Flexible Fluorescence Correlation Spectroscopy

0 downloads 0 Views 49MB Size Report
Jan 2, 2018 - fitting —ppropri—te models to the ™urveD physi™—l p—r—meters ™—n ˜e ...... A full frame readout speed of 500 images per second (2.
Flexible Fluorescence Correlation Spectroscopy using a programmable diractive optical element and an EM-CCD camera

Diplomarbeit zur Erlangung des wissenschaftlichen Grades Diplom-Physiker vorgelegt von

Thomas Kuckert geboren am 28.01.1985 in Zerbst

Professur für Biophysik der Technischen Universität Dresden 2012

Eingereicht am 28.09.2012

1. Gutachter:

Prof. Dr. Petra Schwille

2. Gutachter:

Prof. Dr. Lukas Eng

Historical chart of important technical inventions, which are utilized in the experimental setup of this thesis.

If I have seen further, it is by standing on the shoulders of giants.

Isaac Newton

At the heart of science is an essential balance between two seemingly contradictory attitudes an openness to new ideas, no matter how bizarre or counterintuitive they may be, and the most ruthless skeptical scrutiny of all ideas, old and new. This is how deep truths are winnowed from deep nonsense. Carl Sagan Scientists tend to resist interdisciplinary inquiries into their own territory. In many instances, such parochialism is founded on the fear that intrusion from other disciplines would compete unfairly for limited nancial resources and thus diminish their own opportunity for research. [Naming territorial dominance, greed, and fear of the unknown, as some of the inuences on the increasing specialization of science]

Hannes Alfvén

Kurzdarstellung In der vorliegenden Arbeit wurde ein Fluoreszenzkorrelationsspektroskopie-(FCS) Aufbau realisiert, welcher mehrere Anregungsmuster erzeugen kann und anschlieÿend eine parallele Datenerfassung/-messung ermöglicht.

Dies geschah unter Nutzung

eines programmierbaren diraktiven optischen Elementes (Parallel Aligned Spatial Light Modulator - PAL SLM). Dabei wurde zuerst charakterisiert, wie sich die Einbindung des PAL-SLM auf die Qualität der Punktspreizfunktionen auswirkt. Dies fand über Fluoreszenzmessungen unter Nutzung einer dünnen Lipdmembran statt. Im weiteren Verlauf wurde die Auswirkung der Erzeugung von mehreren Spots auf die Qualität von FCS-Messungen beschrieben.

Die Messungen wurden zu Beginn

mit Avalanche Photodioden durchgeführt. Im weiteren Verlauf wurde eine EM-CCD eingebunden, mit deren Hilfe verschiedene Anwendungen von Mehrfoki-Messungen und unterschiedlichen Anregungsmustern getestet wurden.

Abstract An FCS-setup has been realized, which enables to produce several excitation patterns simultaneously and allows data acquisition accordingly. This was accomplished with a programmable diractive optical element, in this case a parallel aligned spatial light modulator (PAL-SLM). As a rst step, the consequences of using a PAL-SLM for excitation on the quality of the point spread function (PSF) are described. Imaging the PSFs was achieved through uorescence measurements. In the course of the diploma thesis, patterns with several spots are used for FCS-measurements and the quality is described. These performance tests were ran using avalanche photo diodes (APDs). In the further progression an EM-CCD was included, allowing the application of dierent multiple foci measurements and alternating excitation patterns as well.

iv

Table of Contents 1 Introduction

1

2 Theoretical & Technical Background

5

2.1

Fluorescence Correlation Spectroscopy

. . . . . . . . . . . . . . . . .

2.1.1

Spatial Cross-Correlation between foci in the presence of ow

2.1.2

Spatial Cross-Correlation between an outer circular region and

5 12

inner spot . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

Fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

2.2.1

Properties of Fluorescence

. . . . . . . . . . . . . . . . . . . .

21

2.2.2

Used dyes

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

2.3

Geometrical and wave optics . . . . . . . . . . . . . . . . . . . . . . .

24

2.4

Phase hologram computing algorithms

. . . . . . . . . . . . . . . . .

31

2.5

Physics of lipids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

2.5.1

The lipid bilayer and other model systems

. . . . . . . . . . .

37

2.5.2

EggPC SLB as a model system

. . . . . . . . . . . . . . . . .

41

2.2

3 Development of a exible excitation and detection FCS Setup 3.1

45

Programmable Phase Modulator . . . . . . . . . . . . . . . . . . . . .

46

3.1.1

The PAL-SLM principle

47

3.1.2

Characterization of X8267 PAL-SLM model

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

EM-CCD detection . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

3.2.1

Readout mode . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

3.2.2

Implementation in the setup . . . . . . . . . . . . . . . . . . .

55

3.3

Description of whole setup including adapted software . . . . . . . . .

56

3.4

Data evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

3.2

4 Creation and Characterization of dierent excitation patterns

61

4.1

PSF imaging

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

4.2

Multiple Foci

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

5 Calibration and Validations of the exible FCS setup

71 v

5.1

Calibration of the setup

5.2

Probing the EggPC model SLB

5.3

5.4

. . . . . . . . . . . . . . . . . . . . . . . . .

71

. . . . . . . . . . . . . . . . . . . . .

76

5.2.1

Validation measurements . . . . . . . . . . . . . . . . . . . . .

76

5.2.2

EM CCD measurement on an EggPC model system . . . . . .

83

5.2.3

Discussion - Further use in next experiments . . . . . . . . . .

85

Multiple foci measurements

. . . . . . . . . . . . . . . . . . . . . . .

88

5.3.1

Results of slow diusion in a supported lipid bilayer . . . . . .

88

5.3.2

Discussion of results

. . . . . . . . . . . . . . . . . . . . . . .

97

Fast diusion in a monolayer . . . . . . . . . . . . . . . . . . . . . . .

99

6 Applications: FCS and FCCS with fully exible excitation patterns

103

6.1

Nanobeads in Sucrose . . . . . . . . . . . . . . . . . . . . . . . . . . .

103

6.2

Flow measurements with Nanobeads

108

. . . . . . . . . . . . . . . . . .

6.2.1

Construction of a micro-uidic system

. . . . . . . . . . . . .

108

6.2.2

Cross-Correlation with 4 spots in line . . . . . . . . . . . . . .

110

6.2.3

Cross-Correlation using a 3-spot pattern and velocity vector determination . . . . . . . . . . . . . . . . . . . . . . . . . . .

113

6.3

Circle FCS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

116

6.4

Measuring on a two phase-model-system

. . . . . . . . . . . . . . . .

120

6.4.1

Two phase SLB on mica

. . . . . . . . . . . . . . . . . . . . .

120

6.4.2

Two phase monolayer . . . . . . . . . . . . . . . . . . . . . . .

121

7 Conclusion and Outlook

125

A Appendix

127

A.1

Optical setup specications

A.2

Additonal measurement supplements

. . . . . . . . . . . . . . . . . .

127

A.3

Operating and evaluation software . . . . . . . . . . . . . . . . . . . .

128

Bibliography

vi

. . . . . . . . . . . . . . . . . . . . . . .

127

133

List of Figures 2.1.1

Principle of FCS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1.2

Two foci cross-correlation parameters

. . . . . . . . . . . . . . . . .

13

2.1.3

Triangular excitation pattern . . . . . . . . . . . . . . . . . . . . . .

15

2.1.4

Model cross-correlation ow functions for triangular pattern

. . . .

16

2.1.5

Peak time and Amplitude dependency of ow angle alpha . . . . . .

17

2.1.6

Cross-Correlation amplitude dependency of D and v . . . . . . . . .

18

2.1.7

Angular resolution of ow directions . . . . . . . . . . . . . . . . . .

18

2.2.1

Chemical structure of Alexa 546 . . . . . . . . . . . . . . . . . . . .

23

2.2.2

Dye spectra used in this work

24

2.3.1

TEM mode intensity distribution

2.4.1

Phase determining Gerchberg-Saxton algorithm

. . . . . . . . . . .

32

2.4.2

Holographic Optical tweezers setup and explanation . . . . . . . . .

35

2.5.1

Lipid molecule structure and formation . . . . . . . . . . . . . . . .

38

2.5.2

Space lling lipid model and lipid bilayer . . . . . . . . . . . . . . .

39

2.5.3

Bilayer phase occurance

40

2.5.4

Fatty Acid Distribution within EggPC

2.5.5

3D molecule model of predominant DOPC

. . . . . . . . . . . . . .

44

2.5.6

Chemical structure of predominant DOPC

. . . . . . . . . . . . . .

44

2.5.7

Phospholipids Fluorescent Marker DiI as Fatty Acid Analog and its membrane incorporation

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

3.1.1

Programmable Phase Modulator scheme

3.1.2

Principle of PAL-SLM

7

27

43

44

. . . . . . . . . . . . . . .

48

. . . . . . . . . . . . . . . . . . . . . . . . .

49

3.1.3

Interference images for atness correction . . . . . . . . . . . . . . .

50

3.1.4

Parallel beam correction images

51

3.1.5

Gray value phase shift dependency

. . . . . . . . . . . . . . . . . .

52

3.1.6

Phase shift validation images . . . . . . . . . . . . . . . . . . . . . .

52

. . . . . . . . . . . . . . . . . . . .

vii

viii

3.2.1

Detection light path . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

3.3.1

Flexible FCS setup scheme . . . . . . . . . . . . . . . . . . . . . . .

58

4.1.1

Foci images with mirror and PAL-SLM . . . . . . . . . . . . . . . .

62

4.1.2

Uncorrected focus image

63

4.1.3

xz-stack cross sections of 3D PSF

4.1.4

PSF theoretically calculated

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

. . . . . . . . . . . . . . . . . . . . . .

65

4.2.1

Two foci PSF images at dierent distance settings . . . . . . . . . .

66

4.2.2

Logarithmic two foci PSF images with dierent spacings

. . . . . .

67

4.2.3

Multiple foci images from 4 to 50 foci . . . . . . . . . . . . . . . . .

68

4.2.4

Image of 8 foci in line (log) . . . . . . . . . . . . . . . . . . . . . . .

69

4.2.5

xz-plane of 8 foci in line imaged

. . . . . . . . . . . . . . . . . . . .

69

5.1.1

Alexa546 FCS tting curve . . . . . . . . . . . . . . . . . . . . . . .

72

5.1.2

Full FCS measurement data on Alexa546 with APD . . . . . . . . .

73

5.1.3

Recorded APD afterpulsing with white light and exponential t model. 74

5.1.4

Several Alexa546 correlation curves obtained with dierent measurement times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

5.1.5

APD FCS curve EggPC SLB . . . . . . . . . . . . . . . . . . . . . .

75

5.2.1

LSFCS data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

5.2.2

Circular Scanning FCS results . . . . . . . . . . . . . . . . . . . . .

79

5.2.3

FRAP border smear analysis . . . . . . . . . . . . . . . . . . . . . .

80

5.2.4

FRAP images

81

5.2.5

Example Intensity recovery curve

5.2.6

Results of EMCCD measurement on an EggPC SLB.

. . . . . . . .

83

5.2.7

Traces and exposure picture of EMCCD measurement . . . . . . . .

84

5.2.8

Countrate of SLB measurement, APD with similar settings. . . . . .

85

5.3.1

One focus EM CCD FCS curve EggPC SLB

. . . . . . . . . . . . .

89

5.3.2

Two, Three and Four EMCCD FCS curves

. . . . . . . . . . . . . .

90

5.3.3

Seven Foci EMCCD FCS curve

. . . . . . . . . . . . . . . . . . . .

90

5.3.4

Four foci EMCCD FCS curves, settings adapted . . . . . . . . . . .

91

5.3.5

Two and Seven foci EMCCD FCS curves merged . . . . . . . . . . .

92

5.3.6

Statistical distribution of

5.3.7

Statistical

τD

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

τD

. . . . . . . . . . . . . . . . . . .

81

values for dierent number of foci . . .

93

distribution within foci of one-four spot patterns . . .

94

τD

5.3.8

Statistical

distribution within foci of seven spot pattern

. . . . .

95

5.3.9

Average EM CCD traces for one to seven foci patterns . . . . . . . .

97

5.4.1

Fitted Autocorrelation function for 1 focus on monolayer

. . . . . .

99

5.4.2

Calculated Autocorrelation functions for 3 foci on monolayer. . . . .

100

5.4.3

Statistical evaluation of monolayer EM CCD data

. . . . . . . . . .

101

6.1.1

Example EM CCD FCS curve for nanobeads in water. . . . . . . . .

105

6.1.2

FCS data, nanobeads in aqueous sucrose solutions . . . . . . . . . .

106

6.1.3

Stokes-Einstein-behaviour measured with NanoBeads

. . . . . . . .

107

6.1.4

EMCCD traces of beads measurements

. . . . . . . . . . . . . . . .

107

6.2.1

PDMS ow channel sample . . . . . . . . . . . . . . . . . . . . . . .

109

6.2.2

Four foci Excitation pattern and ow direction . . . . . . . . . . . .

110

6.2.3

3 CCF and t to one measured data set . . . . . . . . . . . . . . . .

111

6.2.4

CCF for dierent distances and corresponding shift in CCF peak . .

112

6.2.5

Flow-CCF data 3 foci pattern for 180° angular direction . . . . . . .

114

6.2.6

Flow-CCF data 3 foci pattern for 270° angular direction . . . . . . .

114

6.2.7

Flow-CCF data 3 foci pattern for roughly 315° angular direction . .

115

6.3.1

Circle FCS excitation patterns . . . . . . . . . . . . . . . . . . . . .

117

6.3.2

Circle FCS EM CCD data and curves . . . . . . . . . . . . . . . . .

118

6.3.3

CircleFCS curves and cross-correlation

. . . . . . . . . . . . . . . .

119

6.4.1

Two phase SLB image

. . . . . . . . . . . . . . . . . . . . . . . . .

121

6.4.2

Phase separated monolayer image

. . . . . . . . . . . . . . . . . . .

122

6.4.3

EMCCD acquisition in 2 phases . . . . . . . . . . . . . . . . . . . .

122

6.4.4

EMCCD FCS data of 2 phase measurement

. . . . . . . . . . . . .

123

A.1.1

Transmission plot of dichroic mirror . . . . . . . . . . . . . . . . . .

127

A.1.2

Transmission plots of emission lter (provided by AHF

. . . . .

128

A.3.1

User interface of BlueTweezers software . . . . . . . . . . . . . . .

129

A.3.2

EMCCD-FCS acquisition software: LabVIEW front panel, the user

®) .

interface with controls and indicators [Bur10].

. . . . . . . . . . . .

130

ix

List of Tables 2.4.1 Summary of the theoretical performance of holographic algorithms . .

36

4.1.1 Fit values to both foci from SLM and reference mirror with 2D Gaussian assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

5.2.1 FRAP data obtained with Zeiss ZEN software . . . . . . . . . . . . .

82

5.2.2 Results of dierent valid measurements . . . . . . . . . . . . . . . . .

86

5.2.3 Transition temperatures for EggPC lipids, most relevant in bold [Ava12]. 87 5.3.1 Fit data for chosen (best) and averaged curve data (with standard deviation given for

τD

and

D

of overall average) for all patterns

5.3.2 Data on Average Traces as seen in 5.3.9.

. . .

96

Cpp rate decreases faster

than the foci number increase (relative values according to spot 1).

.

98

measured diusion times . . . . . . . . . . . . . . . . . . . . . . . . .

105

6.1.1 Viscosity, refractive index behavior for water-sucrose solutions and

6.2.1 Average values and standard deviation of auto- and cross-correlation

x

functions with ow contribution . . . . . . . . . . . . . . . . . . . . .

111

6.2.2 Calculated ow data from cross-correlation . . . . . . . . . . . . . . .

115

1. Introduction Fluorescence Correlation Spectroscopy (FCS) is a well-established and highly versatile method commonly applied in the elds of chemistry, biology and biophysics [HS07]. A detailed description on this experimental method is given in section 2.1.

The

parameters obtained with FCS are used to deduce information about the kinetics of chemical reactions, to characterize diusion, molecular aggregation, dynamics of photophysical processes, conformational uctuations, molecular interactions in solutions and cells [Tho02]. FCS has even been employed as a pharmaceutical screening method [SH97]. Through the course of the last 40 years its use has increased tremendously and was accompanied by a number of improvements [Els04] for a better data acquisition and discrimination of parameters [TLA02]. Dierent interrogations by the experimentator to a sample of interest led to advances of FCS to deduce various information as mentioned above - way beyond its origin as an one-point (focus) measurement [MEW72].

Among these are LineScan-FCS, Circular Scanning

+ FCS, multipoint FCS approaches and imaging FCS [SMG 09] using modern CCD cameras. These advances were introduced to achieve i) a more exact determination of absolute diusion coecients, ii) a better discrimination of dierent contributing parameters (photophysics, multiple species) to the FCS function, iii) extending its ability, e.g. towards spatial correlation for ow measurements or to determine the permeability of membranes and iv) the mapping of numerous properties within a cell [SKW99] or any other biological system that comprises inhomogeneities such as phases or structural properties. This diploma thesis focuses on the generation of exible excitation patterns and a matching detection capability. In fact, as mentioned in an experimental work by Blancquaert in 2008 [BGDD08], the ideal multiconfocal experiment would involve: i) a exible way to position simultaneously the desired laser spots at various locations within the biological medium; ii) a matrix of fast, point-like detectors. The thesis highly prots from the advancements of commercially available programmable spatial

1

1 Introduction light modulators and modern EM-CCD cameras, whose implementation for FCS measurements has been thoroughly described by Markus Burkhardt [Bur10] in his PhD thesis in 2010. A spatial light modulator (SLM) was chosen, since it allows to operate beyond the simple extension to multiple foci. This intended use could rely on experiences, that were made due to holographic optical tweezers, which required design and development of computing algorithms as well as an extensive coverage of questions addressing particularities to implement it into an optical setup. Doubtless, the most undemanding and straightforward way to extend the number of foci is the introduction of additional laser paths in a FCS setup.

This can be

achieved by extra laser sources, beam splitting or the usage of Nomarski or Wollaston prisms [Tho08], supporting alternating generation of spatially shifted spots. There are achievements by Arbour [AE10], applying dual-focus FCS in microuidic ow

+ measurements, and Müller [MLP 08], using it for multi-color FCS. Other approaches for generation of multiple foci or alternative excitation patterns exist, involving either passive diractive optical elements (DOEs) or specic engineering of optical parts such as bers and lenses. The manufacturing of specic passive DOEs demands a predesign and will greatly reduce the exibility after its assembly in the setup. However, a number of promising results where obtained by Blom

+ + + + [BJH 02], [BJG 02] and Gösch [GBA 05], [GSA 04]. Tailoring of a single excitation volume has been proposed by Asai [Asa80], carried out by Blancquaert [BDDJ06] and using stimulated emission depletion by Kastrup [KBEH05], that opens an alternative path to develop FCS further. The application of a programmable DOE to the eld of FCS is rather new and

+ + was done by Colyer [CSK 10], [CSR 10]. However, you will nd the use of programmable DOEs in FCS restricted to simplications by solely creating Fresnel lenses or elementary phase patterns to approach this new potential. As a result, achievements

+ were presented towards high-throughput FCS [CSV 11] enabling to collect several FCS curves at the same time from dierent spatial patterns. The non-holographic access is less complex and straightforward, but suered from typical issues such as unequal intensity distribution, requiring a correction via uniformity by normalization of each curve afterwards.

