[Show abstract][Hide abstract] ABSTRACT: A Langevin dynamics based formulation is proposed to describe the shape fluctuations of biopolymer filaments. We derive a set of stochastic partial differential equations (SPDEs) to describe the temporal evolution of the shape of semiflexible filaments and show that the solutions of these equations reduce to predictions from classical modal analysis. A finite element formulation to solve these SPDEs is also developed where, besides entropy, the finite deformation of the filaments has been taken into account. The validity of the proposed finite element-Langevin dynamics (FEM-LD) approach is verified by comparing the simulation results with a variety of theoretical predictions. The method is then applied to study the mechanical behavior of randomly cross-linked F-actin networks. We find that as deformation progresses, the response of such networks undergoes transitions from being entropy dominated to being governed by filament bending and then, eventually, to being dictated by filament stretching. The levels of macroscopic stress at which these transitions take place were found to be around 1% and 10%, respectively, of the initial bulk modulus of the network, in agreement with recent experimental observations.
Journal of the Mechanics and Physics of Solids 01/2014; 62:2–18. · 4.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: It is widely known in adhesive contact mechanics that a spherical particle will not detach from an elastic half-space unless a critical level of pulling force is reached, as already revealed by JKR or DMT type of deterministic models. This paper focuses on the scenario of particle-substrate adhesion where the size of particles is down to nanometer scale. A consequence of particle size reduction to this range is that, the energy scale confining the state of system equilibrium becomes comparable to the unit of thermal energy, leading to statistical particle detachment even below the critical pull-off force. We describe the process by Kramers' theory as a thermally activated escape from an energy well, and develop Smoluchowski partial differential equation that governs the spatial-temporal evolution of adhesion state in probabilistic terms. These results show that the forced or spontaneous separation of nanometer-sized particles from compliant substrates occurs diffusively and statistically, rather than ballistically and deterministically as assumed in existing models.
[Show abstract][Hide abstract] ABSTRACT: Cell adhesion with extracellular matrix depends on the collective behaviors of a large number of receptor-ligand bonds at the compliant cell-matrix interface. While most biological tissues and structures, including cells and extracellular matrices, exhibit strongly anisotropic material properties, existing studies on molecular adhesion via receptor-ligand bonds have been largely limited to isotropic materials. Here the effects of transverse isotropy, a common form of material anisotropy in biological systems, in modulating the adhesion behavior of a cluster of receptor-ligand bonds are investigated. The results provide a theoretical basis to understand cell adhesion on anisotropic extracellular matrices and to explore the possibility of controlling cell adhesion via anisotropy design in material properties. The combined analysis and simulations show that the orientation of material anisotropy strongly affects the apparent softness felt by the adhesive bonds, thereby altering their ensemble lifetime by several orders of magnitude. An implication of this study is that distinct cellular behaviors can be achieved through remodeling of material anisotropy in either extracellular matrix or cytoskeleton. Comparison between different loading conditions, together with the effects of material anisotropy, yields a rich array of out-of-equilibrium behaviors in the molecular interaction between reactant-bearing soft surfaces, with important implications on the mechanosensitivity of cells.
[Show abstract][Hide abstract] ABSTRACT: We report a theoretical study on the cyclic stretch-induced reorientation of spindle-shaped cells. Specifically, by taking into account the evolution of sub-cellular structures like the contractile stress fibers and adhesive receptor-ligand clusters, we develop a mechanochemical model to describe the dynamics of cell realignment in response to cyclically stretched substrates. Our main hypothesis is that cells tend to orient in the direction where the formation of stress fibers is energetically most favorable. We show that, when subjected to cyclic stretch, the final alignment of cells reflects the competition between the elevated force within stress fibers that accelerates their disassembly and the disruption of cell-substrate adhesion as well, and an effectively increased substrate rigidity that promotes more stable focal adhesions. Our model predictions are consistent with various observations like the substrate rigidity dependent formation of stable adhesions and the stretching frequency, as well as stretching amplitude, dependence of cell realignment. This theory also provides a simple explanation on the regulation of protein Rho in the formation of stretch-induced stress fibers in cells.
