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J. Cell Sti. 83, 313-340 (1986)

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Printed in Great Britain © The Company of Biologists Limited 1986

ALIGNMENT OF FIBROBLASTS ON GROOVED SURFACES DESCRIBED BY A SIMPLE GEOMETRIC TRANSFORMATION G. A. DUNN AND A. F. BROWN MRC Cell Biophysics Unit, 26-29 Drury Lane, London WC2B 5RL, UK

SUMMARY The response of chick heart fibroblasts to grooved substrata was studied using microfabricated grooves and new measures of shape and alignment derived from the moments of cell shapes. Cell shape and alignment were measured on 23 different sets of regular, parallel grooves, which ranged in width from 1-65 to 8-96^m, and in repeat spacing from 3-0 to 32-0^m. The grooves were of constant depth, 069fim. Digitized video images were analysed to extract the zero-, first- and second-order moments of the cell shapes, from which were calculated three measures of cell shape, and three measures of cell alignment. Regression analyses of the measures against parameters of the substratum such as groove width, repeat spacing and the ridge width between grooves show that ridge width is the main parameter affecting cell alignment (alignment being inversely proportional to ridge width), although groove width has a small additional effect. All the differences in cell shape between the different grooves can be summarized to a very good approximation as simple geometrical stretch transformations of the shapes of cells on planar surfaces. Our principal measure of cell alignment, paraxial elongation, is a measure of the necessary transformation. This finding has the interesting biological implication that the shape and orientation adopted by cells, in response to the grooves, are not governed by independent cellular mechanisms.

INTRODUCTION

The problem of how cells align themselves in response to structural or mechanical anisotropy in their environment is still unresolved, even at the level of understanding which properties of the environment are most effective at eliciting the cellular responses (Dunn, 1982). One reason is that the microproperties of the environment are not easy to control or measure, even in tissue culture, but we feel that an equally important reason lies in the current inadequate methods for quantifying the cellular response, which generally extract only a small part of the information presented by the cell behaviour. As an approach to the first problem, we have used chick heart fibroblasts cultured on a range of substrata consisting of regular arrays of parallel grooves made in plane quartz surfaces. These substrata were manufactured using microfabrication techniques developed for the electronics industry. The grooves have rectangular crossKey words: fibroblasts, contact guidance, grooved substrata, microfabrication, image analysis, moments, cell shape, cell alignment, cell orientation, immunofluorescence, actin, microfilaments, microtubules.

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sections of constant depth, but vary in width and repeat distance. The technology for producing these substrata is now readily available and offers much better control over groove profile and dimensional parameters than the use of engine-ruled substrata such as diffraction gratings. To tackle the second problem, the response of the cells as a function of the groove parameters was quantified by using the method of moments to analyse the static shape of fixed cells. It has long been recognized that certain mathematically defined quantities known as moments are valuable for describing irregular two-dimensional shapes. Their use is common in the field of computer pattern recognition, but their potential for analysing cell shape has been largely ignored. Perhaps the reason for this is the difficulty of calculating moments from polygonal approximations of cell outlines. However, their calculation is particularly simple now that methods for digitizing cell images are readily available. Moments have the important property that any shape can be described to an arbitrary degree of accuracy by including as many of the infinite series of moments as are required in the description. Thus the accuracy of the description can be limited by taking only the first few moments of lower orders. In the case of cells, this gives a description of shape that ignores the fine details of the cell outline. This is generally a much more useful description than the commonly used measures of cell shape that take account of the length of the cell perimeter or the 'caliper widths' of a cell, and are therefore excessively sensitive to the presence of fine processes while ignoring the basic shape of the cells. Furthermore, any method for measuring the fine detail of perimeters is subject to errors that are inevitably introduced by the method of approximating the outline; in the worst cases, the measures are more dependent on this method than they are on the shape of the cell. Moments can be made to have all the invariance properties that are desirable in any measure of cell shape: measures can be obtained from them that are independent of the position, size and orientation of the shape with respect to the coordinate system (Hu, 1962). Unfortunately, these moment invariants described by Hu are not easy to interpret and are largely restricted to empirical use. We have remedied this by deriving new moment invariants that are not only easier to interpret, since they conform to intuitive notions of shape, but that are particularly meaningful in the biological system that we use here. Furthermore, our measures differ from each other in their invariance properties so that they can be used to measure different aspects of cell behaviour. For example, some of the measures are not invariant under rotation, so that they can be used to measure cell orientation, and other measures have invariance properties in addition to those already mentioned. MATERIALS AND METHODS