+ According to the available, recently published scientic work [GGK 11], this thesis demonstrates for the rst time the implementation of a programmable DOE using holographic algorithms to generate exible excitation patterns and its simultaneous

2

1 Introduction detection by a fast EM-CCD chip.

The main advantage of the setup constructed

within this work is the exibility of the excitation and detection pattern, with less than a minute required to change the number and positions of spots. It is achieved with less artifacts from unequal intensity distribution than the Fresnel lenses approach. Additionally, it is possible to utilize tailored excitation volumes. Chapter 2 gives the theoretical background and basic properties regarding uorescence correlation spectroscopy, which includes a brief discussion of uorescence in the context of this setup. More explicitly considered are spatial cross-correlation in the presence of ow and adapted for a circle FCS pattern. The chapter explains the usage of algorithms for holographic calculation and depicts the fundamental principles of membrane biophysics related to model systems used in the experiments. Chapter 3 supplies all necessary information related to the construction of a exible FCS (fFCS) setup. It addresses the programmable phase modulator, the EM-CCD detection and data evaluation. Chapter 4 focuses on the quality of the foci (shape of the point spread function) and the inuence of the number of foci on the pattern appearance. The following 3 chapters present the experimental results in this order: the calibration and validation of basic functionality followed by multiple foci measurements (particular attention to section 5.3), performed using model systems with dierent diusion regimes, and nally spatial cross-correlation approaches (particular attention to section 6.2) made possible by the exible nature of this method.

3

2. Theoretical and Technical Background This chapter supplies the foundation of uorescence and uorescence correlation spectroscopy (FCS) constrained to the information relevant for this experimental work. Fluorescence is described briey concerning its physical properties with reference to the used dyes, substances and optical parts in the experiment. Algorithms to compute phase holograms are introduced in general and the algorithms chosen are discussed in detail. The chapter closes with an overview on the physics of lipids, focusing on the fundamentals of membrane biophysics and current research questions addressed. Where the latter is the scientic territory of investigation, the FCS method and its underlying principles provide the means to navigate within biophysical research and determine unknown parameters.

2.1. Fluorescence Correlation Spectroscopy (FCS) In its origin, FCS was developed by Magde, Elson and Webb exactly 40 years ago to monitor thermodynamic uctuations in a reacting system [MEW72]. It served as a miniaturization of dynamic light scattering with a new concept, taking advantage of the temporal uctuations of uorescence by correlating them. In brief words, FCS is commonly realized by focusing laser light into a tiny volume and by recording the temporal statistics of uorescence photons through a highly sensitive detector [MEW74].

These photon counts are then correlated with itself (autocorrelation)

and give a characteristic autocorrelation curve (ACF), whose behavior depends on the underlying experimental conditions such as concentration and diusion speed or ow, as well as on photophysical parameters such as triplet state behavior [WMR95] and quenching.

5

2 Theoretical & Technical Background 2.1 Fluorescence Correlation Spectroscopy Subsequently, to exploit the ability of FCS, it depends on the inventiveness (even inverse-FCS, proposed by Wennmalm [WTXW09]) of the experimenter to utilize the method in such a way, that queries of interest on a sample can be answered appropriately. The depicted parameter landscape of the ACF, including interdependencies, usually asks for a prior knowledge of contributing factors for precise interpretation of obtained values.

However, the method of FCS serves well to distinguish many

parameters like diusing times, compared relative to each other and given similar experimental conditions.

It can answer boolean type yes-or-no questions, e.g.

if

agglomeration or quenching occurs, additionally FCS is quantitative. The sophistication of FCS, after its nalized theoretical treatment for the most part, depends on improved technical approaches such as dual-color or spatial crosscorrelation, scanning FCS [PS08], [RCS09], total internal reection FCS, to name just a few. To the rst group of technical improvements [MHW97] belong enhanced optics such as lenses, objectives and state-of the art lasers, the optimization of confocal pinholes [RMWK93] to reduce the sample volume [ER94], which gave the technique a great rise in science, as well as yet more sensitive detectors and the design of specic dyes or other uorescent materials.

Brief derivation of FCS functions The theoretical fundamentals of FCS are drafted in the following. For a more detailed and explicit covering of this subject, please refer to [Bur10], [Sta10], a coherent derivation can be found for example in [EM74] and [AP75]. The detected uorescent signal F can be written as the sum of average and uctuation

F (t) = hF i + δF (t)

with

hF i =

1 tmeas

Z

tmeas

F (t)dt

.

(2.1.1)

0

Autocorrelation of the uorescence signal F is then dened by its uctuations and average uorescence signal

G(τ ) =

δF

hF i

hδF (t)δF (t + τ )i hF (t)F (t + τ )i = −1 2 hF (t)i hF (t)i2

.

(2.1.2)

This is a test of the self-similarity of the uorescence signal F, which can be described as

6

2 Theoretical & Technical Background 2.1 Fluorescence Correlation Spectroscopy

F (t) =

n X

Z

Iex (~r)S(~r)Ci (~r, t)d3~r

κi σex,i φi

.

(2.1.3)

V

i=1

The compact gure 2.1.1 pools the principle of FCS in a few graphics.

(a) A confocal volume is created by focusing a laser through the objective. The emitted uorescence is collected with the same objective, spectrally and spatially altered by a bandpass lter and a pinhole, respectively, and detected by an APD. (b) Molecules diuse through the confocal volume and give rise to a uctuating intensity trace (c). The autocorrelation curve (d), which is a measure for the self similarity of the signal is calculated from the intensity trace. By tting appropriate models to the curve, physical parameters can be extracted. Taken from [Sta10]. Figure 2.1.1.:

In equation 2.1.3, n represents dierent uorescent molecule species, whereas denotes detector eciency,

σex

uorophore extinction coecient and

φ

κ

the quantum

Iex (~r) and the normalized collection eciency functhe confocal volume, and C(~ r, t) is the concentration of the Introducing molecular brightness η and molecule detection

yield. Excitation intensity prole tion

S(~r)

characterize

uorescent molecules. function

W (~r)

as

ηi = κσex,i φi I0 W (~r) = one obtains for uorescence signal

F

,

Iex (~r) S(~r) I0

(2.1.4) ,

and its uctuations

7

δF

2 Theoretical & Technical Background 2.1 Fluorescence Correlation Spectroscopy n Z X

F (t) =

(2.1.5)

n Z X i=1

,

V

i=1

δF (t) =

W (~r)ηi Ci (~r, t)d3~r

W (~r)δ(ηi Ci (~r, t))d3~r

.

V

Inserting equation 2.1.5 into 2.1.2, considering only one species n=1, it is necessary to separate the uctuation term in equation 2.1.5, assuming constant molecular brightness, we arrive at

R G(τ ) =

V

0

R V

W (~r)W (~r0 )Φ(~r, (~r0 , τ ))d3~rd3 r0 R ( V W (~r)hCi (~r, t)id3~r)2

.

(2.1.6)

The assumption of constant molecular brightness deviates from the experimental reality, where photophysical eects change this parameter and cause distortions in the correlation curve. More artifacts are discussed in the corresponding subsection 2.1.

W (~r) and the concentraΦ(~r, (~r0 , τ )) = hδC(~r, t)δC(~r0 , t + τ )i,

Inserting the expressions for the molecule detection function tion correlation function (diusion propagator)

which are outlined for its relevant consideration in the following paragraphs, one obtains:



 G3D (τ ) =

1 Vef f · hCi

·



1 1 τ · q ω2 1 + τD 1 + z20 0

τ · τD



.

(2.1.7)

The rst factor in equation 2.1.7 is the inverse of the average particle number

hN i

in the eective focal volume, therefore the local concentration of uorophores can be determined from the amplitude

G(0) = 1/hN i.

The molecular detection function is a product of excitation

S(~r)

point spread function, normalized by its amplitude

W (~r) =

Iex (~r) · S(~r) I0

,

whose properties are described in the next paragraph.

8

Iex (~r)

and detection

I0 , (2.1.8)

2 Theoretical & Technical Background 2.1 Fluorescence Correlation Spectroscopy

Excitation and Detection Prole In general, the focused laser beam is described theoretically by a three-dimensional Gaussian as

  2(x2 + y 2 ) 2z 2 − 2 W (~r) = exp − ω02 z0

,

(2.1.9)

ω0 is the lateral radius, 2 where the intensity of the focused laser beam has fallen to 1/e . 2 · z0 is the axial z length of the focus and usually substituted by the structural parameter S = 0 , that ω0 which allows the analytical solution given in equation 2.1.7.

can serve as a quality control, since it should be stable for all measurements and typically falls in between 4 and 8.

Equation 2.1.9 will give an eective volume of

3 2

Vef f = π ω02 z0 . The lateral extension of the observation volume is determined by the focus, whose radius is calculated from Gaussian beam optics

ω0 = where

λ

λf nπωL

denotes the excitation wave length,

refractive index of the immersion liquid and

,

(2.1.10)

f the focal length of the lens, n the ωL the beam radius before the focus.

The focus radius is small versus the beam radius before focusing, which allows to approximate the focus angle

tan δ =

ωL and changes equation 2.1.10 to f

ω0 =

λ . nπ tan δ

(2.1.11)

Numerical aperture of the objective is described by detection angle

NA = n sin α

α

.

(2.1.12)

However, the real experimental excitation point spread function will dier from that Gaussian approximation [HW02]. The excitation intensity follows

  r2 ω 2 I0 Iex (r, z) = I0 (z) · exp − 2 , with I0 (z) = 20 ω (z) ω (z)

,

(2.1.13)

in which the dependency for the z-position of the beam waist radius is obtained from Gaussian beam optics

9

2 Theoretical & Technical Background 2.1 Fluorescence Correlation Spectroscopy

ω 2 (z) = ω0 +

z 2 λ2 ω0 n2 π 2

(2.1.14)

that can be simplied by using equation 2.1.11

ω 2 (z) = ω0 + z 2 tan2 δ

.

(2.1.15)

As a result only for very small pinhole sizes, where the axial Lorentzian prole is suppressed, the three-dimensional Gaussian model is a good approximation.

Oth-

erwise a Gauss-Lorentz-model is necessary, which has no direct analytical solution. An ideal model would be the use of the previously experimentally determined excitation and detection point spread function for tting, which is in reach with modern computing power. In spite of that, a perfect description of the molecule detection function is not necessary when FCS is used to determine parameters relative to a known reference dye in standard one-focus FCS. The need to introduce the GaussLorentz-model appeared, when an unusual big pinhole was needed to detect the signal from two foci, that were excited alternating for spatial cross-correlation. This is not the case in the setup of this work, as chosen pinhole sizes stayed small (pinhole size is variable through the choice of number of pixels).

Diusion and ow Brownian translational diusion, as the most prominent source of intensity uctuations in FCS, causes constant change of the local concentration within a small confocal volume

V0

in contrast to the constant macroscopic concentration

hCi

in the

sample over time. The number of particles is Poisson-distributed. Free diusion is described by the following equation, also known as Fick's second law:

∂C(~r, t) = D∇2 C(~r, t) ∂t

.

(2.1.16)

The diusion coecient has been derived by Stokes and Einstein for a spherical particle in the case of a homogeneous, interaction-free and isotropic environment:

D= where

kB

is the Boltzmann constant,

T

kB T 6πηr

,

the temperate,

10

(2.1.17)

η

the viscosity of the medium

2 Theoretical & Technical Background 2.1 Fluorescence Correlation Spectroscopy and

R0 the hydrodynamic radius of the diusing particle.

Since the viscosity depends

directly on temperature, the overall behavior of temperature dependence is strong and has to be considered even within the small area of room temperatures

[20..25]◦ C ,

changing roughly about 20 % in this interval [Kap10].

Φ(~r, ~r0 , t)

To acquire equation 2.1.7, the concentration correlation function

is de-

termined by solving the diusion-transport-reaction-equation [Hau05]

n

X ∂δCi (~r, t) = Di ∇2 δCi (~r, t) + Tij δCi (~r, t) − ~v (~r, t)∇δCi (~r, t), ∂t j=1 where

Di

denotes the diusion coecient of the molecular species i,

of the reaction matrix

T

and

~v (~r, t)

Tij

(2.1.18)

as elements

the ow velocity. Considering just translational

diusion, equation 2.1.18 simplies and by inserting into equation 2.1.6, the relationship 2.1.7 is obtained. Denitions

hN i = hC(~r, t)iVef f τD =

ω02

4D z0 S= ω0

,

,

(2.1.19)

are used. Extending the previous consideration to the situation of active transport, solving the diusion-transport-reaction equation 2.1.18 for the case of one uorescent species reveals the concentration correlation function

Φ(~r, ~r0 , τ )

with a ow velocity

term and results in an autocorrelation function including ow





1 1  1 GAC (τ ) = τ · q ω2 hN i 1 + τD 1 + z20 0

τ · τD

 exp



−v 2 τ 2 ω02 + 4Dτ

 ,

where ow is considered to be perpendicular to the optical axis (vz

k~v k =

p

vx2 + vy2

(2.1.20)

= 0)

and

v =

represents the absolute value of the velocity.

Artifacts in FCS An in-depth examination of a great number of contributing factors, that will distort the results, exists in the article of Enderlein [EGPF04]. Accordingly, precautions have to be taken towards i) the laser power density avoiding under- and over saturation,

11

2 Theoretical & Technical Background 2.1 Fluorescence Correlation Spectroscopy ii) too high or too low concentrations, iii) cover glass thickness, iv) light polarization eects and v) varying refractive indexes to correct for wrong estimations of diusion coecients and number of particles. As photophysical parameters are naturally unknown for a given sample, neglecting the triplet fraction or plainly losing that information, will lead to an underestimation of particle concentration [WRM94].

Furthermore, uncorrelated background,

afterpulsing and astigmatism contribute to a misleading parameter determination after tting, if they are not considered and checked for.

2.1.1. Spatial Cross-Correlation between foci in the presence of ow FCS allows the determination of ow, which is described by speed, direction and its prole, representing the spatial dependency of ow velocities within a sample. However, the parameter landscape of the model tting functions applied to a onefocus FCS curve, assuming several unknown properties of the sample leads to large uncertainties if extra variables like ow properties or multicomponent diusion have to be determined. cient

D

In fact, even with basic properties such as the diusion coe-

and particle number

N

measured beforehand, without the presence of ow

and multiple components, artifacts and noise of a one-focus FCS measurement demand minimum requirements (to distinguish ow velocity or multiple components having dierent diusion times).

Considering ow, its velocity has to be distinct-

ively higher (roughly 0.5 mm/s) than the particle diusion to achieve reasonable results [BDSE99]. Likewise the diusion time of multiple components has to dier by a factor much bigger than 1.6 to be distinguishable in FCS curves even in optimal measurement situations [MWRV99a]. However, the determination of ow direction is not possible because of the circular (symmetric) shape of the FCS spot. The idea of spatially separated foci has been introduced early and realized (e.g.) in 1995 by Brinkmeier [BR95]. This adaption of an FCS measurement greatly improves the possibility to obtain and distinguish ow properties and multiple diusing components, noting that the determination of ow direction remains tedious. This section briey gives a general description of spatial uorescence cross-correlation spectroscopy (sFCCS) by theory and introduces a 3 foci cross-correlation method according to the experimental realization in this work. The sFCCS function by cross-

12

2 Theoretical & Technical Background 2.1 Fluorescence Correlation Spectroscopy correlating uorescence signals

∆)

I1 (t) and I2 (t), emitted from two spatially shifted (by

observation volumes, follows as:

GCC (∆, τ ) = with

hI1 (t)I2 (t + τ )i hδI1 (t)δI2 (t + τ )i =1+ hI1 (t)I2 (t)i hI1 (t)I2 (t)i

δI1,2 (t) = I1,2 (t) − hI1,2 (t)i

,

being the deviations from the temporal averages

of the signals. Fluctuations of the concentration of uorescent molecules, the observation volumes,

W1

and

(2.1.21)

W2 ,

δC ,

within

give rise to these deviations.

The two spatial cross-correlation functions for ow are derived using equation 2.1.21 and similar considerations as sketched above in section 2.1





 2 2  2 1 v τ + R − 2Rvτ cos α 1  1  exp − · q GCC,f orward (τ ) = ω02 hN i 1 + ττD ω02 + 4Dτ τ 1 + z 2 · τD 0    2 2  2 1 v τ + R + 2Rvτ cos α 1  1  exp − · q GCC,backward (τ ) = . ω02 hN i 1 + ττD ω02 + 4Dτ τ 1+ · z02

τD

(2.1.22) The distance R between the foci has to be determined precisely beforehand, on its accuracy depends the quantication of ow properties.

See gure 2.1.2 for the

denition of the angle alpha between ow and spot distance R.

α 1

2

R

2 foci pattern. Denitions of distance R (black), angle α between the direction of ow (orange vector) and connecting line (dashed black) of foci.

Figure 2.1.2.:

Due to the increasing number of t parameters, a preceding independent measurement to specify the diusion coecient and particle concentration should be considered. Both the amplitude and the temporal position (τ ) of the cross-correlation peak depend on the ow velocity and its angle

α.

This prohibits a precise determin-

ation of ow velocity and direction by just one measurement using two spots. While

13

2 Theoretical & Technical Background 2.1 Fluorescence Correlation Spectroscopy rotating the two spots, the maximum amplitude of the correlation peak has to be found, demanding a number of succeeding data acquisitions. In this work it is proposed to extend the 2-foci pattern by an extra third spot, creating a triangular excitation pattern which can be arbitrarily adjusted and simultaneously detected. Hence the spatial cross-correlation is fetched into 2 dimensions. The benets of this approach, a more precise ow velocity identication and obtaining of its direction within 10 degree accuracy, are theoretically presented and subsequently veried. The foci should be adjusted such that the ow occurs in the xy-plane. Flow with a

vz

component has to be treated in addition, but will lead for the main part to a

decrease of the cross-correlation amplitude. Figure 2.1.3 displays the applied triangular spot pattern used in this work (drawn to scale including Gaussian beam waists) and generally considered options of ow direction relative towards it, enabling an immediate

α (see gure 2.1.7).

45◦ ± 25◦

angular resolution of

Model cross-correlation functions (CCF) are plotted accordingly

(gure 2.1.4). Cases are numbered from 1 to 4, the respective opposite (180°) ow direction inherits a negative sign, since its model function will have the same appearance symmetric to the x-axis. The optimal choice allowing immediate resolution of

30◦ ± 15◦

α would be an equilateral triangle, because two additional angle bisector

cases orthogonal to the two opposing spots for cross-correlation would be distinguish-

82◦ γ angle, ow along the spot vectors 1 → 3 orthogonal to 2 → 3 and 1 → 3, respectively.

able. Due to the almost

and

2→3

is here

Each measurement gives three cross-correlation ow functions. To reach a more exact resolution the dierent correlation peak amplitudes and their temporal position (see model functions in gure 2.1.4) have to be taken into consideration. An option presented here is the weighted velocity vector addition as in equation 2.1.23. Velocity values are extracted from the separated ts of the CCF. However, amplitude and peak time both depend on angular direction and ow velocity (plotted in gure 2.1.5, taken from [BDSE99]), the latter ones being the unknowns to be calculated from the rst ones. This implicit dependency asks for a more detailed analytical solution than presented in equation 2.1.23. It has to be taken into account, that dierent diusion speeds and ow velocity will change the amplitude of the CCF as well, as plotted in the theoretical calculation by gure 2.1.6, which represents the values for the experimental

14

2 Theoretical & Technical Background 2.1 Fluorescence Correlation Spectroscopy

Figure 2.1.3.: Triangular excitation pattern with angular distribution and foci distances. Dierent highlighted ow directions for immediate angular resolution from CCF are shown. Triangle angles α = 45◦ , β = 53◦ , γ = 82◦ . Obtained by CCD imaging with 100 nm resolution and not optimized towards α = β = γ .

situation in this work.

However, for an angular ow direction distinction of 25° with a reasonable error of 15 degree, in any biological system such as cells, where active transport and its direction is questioned, the approach of equation 2.1.23 is sucient. The weights in equation 2.1.23 assume a linear relationship for the amplitude and

τmax

dependency

of velocity and angular direction as a working approximation. Because the excitation pattern supplied a non equilateral triangle, a correction towards uniformity for the extracted velocity values from

τ

is introduced in 2.1.24.

