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Microscopy: Science, Technology, Applications and Education A. Méndez-Vilas and J. Díaz (Eds.) ______________________________________________

Introduction to Atomic Force Microscopy Simulation E. F. Franca1, A. M. Amarante2, and F. L. Leite2 1

Chemistry Institute, Federal University of Uberlândia (UFU), P.O. Box 593, Uberlândia, 38.400-902, Minas Gerais Brazil 2 Federal University of São Carlos (UFSCar), Sorocaba, 18052-780, São Paulo – Brazil The atomic force microscopy (AFM) is a powerful for single-molecule force experiment that can characterize physical and chemical properties of biological and polymeric matter at the nanometer scale. However, it does not reveal the molecular mechanisms behind the binding of ligands and conformational changes in biomolecules in atomic time scale. This information can only be addressed by molecular dynamics (DM) simulation, which simulates the AFM experiments through methodology called Steered Molecular Dynamics (SMD). The AFM simulation is usually obtained by integrating the mean force from an ensemble of configurations resulted from a molecular mechanics calculation. In this chapter, we shall concentrate on simulation of the atomic force spectroscopy (AFS), which procedure consist in perform a constant velocity molecular dynamics simulation, recording force and position at each time point, to reproduce and predict the atomic force curves. The AFM simulation showed to be very useful to provide qualitative and quantitative information about ligand binding pathways in enzymes and the mechanical properties of biological and synthetic polymers. Keywords: Molecular Dynamics; AFM simulation; Atomic Force Spectroscopy, Potential of Mean Force, Steered Molecular Dynamics.

1. Introduction The most striking progress towards the implementation of a nano-scale science and engineering was realized with the invention of the Scanning Tunneling Microscope (STM) in 1982 [1], followed by the invention of the Atomic Force Microscope (AFM) in 1986 [2]. The STM and AFM have provided revolutionary tools for the nanoscopic investigation of the morphology and electronic structure of material surfaces, and have made possible the purposeful manipulation and structural modification of these surfaces on atomic and molecular scales [3]. These probe-based techniques are now supplemented with Computer-based numerical simulations, based on the Molecular Dynamics (MD) technique, have successfully provided a framework for modeling nano-scale processes. Computer-based nanoscopic simulations form the standard numerical modeling tool for investigating the physics of materials, particularly the structure and properties of solid-state surfaces, on retained temporal and spatial scales. Numerical simulations together with the scientific visualization of their results are now collectively referred to as the Computational Nano-science. This field allows us to explore the detailed structure of the phase-space of complex manybody systems, in any type of topology, and to derive their dynamics and emergent properties in terms of the dynamics of their underlying micro-states. Numerical simulations have been performed via several distinct methodologies. The most well known and widely used is the MD method [4]. Today, one of the greatest interests is the study of biomolecular systems to understand the mechanisms that establish their functions, which is very useful to comprehend many cellular processes. This knowledge is highly important to propose new pharmaceutical products, such as the HIV protease inhibitors [5,6]. The proposition of new inhibitors requires the understanding the specific ligand-receptor interactions in the biochemical processes. Thus, the binding and unbinding process involving biomolecules is essential to underlying the mechanisms of enzyme reactions and molecular recognition for drug design [7]. The experimental study of the binding properties of biomolecules requires the application of mechanical forces to single molecules in small assemblies through AFM. Similar approach can be done using molecular dynamics adding external forces to reduce energy barriers and speed up the kinetics [7]. The molecular dynamics methodologies capable in doing this are called Steered Molecular Dynamics (SMD) or Potential of Mean Force (PMF) molecular dynamics. Thus, a further description of biological systems and the drug design process require a combined experimental-computational approach. The aim of this review is to provide a glimpse of the potential and limitations of the AFM simulation for applications in molecular characterization of the mechanical response of biological molecules and polymers at the nanometer scale, as realized by single-molecule force experiments.