Microfabricated substrata The microfabricated substrata were kindly produced by Mr F. Goodall at the Rutherford Appleton Laboratory of the SERC. Briefly, a mask of the desired pattern was made on chromiumplated quartz by electron beam lithography, the pattern being controlled by a computer programme written in GAELIC. The mask pattern was then contact printed onto photoresist-coated

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quartz by deep ultraviolet irradiation (200-260 nm), and the grooves were produced in the quartz by ion-milling. The grooved substrata consisted of an array of 2 mm X 2 mm areas, each area containing regular parallel grooves of constant width and repeat distance. The combinations of width and repeat used are shown in Table 1. Each grooved area was separated from its neighbours by a margin 0-125 mm wide, and the grooves in each area were arranged to be oriented perpendicularly to those of the nearest neighbouring areas. Grooves were nominally 1-0, 2-0, 4-0 or 8-0 fim wide, but measurement by scanning electron microscopy and by light microscopy showed the true widths to be 1-65, 2-85, 4-85 and 8-96nm, respectively. The mean depth of the grooves as measured by Jamin-Lebedeff interferometry using Senarmont compensation (Publication no. G40-560/l-e, Zeiss, Oberkochen) was 0-69 Jim; this value never varied by more than 0-035 fim.

Chick heart fibroblast culture Chick heart fibroblasts were isolated as explants from 7-day-old embryos and grown in medium 199 containing 10% foetal calf serum, 0-2mM-glutamine, 0"35gl~' bicarbonate, lOOunitsml" 1 penicillin and lOOunitsml" 1 streptomycin, in an atmosphere of 5 % CO2 in air at 37°C. After 2 days in culture the explants were removed and cell outgrowths were dissociated with 0-05 % (w/v) trypsin, containing lOmM-EDTA, resuspended in fresh medium, and seeded onto the grooved substrata at a density of 30 cells mm" 2 . After 24 h, the cells were fixed in 2-5 % glutaraldehyde for 1 h, washed in PBS, and stained for 2 days in Mayer's Haemalum (BDH Chemicals Ltd). The long staining period produced very heavily stained cells, which facilitated image enhancement. The culture was then dehydrated in ethanol, air dried and mounted in DPX.

Microfilament and microtubule staining After 24 h in culture on grooved substrata, cells were rinsed with phosphate-buffered saline (PBS), fixed in 0-25 % glutaraldehyde in PBS for 5 min, washed in Ca 2+ /Mg 2+ -free salts solution (CMF) for 2min, extracted with 0 1 % Triton X-100 in CMF for 15 min, washed in CMF for 2 min, and fixed again in 0-25% glutaraldehyde for 5 min. Autofluorescence was quenched by immersing the culture in two changes of 2mgml~' NaBH 4 in CMF at 0°C for 5 min. Actin filaments were then stained with 2^/gmP 1 rhodamine-labelled phalloidin for 30min at room temperature. Microtubules were stained with YL1 monoclonal rat anti-tubulin (Serotec) for 30 min, followed by FITC-labelled goat anti-rat immunoglobulin G for 30 min. The culture was then washed for 2min in 1 % bovine serum albumin in CMF.

Scanning electron microscopy Cells were cultured for 24 h on grooved substrata as described above, fixed in 2-5% glutaraldehyde for l h , post-fixed in 1% OsO4 for 1 h, dehydrated through 30%, 50%, 70%, 9 5 %

Table 1. Number of cells analysed on grooved substrata Groove width No. of cells analysed 8-96 4-85 2-85 1-68

— — — 239

— — 114 176

— 158 116 115

3-0

4-0

6-0

Planar quartz control: 146 cells.