Thus it is outlined, how

an arbitrary triangle pattern can be deployed in the sample in a exible way, if certain conditions require to deviate from the equilateral triangle optimal for analytical calculations.

The highest amplitude

Gmax (τmax )

determines the weights

15

A13,12,32

in equation

2 Theoretical & Technical Background 2.1 Fluorescence Correlation Spectroscopy 0 .1 0 0 .1 2

C C F 1 2 C C F 1 3 C C F 2 3

0 .1 0

0 .0 8

0 .0 8

0 .0 6

G ( τ)

G ( τ)

0 .0 6

0 .0 4

0 .0 4 0 .0 2 0 .0 0 .0 0 .0 0 .0

0 .0 2

0 .0 0 1 E -3

0 .0 1

0 6 0 4 0 2 0 0 1 E -3

0 .1

0 .0 1

L a g tim e [s ]

0 .1

L a g T im e [s ]

(a) Case 1

(b) Case 2

0 .0 3 5

0 .1 4

0 .0 3 0

0 .1 2 0 .1 0

0 .0 2 5

0 .0 8

G ( τ)

0 .0 2 0

0 .0 6

0 .0 1 0

0 0 0 0 0 0 0 0 0 0 0 0

0 .0 2 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0

0 .0 0 5 0 .0 0 .0 0 .0 0 .0

0 .0 4

G ( τ)

0 .0 1 5

1 5 1 0 0 5 0 0 1 E -3

0 .0 1

0 .1

0 3 0 0 2 5 0 2 0 0 1 5 0 1 0 0 0 5 0 0 0 1 E -3

0 .0 1

L a g T im e [s ]

0 .1

L a g T im e [s ]

(c) Case 3

(d) Case 4

Model cross-correlation ow functions for all 4 cases of gure 2.1.3. Y-axis of (b)-(d) are split to resolve the low amplitude CCFs better. Figure 2.1.4.:

2.1.23:

Gmax (τmax ) = max{G13,12,32 }

and

τmax = max{τ13,12,32 }

~v = A13 · v~13 + A12 · v~12 + A32 · v~32 G13,12,32 · τ13,12,32 with A13,12,32 = . Gmax · τmax

The velocity vector is made up of two components for 2 dimensions: Due to dierent side lengths, correction terms are introduced:

16

(2.1.23)

  x ~v = . y

2 Theoretical & Technical Background 2.1 Fluorescence Correlation Spectroscopy

Dependency of peak value time and amplitude due to ow-foci vector α. Experimentally and theoretically determined by Brinkmeier [BDSE99]. Peak time τ decreases with increasing deviation from α = 0◦ . Figure 2.1.5.:

  0.75 v~12 = 0

and

  0.57 v~13 = 0.56

with

 and

v~32 =

 0.43 −0.56

|v13,32 ~ | = (0.8, 0.7)

(2.1.24)

0

G(τ12 ) = 1.3 · G(τ12 ) 0 τ12 = 0.75 · τ12

.

The absolute value for the ow velocity is therefore determined by angular dierence

α1

τmax

and the

between the direction of the highest cross-correlation amplitude

and the determined ow velocity vector

|~v | =

~v

:

R · cos(α) τmax

17

.

(2.1.25)

2 Theoretical & Technical Background 2.1 Fluorescence Correlation Spectroscopy

0 .8 R

ω 0 .6

S

G ( τm

a x

)

α 0 .4

0 .2

=

1

. 5

µ

m

=

0

. 3

µ

m

=

6

. 5

=

0

°

v =

1

v =

2

0

0

0

0

µ

µ

m

m

/ s

/ s

v =

5

0

µ

m

/ s

v =

2

0

µ

m

/ s

0 .0 1

1 0

1 0 0 2

D

[ µ

m

/ s ]

The amplitude of the cross-correlation G(τ ) in dependency of diusion coecient D is plotted for dierent ow velocities, parameters correspond to performed experiment.

Figure 2.1.6.:

Figure 2.1.7.: Angular resolution of ow directions by immediate evaluation of CCF peak amplitudes. Number 1 to 4 correspond to particularized cases in gure 2.1.3 .

18

2 Theoretical & Technical Background 2.1 Fluorescence Correlation Spectroscopy

2.1.2. Spatial Cross-Correlation between an outer circular region and inner spot While the idea of spatial uorescence cross-correlation spectroscopy (sFCCS) between two focal volumes has been thoroughly studied, the tailoring of one or more detection volume shapes itself is another direction of progress within FCS but rather weakly investigated. A new sFCCS optical geometry has been proposed by Blancquaert et al. [BDDJ06].

Two pinholes, a ring and core, were encapsulated one in the other

by coating optical bers and a specic design of the detection paths in the setup to cross-correlate between the outer ring and inner spot.

The ultimate goal is to

achieve a better precision of the diusion coecient measurement in addition to a better discrimination between diusion and other processes that bias the intensity uctuations at shorter times (singlet-triplet, photobleaching dynamics) [BDDJ06]. It would allow to distinguish better between dierent diusing species as well, ordinarily exacerbated by the complicated parameter landscape of the multicomponent FCS t functions for only one-point detection. Blancquaert et al. suggested to explore this area further after rst results, due to the new capabilities oered by spatial light modulators. Hence a principle feasibility to generate the proposed excitation pattern and its detection via a fast EM-CCD chip is presented in section 6.3. In contrast to the work of Blancquaert in 2006, where the two FCS volumes were generate via designed ber pinholes, the programmable SLM allows to achieve an excitation pattern in a 2D plane, which corresponds to an outer circle and inner spot. Thus uorophores will only be excited in the regions of interest, and a large improvement towards more uniformity of power density between the two volumes is expected as well.

A special calibration or engineering of bers is not necessary,

due to the 2D spatial detection capability of the EM-CCD. It follows a theoretical consideration restricted to 2D, adapted from [BDDJ06]. The function Molecule Detection Eciencies

M DEin (r)

describes the probabil-

ity to collect the signal of a uorescent molecule for the FCS measurement. a product of the Collection Eciency Functions proles

I(r).

CEFin (r)

It is

and respective excitation

As stated in section 6.3, the ideally achieved case is a center spot corres-

ponding to a Gaussian shaped point spread function and an homogeneously shaped outer region. However, the latter one was characterized by a varying distribution of excitation light around the inner spot with a radius of circa

19

2.2 µm.

The outer ring

2 Theoretical & Technical Background 2.1 Fluorescence Correlation Spectroscopy inherited a width of roughly

1 µm.

Both inner and outer MDE functions are very close to Gaussian ones. The inner volume is described by

" 2D (r) = Ain · exp −2 M DEin



r ωin

2 # (2.1.26)

and the outer volume by an annular Gaussian :

" 2D M DEout (r) = Aout · exp −2

where

2

1/e

rout

is the radius and

ωout



r − rout ωout

2 # ,

(2.1.27)

the radius, where the intensity has dropped to

. In contrast to the approach of Blancquaert et al., a much higher outer MDE

was feasible, since the excitation pattern did not depend on one single expanded focus spot. By integrating the product of the diusion propagator time with the two MDE functions (using imaginary Bessel function

J0 ),

one obtains the following cross-

correlations functions:

GCC (τ ) = 1 +

1 2 Cπωef f

  r2 exp − 1+ ττ D  · 1 + ττD

,

(2.1.28)

where C is the concentration of uorescent molecules in 2D and D the corresponding 2D diusion coecient. Equation 2.1.28 includes parameters

2 ωef f =

2 2 2 ωef (ωin + ωout ) rout f ; τD = ; r= 2 4D ωef f

.

(2.1.29)

Subsequent, equation 2.1.28 exhibits a maximum located at:

τmax =

2 2 rout − ωef f 4D

.

(2.1.30)

In this thesis only 2D model systems were studied to characterize the performance of the approach, therefore no discussion towards a 3D characterization is outlined in this section. A more detailed theoretical consideration can be found in [BDDJ06].

20

2 Theoretical & Technical Background

2.2 Fluorescence

2.2. Fluorescence 2.2.1. Properties of Fluorescence Fluorescence, as a physical phenomena, is used by scientists from many disciplines as one of the core tools to study systems in biochemistry and biophysics.

It is

advancing remarkably in the past 20 years and expanding to more and more areas such as biotechnology [Lak06]. This dramatic growth is due to the development of a broad range of dyes, suiting almost any special demand, and the vast improvement of optical systems and detector capabilities in this time period. Luminescence is the superior classication, referring to the emission of light from any substance and occurs from electronically excited states [Lak06]. Depending on the nature of excited states, its most common types encountered in organic dyes are uorescence and phosphorescence. Because of excited singlet states, where the excited electron is paired with opposite spin to the ground state orbital, the rst category implicates rapidly return of the electron within roughly 1-10 ns by emission of a photon. The latter one refers to emission of photons from excited triplet states, whose return to the ground state is forbidden because of the same spin orientation. Phosphorescence has a typical lifetime of milliseconds to seconds. The processes that occur between the absorption and emission of light are usually illustrated by the Jablonski diagram [Lak06]. It illustrates the complex nature of uorescence including dierent electronic states, vibrational energy levels and attributes leading to quenching, energy transfer and solvent interactions. Stokes shift refers to the increase of wavelength between the absorbed and emitted photon, that is caused by relaxation from higher vibrational levels or higher excitation states to the lowest energy vibrational level of occurs.

S1 ,

from where the uorescence emission generally

Hence the spectra of absorption and emission have a characteristic band-

width but with dierent probabilities, also having an intersection, termed resonance uorescence. A mirror image rule outlines, that a symmetry between emission and excitation (absorption) spectra exist.

The distinctive spectra of dierent molecule

will change in dierent environments, that can be used as an additional descriptive factor for probing in biological systems. For example, uorescence commonly occurs from aromatic rings at certain wavelengths. Fluorescence lifetime and quantum yield are important characteristics of a uoro-

21

2 Theoretical & Technical Background

2.2 Fluorescence

phore. Whereas the rst one is dened as

 [S1] = [S1]0 · exp with

[S1]

as the

[S1]0

t − τ

 ,

(2.2.1)

concentration of excited states molecules at time

the initial concentration and

τ

t, [S1]0

as

the uorescence lifetime. Hence it describes the time,

when the number of uorescent molecules has decreased to

1/e.

Quantum yield is

the number of emitted photons relative to the number of absorbed photons. Fluorescence molecules can be attached to biological relevant molecules without inuencing their basic overall behavior. This allows to visualize processes on a molecular scale, that would be hidden from any optical imaging system. Their range is broad, spanning the whole wavelength spectra, from dyes that are similar to the studied system (such as the amphiphilic DiI in membranes), uorescent proteins that are expressed by the DNA and various ways of chemical bonding to the substance of interest. The following subsections contain information about the used dyes, their spectra and physics according to the optical setup.

2.2.2. Used dyes In one-point Fluorescence Correlation Spectroscopy (see next section 2.1) it is crucial to have a well-behaving reference dye for calibration. This work made use of an isomeric mixture of Alexa Fluor

® 546 Carboxylic Acid, Succinimidyl Ester (Molecu-

lar Probes, Invitrogen, Life Technologies). It belongs to the group of amine-reactive uorescent dyes widely used in life sciences for conjugating to proteins or other aminecontaining compounds. The choice for system calibration fell upon this uorophor, since it is well excitable by HeNe (543.5 nm) laser and its absolute diusion coecient is known [PS08]. Invitrogen

® supplies the molecular formula as C50H62Cl3N5O14S3,

its molecular weight as 1159.6 (or 1.16 kDa). After calibration, DiIC18 (3) (Molecular Probes, Invitrogen, Life technologies) , a lipophilic membrane stain that diuses laterally to stain the entire cell, was employed for measuring diusion within a membrane. It is weakly uorescent until incorporated into membranes.

This orangered-uorescent dye, which is spectrally similar to

tetramethylrhodamine, is often used as a long-term tracer for neuronal and other

22

2 Theoretical & Technical Background

Figure 2.2.1.:

2.2 Fluorescence

Chemical structure of Alexa 546. Taken from [Inv12]

cells [Inv12]. It is an indocarbocyanine dye with a 18 carbon long alkyl hydrocarbon tail and a 3 carbon bridge between the indoline nuclei.

Its chemical name is 1,1'-

dioctadecyl-3,3,3'3'-tetramethylindocarbocyanine perchlorate, the chemical formula is C59 H89 CIN2 O4 . In this experimental work the use of NanoBeads and Quantum Dots was considered as well. Both are tiny particles on the order of a nanometer in size. Quantum dots are composed of a hundred to a thousand atoms and made from semiconductor materials such as CdS and CdSe.

They dier in color depending on their size and are very

bright in comparison to uorescent molecules. The light emission can be compared to uorescence, but strictly its origin is caused by a semiconductor property which is the band gap. They are very stable and will not photobleach, however, they display other properties such as blinking on longer timescales [HSC07].

NanoBeads are labeled

polymer beads varying from 10 nm to micrometer in size. They are also very bright and stable to photobleaching or triplet blinking, since a large number of uorescent molecules is attached or included in these spheres.

The high brightness of both

particles enables application in biological research such as single particle tracking and often ll a gap, where traditional dyes are unable to meet the expectations [WNS09]. The used NanoBeads in the work were FluoSpheres

®carboxylate-modied micro

spheres of 14 nm size and orange uorescent (540/560). They were applied for imaging calibration (determination of detection point spread function, where NanoBeads served as a point-like light source), to demonstrate the feasibility of acquiring exact FCS curves based on the Stokes-Einstein-relation and ow measurements.

Since

quantum dots were not available in the desired wavelength range and are strong in blinking (frequently, quantum dots switch into a dark state on milliseconds to second time scale), their use was not further considered in this experimental work. Dyes used for membrane staining, such as DiI, exhibit in general a preference

23

2 Theoretical & Technical Background

2.3 Geometrical and wave optics

for a certain phase, if phase separation occurs in studied systems. One attempt in this work was to demonstrate the simultaneous measurement of dierent diusion coecients in two phases. To guarantee a sucient number of dye molecules in both phases, but being able to distinguish both phases by pure visualizing, BD-TMR Chol (AC) was chosen due to its distribution in both lipid phases.

Spectra of used dyes in accordance to setup characteristics, relative percentage values plotted to λ in nm .

Figure 2.2.2.:

2.3. Geometrical and wave optics A sophisticated approach that uses modern optics for diraction limited spots, highly sensitive detection and holographic excitation pattern generation is a prerequisite to achieve the designated aim of a exible FCS platform.

This section will outline

the fundamental knowledge and essential considerations to realize a functioning FCS system. Furthermore, the limits of resolution and the generation of the point spread function are explained via geometrical or wave optics. The properties of light can be described by dierent models. Geometrical optics describes light as non-interacting rays, whereas wave optics explain light as electromagnetic waves that can also interact with each other. Geometrical optics serve well to understand dierent optical systems involving lenses for imaging, magnication and focal points. Wave optics are necessary to understand diraction, interference, polarization, and other phenomena where the ray approximation for geometrical optics is not valid anymore.

24

2 Theoretical & Technical Background

2.3 Geometrical and wave optics

Laser beam properties Rooted in the Maxwell equations, we obtain from the homogeneous form of the electromagnetic wave equations

  ∂2 2 ∇ − µ 2 u = 0 ∂t

,

(2.3.1)

u refers to the the electric eld E or magnetic eld B, respectively (boundary condition E ⊥ B ⊥ S and ρ = 0). The speed of light in any medium is dened by √ −1 c= µ . where

Re is

The general solution to this equation is a linear superposition of n waves ( real part):

u(r, t) = Re

Z

dn k a(k)ei(kr−|k|ct)

(2.3.2)

a(k), containing phase φ(k) and the angular frequency ω = |k| c serving as a complete set to describe a propagating light source. u serves again as a placeholder for E or B. k is the wave propagation vector, its magnitude . |k| the wavenumber connected to the wavelength through k = 2π λ with the complex amplitude

The magnetic properties of media mostly used in optics such as glass, air and vacuum, can be neglected most often and equation 2.3.1 reduces to

∂ 2 E(r, t) = −∇ ∇ E(r, t) − µ0 (x) ∂t2 2

E(r, t)



1 E(r, t) · ∇(r) (r)

describes the electric eld vector at position

eld constant

(r)

r



and time

.

t.

(2.3.3)

The electric

can contain a spatial dependence of the refractive index from the

medium. The following considerations simplify, if we introduce a restricted ansatz by monochromatic, linear polarized electric elds, as they occur by the laser after the polarizing element in the setup:

"

E(r, t) = e · E(x, y, z) · eiωt

with

a1 eiθ1 e= a2 eiθ2

# .

(2.3.4)

Equation 2.3.4 contains a time-independent electrical eld amplitude and the complex polarization vector

e,

also referred to as Jones vector describing amplitude and

25

2 Theoretical & Technical Background

2.3 Geometrical and wave optics

phase of the electric eld in x and y direction. Inserted into equation 2.3.3 gives

∇2 E(x, y, z) + k(r)2 E(x, y, z) = 0

Here,

k 2 (r)

related by

k 2 (r) = ω 2 µ0 (r)

.

(2.3.5)

is only valid for non-conducting, loss-free

media. Plane waves are a possible solution to this equation

E(r, t) = e · E0 · exp(i(ωt − kr)) where polarization vector

e ⊥ k.

,

(2.3.6)

Such elds have an innite extension.

In the

experimental situation though, approximations towards spatially limited light beams are of interest. This is introduced by beams propagating along the z-axis

E(x, y, z) = E0 X(x, z)Y (y, z)e−ikz . The enveloping functions

X(x, z), Y (y, z)

(2.3.7)

vary much faster in the (x,y) plane than

along the z-axis, which is referred to as a paraxial beam approximation. 2 ∂ ∂2 , ∂ , k ∂z done by assuming ∂x2 ∂y 2



This is

∂2 , ∂ () ∂ (), which uncouples the (x,y) and (y,z) ∂z 2 ∂z ∂z

fraction. This yields



∂ ∂2 − 2ik 2 ∂x ∂z



 X(x, z) = 0,

∂2 ∂ − 2ik 2 ∂y ∂z

 Y (y, z) = 0

.

(2.3.8)

The solution of the paraxial form of the Maxwell equations is rather complex, therefore the nal solution solved in Cartesian coordinates listing all contributing functions and factors is stated here (containing Hermite polynomials

Hn,m ,

linear

superposition of these is solution as well):

Em,n (x, y, z, t) = e · E0 Xm (x, z)Yn (y, z)e−ikz eiωt   √ x ω0 x2 kx2 2m + 1 Xm (x, z) = Hm ( 2 )exp − 2 −i +i η(z) ω(z) ω(z) ω (z) 2R(z) 2   r √ y ω0 y2 ky 2 2n + 1 Yn (y, z) = Hn ( 2 )exp − 2 −i +i η(z) ω(z) ω(z) ω (z) 2R(z) 2 r

26

(2.3.9)

2 Theoretical & Technical Background

2.3 Geometrical and wave optics

with

zR =

πω02 n λ s

ω(z) = ω0   zR2 R(z) = z 1 + 2 z

Rayleigh length,

1+

z2 zR2

beam radius, (2.3.10)

curvature radius of the wavefront,

η(z) = arctan( This set of solutions is called

z ) zR

Gouy phase.

Hermite-Gaussian-modes,

also TEMm,n modes

(transversal electro-magnetic, analog to waveguides). With a xed wavelength parameters

ω0 , m, n

λ, the

and origin of the z-axis/ waist position give a complete set of

information for the beam. All modes are visible and contribute to the laser beam after it is coupled out from the laser. The most important mode TEM0,0 has 0 knots and is rotationally symmetric. Possible modes are depicted in gure 2.3.1.