2. AFM Force Spectroscopy AFM can be used to determine the dependence of the interaction on the probe-sample distance at a given location [8], in the so-called atomic force spectroscopy (AFS). AFS may be performed in two ways: local force (LFS) and force imaging spectroscopy [9]. In LFS, the force curve is determined at a particular location on the sample surface, as shown schematically in Fig. 1 [10]. Force curves are plots of the deflection of the cantilever (force) versus the extension of the

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piezoelectric scanner (sample displacement); if the cantilever spring constant is known, then the deflection can be converted into force. These curves can be used to measure the vertical force that the tip applies to the sample surface and to study the surface properties of the sample, including the elastic deformation of soft samples. They can also be used to monitor the unfolding of protein molecules as the latter are pulled from the sample surface by the AFM tip. F (nN)

d

c-d Pull-on Force

b-c

a-b

b e

a JTC

g

c

h g-h Pull-off Force

d-f

f-g f

JOC

Sample Displacement (nm) Fig. 1. Force curve on a wood surface illustrating the points where jump-to-contact (JTC) (approach) and jump-off-contact (JOC) (withdrawal) occur and the maximum values of the attractive force (pull-on force and pull-off force) (Reprinted from reference [10]).

In the diagram of Fig. 1 is shown a typical F vs D curve obtained with a soft cantilever on a hard sample. Segment ad represents the first half cycle (approach curve) while segment d-h is the second half cycle (withdrawal curve) of the curve. The most interesting regions of the force curve are two non-contact regions, containing the jump-to-contact and the jump-off-contact. The non-contact region in the approach curve provides information about attractive (vdW or Coulomb force) or repulsive forces (vdW in some liquids, double-layer, hydration and steric force) before contact; this discontinuity occurs when the gradient of the tip–sample force exceeds the spring constant of the cantilever. The maximum forward deflection of the cantilever multiplied by the effective spring constant of the cantilever is the pull-on force [11]. The non-contact region in the withdrawal curve contains the jump-off-contact, a discontinuity that occurs when the cantilever’s spring constant is greater than the gradient of the tip–sample adhesion forces. The maximum backward deflection of the cantilever multiplied by the effective spring constant of the cantilever is the pull-off force [11]. At the start of the cycle (point a) a large distance separates the tip and the sample, there is no interaction and the cantilever remains in a non-interacting equilibrium state. As separation decreases, in a-b the tip is brought into contact with the sample at a constant speed until it reaches a point close to the sample surface (point b). Once the total force gradient acting on the tip exceeds the stiffness of the cantilever, the tip jumps to contact (JTC) with the sample surface (b-c). JTC is often due to capillary forces from the moisture layer that covers the tip and the sample surface (not present in vacuum). In (c-d), the tip and sample are in contact and deflections are dominated by mutual electronic repulsions between overlapping molecular orbitals of the tip and sample atoms. The shape of segment (c-d) indicates whether the sample is deforming in response to the force from the cantilever. The slope of the curve in the contact region is a function of the elastic modulus and geometries of the tip and sample [9]. Segment (d-e) represents the opposite movement to segment (c-d), with the tip being withdrawn. If both segments are straight and parallel to each other, there is no additional information content. If they are not parallel, the hysteresis gives information on plastic deformation of the sample [12,9]. In segment (d-f) the sample is being retracted and adhesion or bonds formed during contact with the surface cause the tip to adhere to the sample. As the sample continues retracting, the spring force of the cantilever overcomes the adhesion forces and the cantilever pulls off sharply (f-g). In this segment several long and short-ranged forces become effective. The force at point f is the total adhesive force between the tip and the sample. In segment (g-h) the cantilever is moved upwards to its undeflected or noncontact position.

3. Single-Molecule Force Spectroscopy (SMFS) In the past several years, the AFM has emerged as a powerful tool for measuring the dynamic strength of intermolecular bonds [13]. The unbinding properties of various ligand–receptor systems including avidin/biotin, antibody/antigen, and p-selectin/carbohydrate pairs [14] have been characterized by force spectroscopy. These experiments are used to resolve interactions down to a single ligand–receptor pair under well-defined conditions and mechanical properties of polymers.

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SMFS relies on the force–distance curves obtained from the approach where the cantilever tip catches and draws the single polymer chains adsorbed or immobilized on the substrate surface or vice versa (Fig. 2) [15].

Fig. 2. The anatomy of a typical force–distance curve for poly (o-ethoxyaniline) (POEA) in the collapsed state. (I) Tip approaches surface: no interaction. (II e III) Tip compression of brush: “hard-sphere” type interaction. (IV) Retraction: force acting on the tip decreases as the sample is moved away. (V, VI e VII) Tip pulled down: indicating adhesion/multiple-chain pulling events. (VII) Polymer detaches from the tip (Reprinted from reference [15]).

