[Show abstract][Hide abstract] ABSTRACT: In this paper, we develop a mechanochemical modeling framework in which the spatial-temporal evolution of receptor-ligand bonds takes place at the interface between two compliant media in the presence of an externally applied tensile load. Bond translocation, dissociation and association occur simultaneously, resulting in dynamic aggregation of molecular bonds that is regulated by mechanical factors such as material compliance and applied stress. The results show that bond aggregation is energetically favorable in the out-of-equilibrium process with convoluted time scales from bond diffusion and reaction. Material stiffness is predicted to contribute to adhesion growth and an optimal level of applied stress leads to the maximized size of bond clusters for integrin-based adhesion, consistent with related experimental observations on focal adhesions of cell-matrix interaction. The stress distribution within bond clusters is generally non-uniform and governed by the stress concentration index.
[Show abstract][Hide abstract] ABSTRACT: The rapid development of fabrication and processing technologies in the past two decades has enabled researchers to introduce nanoscale features into materials which, interestingly, have been shown to greatly regulate the behavior and fate of biological cells. In particular, important cell responses (such as adhesion, proliferation, differentiation, migration, and filopodial growth) have all been correlated with material nanotopography. Given its great potential, intensive efforts have been made, both experimentally and theoretically, to understand why and how cells respond to nanoscale surface features, and this article reviews recent progress in this field. Specifically, a brief overview on the fabrication and modification techniques to create nanotopography on different materials is given first. After that, a summary of important experimental findings on the mediation of nanoscale surface topography on the behavior of various cells, as well as the underlying mechanism, is provided. Finally, both classical and recently developed approaches for modeling nanotopography-mediated cell adhesion and filopodial growth are reviewed.
International Journal of Smart and Nano Materials 01/2015; 5(4):227-256. DOI:10.1080/19475411.2014.995744
[Show abstract][Hide abstract] ABSTRACT: By combining optical trapping with fluorescence imaging, the adhesion and deformation characteristics of suspension cells were probed on single cell level. We found that, after 24 h of co-culturing, stable attachment between non-adherent K562 cells and polystyrene beads coated with fibronectin, collagen I, or G-actin can all be formed with an adhesion energy density in the range of 1-3 x 10(-2) mJ/m(2), which is about one order of magnitude lower than the reported values for several adherent cells. In addition, it was observed that the formation of a stronger adhesion is accompanied with the appearance of a denser actin cell cortex, especially in the region close to the cell-bead interface, resulting in a significant increase in the apparent modulus of the cell. Findings here could be important for our understanding of why the aggregation of circulating cells, like that in leukostasis, takes place in vivo as well as how such clusters of non-adherent cells behave. The method proposed can also be useful in investigating adhesion and related phenomena for other cell types in the future.
[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(1):2–18. DOI:10.1016/j.jmps.2013.06.006 · 3.60 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: 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 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. DOI:10.1371/journal.pone.0065864 · 3.23 Impact Factor
[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 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. DOI:10.1016/j.jmps.2012.06.004 · 3.60 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 02/2011; 59(2):251-264. DOI:10.1016/j.jmps.2010.10.008 · 3.60 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We developed a transient model for actin-based motility. Diffusion of actin monomers was included in the formulation and its influence on the speed of actin-driven cargos was examined in detail. Our results clearly demonstrated how actin polymerization accelerates cargos that are initially stationary, as well as how steady-state is eventually reached. We also found that, due to polymerization and diffusion, actin monomer concentration near the load surface can be significantly lower than that in the rest of the comet tail, suggesting that many previous models may not be very accurate.
[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
[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 04/2010; 58(4-58):502-514. DOI:10.1016/j.jmps.2010.01.010 · 3.60 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.
[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. DOI:10.1016/j.ijsolstr.2006.09.006 · 2.21 Impact Factor