Transversal intensity distribution of Hermite-Gaussian-modes. Shown are TEM0,0 , TEM1,0 , TEM2,5 and the superposition of TEM1,0 + iTEM0,1 , the so-called donut-mode. Figure was taken from [Fac10]. Figure 2.3.1.:

The experimental important value of intensity

I

(transported energy per unit area,

perpendicular to the main propagation direction, and time) is determined from the electrical eld by

I = c ·  · |E|2

(2.3.11)

The solution for the TEM0,0 mode in a plane perpendicular to the z-axis gives

I(rx,y , z) = I0 (z) · e



2r2 x,y ω 2 (z)

(2.3.12)

This Gaussian intensity prole is the eponym for the name Gaussian beams. The

27

2 Theoretical & Technical Background parameter

ω(z)

2.3 Geometrical and wave optics

is a measure for the local radius of the Gaussian beam along its

optical axis: The electrical eld has dropped for

1 I . At e2 0

ω0 ,

z=0

rx,y = ω(z)

to

1 E , the intensity to e 0

the Gaussian beam reaches its minimum radius

ω(z),

which is here

which is the focus or the beam waist. Its radius changes hyperbolically along the

direction of propagation according to equation 2.3.10 with a characteristic length For large z the Gaussian beam diverges linearly with the angle of divergence

ω(z) ω0 λ = = z→∞ |z| zR πω0 n

tan Θ = lim

,

zR .

Θ

(2.3.13)

a complete calculation of the Gaussian beam path with given vacuum wavelength

λ

is possible.

Laser focusing, resolution and spatial ltering Various methods exist to determine the waist of a Gaussian beam. A common one is the knife-edge-method. A razor blade is inserted between the laser and a power meter to check, until when the detected power has dropped to a particular value (e.g. 10 %). Because the laser specications used in this setup was provided with a technical specication, that contained the divergence angle, a complete calculation of the beam path values were possible with the well-dened properties of the established optical components. To simulate the shape of the laser beam in the focus, which is often referred to as

® program was deployed. The

the excitation point spread function (PSF), a MatLab

program uses an integral representation of the light intensity in the focus region taking several system-relevant factors into account [NWH07]. The results of this calculation and a comparison to experimentally obtained PSFs are outlined in section 4.1. In the setup of this work, it was necessary to expand the laser beam to fully illuminate the active spatial light modulator (SLM) surface and to use the maximum possible area of the objective's back aperture (see section 3.3). By expanding, the divergence angle is reduced by the same factor as the beam is expanded, dened by the focal distance

f

relation of the set of lenses

f1 /f2 .

This allows the laser beam

to travel a longer distance still being bundled and conned. A concave lens, which has a negative focal length, can be used to reduce the length of the beam expander, but in this setup higher modes than TEM0,0 were spatially ltered by introducing a

28

2 Theoretical & Technical Background 5

µm

2.3 Geometrical and wave optics

pinhole at the intermediate focal plane, calculated by

Pinhole diameter (microns) with

f

=

8·λ·f , D·π

as the focal length of the objective lens and

D

(2.3.14)

the input beam diameter.

The theoretical limit to the focusing of a laser, which is called the diraction limit, is given by equation 2.1.10. According to this Abbe derived the resolution

r=

0.61 · λ . NA

r

as

(2.3.15)

It corresponds to the minimum distance of two closely spaced airy disks (equal to the PSF) in the diraction pattern that are still distinguishable. Typically it means, that the maximum of one airy disk falls into the minimum of the second one(at angle

θ ≈ 1.22 λd

θ

for small angles

and far away from the aperture). The 60x high-

quality water immersion objective with a numerical aperture (NA ) of 1.2 therefore gives a theoretical value of

λ/2

or 272 nm in the setup situation. This should not

be confused with the size of the detection PSF, which will be determined in this experimental work using a point-like nanobead and will give a smaller value, but well

+ in agreement with another theoretical consideration done by [CSR 10] for exactly the same objective. Regarding confocal microscopes, the full width-half maximum of the PSF is used more often instead of the more complex airy pattern description, resulting to

r = 0.4λ/NA ,

giving 181 nm in our 543.5nm laser wavelength setup.

Because both the excitation and the detection PSF can be approximated by a Gaussian function, their product corresponds to a convolution of two Gaussians with their specic standard deviation

σ1,2 .

The resulting width is

σres =

p σ12 + σ22 .

It

should be noted that the detection PSF from a point-like source will be signicantly smaller than the excitation PSF, thus the visualized PSF will almost correspond to the excitation PSF. Another important factor is the ability to acquire all necessary information from the optical system via a CCD detector, which samples the image.

For this, the

Nyquist theorem is applied. In brief words, the Nyquist theorem accounts, that the frequency of the sampling rate should be roughly twice as high than the measured frequency to acquire all information over the whole bandwidth. In terms of an optical system, it means about 2 pixels should be available for the FHWM of the Gaussian

29

2 Theoretical & Technical Background

2.3 Geometrical and wave optics

PSF. Because the CCD is a two-dimensional array, the value should be multiplied



by

2,

giving roughly 3 pixel per FHWM. Section 4.1 will show, that this condition

is well satised in the setup.

Properties of optic materials Dierent optic media are used in this setup. They can be described by properties such as their refractive index, reection, transmission and absorption. The refractive index

n(λ)

indicates the property of a medium to refract light, calculated in terms

of geometrical optics by the relation of the two refractive indexes after the transition of the light beam

n2 sin θ1 = . sin θ2 n1

(2.3.16)

Its variation with the wavelength is called the dispersion relation and is unique for each material. By dening a complex index of refraction the dielectric eld are introduced and

n ˜ = n + iκ, the properties of

κ indicates the amount of absorption loss when

the electromagnetic wave propagates through the material. The reectivity can be calculated at normal incidence by

 R=

n1 − n2 n1 + n2

All three optical properties (absorptivity related by

A,

2 .

reectivity

(2.3.17)

R,

transmissivity

T)

are

A + R + T = 1.

Typical deviations from an ideal lens, such as aberration and its eect of astigmatism, are related to the optical properties outlined above.

However, staying within

the paraxial approximation of the wave equation will not yield these eects, since the dimensions of the lens within the x-y plane have to be considered. Aberration is divided in two categories:

spherical aberrations, which describe the change of

focused light dependent of the distance from the center of the lens and chromatic aberrations, which are due to the dispersion relation and will focus light dependent on its wavelength at dierent spatial positions from the focal distance of a lens. Astigmatism occurs, if light will be incident non-parallel to the optical axis of a lens. Such imperfections cause an enlargement and distortion of the ideal considered paraxial-wise assumed, diraction-limited focus.

30

2 Theoretical & Technical Background 2.4 Phase hologram computing algorithms

Fourier optics Fourier optics is the study of classical optics using Fourier transforms, in which the wave is regarded as a superposition of plane waves which are not related to any identiable source. It serves well for description of (Fraunhofer or Fresnel) diraction, is used in image processing techniques and touches the work of this thesis due to the fact, that a Fourier transform algorithm is applied in an optical system based on a diractive element.

2.4. Phase hologram computing algorithms The experimental setup presented in this thesis utilizes an active, programmable diractive optical element (DOE). Its technical details and working principle is described in the section 3.1 of the following chapter. In brief words, it is a 2D array of pixels that can alter the phase and amplitude of light individually. For underlying optical principles please refer to section 2.3. The term hologram arises, if the wave properties of light are used to create images. Due to the electromagnetic wave-like nature of light, which is characterized by phase, amplitude, polarization and its direction of propagation, and the fact, that a lens produces the Fourier transform of an input image at its focal plane, a spatial light modulator can be used to create a hologram by modulating amplitude and phase of the incident light. Thus, in principle, an SLM creates any desired excitation pattern in the image plane [Sch05]. However, in reality, a spatial light modulator (SLM) will not be able to address both parameters in that straight-forward way. Thus a signicant amount of commercially available SLMs are build to be switchable either for pure amplitude or pure phase modulation of the incident light. Phase-only modes allow to modulate the laser light in such way, that laser light is used eciently to generate particular patterns when the light recombines in the image plane.

Because there

+ is no analytical solution to calculate the corresponding Fourier transform [DSD 01] of any desired pattern in the image plane by phase-only alternation, a wide range of algorithms have been introduced in the eld of holographic optical tweezers. In the following, I will introduce a number of important algorithm and their theoretical principle. In 1972, Gerchberg-Saxton (GS) presented a practical algorithm for the determina-

31

2 Theoretical & Technical Background 2.4 Phase hologram computing algorithms tion of phase from image and diraction plane pictures [GS72]. This algorithm works iterative and retrieves the phase of the complete wave function, whose intensities in the diraction and imaging plane are known, related by a propagating function such as the Fourier transform. Originally intended to be protable in electron microscopy, crystallography and possibly photography, this algorithm has become one foundation for the computation of phase holograms to achieve the desired excitation patterns in holographic optical tweezers. It should be noted, that the algorithm gives here the necessary phase hologram to the given, desired intensity distribution of light in the specimen plane. Figure 2.4.1 summarizes the principle of the GS-algorithm in a schematic drawing:

Figure 2.4.1.:

Phase determing Gerchberg-Saxton algorithm.

The rst step is to supply the source intensity (in form of a 2D or 3D array) and an initial-guess for the phase hologram that will give the desired target intensity pattern after the Fourier transformation (FT). This guess can be completely random, however, a more intelligent guess retrieved from a fast calculation will decrease the time until the algorithm converges signicantly.

This immediate set of phase and

amplitude is then Fourier transformed, and the obtained intensity gives the target intensity in the image plane. In the next step, the phases from the image plane are fed into a back loop of the algorithm, but the target intensity will be replaced by the desired intensity pattern.

Another inverse Fourier transform follows, and the

obtained phases represent the necessary phase hologram. Then the loop repeats by the rst step. Holographic optical tweezers, which was the rst eld in optics and biophysical re-

32

2 Theoretical & Technical Background 2.4 Phase hologram computing algorithms search that adapted this basic theoretical work of Gerchberg-Saxton, impose specic needs on the ability of these algorithms. At rst, they should be ecient, so that laser power loss is reduced to a minimum from the source to the specimen plane. Secondly, they should be eective to create the desired patterns suciently precise in terms of shape. Thirdly, they should be fast to allow video-rate manipulation [HPL09] while performing the experiment.

Lastly, a minimum of uniformity for multiple traps is

desired to avoid the o-line normalization of the amplitudes from autocorrelation curves.

A catalog of dierent algorithms exists that have been evaluated with re-

spect to these properties, and usually demand a trade-o depending on the most important attribute that shall be fullled. Because a state-of-the-art computing power was available for this project, and the FCS patterns were not changed with the measurement time, video-rate calculation speeds were not essential. In spite of this, it was crucial to have diraction-limited spots that were eectively produced by phase holograms to provide point spread functions as close as possible to the assumptions from the 3D Gaussian model. Additionally, uniformity between the spots and a sucient level of eciency was desirable, due to the rather low laser power available. The GS-algorithm provides sucient eciency and eectiveness after more than 30 iterations, which took about 15 seconds to compute. Yet it lacked adequate uniformity of intensity distribution to be considerably superior to the less complex Fresnel

+ lenses approach chosen by Colyer [CSR 10]. Therefore an existing adaption of the GS-algorithm, direct towards almost perfect uniformity between the generated spots, was implemented, called the Gerchberg-Saxton weighted algorithm. Weights are introduced to correct the initially achieved solutions with a bias toward uniformity. In the setup situation with the PPM included, all algorithms utilize the phase shifts

∆m j picked up by the light (of wavelength m

λ)

as it propagates from pixel

j

to spot

(the following description according to [SCDL08]). Phase shifts are calculated by

scalar diraction theory, where the complex amplitude of the electric eld at the

j th

pixel (see also gure 2.4.2)

uj = |u| exp(iφj ) is taken to the location of the

mth

,with phase shift

φj ,

spot in the image space [Goo05].

up the contributions from all N pixels we obtain the complex amplitude

33

(2.4.1)

Summing

vm

for the

2 Theoretical & Technical Background 2.4 Phase hologram computing algorithms electric eld at the position of spot

m,

X

vm ∝

|u| exp(i(φj − ∆m j )

(2.4.2)

j=1,N the phase shifts

∆m j

are given by

πzm 2 2π (xj xm + yj ym ) (xj + yj2 ) + 2 λf λf

∆m j = with

xj , yj , xm , ym , zm

,

(2.4.3)

according to gure 2.4.2 (b).

The normalized eld at spot

m

Vm =

is given by the equation

N X 1 m exp(i(φj − ∆j ) N j=1

and is related to the normalized intensity at spot

m

,

by

(2.4.4)

Im = |Vm |2 .

A perfect

uniform, eective and ecient hologram would create a single diraction-limited focus at the position of the

φj

at each pixel

that for

φj =

j

mth

spot, theoretically possible by choosing the phase

to cancel out the phase shift as the light propagates to spot

m,

∆m j all pixels (j =1,...,N) interfere constructively at the position of spot

m. For this ideal Im = |Vm |2 = 1.

situation, all terms in sum 2.4.4 are real and equal to

1/N ,

so

Since the target intensity is an array of bright spots surrounded by darkness, it is not necessary to calculate the complex eld in points whose intensity will be replaced by zero before back propagation.

Concerning the GS algorithm, the Fast Fourier

Transform (FFT) has drawbacks, which can be avoided, by directly calculation the eld at the spot locations as done in equation 2.4.4. Table 2.4.1 summarizes dierent properties of existing algorithms. The performance is quantied by the three measures eciency, uniformity and the standard deviation:

e=

X m

Im , u = 1 −

p max[Im ] − min[Im ] , σ = h(I − hIi)2 i/hIi max[Im ] + min[Im ]

(2.4.5)

Eciency describes, how much of the source intensity will be transformed into the trap intensity. Uniformity is a measure to illustrate how equal the power distribution

34

2 Theoretical & Technical Background 2.4 Phase hologram computing algorithms

(a) The beam from a laser is widened in

(b) Geometry of pixel and trap positions relative to

a beam telescope and illuminates an SLM. The rst-order diracted beam is collected by the Fourier lens; as the SLM is positioned in the front focal plane of the Fourier lens, the complex amplitude in the back focal plane, F, is the Fourier transform of the complex amplitude in the SLM plane. The remaining combination of lenses, including a microscope objective, images the beam in the Fourier plane into the central trap plane, P.

the (eective) Fourier lens's focal planes. The transverse position of the jth pixel in the SLM plane is (xj ; yj ), the position of the mth trap relative to the centre of the Fourier plane is (xm ; ym ; zm ). x and y are the two transverse coordinates, z is the longitudinal coordinate.

Figure 2.4.2.: (a)Simplied standard holographic optical tweezers (HOT) setup and (b) Schematic HOT explanation.Both taken from [SCDL08].

is between spots, and the standard deviation is a more descriptive indicator of the occuring power variation. Some algorithms, such as Random Mask Encoding (RM), Superposition (S) and Random Superposition (SR) serve outstanding in terms of small computational cost and very fast converging results after a handful of iterations. However, being useful for video-rate manipulation in HOT, they suer in low eciency, bad uniformity and if checked, will most probably not achieve the demands of a diraction-limited PSF as desirable for FCS. Considering that computational cost is not a limiting factor, the weighted Gerchberg-Saxton (GSW) algorithm gives the best results in terms of uniformity and high eciency. This experimental work employed rst the less complex Gerchberg-Saxton (GS) algorithm, to check the performance in terms of 3D Gaussian foci. After successful runs, the GSW algorithm proved its brilliant performance for any given pattern. It should be noted, that the table displays the results for two dierent patterns, which were either symmetric or less-symmetric. In many cases, slight changes of the desired excitation patterns towards less symmetry

35

2 Theoretical & Technical Background 2.4 Phase hologram computing algorithms algorithm

e

u

σ

K

scaling

RM

0.01 (0.07)

0.58 (0.79)

16 (13)

1 (1)

N

S

0.29 (0.69)

0.01(0.52)

257(40)

1 (1)

N x M

(%)

SR

0.69 (0.72)

0.01 (0.57)

89 (28)

1 (1)

N x M

GS

0.94 (0.92)

0.60 (0.75)

17 (14)

30 (30)

K x N x M

AA

0.93 (0.92)

0.79 (0.88)

9 (6)

DS

0.68 (0.67)

1.00 (1.00)

0 (0)

GSW

0.93 (0.93)

0.99 (0.99)

1 (1)

30 (30) 5 7.5 x 10 (1.7 x 30 (30)

K x N x M

5

10

)

K x P x M K x N x M

Summary of the theoretical performance of some algorithms for shaping of a highly symmetric 2D and a less symmetric 3D structure (in brackets). The algorithms are random-mask encoding (RM), superposition (S), random superposition (SR), Gerchberg-Saxton (GS), adaptive-additive (AA), direct search (DS), and weighted Gerchberg-Saxton (GSW). The 2D target trap structure is a 10 x 10 square grid of bright spots, the 3D target structure consists of 18 traps located on the sites of a diamond-lattice unit cell. The eciency, e, and uniformity measures, u and σ , are calculated after K iterations. The right-most column refers to computational cost scaling, where M is the number of traps, N is the number of pixels in the hologram, and P is the number of gray levels (256 here). [DLIR07]. Table 2.4.1.:

led to a faster computation, fewer ghost traps and an overall better performance of the hologram calculation. The GS algorithm oers the opportunity to be extended into 3D and shaping each focus individually [CKG02], allowing even more degrees of freedom for excitation. However, a corresponding exible FCS detection unit does not yet exist. Either a set of single APDs would have to be calibrated for each spot, or a smart optic - which could involve another SLM as well- could image the pattern onto an advanced CCD chip.

M additional degrees of freedom wm and maximizing the weighted sum m wm |Vm | with the constraint that all |Vm | are equal. The weights for the current (k th) iteration are calculated The chosen GSW algorithm has been derived by introducing

P

according to

k−1 i h k−1 Vm k wm = wm |Vmk−1 |

(2.4.6)

before the phase hologram is calculated using

" φj = arg

# X

k m wm exp(i(∆j + θm )) .

m

36

(2.4.7)

2 Theoretical & Technical Background

2.5 Physics of lipids

An example hologram for an 8 spot excitation pattern, with added correction picture (see section 3.1) is shown in the appendix A.3.

2.5. Physics of lipids Biophysics uses the methods and theories from physical science to study biological systems. The understanding of biological functions has increased tremendously during the past 50 years, accompanied with progress in physics and technology, and has reached a point, where macroscopic biological processes are related to molecular interactions on a nanoscale.

Cells of arbitrary function from any organism have a

bouquet of fundamental features in common. To one of the most important compartments belongs the membrane, as a precondition to maintain the spatial organization of life. In order to fulll a variety of tasks for an organism to function, the membrane exhibits highly specialized constituents. The best barrier between aqueous compartments is a hydrophobic layer, because water-soluble components of the cell will not pass it directly, the structure is exible and allows growth for the cell, as well as the fact, that it assembles spontaneously.

Cells are of microscopic scale and even the

smallest ones are visible by light microscopy. However, the very core of membranes, which are the essential barrier of the cell to the external environment, cannot be resolved by the same method, being only 5 nm in thickness.

2.5.1. The lipid bilayer and other model systems This hydrophobic layer is made of lipid molecules. They are amphiphilic molecules, therefore polar on one end and non-polar on the other end. A broader understanding of the underlying physical processes, that occur at the interaction to water, the inclusion of active membrane proteins and the phase organization of complex lipid mixtures, as found in biological membranes, will lead to the knowledge of basic and crucial processes of life. This section will briey summarize known properties regarding biological membrane model systems such as lipid vesicles, supported lipid bilayers (SLBs) and monolayers, which are used in this experimental work. At low concentrations, lipids dissolve in water. However, at a critical concentration they form into structures, whose shape is dependent on the form of the lipid molecules and can aggregate to a number of possibilities (see gure 2.5.1).

37

2 Theoretical & Technical Background

2.5 Physics of lipids

(a)

(b)

(c)

(a) dierent lipid molecules, (b) chemical details of a phospholipid containing a negative phosphate in the head group and (c) lipid formation. Images (a) [Tif11] and (c) by Mariana Ruiz Villarreal.