The present chapter is focused on force unfolding of proteins and enzymes by AFM simulation. Protein folding remains one of the most fascinating mechanisms of biology. AFM provides experimenters with the means to manipulate single molecules under physiological conditions. This powerful new tool can produce the forces necessary either to rupture ligand-receptor bonds [16] or to stretch DNA and RNA [17,18]. More recently, the AFM has been applied to unfold proteins [19]. The unfolding of proteins by applying a force to single proteins attached between a surface and an AFM tip complements more classical technical using temperature or chemical as denaturants. The general scheme for force unfolding of protein resembles a “fishing” experience. Proteins are attached on a surface are picked up with a silicon-nitride or silicon tip of a flexible cantilever (Fig. 3) [20]. The probability of fishing on or more molecules depends not only on the density on the surface but also on the interactions between the tip and the protein. Once a protein is picked up, it can be stretched to more than 10 times its folded length (depending on its folded structure) reaching almost its total contour length [21]. The extension of the elastic, already unfolded part of the protein produces a restoring force that bends the cantilever. This bending, and therefore the force, can be measured with the high precision of the AFM. With proper sample preparation and well-adapted instrumental techniques, single – molecules unfolding processes generate a signature, i.e., a force-distance profile, which can be clearly distinguished from background noise and other events not related to unfolding process.

Fig. 3. Left: Schematic diagram of the AFM SM-FS study on the guanine quadruplex formation (chromosome ends that govern gene stability, and other parts of the genome, especially in promoters). Gold-coated AFM probe and surface are coated with a SAM of a thiolated 3G or 4G DNA, where each contains two G-rich domains (colored in brown) and an A12 spacer sequence (black), diluted by the spacer-DNA (A10) at 1:5 molar ratio. Right: a typical force-distance curve obtained from the unbinding of an inter-surface Gquadruplex (Reprinted from reference [20]).

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2. Molecular Dynamics Simulation MD simulation, which is based in the laws of classical mechanics, have been applied on a increasing scale of problems in physics, chemistry, material science, biology, and recently in the field of nanoscience [3]. The MD methodology consists in solve the Newton’s equations of motion for a system of N interacting atoms:

∂ 2 ri Fi = mi 2 , i = 1,2,..., N . ∂t

(1)

The forces are the negative derivates of a potential function V (r1,r2,…, rN):

Fi = −

∂V . ∂ri

(2)

The potentials are described by the interactions between atoms through force fields [22-26]. The equations are solved simultaneously in small time steps, in the order of femtoseconds (1 fs = 10-15 seconds). In a typical MD simulation, initial coordinates of the atoms are obtained from crystallographic or Nuclear Magnetic Resonance (NMR) structures. Thus, through integration of Newton's equations, the molecular dynamics simulation can extend static structural data into dynamics [22-27]. The time-evolved snapshots of atomic coordinates, combined sequentially into sets called trajectories, result in an detailed ‘‘movies’’ of how the molecules behaves over time under a variety of conditions [27]. The limitations of the MD are the limited size of biomolecule simulated and the limited time-scale covered by the methodology. Today, these difficulties do not permit a realistic simulation of most integral cellular components, which often involve many millions of atoms, or from reaching simulation of the millisecond timescale relevant for the fastest cellular processes. Thus, to overcome the size and timescale limitation, MD descriptions have been simplified through so-called coarse-graining [28-30] and biomolecular processes have been accelerated by applying external forces in socalled steered molecular dynamics (SMD) simulations [31-35].