PLoS ONE 06/2013; 8(6):e65864. · 3.53 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We theoretically and numerically investigate the interplay between diffusion of a surface-bound receptor and its reaction with an opposing ligand. Special attention has been paid to the mechanical regulation of bond association by varying the initial gap distance and relative separation speed between the protein-bearing surfaces. Such diffusion-reaction coupling effects can cause the apparent on-rate or reciprocal of the average waiting time for bond formation, to be not constant, but instead a function sensitive to the system parameters that affect the transport of proteins. The results provide a quantitative understanding of how significantly the transport mechanism can affect overall binding behavior of molecular interactions and call for a paradigm shift in modeling receptor-ligand bond association when the protein-bearing surfaces are in relative separation.
[Show abstract][Hide abstract] ABSTRACT: We examine the force needed to extend/compress a bio-filament, a key issue in the study of cytoskeleton mechanics and polymer physics, by considering both the associated stretching and bending deformations. Specifically, closed form relationships are derived to predict the buckling of stiff filaments such as F-actin and microtubules. Our results clearly demonstrate that the maximum force a 2D filament can sustain is higher than the Euler buckling load whereas the force in a 3D filament is always below it, and hence clarify some of the ambiguities in the literature. In addition, analytical expression is also obtained to describe how the extensional force increases when a flexible molecule, like DNA, is stretched close to its contour length, which has been shown to fit a variety of experimental data very well. Our theory provides important corrections/improvements to several well-known existing models.
Journal of the Mechanics and Physics of Solids 11/2012; 60(11):1941–1951. · 4.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Micro-pillars of anodic aluminium oxide with nano-sized honeycomb channels along the pillar axis exhibit compressive stress–strain response with large excursions corresponding to discrete, inhomogeneous deformation events. Each excursion is found to associate with the severe distortion of a material layer at the pillar’s head, whereas the remaining of the pillar remains intact. The stresses at which these excursions occur do not exhibit any significant dependence on the pillar size. A simple model is proposed to describe the response of pillars under compression, which energetically, as well as kinetically, explains as to why the localized deformation always takes place at the pillar head. Predictions on the occurrence of instability events from this model also quantitatively agree with the experimental observations.
Journal of the Mechanics and Physics of Solids 01/2011; 59(2):251-264. · 4.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We consider the energy needed to separate two surfaces connected by molecular bonds, whose formation and breakage can be described
by the classical rate equation. We find that this adhesion energy is strongly rate-dependent due to the chemical kinetics
involved. Two cases where the separation between surfaces grows linearly, or exponentially, with respect to time are studied
in detail, scaling relations between the adhesion energy and separation speed, or the exponential factor, are derived in each
case. As an example of application, the peel test of a membrane in adhesive contact with a substrate is also studied. We will
show that findings obtained here can be directly used to predict the relationship between the applied tension and the peeling
velocity, which is of central interest to this type of experiment.
KeywordsAdhesion-Adhesion energy-Molecular bond-Peel test
Cellular and Molecular Bioengineering 09/2010; 3(3):247-255. · 1.23 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Using a generalized Brownian ratchet model that accounts for the interactions of actin filaments with the surface of Listeria mediated by proteins like ActA and Arp2/3, we have developed a microscopic model for the movement of Listeria. Specifically, we show that a net torque can be generated within the comet tail, causing the bacteria to spin about its long axis, which in conjunction with spatially varying polymerization at the surface leads to motions of bacteria in curved paths that include circles, sinusoidal-like curves, translating figure eights, and serpentine shapes, as observed in recent experiments. A key ingredient in our formulation is the coupling between the motion of Listeria and the force-dependent rate of filament growth. For this reason, a numerical scheme was developed to determine the kinematic parameters of motion and stress distribution among filaments in a self-consistent manner. We find that a 5-15% variation in polymerization rates can lead to radii of curvatures of the order of 4-20 microm, measured in experiments. In a similar way, our results also show that most of the observed trajectories can be produced by a very low degree of correlation, <10%, among filament orientations. Since small fluctuations in polymerization rate, as well as filament orientation, can easily be induced by various factors, our findings here provide a reasonable explanation for why Listeria can travel along totally different paths under seemingly identical experimental conditions. Besides trajectories, stress distributions corresponding to different polymerization profiles are also presented. We have found that although some actin filaments generate propelling forces that push the bacteria forward, others can exert forces opposing the movement of Listeria, consistent with recent experimental observations.