Figure 2.5.1.:

Water, being crucial for life due to its unusual properties of dissociation and polarity, forces the lipid molecules in an energetically favorable state where the unpolar (hydrophobic) region is shielded o and the polar (charged, can be either positive or negative), hydrophilic group is exposed to water. As seen in gure 2.5.1 (a), lipids can have one, two or three hydrophobic tails. The sterol is a more compact and curved lipid than the other membrane components. Therefore the spatial appearance of lipids varies, being described by dierent factors to relate the volume of the head group to the tail. A micelle is the smallest possible aggregate, mostly favored by lipids with one tail.

Lipids with two tails in a sucient concentration tend to form liposome

vesicles. This process can be speeded up by sonication and is an essential step for the forming of lipid bilayers. These small uni(/-multi)lamellar vesicles (SUVs) can be forced to bigger sizes, which approach the macroscopic size of a cell and therefore are a popular object in biophysics. Their large radius, which is the membrane curvature, allows to approximate a lipid bilayer with low curvature if studied at the top of the giant unilamellar vesicle (GUV). Bilayers are used in scientic and practical applications for many reasons [CB07], including a well-dened orientation and position, hence providing a good accessibility for dierent surface-sensitive techniques. SLBs can only be prepared guaranteeing proper execution of dierent steps. An interim stage of the protocol is the formation of lipid vesicles, that can be used

38

2 Theoretical & Technical Background

2.5 Physics of lipids

themself as a model system. Monolayers, representing the third model system, emerge on top of a water surface with a boundary to air.

Taking the nature of lipids in

account, a sucient amount of added organic solution on the water surface will ow with the head group directed towards the air-water-boundary. This simple system will exhibit similar behavior as seen on GUVs and SLBs, and is therefore of scientic relevance. The exact lipid composition will determine several properties of this bilayer, in

+ interdependence of phase transition temperatures and shapes [KSB 03].

(a)

(b)

(a) Space lling model of sphingomylin and cholestoral to demonstrate the shape, (b) Inuence of curved(unsaturated) chains on bilayer formation. Figure 2.5.2.:

Biological lipids originate from two distinct types of biochemical precursors: ketoacyl

+ and isoprene groups [FSM 09]. Following this approach lipids can be classied into two categories and their further subgroups: fatty acids, glycerolipids, glycerophospholipids, sphingolipids, saccharolipids and polyketides, which are constituted from ketoacyls, as well as sterol lipids and prenol lipids, which originate from isoprene groups. Of these, three major subgroups constitute a biological lipid membrane: (glycero)phospholipids, glycolipids (either glycero- or sphingolipids with a carbohydrate attached) and cholesterol (a sterol lipid). A lipid bilayer can occur in dierent phases [SKS03]: a solid phase, a gel-like phase (liquid ordered) and a very mobile liquid disordered phase (see gure 2.5.3).

39

2 Theoretical & Technical Background

2.5 Physics of lipids

Dierent bilayer phases, from left to right: solid, liquid-disordered and liquid-ordered phase. [BS05]. Figure 2.5.3.:

The solid phase is characterized by a high order with almost no translational diusion. In the liquid ordered-phase, often present in combination with cholesterol, the lipid chains remain in conformational order (not the case in liquid-discorded phase anymore) but translational diusion is allowed. Phase occurance depends on the temperature and lipid composition. There are dierent methods to form these bilayers. In this work, an established protocol of the Schwille lab to constitute a supported lipid bilayer (SLB) on glass or mica was followed.

A lipid mixture diluted in an organic solvent (chloroform

or methanol) is dried by nitrogen to avoid oxidation of unsaturated tails, that will then be found as multilamellar layers attached to the surface of a glass vial. After adding a buer suited to maintain the pH value and to stabilize the conditions of the bilayer, the ask is sonicated for SUV formation. Pipetting these SUVs on a prepared chamber and adding a calcium ionic solution causes the SUVs to burst, after they sediment and settle on the glass or mica surface. A small fraction of these lipids will form a lipid bilayer, which is separated by a thin layer of water from the support, thus allowing to treat it as a free lipid bilayer to some extent [Sac96]. However, interaction with the support is present and should not be neglected, which is observable by the lesser interaction of mica with the SLB due to less surface impurities. The translational diusion of lipid molecules in a bilayer is often studied by uorescence, which is described in section 2.2. This is possible by incorporation of lipidsimilar molecules with an amphiphilic nature into the membrane, or by labeling a membrane compartment with a uorophore. For both techniques, it must be ensured, that the observed membrane stains will behave similar to the overall lipid behavior in the membrane to draw valid conclusions from the observation. For the membrane dye DiIC18 (3), this was done by Muddana et al. [MGMB11] in a theoretical treatment. It proved, that the relative behavior of DiI diusion scales with the overall change

40

2 Theoretical & Technical Background

2.5 Physics of lipids

in diusion, though the absolute diusion coecient is slightly smaller than for the lipid molecules. The situations described are of principle model character, whose theoretical understanding and experimental conrmation is a key strategy towards comprehending the far more complex biological membranes.

The experimental validation of the

theoretically proposed rafts is still under extensive investigation since many years now [BSKS04].

Due to the short timescale of their presence and their tiny size,

even less than the currently available resolution of Stimulated Emission Depletion (STED) Microscopy, they have not been conrmed in measurements by now. However, their presence appears to be important for central biological functions within membranes such as the clustering of membrane proteins [PT89].

The situation is

further complicated by the high level of heterogeneity that exists within and between cell membranes [WT05] due to dierent lipid compositions. A measurement system to obtain this temporal and spatial dependency such as the setup presented in this work, is of key interest to grasp more aspects of the complexity within cells [BKS06].

2.5.2. EggPC SLB as a model system To demonstrate the feasibility for FCS of this setup, it was necessary to work with a model system, that fullls as many as possible out of ve requirements. Firstly, it should supply reproducible and stable results. Secondly, the diusion coecient should ideally lie close to the order of magnitude of

100 µm2 /s

and not vary across

dierent spatial positions in the sample. Thirdly, the concentration of uorophores should be controllable, sucient in its emission intensity and stable to bleaching or quenching. Fourthly, the eort to produce a model system should be kept to a minimum and the handling within FCS measurements should be as easy as possible. This guarantees, that artifacts and experimental limitations will cast no doubt on the obtained results from a new platform using a novel approach within the eld of FCS. A supported lipid bilayer, constituted from EggPC, on glass and stained with a DiIC18 (3) membrane stain satised all out of the ve conditions mentioned above. As described in section 2.5, a supported lipid bilayer is a widely used system, that provides a good base to investigate the behavior of membranes. Within the Schwille group, protocols (the chosen one is briey explained in the next paragraph) and years

41

2 Theoretical & Technical Background

2.5 Physics of lipids

of experience were available to prepare SLBs on dierent supports and for dierent purposes. The advantage of an EggPC lipid composition in comparison to the commonly used DOPC is its better tendency to form well-behaving SLBs. However, the lipid distribution is a complex potato-salad and not completely determined. Diffusion within DOPC SLB membranes was measured before at

2 µm2 /s

+ [PSH 06].

Another advantage is the constraint of diusion within 2 dimensions, that allows a less complex tting model. DiI nicely incorporates into the membrane at manageable concentrations and no major photobleaching at moderate laser powers is observed. To ensure steady and uniform conditions across the membrane surface, it was crucial to follow the protocol precisely. Once obtained, a sample could be used for a period of about 2 days. The rst step in SLB formation is the production of SUVs via sonication. The previously pipetted aliquots, at an EggPC concentration of roughly 4 mg/ml and already added DiI at 0.01 mol %, were sealed with an Argon gas atmosphere to prevent oxidation and placed into the sonicator for at least 15 min until the liquid became transparent.

This optically indicates, that the solution has switched from

the prior (milky) multilamellar vesicles and lipid structures to the desired unilamellar SUVs. These aliquots can be either stored at -20°C, or directly used for the next step of SLB formation.

SLBs can be constituted on mica or glass surfaces.

The latter

ones are less labor-intensive but require a thoroughly cleaning process, to remove as much surface impurities as possible from the cover glasses, and were plasma cleaned to achieve a polar surface that facilitates the SLB formation process. A chamber was built by glueing the wide end of a cut pipette tip to the cover glass. This provided a large volume to assure sucient amounts of buer on top of the SLB as well as a large area for FCS measurements. 0.1 M calcium ionic solution was added after the SUV aliquots were lled in the chamber and it was allowed to stand for 5 min so the SUVs settle on the glass surface, which leads to the bursting of SUVs and forms the membrane only from a small fraction of the lipid amount available. At the end follows a multi-step washing process to remove abundant SUVs and to regain the desired SLB buer conditions, eliminating all calcium ions. Figure 2.5.4 illustrates the lipid composition of EggPC. In contrast to a DOPC model lipid system, EggPC is already far closer to natural conditions concerning its lipid contents, yet will not show a 2 phase behavior.

Incorporation of membrane

proteins would be the next step towards a more biological environment.

42

2 Theoretical & Technical Background

Figure 2.5.4.:

2.5 Physics of lipids

Fatty Acid Distribution within EggPC, [Ava12].

As displayed, EggPC has a complex mixture of dierent lipids. The main components are DOPC (18:1), 18:2 unsaturated, 18:0 saturated and 16:0 saturated. Minor distributions come from shorter lipids as 14:0 and < 3% from long-chained lipids. A 3D model of the main compartment (DOPC) and its chemical structure is shown in the gues 2.5.5 and 2.5.6.

Containing one unsaturated bond in its side chain, the

transition temperature of DOPC is below the freezing temperature of water and will cause a high mobility in the membrane as explained in section 2.5. Other lipids with no unsaturated side chains, characterized by a transition above room temperature, will rather slow down membrane diusion. Other factors that might contribute to slower diusion is the variation of overall chain lengths, where the diusion coecient decreases with longer chains [KS06], additionally in EggPC this can cause friction due to short-time locking of the upper and lower leaet. The applied membrane stain is shown in gure 2.5.7, illustrating its chemical lipidanalogue structure and resuling membrane incorporation. The neutral eect of DiI in membranes at low concentrations and its behaviour according to the lipid dynamics was shown by Muddana et al. [MGMB11] (see section 2.5). Even though gure 2.5.7 (b) indicates, that the DiI molecule will slightly stick

43

2 Theoretical & Technical Background

2.5 Physics of lipids

Figure 2.5.5.:

3D molecule model of predominant DOPC [Ava12].

Figure 2.5.6.:

Chemical structure of predominant DOPC. [Ava12].

Phospholipids Fluorescent Marker DiI as Fatty Acid Analog and its membrane incorporation. [Inv12]. Figure 2.5.7.:

out the lipid plane. However, as Muddana et al. [MGMB11] calculated, the overall DiI prole will rather be directed more towards the center hydrophobic region. The SLB membrane can be split into the upper and lower (directed towards the support material surface) leaet.

Furthermore, DiI will switch very seldom - likewise the

membrane lipids- between both leaets.

It was suggested, that interaction of the

SLB with the support might be stronger for the lower leaet and could cause higher immobile fractions, but this was not clearly shown yet [FSG05].

44

3. Development of a exible excitation and detection FCS Setup This section describes dierent steps to build a exible FCS (fFCS) setup.

Two

main modications are carried out in comparison to a standard one-point FCS confocal setup: before the light enters the objective, the programmable phase modulator (PPM) is placed in a position, conjugate to the back focal plane of the objective's back aperture. Secondly, the standard APD with a glass ber acting as a pinhole is replaced by the EM-CCD. Regarding the excitation part, the inclusion of the PPM requires optical considerations, that are outlined in the following section 3.1.

Be-

cause an easy switching between APD and hardware correlation towards EM CCD detection and oine evaluation is crucial to cross-check measurements and pre-check conditions within the measurement, the detection path is alternated as well (see section 3.2).

Both elements, the EM-CCD as well as the PPM, are controlled by

LabView programmed software. The deployment of these elements and the software development, due to its rather complex nature of technical considerations, has to be taken into account and is there outlined in the following sections.

Concerning

the required spatially resolved detection, using the EM-CCD camera and oine data evaluation, this part of the exible FCS platform relied on the provided foundations of Burkhardts PhD thesis [Bur10]. To control the PPM and calculate phase holograms, the Blue Tweezers (Optics Group, Physics and Astronomy, University of Glasgow, http://www.gla.ac.uk/schools/physics/research/groups/optics/) software, made freely available under the General Public License, was adapted towards the means of this setup.

45

3 Building a exible FCS setup

3.1 Programmable Phase Modulator

3.1. Programmable Phase Modulator The introduction of this thesis outlined dierent approaches to extend one-focus FCS to two or more foci. Among these, one of the rst available optical components were especially designed diractive optical elements, abbreviated DOEs.

DOEs belong

to the group of phased-array optics, that modify the properties of electro-magnetic waves such as light to design lenses (or other) systems.

A known example is the

building of Fresnel lenses in light towers more than hundred years ago, which were much thinner and lighter than its counterpart, the convex lens. Describing the optical properties of lenses by geometrical means (ray optics), the curvature of the airglass-boundary determines the focal lengths.

Switching to wave optics, only the

dierences in phase depending on the spatial position will be of relevance for the determination of the focal point, being the plane in a certain distance, where only a spot of constructive interference remains. Therefore a thick lens can be substituted by a thin lens, theoretically no thicker than the wavelength of the light. Its surface will than vary from

0 .. 2 π

in the same nature as its complete counterpart.

Such approach, in a more complex manner, allows to fabricate a lens in form of a DOE, that possesses multiple spot in its focal plane, therefore more points of constructive interference.

Customly manufactured lenses were used by Goesch et

+ al. [GBA 05] to realize a parallel dual-color FCCS setup. Two DOEs, designed for red and blue laser wavelengths, produced 4 spots, that were then coupled into optical bers and detection was carried out using APDs and succeedingly correlation. Earlier

+ + works by Blom et al. [BJH 02], [BJG 02] used a 4x1 pattern for ow measurements. These DOEs were the result of photolithography, printing pre-calculated and designed micro-structures on glass slides. Their quality and optical outcome therefore depended on the precision of this fabrication process, and was accompanied by the disadvantage of long fabrication time and no further exibility in the setup.

This

type of DOES is nowadays widely deployed in dierent elds such as photo techniques, vehicle engineering, security and image processing; being a versatile tool also for beam shaping and beam separation. Parallel to manufactured DOE lenses, another path was opened by computer controlled spatial light modulators (SLMs).

This term refers to controllable optical

devices, that change the intensity (amplitude) or phase of incident light. If the latter property is modied, they might be referred to equally as programmable phase

46

3 Building a exible FCS setup

3.1 Programmable Phase Modulator

modulator. Dierent approaches exist, to allow computer-based control: Either by electrically or optically addressing of the SLM matrix.

Liquid Crystal on Silicon

(LCoS) is a common technique also present in the device of this setup, previously the SLM matrix optical addressing by laser, which recently was replaced by a Complementary metaloxidesemiconductor (CMOS) array for a succeeding model. The much broader exibility of SLMs, that are increasingly comparable to premanufactured DOE lenses in terms of optical quality, make them a versatile tool in astronomy, atom optics, holographic displays, often in combination with a ShackHartmann-wavefront-sensor to construct an adaptive optics system.

3.1.1. The PAL-SLM principle

® Photonics, X8267 PPM) was used in

A parallel-aligned (PAL)-SLM (Hamamatsu

this work. Its name refers to the type of liquid crystals, that are present in the device. More generally spoken, an SLM can be reective or transmissive, where both options use technology similar to those found in liquid crystal display (LCD). An LCD makes use of the light modulating properties of liquid crystal, which are characterized by their type of ordering (LC phases). Positional and orientational order dene chiral, smectic and nematic phases, to name the most important ones. A nematic phase is the LCD type in the PAL-SLM used in this setup. A reective SLM, as used in this work, allows a much higher diraction eciency (percentage of incident light that is diracted to the desired phase shift) while just slightly absorbing and diusing the laser light.

An electric eld, which is controlled via a laser diode, addresses each

individual pixel made up by several LCs.

This electric eld is induced by a laser

beam matrix modulated through another LCD as seen in gure 3.1.1 (b). This laser diode induced modulation is done to reduce optical aberrations within the phase modulation process. The electric eld in between

0 .. 3 V

will cause the LCs to align from their ori-

ginal PAL positioning in a nematic phase, as depicted in gure 3.1.2 (b), towards a horizontally aligned position, if the full voltage is employed. As any other optically active material, these LCs inherit a refractive index with a certain dispersion relation. Closely looking on gure 3.1.1 (a), a knob is visible, which will rotate the PPM surface 45 ° and lock in another position. This switches between amplitude- or phase-only modulation. The amplitude modulation is a simple relationship of redu-

47

3 Building a exible FCS setup

3.1 Programmable Phase Modulator

(a)

(b)

LCD active surface of the PPM with knobs for mode-switch(left) and cross-section through functional layers of PPM (right,taken from [Pho03]). LD refers to laser diode module. Figure 3.1.1.:

cing the amount of the reected laser pixel-addressed, as known from monochrome calculator displays, whereas the second mode addresses the phase and changes it at least in an interval of

[0..2π],

depending on the incident wavelengths, but sucient

for arbitrary modulation in the visible spectra. Figure 3.1.2 (a) shows the principle of this phase-only modulation, in a transmission graphic for simplication. The liquid crystals, arranged parallel, will align horizontally with voltage applied and thus inducing a phase change only on the light which has polarized along the molecular axis. Perpendicular polarized light will stay totally unaected.

3.1.2. Characterization of X8267 PAL-SLM model To use the PAL-SLM abilities to full scale and best quality, a number of controls play a role. Every PAL-SLM model comes along with specic properties, that have to be regarded for implementation and are described in this subsection. Firstly, a laser beam has to be expanded in such a way, that the whole active square-shaped surface of the SLM is illuminated with polarized light parallel to the vertical sides of the LCD. A precondition to achieve results of high-quality is a uniform intensity over

48

3 Building a exible FCS setup

3.1 Programmable Phase Modulator

Figure 3.1.2.: Principle of phase modulation (a) and parallel aligned liquid crystals of the spatial light modulator (b). Adapted from [Ham05]. Input light leaves the PAL-SLM at the same polarization plane but with changed phase relative to other pixels, depending on voltage address and corresponding change of refractive index.

the whole surface. The SLM will achieve its best performance, if the incident light reaches the surface exactly perpendicular.Under these preconditions, two additional technical limitations have to be checked and calibrated.

Flatness correction Due to manufacturing reasons, the SLM surface will not be at. The LCs will rest in a sinkhole-like plane, being rather at and low in the center, but with increasing curvature and height towards the edges.

The following check by a Michelson-

interferometer gave proof to a height dierence trespassing 4 wavelengths, varying mostly at the edges. This requires a atness correction, which was crucial to obtain well-dened diraction-limited spots. An interferometer was built in such way, that the reections from the SLM surface and a very at

λ/10

mirror were recorded by

a CCD chip. Figure 3.1.3 shows these recordings. The left image (a) was handed over to Hamamatsu. The company demanded more than fty lines lling the active SLM area, which was realized by tilting the mirror. Both pictures visualize the active SLM surface and the overlling of it, present by the less intense reection from the mirror surrounding the square area of interference.

The bending of the lines

in the left image are due to the non-at surface. From this picture a atness correction image was calculated, representing the height topography in terms of a 256 gray value picture. This is possible by Zernike polynomials, as described in previous

49

3 Building a exible FCS setup works [HLS04], [OAMPC07].

3.1 Programmable Phase Modulator

This article is a good reference for a more detailed

covering of correction and calibration of SLMs.