3. Steered Molecular Dynamics (SMD) to Simulate AFM Experiments The SMD was inspired by the AFM technique, which have been used extensively to study the binding properties of biomolecules and their response to external mechanical manipulations [32,33]. The SMD calculations was first introduced by Izrailev in 1997 [36,37], with the objective to the study of the dynamics of binding–unbinding events in biomolecular systems and of their elastic properties on time scales covered by molecular dynamics simulations, which is typically in nanoseconds. The single-molecule experiments provided a greatly advanced knowledge about many mechanical properties of biopolymers regarding numerous functions of cells [33]. Regarding these information, the SMD method can provide complements to these observations, providing atomic level descriptions to underlying experimental events. Thus, compared with the AFM experiments, the SMD applies external forces to manipulate biomolecules in order to probe mechanical functions and determine enzymatic reaction pathways. The SMD is closely related to the well-known umbrella sampling and free energy perturbation methods [38], which was proposed to determine energy landscapes. The SMD simulations are equivalent to umbrella sampling only when applied forces are weak, involving only small conformational changes [32]. The interest of these new methodology is to induce major changes, e.q., a ligand is extracted from an enzyme or a protein’s termini are stretched to initiate unfolding, and when superimposed forces change rapidly in time, leading to significant deviations from equilibrium. The SMD has two typical protocols. In the first protocol, a constant force is applied to one or more atoms; extension or displacement is then monitored throughout dynamics. Customized time-dependent forces may be applied as well. In the second protocol, called constant velocity SMD, a harmonic potential (spring) is used to induce motion along a reaction coordinate [23,36]. The constant velocity SMD is the best option to mimic the AFM experiments in which a molecule is stretched by a cantilever moving at constant velocity. According to Izrailev [32,39], one way to apply external forces to a protein-ligand complex is to restrain the ligand to a point in space (restraint point) by an external, e.g., harmonic, potential. The restraint point is then shifted in a chosen direction [32,40-43] forcing the ligand to move from its initial position in the protein and allowing the ligand to explore new contacts along its unbinding path. Assuming a single reaction coordinate x, and an external potential V = K(x – x0 vt)2/2, where K is the stiffness of the restraint, and x0 is the initial position of the restraint point moving with a constant velocity, v, the external force exerted on the system can be expressed as

F = K ( x0 + vt − x ).

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This force corresponds to a molecule being pulled by a harmonic spring of stiffness K with its end moving with velocity v. Alternatively, a fixed restraint point at a distance much larger than the length of the unbinding pathway may be chosen. In this case, the end of the spring does not move and its stiffness is linearly increased with time [36], i.e., K= αt, and the force is

F = αt ( x0 − x ).

(4)

Other external forces or potentials can also be used, e.g., constant forces or torques applied to parts of a protein to induce rotational motion of its domains [44]. The SMD simulations require selection of a path, or a series of directions of the applied force. In some cases a straight-line path is sufficient, but in the others, the forced unbinding of the ligand requires the direction of the force to be changed during the simulation to avoid distortion of the surrounding protein. The direction of the force can be chosen randomly [45] or by guessing a direction on the basis of structural information [39,40]. A force is then applied to the ligand in the chosen direction, and this direction is accepted or rejected based on factors such as conservation of secondary structure of the protein, deformation of the protein, the magnitude of the force applied, the average velocity of the ligand along the unbinding pathway, etc [32,39,46]. The Fig. 4 shows a SMD simulation, which a time-dependent external force is applied in one direction to facilitate the unbinding from a protein [39].

Fig. 4. Extraction of a ligand from the binding pocket of protein. The force (represented by an arrow) applied to the ligand (show in van der Waals spheres) leads to its dissociation from the binding pocket of the protein (a slice of the protein represented as a molecular surface is shown) (Reprinted from reference [39]).

A limitation of the modeling approach is the short time scale accessible to MD, several orders of magnitude shorter than the time scale of AFM observations. As a result, peak forces calculated in SMD simulations are typically one order of magnitude higher than those obtained from AFM experiments [47]. The results obtained from SMD simulations, which are typically force and extension as a function of time, need to be analyzed in terms of quantitative measures of the molecules mechanical properties, such as elastic module or potential of mean force (PMF) along a stretching direction [47].