[Show abstract][Hide abstract] ABSTRACT: A rolling model for cell motility is proposed here where the movement of cell is treated as a result of the continuous release and growth of adhesions at the trailing and leading edge of the cell, respectively. The appearance of actin polymerization is key in this model as it breaks the symmetry of adhesion characteristics. The cell speed predicted here is in the correct range and exhibits a biphasic relationship with the cell–substrate adhesive strength which is consistent with experimental observations. We will show that this biphasic dependence of cell speed on adhesivity is due to the interplay between the energy dissipation associated with cell movement and the thermal fluctuations of actin filaments necessary for polymerization. Our results also suggest that the mobility of adhesion molecules is not only unnecessary but may actually limit cell motility.
Journal of the Mechanics and Physics of Solids 01/2010; · 4.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Focal adhesions are clusters of specific receptor-ligand bonds that link an animal cell to an extracellular matrix. To understand the mechanical responses of focal adhesions, here we develop a stochastic-elasticity model of a periodic array of adhesion clusters between two dissimilar elastic media subjected to an inclined tensile stress, in which stochastic descriptions of molecular bonds and elastic descriptions of interfacial traction are unified in a single modeling framework. We first establish a fundamental scaling law of interfacial traction distribution and derive a stress concentration index that governs the transition between uniform and cracklike singular distributions of the interfacial traction within molecular bonds. Guided by this scaling law, we then perform Monte Carlo simulations to investigate the effects of cluster size, cell/extracellular matrix modulus, and loading direction on lifetime and strength of the adhesion clusters. The results show that intermediate adhesion size, stiff substrate, cytoskeleton stiffening, and low-angle pulling are factors that contribute to the stability of focal adhesions. The predictions of our model provide feasible explanations for a wide range of experimental observations and suggest possible mechanisms by which cells can modulate adhesion and deadhesion via cytoskeletal contractile machinery and sense mechanical properties of their surroundings.
[Show abstract][Hide abstract] ABSTRACT: We present here a mechanics model for the force generation by actin polymerization. The possible adhesions between the actin filaments and the load surface, as well as the nucleation and capping of filament tips, are included in this model on top of the well-known elastic Brownian ratchet formulation. A closed form solution is provided from which the force-velocity relationship, summarizing the mechanics of polymerization, can be drawn. Model predictions on the velocity of moving beads driven by actin polymerization are consistent with experiment observations. This model also seems capable of explaining the enhanced actin-based motility of Listeria monocytogenes and beads by the presence of Vasodilator-stimulated phosphoprotein, as observed in recent experiments.
[Show abstract][Hide abstract] ABSTRACT: The strength of a bonded interface is considered for the case in which bonding is the result of clusters of discrete bonds distributed along the interface. Assumptions appropriate for the case of adhesion of biological cells to an extracellular matrix are introduced as a basis for the discussion. It is observed that those individual bonds nearest to the edges of a cluster are necessarily subjected to disproportionately large forces in transmitting loads across the interface, in analogy with well-known behavior in elastic crack mechanics. Adopting Bell's model for the kinetics of bond response under force, a stochastic model leading to a dependence of interface strength on cluster size is developed and analyzed. On the basis of this model, it is demonstrated that there is an optimum cluster size for maximum strength. This size arises from the competition between the nonuniform force distribution among bonds, which tends to promote smaller clusters, and stochastic response allowing bond reformation, which tends to promote larger clusters. The model results have been confirmed by means of direct Monte Carlo simulations. This analysis may be relevant to the observation that mature focal adhesion zones in cell bonding are found to have a relatively uniform size.