(a)

(b)

Acquired interference lines image forwarded to Hamamatsu for correction (a) and achieved result after correction image (b). Figure 3.1.3.:

Figure 3.1.3 (b) demonstrates how these lines are corrected, and hence are straight after the correction image is displayed on the SLM surface. However, looking closely, another drawback is visible: Due to the fact, that the height of the SLM surface varies by more than one wavelength, the correction picture reects this by a phase jump from gray value 256 to 0. Accordingly, the corresponding LCD pixels will have a jump in voltage from roughly 2V to 0V. This sharp edge is not maintained and is blurred by pixel bleeding, referring to the penetration of the electric eld from the 2V pixels into the 0V pixels. The eect is visible by black lines according to the gray value steps as in the correction picture from gure 3.1.4 (a). The oset between the same line after a phase jump is due to the reason, that the dispersion relation is not considered yet. Alternatively, the height landscape of the SLM can be imaged directly by tilting the reecting mirror of the Michelson-Interferometer in such a way, that both reection beams are exactly parallel aligned.

Figure 3.1.4 (b) illustrates that non-atness

according to the 543.5 nm HeNe laser wavelength, and its correction (c). edges, this correction lacks exactness, since the curvature increases strongly.

50

At the

3 Building a exible FCS setup

(a)

3.1 Programmable Phase Modulator

(b)

(c)

Figure 3.1.4.: Correction Image(a), Michelson-interferometer set to parallel mirror-SLM beam path without (b) and with correction image applied (c).

Phase modulation calibration In the next step wavelength dependencies were evaluated.

The company supplied

measurement data according to a 633 nm laser wavelength and theoretical calculations for other wavelengths (see gure 3.1.5. However, a cross-checking of the true dispersion relation behavior via phase images was performed. Although the experimental obtained phase shift was close to the theoretical consideration, the technical (analog) nature of addressing the LCD via a VGA signal does not guarantee the same conditions, due to the analog voltage conversion. As a VGA splitter was introduced for hologram observation, this step guaranteed a satisfying blaze control, as the function was named for translating the

[0..256]

gray value interval into the

[0..2π]

phase shift. Figure 3.1.6 shows two applied control situations. The supplied phase picture was an image, split into two horizontal halves, whereas the upper half was set to black (gray value 0) as a reference and the lower half to the gray value (only the green channel from RGB was important, therefore a green rectangle) that was checked for its according phase shift. Thus crucial data points to correct the gray values towards 1 and 2

π

and dierent fractions of

π

were obtained and guaranteed the desired

modulation.

51

3 Building a exible FCS setup

3.1 Programmable Phase Modulator

3.1.5.: Phase shift according to applied gray value for dierent wavelengths due to refractive index dependency of λ . Figure

Images for phase shift validation: Gray value of 109 according to 1 π shift (2 images on the left, smaller image is zoomed cut-out of center area), and gray value of 150 according to 2 π shift (2 images on the right). Figure 3.1.6.:

52

3 Building a exible FCS setup

3.2 EM-CCD detection

3.2. EM-CCD detection Within the group of Prof. Schwille, a former PhD student,Markus Burkhardt, showed how to adapt an EM-CCD for FCS detection [BS06]. This section will briey summarize the most relevant conclusions and technical elements of that work. The classic Charge Coupled Device (CCD) technology works by photons that cause the lling of electron (potential) wells which are read out in the following. A so-called standard gain, which is the conversion factor of this readout signal, is possible but done after acquisition. In contrast, the EM-CCD increases the sensitivity to photon detection tremendously by a pre-readout electron gain. For the camera pixels, an electron multiplication exists, that can be set to a certain on-chip gain approaching single-photon sensitivity. In this setup, a Fast EM-CCD was employed. Its readout speed is at least ve times faster than comparable EM-CCDs, however, the total number of pixels is limited to 128x128, but was more than sucient in this work for a limited number of excitation spot and a limited detection area. Burkhardt [Bur10] showed, that an EM-CCD approach is comparable to the APD detection. Instead of the entrance from the glass ber, that serves as a pinhole and is found at a typical

50 µm in diameter, the EM-CCD pixels (square, side length 24 µm)

itself replace the pinhole and provide a useful spatial information additionally, that

+ has been used in other works for imaging FCS [KGS 07]. A direct comparison from the APD, which is single-photon sensitive and reaches about 75 % in terms of quantum eciency (QE), this value is almost achieved by the EM-CCD at its best settings. However, this is reduced to an eective QE due to read-out processes governed by the stochastic nature of amplication, and falls further to about 50 % QE. A full frame readout speed of 500 images per second (2 ms correlation lag time) is possible, up to 5000 pictures per second (µs range of lag times) in specic readout modes using binning or sub-arrays [Tec03]. Because of the on-chip amplication of even single-photon related electrons above noise level, the read noise is is very small in comparison to other CCDs. Burkhardt put a focus in his work to reach comparable properties for the EM-CCD in terms of lag times. Whereas the APD and hardware correlator lag time is found at the order of 100 ns, such speeds are out of reach even for a high-speed Fast-EM-CCD due to the technical readout process. Dierent readout modes are briey described

53

3 Building a exible FCS setup

3.2 EM-CCD detection

in the following subsection, with a main emphasis on the one used in this work.

3.2.1. Readout mode The standard readout of the EM-CCD, as used to obtain single images, is called the Frame Transfer or kinetic mode. After the exposure (up to the whole 128x128 chip), this frame is shifted rapidly (∼

40µs)

in a vertical way to an optically shielded chip

below. This storage chip is then read out, allowing to obtain the next exposure in parallel. A full frame can be read out at its fastest within 2 ms, that are mainly due to 1.6 ms of the sequential readout of the storage chip. If only a subregion of the chip is used, the EM CCD will bin the unused rows together, allowing a higher time resolution.

It should be noted, that limiting the

number of columns will not speed up the readout but still reduce the data size. Subregions below 8x8 pixels did not speed up the readout process signicantly anymore, being characterized by a kinetic cycle (lag) time of 0.3 ms. Two determining gain factors have to be set as described above.

The on-chip

multiplication of electrons before readout (EM-Gain) was set to its maximum value of 255, while the EM-CCD was cooled down to a stable temperature of -40 °C via air cooling. A calibration done by Burkhardt showed, that the actual gain is then 450. The pre-amplier gain, done while analog-to-digital-conversion (ADC), was set as well to its maximum (5x), which allows a better use of the dynamic range in terms of the gray scale at low light levels. A baseline clamp option was activated, which corrects the varying electron oset of the ADC. Without baseline clamp, uctuations in an FCS measurement are dominated by uctuations of the baseline, leading to largely distorted autocorrelation curves. Mostly internal camera exposure noise caused by thermally emitted electrons and clock-induced charges will cause dark noise, without any illumination present.

To

subtract so-called dark noise, every measurement with changed settings required the recording of a dark image, that was used in the o-line, step-by-step data evaluation. The dark images often exhibited xed patterns of rows with varying brightness, which can be due to the horizontal readout process as stated by the manufacturer. At decreasing light levels, the removal of such regularities becomes increasingly important. During the FCS measurements, a large amount of data (∼

54

50

MB) is collected

3 Building a exible FCS setup within short times (.

30s).

3.2 EM-CCD detection

The internal circular buer is limited to 50 MB, which

has to be considered while adjusting the settings. Nevertheless, there is a spooling mode available for the Andor cameras, which allows data transport to the computer while measuring. To drive the readout process even faster, another readout mode, called the fast kinetic mode, allows practically lag times down to

∼ 20µs

[Bur10]. In this mode,

exposed rows are shifted on the image ship to an additionally optical shielded area of the imaging chip for storage, and handed over to the storage ship after an image series. That mode reaches the limits of camera tuning, and is more complicated to operate. Furthermore, it requires the insertion of a well-calibrated razor blade in the detection path to shield a part of the image chip o from light.

Though it would

provide the ability to measure dyes in free solution, the fast kinetic mode was not applied in this work. Diusion coecients greater than

D ∼ 20µm2 /s

are very rare

in the high viscose biological environment of a cell [SSML03], and therefore of less interest.

3.2.2. Implementation in the setup The emitted uorescence light is coupled out over the right side port of the Olympus IX70 microscope. A lens system was built, to facilitate a switch between APD and EM-CCD detection. This is shown in photograph 3.2.1. This part of the setup was enclosed in a blackened box, to prevent exposure by external light, allowing to avoid any further more tedious built-in shielding of the detection path. Once the EM-CCD was adjusted in the optical axis, no further manipulation was necessary and hence no micron screw stage constructed, that suered problems in the work of Burkhardt due to the 5 kg weight load of the EM-CCD. This diculty was overcome by adjusting the detection light path via a mirror. In contrast to the entrance pinhole of the glass ber towards the APD, the EM-CCD chip with a roughly 1.5 mm side length chip oered enough area to cover with small depositioning of the detection path. The EM-CCD was controlled by LabView software on the same PC, that computes the SLM holograms. Furthermore, the eld of view from the EM-CCD corresponded almost to the hologram interface are for spot placement after proper adjustment, which simplied manipulation. Typically, no more than a 40x20 pixel area of the 128x128 pixel EM-CCD was used

55

3 Building a exible FCS setup

3.3 Description of whole setup

Detection light path after coupling out of the IX 70 side port(M). A lens (focal length 200 mm) re-images the detection plane onto the EM CCD chip(E). If a mirror is inserted on the holder in the center, the APD glass ber entrance(F) is illuminated. Light path in orange.

Figure 3.2.1.:

for acquisition, especially multiple spot patterns with less than 4 spots in spatial proximity allowed to restrict the readout area to less than a 20 pixel square and hence enabling short lag times and sucient overall recording time. If settings, such as the total measurement time, lag time or the used subregion where changed, a corresponding Dark Noise image was acquired by blocking the excitation laser light from the sample.

3.3. Description of the whole setup including adapted software Figure 3.3.1 shows a complete sketch of all relevant parts from the exible FCS (fFCS)-setup. The inclusion of a spatial light modulator gives rise to specic demands

+ in the design of the optical setup [MBMUC 07].

® cylindrical Helium Neon

Excitation laser light is provided by a CVI Melles Griot

56

3 Building a exible FCS setup

3.3 Description of whole setup

2 laser system. Output power is 2 mW, beam diameter (1/e ) 0.86 mm, beam divergence 0.81 mrad and random polarization. More than 90 % of the laser power are within the desired TEM0,0 mode, the

M2

ration is

< 1.05

the laser is stable after 15

minutes and exhibits less than 2 % power drift. Because the HeNe laser produces not only the desired and well-behaving Gaussian shaped TEM0,0 mode, a preceding spatial lter is introduced. The same eect could be achieved by coupling the laser into a single mode ber (transmitting only the TEM0,0 mode), but is realized by an according

5µm

pinhole (for calculation see

section 2.3) which could be inserted in the beam expander. An optical density lter assures control of the laser power, that is transmitted towards the specimen plane. After the beam expander (40x,

f1 =7.5mm, f2 =300mm),

the laser beam diameter is 34.4 mm and passes a polarizing lter to achieve linear polarization, that is necessary for the PAL-SLM. The active SLM surface is a square with 20 mm side length, that reects the laser beam now with the imprinted phase hologram. The laser hologram is further reected by a beamsplitter towards a telescope (4f-setup with 2 lenses), to couple the excitation laser hologram into the microscope and towards the back aperture of the objective. The telescope reduces the beam diameter by a factor of 3, to t the square-shaped phase hologram into the 9 mm back aperture, slightly underlling it. Already after the reection of the beamsplitting element in front of the SLM, the laser power has been reduced fourfold. The spatial lter reduces the laser power by a factor of circa 2.5, the lost reection due to over expanding the beam for the SLM by a factor of 2 and the polarizing lter by 2, which means that a laser power no higher than

50 µW

will be available for excitation. A measurement before entering

the objective proved, that the laser power has been reduced to roughly

10 µW ,

which is sucient for FCS but will limit the number of FCS spots to about 10. That problem could be easily overcome by employing a more powerful laser, or by variations in this setup without spatial ltering and a beamsplitter in front of the SLM, but accompanied with a reduction in quality.

+ As suggested in a work done by Polin [PLL 05], an improvement to block the undiracted laser beam would be the insertion of a beam block in form of an opaque pindot. Such pindot was bought from Linos, but its use proved dicult and as further measurements had shown, it did not distort the FCS curves on a relevant scale. Samples were placed on the microscope stage and xed with a weight to reach a

57

3 Building a exible FCS setup

3.3 Description of whole setup

better stability. The objective was mounted on a PiFoc Piezo element, that allowed nanometer precision within the z axis to position the focus exactly. The PiFoc was controlled via PC as well. Two PCs were installed next to the setup.

PC 1 controlled the Coolsnap CCD

camera used for imaging, as well as the APD-hardware-correlator FCS channel.

® based system before Windows Vista®.

Both devices demanded a Windows

PC

2 addressed the hardware driver of the PAL-SLM, the PiFoc and the Andor Ixon EM-CCD. Two monitors allowed the control of all elements while having the actual displayed hologram in site. More Images of the setup, practical considerations for further usage and short explanations of the user-interfaces for the BlueTweezers software, example holograms and the EM-CCD control user interface are outlined in the appendix A.3.

Laser 543,5 nm/ d=0,86 mm

500 mm Optical table 1250 x 1250 mm² with 25 mm M6 grid

Beamsplitter

SLM

Beam Expander M1

M2b

Polarizer 1

Power meter

Olympus IX 70 FCS Setup Microscope L1 M2a Telescope

M2c

Beamblock DC L2 M3

APD/ EMCCD detection unit and Correlator

Flexible FCS setup with optical laser paths, PAL-SLM excitation and APD/EMCCD detection unit. Figure 3.3.1.:

58

3 Building a exible FCS setup

3.4 Data evaluation

Setup information on uorescence detection The light intensity of the emitted uorescence light lies many orders of magnitude below the power density of the excitation lights. Additional photophysical properties require a compromise towards an optimal excitation intensity, which must be high enough to provide enough signal for detection but low enough to prevent oversaturation in the laser focus and to reduce photobleaching and switching into triplet states. Further components are added in the emission light pathway, to exclude external stray light, photons induced by autouorescence and therefore commonly only a dened bandwidth will reach the detector, chosen to cover the maximum interval of the emission spectra if possible. Alternative excitation wavelength can be coupled into the optical path if necessary, but require additional calibration and considerations for the programmable phase modulator 3.1. The laser light is focused in the sample plane, before it is directed towards the back aperture of the objective by a dichroic mirror. This dichroic mirror (D011 Z 543 RDC, further details in appendix) acts as a longpass lter. For the HeNe 543.5 nm excitation wavelength, the dichroic reects approximately 96.5 % into the focal plane. Vis versa emitted light transmission increases from 3.5 % at 543.5 nm to 100 % at wavelengths higher than 569 nm, while the intersection for 50 % transmission is given at 554 nm. The bandpass lter from AHF

®585/65 has a sharp, designed edge for transmission

at 552.5 nm (dichroic transmission here circa 33 %), prohibiting any excitation laser light which has yet passed the dichroic to reach the detectors. Transmittancy is about 97 % to the next sharp cut-o wavelength at 617.5 nm, thus blocking any stray light or undesired autouorescence at longer wavelengths o.

3.4. Data evaluation FCS measurements began with usage of one or two APDs, whose photon counts were evaluated to an ALV-6000 hardware correlator.

This allowed on-line display of

autocorrelation curves and countrates, therefore an ideal reference to check the basic functioning of the FCS setup.

Autocorrelation curves are saved in .asc format.

Fitting was done by using Origin

®

software and user-dened FCS functions.

59

In

3 Building a exible FCS setup

3.4 Data evaluation

the course of the work, a newly developed FCSFit-program by Paul Mueller (personal communications, unpublished program) was utilized, allowing ecient tting of multiple curves and various parameter controls. EM-CCD data was evaluated by Matlab written code and required a number of steps to be controlled. Exposure cycle times, frame pixel size and pinhole size (region of interest for correlation) had to be protocoled and entered manually. Additionally, a dark count picture had to be subtracted. Calculated traces and correlation curves were then treated in the .csv format by using Mueller's FCSFit program. Supplementary informations and comments on code and algorithms are stated in the appendix A.3.

60

4. Creation and Characterization of dierent excitation patterns 4.1. PSF imaging The theoretical considerations in section 2.1 showed, that FCS relies on a well-dened excitation and detection prole close to the 3D Gaussian assumption. Introducing a new optical element such as the SLM in the beam path asks for a cross-check, how the focus remains in comparison to laser beam reected by a at reference mirror. In

+ principal, this can be achieved by FCS measurements in 3D as well [BKK 09]. The advantage of imaging the point spread function (PSF) produced in the sample is a more complete knowledge of the three-dimensional shape and intensity distribution for one focus, as well as a clear comparison between multiple foci whose generation is a main intention in this work. An ideal PSF regarding the Olympus 60x NA1.2W objective in combination with the HeNe laser providing a 543.5 nm excitation light source results in

d = 272.5nm.

This is calculated using the Abbe resolution limit (maximum of airy disk placed in rst minimum of airy disk)

d= with

n sin θ

λ 2(n sin θ)

,

(4.1.1)

being the numerical aperture (NA).

Applying equation

d = 0.4λ/NA

- which applies for the full width half maximum

(FWHM) of intensity, one obtains 181 nm as the lower limit of resolution.

This

denition is easy to apply, since only a Gaussian t is necessary to the PSF data for determination of

d.

PSF imaging was done by imaging z-stacks of an EggPC membrane with sucient (0.5 mol %) dye.

The membrane thickness of roughly 5 nm can be treated as an

61

4 Characterization of excitation patterns

4.1 PSF imaging

innitely thin source in z, however, its x-y-plane will supply an image, which is a convolution of detection and excitation PSF. To obtain the (deconvoluted) excitation PSF, the detection PSF was determined by imaging a 20nm NanoBead.

190 nm

A

d =

(referring to the FWHM) detection PSF was determined by a Gaussian t,

which is in agreement with the theoretical limit of this setup (MatLab based PSF Lab program, [NW10]). Accordingly, the excitation PSF is calculated by using equation

σres =

p σ12 + σ22

(see section 2.3).

The Coolsnap HQ CCD was used to image the PSF, because of its small pixels (6

µm) 0.6 nm

and sucient sensitivity. 1 pixel on the CCD was determined to be

100 ±

(with 1.5x magnication piece inserted, determined with 2 dierent micron

line calibration plates). Expecting a PSF in the range of 272 nm, the Nyquist frequency is fullled and a yet more precise determination was possible by tting a 2D Gaussian function to the obtained images.

2 2

1 6

1 4 0 .0 1 8

1 5 0 .0 2 4

2 8 0 .0

2 9 5 .0

5 1 7 .5 7 7 6 .3

8 1 7 .5

1 0 3 5

2 2

1 0 9 0

2 8

1 2 9 4

1 3 6 3

1 5 5 3

2 4

y

y [1 = 1 0 0 n m ]

5 4 5 .0

2 6

2 0

3 0

1 6 3 5

1 8 1 1 2 6

1 9 0 8 3 2

2 0 7 0

2 1 8 0 3 4

2 8

3 6

3 0 2 2

2 4

2 6

2 8

3 0

3 2

3 4

3 8

3 6

x [1 = 1 0 0 n m ]

4 0

4 2

4 4

4 6

4 8

5 0

x

CCD imaged foci for beam waist value determination and shape control. SLM with correction image applied(left) reference mirror(right). Figure 4.1.1.:

In gure 4.1.1, the SLM focus is shown in Comparison to reference mirror. The focused spot from the SLM without any applied correction is not usable for FCS measurements, as shown in 4.1.2 A 2D image by the CCD, with colors scaled to an RGB lookup table, is illustrated for the center spot (z=0).