4. Calculation of the Potential of Mean Force (PMF) A potential of mean force (PMF) is a potential which is obtained by integrating the mean force from an ensemble of configurations. The PMF plays an important role in a typical investigation of a molecular process which configuration space is described by a reaction coordinate [48]. The PMF is basically the free energy profile along the reaction coordinate and is determined through the Boltzmann-weighted average over all degrees of freedom other than the reaction coordinate. This information provides further description of the modeled process along the reaction coordinate [34]. As described previously, the SMD is an effective method to explore mechanical and molecular processes accessible thought AFM experiments. However, a SMD simulation is a nonequilibrium process, whereas PMF is an equilibrium property. Therefore, to connect the equilibrium and nonequilibrium processes is necessary to use a nonequilibrium statistical mechanics, which can be made thought the Jarzynski’s equality [49,50]. The Jarzynski’s equality is concerned with systems that begin in equilibrium and consequently are driven away form equilibrium, which corresponds to an exact relation between free energy differences and the work done through nonequilibrium processes. Based on Jarzynski’s equality, a new method for sampling trajectories obtained from constant velocity pulling has been proposed to reconstruct the PMF without any assumption on its shape [34]. Thus, for isobaric-isothermal ensembles (constant temperature T and pressure P) the Jarzynski’s equality relates the free-energy difference ∆G = GB - GA, where GA and GB correspond to the free energy at states A and B, to work WAB enforcing the transition A → B nonequilibrium simulations. The equation is

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∆GAB = −k BT log e − βW

AB

(5)

where WAB is the work performed to force the system along one path from state A to B; the angular bracket denotes averaging over repeated realization of the process; β = 1/kBT is the inverse temperature and kB is the Boltzmann constant. The Jarzynski’s equality displayed on the equation (5) has an exponential average difficult to evaluate, because it is strongly dominated by instances in which small work values arise, and a direct application of this equation to calculate a PMF is not practical. According to Park and Schulten [34], this point is illustrated in Fig. 5 [34]. Let P(W) be the probability distribution of the work, which is typically of a bell shape. Then P(W) e-βW is another bell-shaped function, but with its peak shifted toward the left from that of P(W). Most work values are sampled around the peak of P(W), whereas the exponential average ∫ dwP ( w)e − βW cannot be estimated accurately without properly sampling the region around the peak of P(W) e-βW. When the shift is much larger than the width, there is little overlap between P(W) and P(W) e-βW, which makes the estimate of the exponential average impractical. However, this problem can be solved applying the cumulant expansion [50]. For example, the logarithm of an exponential average can be expanded in terms of cumulants,

log e x = x +

(

1 2 x − x 2

2

) + ⋅ ⋅ ⋅,

(6)

where the first and second cumulants are shown. This approximation can only be valid only if the work values follow a Gaussian distribution. In SMD simulations, the use of stiff springs can be made to conform to a Gaussian work distribution and the second order cumulant expansion of Jarzynski’s equality can be applied [34]. The PMF calculation using the Jarzynski’s equality was validated through the SMD simulation of the Helix-coil transition of deca-alanine. The results demonstrated the Gaussian nature of the resulting work distribution, which supported the use of the second order cumulant expansion in practical application of Jarzynski’s equality in SMD simulation [34]. The applications and potentialities of the AFM simulations will be showed in details as follow.

Fig. 5. Difficulty of estimating the exponential average. Typically, the peak of P(W) e-βW is shifted from that of the work distribution P(W). This make 〈e-βw〉 difficult to estimate. On the other hand, 〈W〉 and 〈W2〉 are easier to estimate because P(W) W and P(W) W2 are centered around the peak of P(W) (Reprinted from reference [34]).

5. Application of the AFM Simulation The forced unfolding and unbinding processes in enzymes using virtual AFM is a promising strategy for further studies of enzymatic mechanisms. These AFM simulations through molecular dynamics (MD) permitted the understanding of many important mechanisms into biological processes. In this topic will review the most important biological systems studied with AFM simulation and the most recent application of it. The first two to system are the study of biotin-avidin complex and the unfolding of the enzyme titin. The last two system reviewed correspond to the new application of the AFM simulation to understand elastic properties of polysaccharides and to predict the construction of new enzymebased nanobiossensors.