[Show abstract][Hide abstract] ABSTRACT: The adhesion of a living cell to an extracellular matrix surface is effected through the bonding of receptor molecules in
the cell membrane to compatible ligand molecules on the surface. In a series of experiments on adhesion of cells to a substrate
surface with a controlled density of ligand binding sites, Arnold etal. (ChemPhysChem 5:383, 2004) showed that tight cell
adhesions could form only if the areal density of binding sites on the substrate was higher than some critical value. Furthermore,
this critical value was consistent across the four cell types examined in the experiments. For ligand density below the critical
level, on the other hand, virtually no adhesions formed. In this article, we examine the competition between thermal undulations
of the cell membrane and its adhesion to the substrate. In particular, we show that thermal undulations destabilize membrane
bonding to the substrate unless the bond spacing is below a certain level. By following this line of reasoning in the context
of classical statistical mechanics, we obtain an estimate of the critical value of spacing which is in reasonable agreement
with the observations.
Journal of Materials Science 08/2007; 42(21):8904-8910. · 2.31 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We consider the forced detachment of a thin-walled vesicle bonded to a substrate for two particular cases. In both cases, the configuration is three-dimensional and the bonding is assumed to occur under conditions of axial symmetry for which the adhered area is always circular. Detachment is driven by a force applied to the top of the vesicle in a direction normal to the substrate surface. The first case is the static or time-independent situation of a vesicle for which bonding is the result of nonspecific interactions between the vesicle and substrate surfaces. For this case, it is shown that the radius of the adhesion patch is determined implicitly by the pulling force F. The maximum pulling force Fcr, beyond which the adhered configuration is unstable and the detachment proceeds spontaneously, can also be calculated implicitly. For the particular case of weak adhesion, all significant parameters of the detachment process can be determined explicitly. The second case studied is the time-dependent debonding of a vesicle for which adhesion with the substrate is the result of specific interactions between binders on the two surfaces, typical of biological materials for which the binders are ligand–receptor protein pairs. By treating the detachment process as a result of the debonding of the protein pairs at the edge of the circular adhesion patch, the governing equation for the radius of the adhesion patch is obtained. If a constant force is suddenly applied, it is found that the elapsed time to full detachment is proportional to the magnitude of this force to the power −1.1; alternatively, if the force applied to the vesicle increases linearly in time, it is found that the value of the force at complete detachment is proportional to the applied loading rate F˙ to the power 0.39, in agreement with recent experimental observations.
International Journal of Solids and Structures 03/2007; 44(6):1927-1938. · 2.04 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The phenomenon considered is the potential for adhesion between a membrane and a nearby substrate through bonding of receptor molecules in the membrane to ligand molecules on the sub-strate. The membrane is immersed in a thermal reservoir and, consequently, experiences thermal undulations. The undulations must be suppressed in order to effect bonding, and this competition is the focus of the present discussion. A simple physical model is introduced which incorporates thermal motion of a one dimensional membrane, and its tendency for bonding is represented by an interaction potential with the substrate. The model is analyzed within the framework of classical statistical mechanics, based on a description of adhesion in terms of the standard deviation of the membrane at the potential bonding points. The principal result is in the form of a quantitative rela-tionship between the membrane span and the depth of the bonding potential that must be satisfied in order for bonding to be completed.
Journal of the Mechanics and Physics of Solids 02/2007; 56(1). · 4.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The standard view of mechanical adhesive contact is as a competition between a reduction in free energy when surfaces with bonding potential come into contact and an increase in free energy due to elastic deformation that is required to make these surfaces conform. An equilibrium state is defined by an incremental balance between these effects, akin to the Griffith crack growth criterion. In the case of adhesion of biological cells, the molecules that tend to form surface-to-surface bonds are confined to the cell wall but they are mobile within the wall, adding a new phenomenon of direct relevance to adhesive contact. In this article, the process of adhesive contact of an initially curved elastic plate to a flat surface is studied for the case in which the binders that account for adhesion are able to migrate within the plate. This is done by including entropic free energy of the binder distribution in the total free energy of the system. By adopting a constitutive assumption that binders migrate at a speed proportional to the local gradient in chemical potential, the transient growth of an adhesion zone due to binder transport is analyzed. For the case of a plate of very large extent, the problem can be solved in closed form, whereas numerical methods are invoked for the case of a plate of limited extent. Results are presented on the rate of growth of an adhesion zone in terms of system parameters, on the evolution of the distribution of binders and, in the case of a plate of limited extent, on the long-term limiting size of the adhesion zone.
Journal of the Mechanics and Physics of Solids 01/2004; · 4.29 Impact Factor