Both data sets (x-y-Pixel matrix) were tted by a 2D

z = z0 + A ∗ exp(−0.5 ∗ ((x − xc)/wx )2 − 0.5 ∗ ((y − yc)/wy )2 ) and results 2 shown in table 4.1.1. In the area of an intensity higher than 1/e , the Gaussian

Gaussian are

62

4 Characterization of excitation patterns

4.1 PSF imaging

3 0

1 0 .0 0 4 6 .0 0 4 0

8 6 .0 0

y [1 = 1 0 0 n m ]

1 2 9 .0 1 7 2 .0

5 0

2 1 5 .0 2 5 8 .0 3 0 1 .0

6 0

3 4 4 .0 7 0

8 0 5 0

6 0

7 0

8 0

9 0

1 0 0

x [1 = 1 0 0 n m ] CCD spot image of focused laser beam from SLM without applied atness correction . Figure 4.1.2.:

shape is present, exhibiting only irregularities towards the outer edges.

The SLM

focus smears out to a cross-like shape at the outer edges, whereas the spot of the reference mirror inherits a better homogeneous, circle-like shape. Nevertheless, the quality of the SLM PSF can be regarded as high, since the more important center area agrees well with the Gaussian approximation. As a matter of fact, tting the CCD image data to the 2D Gaussian function, the SLM PSF exhibits yet a smaller spot beam waist radius of 260 nm for the excitation PSF after deconvolution. Reference Mirror

SLM Spot value

sigma

value

sigma

A

1870

8

1952

6

1/e2

253

-

264

-

[nm]

260

1

276

1

[nm] 2

259

1

272

1

wx wy

R

0.97806

0.97509

Table 4.1.1.: Fit values to both foci from SLM and reference mirror with 2D Gaussian assumption

Hence, the implementation of the SLM in comparison to a reference mirror does not enlarge and distort the focus. However, the overall optical conguration demanded by the SLM, will lead to reduced foci quality and a stronger deviation towards the diraction limit. This is mainly due to the input laser hologram, which is of square

63

4 Characterization of excitation patterns

4.1 PSF imaging

shape, into the back aperture of the objective, which is round. To achieve smaller PSFs, it is suggested to slightly overll the back aperture, which is not possible with the holographic imaging of the SLM, because information would be lost otherwise. The z-stage was set to 50 nm step size, with parallel image acquisition.

This

enabled to image the xz-plane image of the foci as seen in gure 4.1.3, exhibiting the expected PSF shape.

y [1 = 1 0 0 n m ] 6

4

6

4

4

6

8 4

x [1 = 1 0 0 n m ]

(a)

2 2 .0 0 8 1 .5 0 1 4 1 .0 2 0 0 .5 2 6 0 .0 3 1 9 .5 3 7 9 .0 4 3 8 .5 4 9 8 .0 8

y [1 = 1 0 0 n m ]

1 5 .0 0 1 7 8 .1 3 4 1 .3 5 0 4 .4 6 6 7 .5 8 3 0 .6 9 9 3 .8 1 1 5 7 1 3 2 0 8

6

8

x [1 = 1 0 0 n m ]

(b)

(c)

(a) CCD spot images transformed to xz-stack to display behaviour of foci in z. xy-plane 200 nm (b) and 500 nm (c) above z=0.

Figure 4.1.3.:

It should be noted, that a slight angle found along the z-axis of the PSF image is due to a corresponding small angle, at which the laser beam carrying the phase hologram reaches the back aperture of the objective.

The focus is very sensitive

to any tiny changes in the previous beam path, because the imaging condition of the 4f-optic is only satised in one conguration.

Microscopic imperfections and

loss of adjustments lead to the acceptable inhomogeneity [LG05] seen in gure 4.1.3. Another contributing factor is the loss of the dened imaging conditions, because the objective is moved up- and downwards, and not the sample carrier stage. For comparison, the theoretical calculated PSFs by PSFLab [NW10] are displayed in gure 4.1.4. The program allows detailed parameter descriptors and was set to simulate the PSF in the xy- and xz-plane, using a NA=1.2x water immersion objective and linear polarized (in x) 543.5 nm laser light. Here the refractive index of water

n1 = 1.333, the Menzel® pre-selected cover glass with precisely 0.17 µm and n2 = 1.5255, whereas the objective is designed for a n2 of 1.515. The xy-plane

is

was calculated to a 100x100 pixel resolution, and kept in the same scale as the experimental obtained images.

64

4 Characterization of excitation patterns

4.1 PSF imaging

3.5 −1

3

y [µm]

−0.5

2.5

2

0

1.5 0.5 1 1 0.5 −1

−0.5

0 x [µm]

0.5

1

(a) xy- plane

(b) xz- plane

Figure 4.1.4.: Theoretically calculated PSF for one focus, regarding the setup situation in this work. Calculation done by PSFLab. ).

A slight mismatch for the designed (objective) and real refractive index of the cover glass causes minor distortions only visible in the z-projection. While the center area with the highest intensity and therefore most relevant contribution is approximable by a Lorentzian function, the edges are not symmetric and exhibit aberration eects. The typical rings of a PSF occur only at negative z towards the objective, at positive z these rings are substituted by a cone-like structure. Other eects occur due to the linear polarized light, that have their maximum impact in the xy-plane at z=0. The focus has two banana-shaped maxima along the x-axis at

y = ± 250 nm.

Polarization

causes the focus to dier from the circular shape towards an elliptical shape, but at low extent and most present in the center.

However, the deviations caused by polarization and refractive index mismatch are one minor contribution to artifacts in this FCS setup.

A more predominant error

source, evoking discrepancy between the Gauss-Lorentz-model and experimental reality, is the slight angle of the PSF as seen in gure 4.1.3, that is already caused by tiny misalignments and therefore hard to correct.

65

4 Characterization of excitation patterns

4.2 Multiple Foci

4.2. Multiple Foci The rst stage to check the performance of the SLM regarding multiple foci was the generation of 2 foci with dierent spacing: from very close and overlapping towards a spacing that reveals no overlap anymore and can be of interest in biological samples, where spatially separated spots for FCS examination of more than

5 µm distance are

likely to be used (see gure 4.2.1).

(a) 0.7 µm distance

(b) 1.4 µm dis-

(c)

tance

3.4µm

CCD imaged 2 foci patterns with dierent spacing to validate pattern appearances(only relevant segment depicted at dierent scale, to be obtained from the spatial separation). Figure 4.2.1.:

At very narrow spacing (∼ by a large overlap

700nm from center to center), that will be characterized considering ω0 ∼ 300nm, the excitation pattern suers strong

distortions and unequal intensity distributions between both foci. This situation is distinctly improved, analyzing the

1.4 µm spacing.

Both foci are very similar in terms

of shape and intensity distribution. A typical characteristic of the diraction nature becomes visible, as 2 near maxima spots of rst order appear along the extended connecting line of both foci center.

Hence, a minimal spacing of

1 µm

between

spots will guarantee a sucient quality. Extending the spacing to larger distances is possible to arbitrary positions, only limited by the eld of view from the EM CCD chip or at macroscopic distances (>

100 µm)

66

by the pixel nature of the SLM, that

4 Characterization of excitation patterns

4.2 Multiple Foci

imitates a blazed grating to achieve spot depositioning. The repetition frequency of this blazing will simply become too large, and it is not possible to display enough lines per mm anymore. The same images are displayed logarithmic for better visibility of near maxima and power distribution caused by diraction of higher order in gure 4.2.2.

Same CCD imaged 2 foci patterns as in 4.2.1 with dierent spacing, scaled to logarithmic intensities (broader segment depicted).Scale bar (right) valid for all logarithmic pictures.

Figure 4.2.2.:

Such near maxima or ghost patterns outside the intended foci will cause loss of intensity, but will not distort the FCS measurements within the selected spots, as shown in the following work. Going on, the performance of the setup while extending to more foci is shown. The following gures in 4.2.3 are set to a logarithmic scale. It highlights the performance of the foci at their boundaries and in all patterns a central pattern becomes visible. It is not a coincidence, that this central pattern looks exactly like the highly distorted spot, if no correction image is applied. A certain amount of the reected beam from the SLM will not be aected by its pixels to imprint a phase shift, but will carry solely the height dierence information in terms of phase, according to the non-at surface of the reective area of the SLM. Therefore it is analog to the uncorrected one-focus setting at much lower intensities (at least one magnitude below). The presence of this spot can not be neglected, however it does not inuence FCS measurements signicantly. The only relevant case is when a focus is placed in the same position as the undiracted spot. The undiracted spot is then almost non-detectable anymore, and its intensity is approximately one magnitude lower, restricting its inuence onto the focus PSF to the boundary region.

This holds only true up to a number of 8

67

4 Characterization of excitation patterns

4.2 Multiple Foci

spots in this setup. Ultimately the power density of every single spot falls to such a low value, that it reaches the intensity of the undiracted spot.

That can be

overcome considering three alternatives, i) increased laser power, ii) by using the

+ pindot [PLL 05] or iii) by introducing the beam at a slightly converging angle into the objective, which will focus the undiracted spot before in a displaced z-plane.

CCD imaged multiple foci patterns, starting with 4 (left), 8 (middle two images) and up to 50 foci (right). Intensities are set to logarithmic scale. Desired equal spot shapes are visible as well as undiracted beam. Figure 4.2.3.:

The relative decrease of intensity within multiple spots would ideally scale by

∼ 1/N ,

using N spots. However, the decrease is stronger due to diraction patterns

and undiracted parts. This is quantitatively analyzed in the measurement of the following chapter, please refer to subsection 5.3.2. As described in section 2.4, the GSW algorithm was introduced to achieve equal power distribution between all spots. The higher the number of multiple foci, the more important was this weighted approach, and its success is described as well in section 5.3. A special case to be considered is the dierence between highly symmetric patterns, or pattern of less symmetry as seen in gure 4.2.3. The Gerchberg-Saxton algorithm will perform inferior in terms of calculation time and its characteristic descriptive values such as eciency, if patterns of strong symmetry are used. This is already noted in the article by Gerberg and Saxton [GS72], where a constant phase as a starting value might not converge. Due to the diractive nature of generating the excitation pattern, less symmetric patterns possess less evident near maxima and keep the power density distribution better restricted within the desired foci. In this work, an excitation pattern of 50 spots was created. Surprisingly, the spots will not increase signicantly in size and keep their well-behaving properties crucial for FCS measurements.

This is a clear advantage against the approach of Fresnel

68

4 Characterization of excitation patterns

4.2 Multiple Foci

+ lens programming installed by Colyer [CSR 10]. The holographic method is superior in terms of smaller spots towards the diraction limit, which is kept even at high numbers of spot. The intensity distribution is almost equal and requires no further normalization through calculative eorts. Here, the highest number of foci generated, does not constitute an upper limit yet. The upper boundary was not tested, because already for the 50 spot pattern there is no sucient laser power anymore available in this setup for FCS measurements. Due to the fact, that the 50 spot pattern proved well-behaving PSFs, successful FCS measurements lay at hand if a more powerful laser is used. An estimated upper boundary of this pattern to create multiple spot excitation pattern is expected beyond 100 spots. A last property to be checked was the behavior of multiple spots in dierent zpositions.

Images where obtained by positioning 8 foci in line (see gure 4.2.4).

Further, z-stacks were obtained and calculated in the xz-plane using ImageJ.

Figure 4.2.4.: Logarithmic CCD image of 8 foci in line with 1 spot kept at the undiracted beam. The undiracted beam does not show signicant inuence anymore if overlapped with foci.

The obtained xz-plane image (see gure 4.2.5) certies, that well-behaving PSF functions occur as well in all 3 dimensions. The varying of intensity between dierent foci is yet presented, because no GSW algorithm was applied.

Figure 4.2.5.:

CCD image of 8 foci in line displayed as recorded xz-stack.

An example hologram necessary for an 8 spot excitation pattern, with added correction picture (see section 3.1) is shown in the appendix A.3.

69

5. Calibration and Validations of the exible FCS setup 5.1. Calibration of the setup An one-focus FCS setup needs a reference dye with a known diusion coecient to determine the t values necessary for succeeding measurements. waist value

ω0

and structure factor

S.

These the beam

As point spread functions (PSF) have been

imaged before in this setup, calibration provided also an additional check if these values agree with each other. It should be noted, that the theoretical assumptions of a 3D Gaussian PSF will dier from the real situation, which will inuence the exact number of both parameters. Alexa Fluor Ester (Molecular Probes

® 546 Carboxylic Acid, Succinimidyl

®) was chosen as a dye to calibrate the setup with APD and

hardware correlator measurements, since it was well suited for the setup as described in Chapter 1. The absolute diusion coecient of Alexa546 is known [PS08] by a precision measurement to

D ∼ 315µ2 /s.

Alexa546 was diluted to 25 nM using 0.1

mM aqueous TRIS buer solution. The diusion time from the t is value

ω0 ∼ 300 ± 20nm,

the PSF imaging.

75 ± 7µs.

This corresponds to a beam waist

which lies reasonably close to the obtained value from

The PAL-SLM was set to a surface correction and the APD

®) in combination with a glass ber (50 µm inner

(SPCM-CD 3017, Perkin Elmer

diameter) serving as a pinhole was used to acquire the trace, which was directly calculated to the correlation curve by an ALV hardware correlator (Photon Counting

®).

Module Type SPCM-CD 3017 by PerkinElmer

To further prove the validity of

the FCS measurement to calibrate the setup with Alexa546, the afterpulsing, eect of measuring time and tting range are briey discussed. The upper curve in gure 5.1.2 shows the whole range of the acquired correlation

71

5 Calibration and Validation

5.1 Calibration of the setup D

0 .2 0

a

M

0 .1 5

o

t a

d

:

e

C

h i^ 2

R

^ 2

A

l:

/ D

G ( τ)

0 .1 0

u d

f o

r m

d

a

t a

0 .0 5

d

if f

r k

u b lin k

c

x a

D

o

5

F

4

C

6

_

S

3

T

F

=

n

t a

le

3

0

=

0

, 9

9

9

0

s

r ip l

1

2

5

. 4

1

E

- 5

1

0

. 3

3

±

0

. 3

6

0

. 0

7

4

±

0

. 0

0

6

. 0

0

0

0

. 4

9

±

0

. 0

2

0

. 0

0

5

±

0

. 0

0

0

7

0

. 0

0

1

±

0

. 0

0

0

8

8

7

[ m

s ]

[ m

s ]

6

0 .0 0 1 0

-3

1 0

-2

1 0

R e s id u a ls

L

0 .0 0 .0 0 .0 -0 .0 -0 .0

a

g

T

i m

-1

e

τ

,

m

1 0

0

1 0

1

1 0

0

1 0

1

s

1 5 0 0 7 5 0 0 0 0 7 5 1 5 0 1 0

-3

1 0

-2

1 0 L

a

g

T

i m

-1

e

τ

,

m

s

Fit to relevant part of Alexa546 curve including triplet fraction

Figure 5.1.1.:

function, which includes the afterpulsing regime. The lower curve displays the countrate, to show that the assumption of uctuations around an average value which stays constant within the measurement time holds true. The average countrate of 12,2 kHz gives a counts per molecule (cpm) rate of 1.2 kHz, which is high enough for good results. The dark count rate of the APD used was approximatley 200 Hz. The fast diusion of Alexa546 in solution leads to diusion times in the magnitude of

µs.

Therefore it is necessary to prove, that the intrinsic property of afterpulsing

from the APD does not inuence the correlation curve in the interval of the t. The upper graph of gure 5.1.3 shows the measured afterpulsing from the APD used. Data was obtained by introducing white light from the Halogen lamp, set to a constant light level, of the microscope onto the entrance of the glass ber. In this case the photon emission represents a random process without correlation. The recorded correlation curve of the APD represents now purely the afterpulsing eect, as seen below. A t is possible with a two-component exponential decay. From the rst data point at

125 ns

up to

1 µs

afterpulsing is the dominating factor within

the correlation curve, seen as well in the full-range display of the Alexa546 curve. Within the range of

[1..10] µs afterpulsing still contributes to the curve,

but reduced

to less than one-fth of its original value and further exponentially decaying. As this

72

G ( τ)

5 Calibration and Validation

5.1 Calibration of the setup

0 .8 0 .7 0 .6 0 .5 0 .4 0 .3 0 .2 0 .1 0 .0 -0 .1

D

L

4

3

1 0

-4

1 0

-3

a

g

t a

:

s e

r

µ

0

W

0

s

A

F

L

m

l e

u

x a

T

5

l l

I n

a

s e

r

e

a

s u

-2

1 0 L

C o u n tR a te [k H z ]

a

a

1 0

i m

e

τ

[ m

4

6

t e

p

o

r e

n

s i t y

w

m

e

e

r

n

d

t

e

n

t i m

s i t y

e

-1

s ]

1 3 .0 1 2 .8 1 2 .6 1 2 .4 1 2 .2 1 2 .0 1 1 .8 1 1 .6

C

0

2 5

5 0

7 5

1 0 0

1 2 5 C

Figure 5.1.2.:

o

1 5 0 u

n

t T

i m

1 7 5 e

0

1 0

2 0 0

2 2 5

o

u

n

2 5 0

t R

2 7 5

a

t e

3 0 0

[ s ]

Full FCS measurement data on Alexa546 with APD

interval overlaps with the data range of the triplet fraction, it would be necessary to correct for this to obtain exact values for the triplet time and fraction as well. For the calibration the value of interest was the diusion time. A t beginning from 20

µs on therefore ensures no inuence of the afterpulsing, but losing the entire data for the triplet fraction as well. The according t conrmed the data with N ∼ 9.8 ± 0.2 and τD ∼ 67 ± 3.5 µs. This ensures the independence of the determined diusion time from the chosen tting interval of data as well. The last relevant test was to ensure the repetitive behavior of curves for dierent measuring times as well. This is shown in the graph 5.1.4, which also displays the improving quality of curves for higher measurement times, a clear sign for the stability of the setup.

73

5 Calibration and Validation

5.1 Calibration of the setup

0 .0 5

A P D A fte r p u ls in g fr o m 1 0 0 k H z tr a c e ( la m p ) a n d 2 0 0 s m e a s u r e m e n t tim e 2 C o m p o n e n t E x p F it o f A fte r p u ls in g

0 .0 4

ExpDec2

Modell

y = A1*exp(-x/t1) + A2*exp(-x/t2) + y0 Gleichung

0 .0 3

7.85388E-7

Chi-Quadr Reduziert

0.98745 Wert

0 .0 2 Average

Standardfehler

y0

7.22307E-4

1.95166E-4

A1

0.01182

8.24008E-4

t1

0.00464

5.3067E-4

A2

0.06778

0.0034

2.98033E-4

2.00015E-5

t2

0 .0 1

0 .0 0

1 E -4

1 E -3

0 .0 1

0 .1

L a g [m s ] Recorded APD afterpulsing with white light. A 2 component exponential t model approximates the afterpulsing behavior suciently. Figure 5.1.3.:

0 .2 4

3 0 ------ 1 8 ------ 1 2 ------ 9 0

0 .2 2 0 .2 0 0 .1 8 0 .1 6 0 .1 4

G ( τ)

G ( τ)

Kor. R-Quadrat

0 .1 2

0 s 0 s 0 s s

0 .1 0 0 .0 8 0 .0 6 0 .0 4 0 .0 2 0 .0 0 1 E -3

0 .0 1

0 .1

1

1 0

L a g [m s ] Figure 5.1.4.:

urement times

Several Alexa546 correlation curves obtained with dierent meas-

74

5 Calibration and Validation

5.1 Calibration of the setup

After the successful calibration, the sample was replaced by the supported lipid bilayer made from EggPC on plasma-cleaned cover slips to serve as a model system for the succeeding EM-CCD measurements. Only the sample, providing a slow diusion coecient in the magnitude of

D ∼ 1 µs,

was exchanged and therefore APD-FCS

data gave a calibration base to continue to EM-CCD measurements as in the next section 5.3. The acquired FCS curve with the APD and tted values are displayed below. EggPC will be present in a liquid phase. The curve in gure 5.1.5 was tted after the afterpulsing but yet in the triplet regime. The correlated data corresponds well to the t model, also giving a realistic value for the triplet fraction of 50 %. The slow diusion of roughly

D ∼ 0.5 µm2 /s

is further considered in the next section.