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5.1. Unbinding Biotin from Avidin Binding and unbinding of ligands to proteins is an essential biochemical process that should be known to understand enzymatic process in biological cells [36]. The AFM and molecular dynamics simulation have reveled that proteins have optimal pathways that guide ligands into binding sites. These characterizations elucidated the energy landscape that controls the kinetics of the binding and unbinding processes [33]. The first reported measurement of the unbinding force of individual ligand-receptor pairs using AFM experiments was realized by Gaub and co-workers [51] in 1994 on biotin-streptavidin complex, which are know for its high binding affinity. In the field of molecular dynamics simulation, the first work regarding AFM simulation was made by Izrailev [36], which performed a SMD simulation on the entire tetramer of avidin with four biotins bound to serve as test bed for the SMD method [39], and to investigate the microscope detail of unbinding of biotin from avidin [36]. The schematic representation of the AFM experiment is shown in Fig. 6 [37]. The experimental results showed that the force needed to rupture the ligand-receptor bond was found to be 160 pN. It means that if the biotin can be pulled out from its 10 Å binding pocket with the constant force of 160 pN, which correspond to a binding energy of 23 kcal/mol [51]. This information provided a great glimpse into ligand-receptor binding. However, this AFM experiment can not underlies molecular structure and energy landscapes [33]. For this propose is advantageously complement AFM observations with molecular dynamics simulations and nonequilibrium statistical mechanics analysis. In the SMD simulation, the rupture of biotin from avidin was induced by means of a soft harmonic restraint, as described by the equation (4) with K = α t ranging from 0 to 120 pN/ Å. The results showed values of rupture forces between 450-800 pN, which exceeded the values observed by AFM experiments, but the SMD simulations did not exhibit any particular scaling of the rupture force with the pulling rate [39], which covered a span of almost two orders of magnitude. These forces differences on rupture forces was explained by the participation of water molecules in breaking the hydrogen bond networks between biotin and residues located near the exit of the binding pocket, which can not be determined on the time scale of the simulation. Spite some experimental and theorical discrepancies, the simulation revealed that flapping motions of one of the loops of the avidin monomer play a crucial role in the mechanism of the unbinding of biotin [39]. Therefore the use of the AFM simulation is highly useful when add of external forces is necessary to reduce the energy barriers and speed up the kinetics of enzymatic pathways [36].

Fig. 6. Schematic representation of atomic force microscopy (AFM) experiment on the avidin-biotin complex. An AFM tip attached to an elastic cantilever is linked to biotin; the agarose bead surface is linked chemically to biotin through stiff bonds; an avidin tetramer binds to two biotins on the head and to two biotins connected with the AFM tip; the cantilever applies forces measured by monitoring the position of the tip (adapted from reference [37]).

5.2. Unfolding of Titin In the nature there are proteins that can be stretched to many times their original size [32]. These proteins are the molecular components of skeletal muscles and the involuntary muscles of heart and intestines of the human body. Among these proteins, the less know is the titin, which is a protein that gives muscle elasticity and mechanical stability [23,52]. The titin is the largest know protein in nature [53], composed of 300 modular domains and a few random coil segments [23]. Thus, due to its mechanical properties the titin protein was chosen to be studied since its highly possible number of trajectories can offers an abundance of experimental and theoretical data [39]. The AFM experiments [54-61] measure the extensions of the isolated Titin as a function of applied force. From these studies was understood how titin reacts to mechanical stretching. However, these experimental studies only described how much force the protein can be stretched without actually rupturing in response to strong forces, which do not offer enough information to specify the molecular mechanisms responsible for the titin’s mechanical resistance. The first SMD simulation [62] revealed that the force-bearing of parts of titin is due to many hydrogen bonds networks between its β-strands, which needs to be

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synchronously break to unfold the protein [23,27]. This SMD simulation, displayed on Fig. 7 [32,39], shed light on how the β-strand pairing guard the titin domain against force unfolding [27]. Moreover, others AFM simulations [63] have suggested that titin can act also as biomechanical sensor when the tension induce exposure of a kinase active site in titin, thereby transforming mechanical force into a biochemical signal [23]. One key discovery, which has been elucidates only thought molecular dynamics simulation, was the role of water molecules participating in the domain unfolding. This simulation reveled that the water molecules competed for the understand hydrogen bonds lowering the unfolding barrier of the titin protein [64], suggesting that these events plays a central role in mechanical folding [27]. Recently, force spectroscopy experiments have validated the molecular dynamics simulation predictions [65]. In addition, multidomain proteins, similar to the titin, have been investigated by virtual and experimental AFM and they showed excellent agreement between the measured and predicted of mechanical stability [23,66-68].

Fig. 7. SMD study of the Titin unfolding under mechanical strain. (a) key steps of Titin unfolding identified by SMD. The domain is drawn in cartoon representation and key hydrogen bonds between strands A-B, and between A’-G are show as dotted lines. Left is a snapshot of Titin extended by 10 Å. Right is a snapshot of Titin extended by 17 Å. (b) Force extension curves of Titin extended by constant velocity stretching SMD with 3 different velocities. (c) Intermediate stages of the force-induced unfolding. All Titin domains are drawn in the cartoon representation of the folded domain; solvating water molecules are not shown. The four figures at extensions 10 Å, 17 Å, 150 Å, and 285 Å are showed for comparison (adapted from references [32,39]).