— 201 138 178

48 167 118 89

68 153 176 103

33 130 109 103

90 57

8-0 12-0 16-0 Groove repeat (/zm)

24-0

32-0

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Fig. 1. Four-frame average of digitized video images of cells on planar (A) and grooved (B) quartz substrata (width 4-85 jUm, repeat 8-0^m). C,D. Enhanced binary images of A,B after residual noise and cells in contact have been removed. Bar, 50 flm. and 100% ethanol, and taken to absolute acetone. The specimen was critical-point dried in liquid CO2, sputter-coated with 10nm gold, and viewed on a Jeol T20 scanning electron microscope.

Image enhancement and analysts Cells were imaged using a Zeiss Standard RA microscope with a X16 plan objective and 80 mm projective eyepiece using bright-field optics, and a Falcon SIT video camera fitted with selective contrast expansion and uniformity correction controls (Custom Camera Design, Wells, UK). This provided a field of view approximately 500 /Um X 500 ^m after image digitization. Image digitization, enhancement and analysis were carried out using a Supervisor S214 imagecapturing/graphics system (Gresham Lion PPL Ltd, Thatcham, UK) linked to a DEC PDP11/44 minicomputer running FORTRAN 77 software. The signal from the video camera was digitized to 64 grey levels at a resolution of 512X512 pixels. For each image, four captured frames were averaged to reduce noise (Fig. 1A,B). Each image of cells was subtracted from a background image to compensate for any unevenness in the illumination and camera response. The resulting image was next converted to a binary (black and white) image by selecting a threshold grey level above which all pixels were set to white and all others to black. This selection was performed under manual control in order to ensure the best correspondence between the original cells and the white areas, which we will call objects, of the binary image. The image was next scanned to remove automatically any objects of less than 300 pixels in size, thus eliminating the residual noise, nearly all the debris, and rounded cells of less than about 20jUm diameter. We assumed that these cells (about 2 - 3 % of the total) were either undergoing mitosis or were dead. In our algorithm for this, the machine recognizes as a single object the whole of an 8-connected group of white pixels. Two pixels are said to be 8-connected if one belongs to the set of eight immediate neighbours of the other. In an alternative algorithm given by Lutz (1979), it is possible to choose either 4-connectivity (in which only the vertical and horizontal neighbours are considered) or 8-connectivity (which also includes the diagonal

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neighbours). Finally, the image was again compared with the original optical image and any remaining objects not corresponding with single isolated cells were removed (Fig. 1C,D). This step avoids the complications of dealing with groups of cells in contact with each other. The enhanced binary image was then scanned again using the same algorithm for object detection and the moments of each cell were stored for subsequent analysis. To avoid excessively large sums in the accumulation of moments, and losses in accuracy during subsequent calculations, we chose the first pixel encountered within each object as the origin of that object's coordinate system. In addition, all computations were performed using the FORTRAN 77 Double Precision Real number facility (7 bytes mantissa, 1 byte exponent).

Calculating the moments Moments of a shape. For each cell, we first calculated the zero-order moment, the two first-order moments, and the three second-order moments of its shape. These six moments describe the basic properties of the shape. The zero-order moment is simply the number (n) of pixels in the digitized image of the cell, and the remaining five moments (m) are calculated by obtaining the following sums from the x andy pixel coordinates of all n pixels:

woo =« mio=Z* mm = Y.y /«2o=Zx 2 m\\ = lLxy ™02=llyZ-

(1)

Because they are calculated by discrete summation instead of by integration, these moments are only estimates of the true moments. But the approximation is very good if n is large (typically 1000 for our cells) and we did not consider it necessary to apply a correction for this. Central moments. Central moments are defined as moments referred to the centroid of the shape as the origin of the coordinate system. They are invariant to translation, i.e. they do not change with changes in the position of the object. The second-brder central moments for each cell were calculated as: (ho = f»2o ~ (wio/wtoo)

Mil = ™n - (wiowoi/woo)

M02 = m02 - (m^/moo).

(2)

Normalized central moments. Normalized central moments are invariant to change in size of the shape. For the second order, these were calculated as follows: »bo = These three moments are the basis for all the subsequent measures.

Calculating the measures of cell shape Hu (1962) has defined two second-order measures of shape that are invariant to rotation: 0i = »?02 + mo