D

0 .0 4 0

M

0 .0 3 5 0 .0 3 0

G ( τ)

0 .0 2 5

a

o

t e

d

n :

f c s 2

C

h i^ 2

/ D

o

R

^ 2

t a

d

t a

0 .0 1 5

g g P

ll:

u d

a

if f

r k

u b lin k

C

_

S

L

B

=

0

. 9

7

4

4

4

0

. 5

2

0

. 0

1

_

D

iI _

A

P

D

D

F

=

n

0 .0 2 0

E

e

. 6

1

5

0

7

2

, 3

2

E

- 6

5

±

1

±

4

. 2

±

0

. 0

2

±

0

. 0

0

1

5

0 .0 1 0 0 .0 0 5 0 .0 0 0 -0 .0 0 5 1 0

-3

1 0

-2

1 0

-1

1 0

R e s id u a ls

L

0 .0 0 .0 0 .0 -0 .0 -0 .0

a

0

g

1 0 T

i m

e

τ

,

1

m

1 0

2

1 0

3

1 0

4

1 0

3

s

0 1 0 0 0 5 0 0 0 0 0 5 0 1 0 1 0

-3

1 0

-2

1 0

-1

1 0 L

a

g

T

i m

0

e

1 0

τ

,

m

1

1 0

2

s

Acquired 2D FCS curve from EggPC SLB via APD measurement, model system is discussed next section.

Figure 5.1.5.:

The membrane was positioned in the center of the laser focus, therefore providing the minimum of the beam waist radius.

Since any shift of the z-position will be

extremely sensitive to the x-y-dimension of the focus, stable positioning was ensured

75

5 Calibration and Validation with the PiFoc

5.2 Probing the EggPC model SLB

® and controlled via the maximum of the countrate and its stability

within the measuring time.

5.2. Probing the EggPC model SLB 5.2.1. Validation measurements To conrm the diusion coecient measured in the EggPC model system obtained via the new setup in this work, various independent FCS and Fluorescence Recovery after Photobleaching (FRAP) methods were used to cross-check on dierent platforms. This was especially necessary due to two reasons: i) there is no FCS measurement available in scientic publication concerning EggPC SLBs on plasma treated glass support, that determined the diusion coecient; ii) the initial FCS measurement on EggPC as shown in section 5.1 resulted in an unexpected low diusion coecient, being more than four times slower than a DOPC SLB membrane as a known reference. For discussion of this observation see subsection 5.2.3, which contains table 5.2.2, that summarizes the results and error statistics of all validation methods.

®(Carl

One point FCS was performed on an established platform, using a ConFoCor

Zeiss, Jena, Germany) setup. Additionally, two dierent calibration-free FCS methods were utilized. FRAP measurements were evaluated using a classical overall intensity recover approach, as well as a dierent model based upon the smearing-out of the initially bleach/ non-bleach border and discussed in the PhD thesis of Martin Loose [Loo10].

LineScan FCS LineScan FCS can be called a calibration-free measurement, once all spatial(line dimension and distance) and temporal information (scanning rate) is known. This introduces additional external parameters, allowing to obtain absolute results without the need of calibration measurements of reference dyes. LineScan FCS is very precise depending on the exact knowledge of the parameters line-distance and scanning rate, but increasing noise if the focus is displaced in z, causing an enlarged x-y-beam-waist radius. The latter fact is highly signicant while performing FCS measurements on membranes, since the positioning of the focus relative to the 5 nm thickness of a

76

5 Calibration and Validation

5.2 Probing the EggPC model SLB

lipid bilayer will inuence the beam waist dimensions in its relative z-plane strongly (see section 2.1 and equation 2.1.15). Yet within

±

100 nm the waist radius of the

focus is not too divergent, staying within an acceptable interval [HBTS12]. For more details please refer to the PhD thesis of Jonas Ries [Rie08]. Figure 5.2.1 (a) shows the 2D matrix of data obtained after a complete scanning process. The x-axis represents the total scanning time of 300s, the y-axis represents the time (or according spatial position) within one scan. A MatLab program aligns the data after adjusting with pre-known scanning speeds to this image and displays the detected intensities. Naturally, this will vary due to membrane inhomogeneities. Another error source is the start and end of each line scan, where positive or negative acceleration of the laser beam position occurs and leads to data that has to be excluded from following data evaluation [Rie08].

(a)

(b)

Region of LSFCS data t (a) and LSFCS spatial correlation with w0 and chi error (b).

Figure 5.2.1.:

After a region of interest is chosen, autocorrelation (AC) curves with a spatial component (x-axis) are calculated from the scanning data (gure 5.2.1 (b)). These dier from the autocorrelation curves over time, and for better clarity an according AC curve is determined as well (data not shown). From the spatial AC curve, the beam waist value was determined to be 234.5 nm, giving a rst parameter for a successful measurement. In our case it agreed nicely with the expected value for a

® setup.

543.5 nm laser beam in the used Zeiss

77

5 Calibration and Validation The diusion coecient of

5.2 Probing the EggPC model SLB

0.24 µm2 /s agreed with the initial measurement on the

setup described in this thesis.

Circular Scanning FCS Another established calibration-free method in the Schwille group is Circular Scanning FCS developed by Zdenek Petrasek, for more details see [PS08]. Its preciseness depends on the knowledge and stability of a set scan radius and frequency. Originally put in place to measure absolute diusion coecients within solution, its robustness against artifacts was proven on membranes as well [PDS11]. Thus Circular Scanning FCS was chosen to verify the diusion coecient of the EggPC SLB model system as well. Results and parameters are summarized in the following gure 5.2.2. DiI was excited by a 488nm diode laser, that provided a weak but yet sucient emission light to be detected. Total measurement time was 100s, scanning frequency was 200 Hz and scanning radius set to

0.385 µm.

78

5 Calibration and Validation

5.2 Probing the EggPC model SLB

−3

8

x 10

EggPC SLB7

S3DG1 model g(0) 0.00303 (N 330) D 0.288 ⋅µm2 s−1 a 0.191 µm (τD=126 ms) ⋅ χ2r 1.19 ⋅

7 6 5

g(τ)

4 3 2 1 0 −1 −1

10

0

10

1

10

2

τ / ms

10

3

10

residuals

4 2 0 −2 −4 −1

10

0

10

Figure 5.2.2.:

1

2

10

10

Circular Scanning FCS results

79

3

10

5 Calibration and Validation

5.2 Probing the EggPC model SLB

FRAP Measurements Two approaches were chosen to extract diusion coecient from the recovery of the bleached region. The rst method used the smearing of the sharp border, induced via the bleaching, due to the diusion of bleached molecules into the bright non-bleached area and uorescent DiI into the bleached area.

Data was obtained using custom

programmed MatLab software by Martin Loose [Loo10]. Results are displayed below in gure 5.2.3.

(a)

(b)

Figure 5.2.3.: (a)Border Smear of bleached region (t example, last image of 50s) and corresponding (b) t of σ 2 for 50 s evaluation

The acquired bleaching image stacks, as shown in gure 5.2.4 and discussed subsequently, were loaded by the MatLab code based program and a rectangular region of interest was dened, that crossed the sharp bleaching borders vertically. Data was then tted to the model in equation 5.2.1, obtained from the solution of the diusion equation 2.1.16 in 1D with an initial square well concentration,

      1 x − x1 x2 − x I(x, t) = A 1 − erf + erf +B , (5.2.1) 2 σ σ √ where erf denotes the Gaussian error function and σ = 4Dt. Thus D was retrieved 2 as 0.26 µm /s. ® setup, a 10 x 20 µm rectangle was bleached and its recovery was On a ConFoCor recorded over a 50s period, obtaining a new image every one second.

Thoroughly

bleaching was assured by using maximum laser power of the 25 mW argon laser lines

80

5 Calibration and Validation

5.2 Probing the EggPC model SLB

(a)

(b)

(c)

a.Before photobleaching,b.1st image after photobleaching,c.Area after 50s recovery time

Figure 5.2.4.:

488nm and 514 nm, while post- and prebleaching acquisition was done by the 2 mW HeNe 543nm laser line set to a minimum power, that guaranteed satisfying imaging and yet did not induce further signicant bleaching. Recovery curves were not recorded till complete recovery, however, the 50s time interval contains the relevant steep recovery curve part and can be tted on longer timescales due to its smoother asymptotic behavior. This exhibited also a signicant immobile fraction . 5 0

4 5

In te n s ity [A b s o lu t]

4 0

3 5

3 0

2 5

2 0

1 5 0

1 0

2 0

3 0

4 0

5 0

T im e [s ] Figure 5.2.5.:

Example Intensity recovery curve

The data was evaluated and tted with Zeiss Zen software (tting data not shown), which allows the correction of background intensity and the change of uorescence according to a reference region. The diusion coecient is then calculated in case

81

5 Calibration and Validation of a circular bleached area by

5.2 Probing the EggPC model SLB D =

βω 2 [YSY82]. 4τ1/2

Parameter

β

depends on the

percentage bleach, which was roughly 33 % in both measurements, corresponding to

β = 1.08 [YSY82].

Though the plotted intensity recovery curve did not reach a stable

plateau, tting of 2 independent measurements provided similar results. Following

I(t) = A(1 − e−τ t ),

τ1/2 =

ln0.5

−τ

,

(5.2.2)

the rst part of the recovery curve contains the main information for the exponential recovery. A more precise t would be done using Bessel functions, as described in the work of Soumpasis [Sou83]. Soumpasis also demonstrated, that an exponential t will yield a rst approximation, that is less accurate [SCEH06]. Because this FRAP analysis was done to provide an additional test on the EggPC model membrane system, a more detailed calculation was not necessary.

absolut mobile recovery intensity fraction [%] time [s]

[s]

immobile fraction [%]

τ1/2

26.6

37.4

208.9

144.8

62.6

23.6

37.7

205.9

142.7

62.3

Table 5.2.1.:

FRAP data obtained with Zeiss ZEN software

Table 5.2.1 shows the extracted t parameters from two independent measurements. Absolute intensities resemble the average gray value (0..256) in the region of interest.

Recovery time corresponds to

τ

in equation 5.2.2 and

τ1/2

was extracted

+ respectively. The corresponding bleached spot radius of the rectangle [DHF 10] was about

11 µm.

ω

The mobile fraction is underestimated by this tting, because the

bleached membrane region recovered to an almost indistinguishable level of uorescence in comparison to the unbleached area, purely looking at the Laser Scanning Microscope images on longer timescales than 50s. However, the diusion coecient determined around

D ∼ 0.23 µm2 /s with an error of 50% (standard deviation of ad-

ditional measurements) was sucient for a last cross-checking method, averaging over a larger area of the membrane than the previous ones and therefore less sensitive to spatial hetereogeneties of the SLB, in size close to the order of the diraction-limited laser focus.

82

5 Calibration and Validation

5.2 Probing the EggPC model SLB

5.2.2. EM CCD measurement on an EggPC model system The lower graph visualizes an FCS curve obtained with the EM CCD. The EMCCD, operated in Kinetic Mode, was cooled down to -40 °C. The exposure time was set to 0.46 ms. In combination with 0.04 ms readout time this gave a lag time of 0.5 ms. The smallest possible region of interest was chosen (8 pixel square size) and the emission path of the focus adjusted thus being placed in the center of a 2x2 square pixel region. The total measurement time was 30s and the laser power slightly reduced

(∼ 10%)

since the uorescent signal from the membrane was high enough.

0 .0 1 2

D

a

t a

:

3

0 .0 1 0 M

0 .0 0 8

G ( τ)

0

4

0 .0 0 6

o

d

C

h

R

^ 2

e

i ^ 2

l :

p

t a

u

d

t _

0

. 5

i x p

i n

h

_

f c s 2

/ D

o

i f f

L

m

s c y c _

8

p

i x _

a

s e

0

4

0

1

2

. 3

0

7

E

r 0

d

F

=

=

n

0 .0 0 4

s t o

0

. 9

8

6

4

2

6

- 7

5

8

5

. 0

±

1

. 1

4

4

. 7

±

2

. 0

m

s

0 .0 0 2 0 .0 0 0 -0 .0 0 2 1 0

0

1 0

1

1 0

R e s id u a ls

L

0 .0 0 .0 0 .0 -0 .0 -0 .0

0 0 5 0 0 2 0 0 0 0 0 2 0 0 5

a

g

T

2

i m

1 0 e

τ

,

m

3

1 0

4

s

0 5 0 5 0 1 0

0

1 0 L

Figure 5.2.6.:

a

1

g

1 0 T

i m

e

τ

,

m

2

1 0

3

s

Results of EMCCD measurement on an EggPC SLB.

In comparison to the APD measurement, the number of data points up to 10 ms is greatly reduced. No afterpulsing eect and triplet fraction is visible. The evaluated diusion time of 45 ms corresponds to the diusion time evaluated with the APD. The particle number is slightly higher in comparison to the APD, which rather represents membrane inhomogeneities of the chosen sample region. This is due to the fact, that switching the detection path to the EM-CCD requires to slightly reposition the focus on the membrane to guarantee that the product of the detection and excitation PSF overlaps in its minimum with the membrane in z. In the following gure 5.2.7 the averaged image of all obtained data is shown after the subtraction of the dark image. Within the 2x2 pixel region the intensity

83

5 Calibration and Validation

5.2 Probing the EggPC model SLB

distribution is reasonably uniform, also the outer region shows a steady decay of brightness essentially following a 2D Gaussian function.

A v T ra c e

T ra c e

1 0 5 0

1 4 0 0

A v T r a c e [G r e y V a lu e ]

T r a c e [G r e y V a lu e ]

1 3 0 0 1 2 0 0 1 1 0 0 1 0 0 0 9 0 0 8 0 0 7 0 0

1 0 0 0 9 5 0 9 0 0 8 5 0 8 0 0

6 0 0 5 0 0

7 5 0

0

5 0 0 0

1 0 0 0 0

1 5 0 0 0

2 0 0 0 0

2 5 0 0 0

3 0 0 0 0

0

5 0 0 0

1 0 0 0 0

1 5 0 0 0

2 0 0 0 0

2 5 0 0 0

3 0 0 0 0

L a g [m s ]

L a g [m s ]

Trace (left), averaged trace (middle) EM-CCD Measurement on SLB and corresponding averaged EMCCD exposure data (right). Figure 5.2.7.:

The traces of the EMCCD shown in gure 5.2.7 do not correspond to the photon

∼ 900 represents the [0..16384]). The obtained

countrate as in case of the APD. The average value of

gray

value of the EMCCD image, which is 14 bit (interval

gray

value is related to the number of electrons, which have been accumulated due to photon impacts during the 0,44 ms exposure time interval. No afterpulsing occurs, however, dierent eects due to the EM-CCD technology are present as discussed in the chapter EM-CCD detection. Displayed EMCCD traces correspond to the signal level after dark image subtraction.

The dark image pixels were commonly within

the range of 243 till 251. Accordingly any value higher than 251 exhibits acquired uorescence from the sample, reaching as low as 375 embodying a yet evaluable signal. A corresponding FCS measurement with an APD reveals a uctuating countrate just about 65 kHz. An oscillating eect with a frequency of roughly 0.5 Hz is visible in both detection platforms (EMCCD and APD). This is apparently induced by two factors: A slightly shaking and vibrating optical table and setup on the one hand, on the other hand undulation of the membrane and the sample on the objective. The latter is described in [GPF08] and takes place in non-solid lipid bilayers on a tens of nanometer scale, if separated by a conned volume of water to the support. However, its frequency would not be constant. The shaking of the optical table, due to pneumatic bearings performing to a limited extent, was observed as well in the

84

5 Calibration and Validation

5.2 Probing the EggPC model SLB

8 5 C o u n tR a te

C o u n tR a te [k H z ]

8 0 7 5 7 0 6 5 6 0 5 5 5 0 4 5 0

1 0

2 0

3 0

C o u n tT im e [s ] Figure 5.2.8.:

Countrate of SLB measurement, APD with similar settings.

monolayer model system with the same frequency and on the ConFoCor setup, being mounted on the same table. APD and EMCCD traces comparison suggests, that an EM CCD gray value of approximately 25 corresponds to one detected photon in the APD. To estimate the matching APD count rate exclusively from EMCCD data,

C=

g 27.7 · texp

(with C= count rate in KHz, g= gray value,

texp =

(5.2.3)

exposure time) has to be cal-

culated.

5.2.3. Discussion - Further use in next experiments All validation methods conrmed the diusion coecient obtained on the platform of this setup by APD and EMCCD measurements (see table 5.2.2). The given standard deviation corresponds to the deviation within the measurement results and reects the bandwidth of possible diusion speeds of the EggPC model system constituted on glass. This is due to the fact, that in spite of a careful cleaning process, a relevant amount of impurities will remain on the glass surface. These impurities will interact with the SLB, and can cause partial immobilization in size lower than the diraction limit and will distort the diusion in general. However, the interval is acceptable and serves as a good system to start the multiple foci measurements. Yet another observation to be discussed is: The slow diusion in comparison to

85

5 Calibration and Validation

5.2 Probing the EggPC model SLB

Method ConFoCor Point-FCS LineScan-FCS Circular-Scanning FCS FRAP-Intensity recovery FRAP-border smear Table 5.2.2.:

D [µm2 /s] 0,2 0,28 0,3 0,23 0,25

σ[±µm2 /s] 0,1 0,04 0,1 0,1 0,05

Results of dierent valid measurements

previously measured DOPC SLBs (which was

2 µm2 /s).

Being more than 4 times

slower, a number of reasons are indicated here that can contribute to this reduction. The only comparable reference, where EggPC SLBs have been measured on baked slides gave a diusion coecient of

∼ 2 µm2 /s

[SCEH06]. Support interaction will

lead to a reduction of D by roughly 2 times in comparison to GUVs, as seen in com-

+ parable DOPC GUV and SLB measurements [PSH 06]. Additionally, the eect of the chosen previous surface treatment of the support is especially strong, changing

+ + the diusion speed by more than three times [SPH 07]. The work of Seu [SPH 07] proved, that etched slides resulted in bilayers that could be treated as almost freestanding bilayers.

The diusion coecient of EggPC SLB on glass is much lower,

positioned at roughly

0.25 µm2 /s.

Because the glass was manually cleaned and

plasma treated, support interaction was not fully eliminated.

Also, as mentioned

above in the description of EggPC (subsection 2.5.2), a major dierence to DOPC is the complex lipid mixture. Dierent chain lengths might cause friction between the upper and lower leaet, however, a main reason of the strongly reduced diusion coecient is likely to be caused by the lipid fraction with a transition temperature above 25 °C. See table 5.2.3, where the lipids in bold represent lipids that contribute signicantly to the overall behavior, and note that 45 % of these lipids have a transition temperature of more than 40 °C. The presence of cholestorol would lead to a 2 phase system, but without it these lipids are most likely to cause an overall reduced diusion coecient.

That process is amplied by the interaction with

a surface, that still contains sucient impurities, along which the SLB can anchor in domains smaller than the diraction limit. Because the number of DiI molecules in the FCS observation area is approximately 50 or higher, an averaged behaviour will be observable. Multi-component diusive behaviour is hard to resolve, especially in the suggested scenario, where lipids or DiI respectively will switch their diusive

86

5 Calibration and Validation

5.2 Probing the EggPC model SLB

behaviour on small timescales and spatial positions way below the focus spot size. An alternative protocol using a mica support with naturally less impurities might prove this by exhibiting a higher diusion coecient.

Lipid product Carbons: Composition Transition name Unsaturation (%) Tm(°C) DMPC

14:0

0.2

23

DPPC

16:0

32.7

41

16:1 PC

16:1

1.1

-36

DSPC DOPC DLPC

18:0 18:1 18:2

12.3 32.0 17.1

55 -20 -53

20:2 (Cis) PC

20:2

0.2