5.3. Elastic Properties and Conformational Transitions in Polysaccharides Pyranose ring-based (five carbon atoms and one oxygen atom) sugars and polysaccharides play fundamental roles in biological systems by providing energy, serving as structural elements, and participating in cellular recognition, signaling, and adhesive events [69]. The polysaccharides are thought to respond to stress by elastic deformation, but the underlying molecular rearrangements allowing such a response remain poorly understood. The AFM measurements of the elasticity of individual polysaccharide chains (Fig. 8a) has been suggested that stressed sugar rings may be significantly deformed by mechanical forces which can twist and bend their bond angles [55]. Other AFM experimental studies suggested that sugar ring in a stretched polysaccharide chain can switch theirs chair-like conformation to a boatlike [69-72], both which are more extended and higher energy. The schematic representation of the AFM experiment is showed on Fig. 8a, and the chair-boat transition of the glucopyranose ring of the amylose is displayed on Fig. 8b. These AFM measurements displayed a large deviations from the simple entropic elasticity of polymers that are prominently displayed by R-linked polysaccharides, such as amylose, dextran, and pectin, whose are α-linked polysaccharides [55,69,70,72-74].

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Fig. 8. (a) Schematic representation of the polysaccharide chain stretching. Increased separation of glycosidic oxygen atoms during chair-boat transitions of the glucopyranose ring explains the extensibility of amylose. (b) The diagrams show that the distance between two consecutive glycosidic oxygens O4–O1 increases during a force-driven chair-boat transition when the glycosidic oxygen O4 is in the axial position (amylose).

The use of the AFM simulations thought SMD simulation reveled atomic details which confirmed that the forceinduced conformation transitions involve rotations of monomers about glycosidic linkages (bond between two sugar monomers) and various conformational transitions of sugar rings [69,70,75]. Moreover, a simulated force-extension curve of amylose reveled similar profile of the measurements realized by the AFM experiments. However, the calculated pulling forces corresponding to this region are in a range of 400-800 pN, which is within a factor of 2 of the forces measured experimentally [69]. These results are a typical problem associated to SMD simulations of various AFM stretching measurements, which overestimate the external forces of the conformational transitions. This limitation is due to the gap between the timescales of computer simulations (nanosecond time scale) and the AFM experiments (second time scale), which means that SMD simulation of polysaccharides achieve qualitative rather than quantitative agreement with the experiment [75]. Thus, better agreement between SMD and AFM experiments can be achieved with significantly slower pulling speeds and longer amylose chains are required. Therefore, to circumvent these problems, many authors suggest the use of the replica exchange method (REM) [75,76] which consists in realize many simulation replicas at different temperatures to overcome the energy barrier between two conformations and sample efficiently the conformation phase space of the desired system [75]. Lu et al. employed combined REM SMD simulations to model the stretching and relaxation of the polysaccharide dextran, which has been extensively studied by AFM [55,70] and SMD [55,77]. Using the REM approach, was produced a forward and backward force-extension curves that display little hysteresis between them and reproduce the experimentally measured data not only qualitatively but also quantitatively [75]. These results are displayed at Fig. 9, which compares the force-extension curves obtained from experiment and simulations. In the REM SMD simulations, a set of SMD simulations (replicas) was conducted on the same molecular system over a range of temperatures [75]. At different temperatures, the replicas exchange configurations at a fixed time interval, with a transition probability satisfying the detailed balance condition [75].

Fig. 9. A comparison between force-extension curves of dextran obtained by AFM, REM SMD, and regular SMD simulations (Reprinted from reference [75]).

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Therefore, the overall AFM simulations of the polysaccharides provided the details of the force-induced conformational changes and reveal the mechanism of the stretching process, which force-induced chair-to-boat transitions of the glucose rings. This observation proves the transitions are responsible for the deviations of amylose elasticity from the freely jointed chain model. 5.4. AFM simulation to Design New Enzyme-Based Nanobiosensors Many analytical techniques have been used to detect pesticides and other residues in the environment, but new prospects for detection have emerged recently with nanobiosensors [78,79], which basically comprise a biological component (e.g. enzyme, antibody) immobilized on a nanoscale detection device. Of particular importance are the nanobiosensors obtained by a deposition of a receptor layer (protein) on microcantilevers with analytes detected at concentration as low as 10-18 mol/L [80] using an AFM. Our group suggests a development of a new nanobiosensors capable to detect selectively enzyme-inhibitor herbicides, particularly acetyl-Coa carboxylase (ACCase) [81], which is necessary for the synthesis of fatty acid in plants. Thus, the use of cantilever biosensors to transduce the recognition event from its receptor-coated surface into a mechanical response. The receptors (enzymes) were covalently anchored to the cantilever (tip surface functionalization). Enzyme inhibitors bind to enzymes and decrease their activity and this force interaction can be estimated from the excess force required to pull the tip free from the surface. Theoretical studies using molecular dynamics and molecular docking reveled that the enzyme ACCase has positive and negative charged groups located at different and specific regions on the protein surface, suggesting that functionalized tips surfaces can affect strongly this enzyme orientation [82]. These results suggested optimized situation which the ACCase enzyme should be immobilized and the AFM tips should functionazed. Moreover, to study the specific interaction between the herbicide diclofop and the enzyme ACCase [81,83], the AFM simulation had been performed molecular dynamics simulation, in nanosecond time scale. This simulation configuration is similar what has been realized to study the unbinding of biotin from avidin, described on topic 5.1. The Fig. 10 shows the ongoing process of extraction of the herbicide diclofop (ligand) from the ACCase active site. The curve force obtained during the AFM simulation procedure (Fig. 10) showed that the adhesion force revealed a distribution with average rupture force of 215.9 pN for the herbicide diclofop. The spring constant used in the simulation was 367 kJ mol-1 nm-1, which is similar to a stiffness of spring constant of the AFM cantilevers of 610 N.m-1. These results predict the possible force response that can obtained from AFM experiments. However, discrepancy in the rupture force can be expected, since the timescale between theory and experimental analysis are significantly different; moreover, it is necessary to distinguish nonspecific adhesion and specific interaction, which is hard from experimental analysis. Although these possible limitations the AFM simulation shade light about the mechanism of specific interaction between the herbicide diclofop and ACCase enzyme. Future studies combining theorical and experimental AFM procedures will indicate if the AFM can be utilized as a convenient nanobiosensing tool for confirming the presence and assessing the strength of herbicide-enzyme interactions on biosensor surfaces.

(b)

(a)

Figure 10. (a) Possible unbinding pathway of the diclofop from ACCase active site. The ∆z is the distance between the ligand and the ACCase active site, F is the acting force and the Kc is the spring (cantilever) constant (b) Force curve for the unbinding pathway showed in (a).

6. Final Remarks The AFM simulation, which has been originated from the necessity to explain the molecular view of AFM experiments, revealed to be a very useful technique that can elucidate many important cellular processes and might be used extensively to design new nanotechnologies based on the mechanical properties of biomolecules. This computational modeling based methodology was successfully used for further interpretation of SMFS experiments performed by the

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AFM. In this chapter, was described that one important information extracted from AFM simulation measurements is the calculation of PMF which is feasible thought Jarzynski’s equality. These calculations showed to be straightforwardly transferred to AFM experiments if sufficiently spring constant of cantilever are chosen during the AFM simulation. According to the theoretical calculations described here, the more significant limitation of the AFM simulation is the restriction of the simulation in nanosecond timescale, which require a use of velocities much more above than those used in AFM experiments, which results in rupture forces significantly different of the experiments. Although these limitations, the AFM simulations has been used successfully to interpret AFM measurements. Therefore, the application of the AFM simulation, described so far, showed that experimentalists and theorists needs to join theirs efforts to guarantee remarkable success to understand the structure, function and mechanical properties of biomolecules in many cellular processes and to use these properties in future technological products. Spite the limitations, the AFM simulation through molecular dynamics is very useful to complement many experimental methodologies and it is becoming a tool for making accurate predictions, which opens new frontiers in the field of nanotechnology. Acknowledgements: The financial support given by FAPESP and CNPq are gratefully acknowledged.

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