Soft matrices suppress cooperative behaviors among receptor-ligand bonds in cell adhesion

A multi-scale clutch model for adhesion complex mechanics

Cell-matrix adhesion is a central mechanical function to a large number of phenomena in physiology and disease, including morphogenesis, wound healing, and tumor cell invasion. Today, how single cells respond to different extracellular cues has been comprehensively studied. However, how the mechanical behavior of the main individual molecules that form an adhesion complex cooperatively responds to force within the adhesion complex is still poorly understood. This is a key aspect of cell adhesion because how these cell adhesion molecules respond to force determines not only cell adhesion behavior but, ultimately, cell function. To answer this question, we develop a multi-scale computational model for adhesion complexes mechanics. We extend the classical clutch hypothesis to model individual adhesion chains made of a contractile actin network, a talin rod, and an integrin molecule that binds at individual adhesion sites on the extracellular matrix. We explore several scenarios of integrins dynamics and analyze the effects of diverse extracellular matrices on the behavior of the adhesion molecules and on the whole adhesion complex. Our results describe how every single component of the adhesion chain mechanically responds to the contractile actomyosin force and show how they control the traction forces exerted by the cell on the extracellular space. Importantly, our computational results agree with previous experimental data at the molecular and cellular levels. Our multi-scale clutch model presents a step forward not only to further understand adhesion complexes mechanics but also to impact, e.g., the engineering of biomimetic materials, tissue repairment, or strategies to arrest tumor progression.

Receptor-Ligand Binding: Effect of Mechanical Factors

Gaining insight into the in situ receptor-ligand binding is pivotal for revealing the molecular mechanisms underlying the physiological and pathological processes and will contribute to drug discovery and biomedical application. An important issue involved is how the receptor-ligand binding responds to mechanical stimuli. This review aims to provide an overview of the current understanding of the effect of several representative mechanical factors, such as tension, shear stress, stretch, compression, and substrate stiffness on receptor-ligand binding, wherein the biomedical implications are focused. In addition, we highlight the importance of synergistic development of experimental and computational methods for fully understanding the in situ receptor-ligand binding, and further studies should focus on the coupling effects of these mechanical factors.

Viscoelasticity Acts as a Marker for Tumor Extracellular Matrix Characteristics

Biological materials such as extracellular matrix scaffolds, cancer cells, and tissues are often assumed to respond elastically for simplicity; the viscoelastic response is quite commonly ignored. Extracellular matrix mechanics including the viscoelasticity has turned out to be a key feature of cellular behavior and the entire shape and function of healthy and diseased tissues, such as cancer. The interference of cells with their local microenvironment and the interaction among different cell types relies both on the mechanical phenotype of each involved element. However, there is still not yet clearly understood how viscoelasticity alters the functional phenotype of the tumor extracellular matrix environment. Especially the biophysical technologies are still under ongoing improvement and further development. In addition, the effect of matrix mechanics in the progression of cancer is the subject of discussion. Hence, the topic of this review is especially attractive to collect the existing endeavors to characterize the viscoelastic features of tumor extracellular matrices and to briefly highlight the present frontiers in cancer progression and escape of cancers from therapy. Finally, this review article illustrates the importance of the tumor extracellular matrix mechano-phenotype, including the phenomenon viscoelasticity in identifying, characterizing, and treating specific cancer types.

A Framework of Paracellular Transport via Nanoparticles-Induced Endothelial Leakiness

Nanomaterial-induced endothelial leakiness (NanoEL) is an interfacial phenomenon denoting the paracellular transport of nanoparticles that is pertinent to nanotoxicology, nanomedicine and biomedical engineering. While the NanoEL phenomenon is complementary to the enhanced permeability and retention effect in terms of their common applicability to delineating the permeability and behavior of nanoparticles in tumoral environments, these two effects significantly differ in scope, origin, and manifestation. In the current study, the descriptors are fully examined of the NanoEL phenomenon elicited by generic citrate-coated gold nanoparticles (AuNPs) of changing size and concentration, from microscopic gap formation and actin reorganization down to molecular signaling pathways and nanoscale interactions of AuNPs with VE-cadherin and its intra/extracellular cofactors. Employing synergistic in silico methodologies, for the first time the molecular and statistical mechanics of cadherin pair disruption, especially in response to AuNPs of the smallest size and highest concentration are revealed. This study marks a major advancement toward establishing a comprehensive NanoEL framework for complementing the understanding of the transcytotic pathway and for guiding the design and application of future nanomedicines harnessing the myriad functions of the mammalian vasculature.

Frustrated endocytosis controls contractility-independent mechanotransduction at clathrin-coated structures

It is generally assumed that cells interrogate the mechanical properties of their environment by pushing and pulling on the extracellular matrix (ECM). For instance, acto-myosin-dependent contraction forces exerted at focal adhesions (FAs) allow the cell to actively probe substrate elasticity. Here, we report that a subset of long-lived and flat clathrin-coated structures (CCSs), also termed plaques, are contractility-independent mechanosensitive signaling platforms. We observed that plaques assemble in response to increasing substrate rigidity and that this is independent of FAs, actin and myosin-II activity. We show that plaque assembly depends on αvβ5 integrin, and is a consequence of frustrated endocytosis whereby αvβ5 tightly engaged with the stiff substrate locally stalls CCS dynamics. We also report that plaques serve as platforms for receptor-dependent signaling and are required for increased Erk activation and cell proliferation on stiff environments. We conclude that CCSs are mechanotransduction structures that sense substrate rigidity independently of cell contractility.

Cells sense mechanical properties of their environment using various cellular structures including focal adhesions. Here, the authors identify flat clathrin-coated structures (CCSs) as mechanosensitive signaling platforms that form independently of contractility and in response to substrate rigidity.

Regulation of Active ICAM-4 on Normal and Sickle Cell Disease RBCs via AKAPs Is Revealed by AFM

Human healthy (wild-type (WT)) and homozygous sickle (SS) red blood cells (RBCs) express a large number of surface receptors that mediate cell adhesion between RBCs, and between RBCs and white blood cells, platelets, and the endothelium. In sickle cell disease (SCD), abnormal adhesion of RBCs to endothelial cells is mediated by the intercellular adhesion molecule-4 (ICAM-4), which appears on the RBC membrane and binds to the endothelial αvβ3 integrin. This is a key factor in the initiation of vaso-occlusive episodes, the hallmark of SCD. A better understanding of the mechanisms that control RBC adhesion to endothelium may lead to novel approaches to both prevention and treatment of vaso-occlusive episodes in SCD. One important mechanism of ICAM-4 activation occurs via the cyclic adenosine monophosphate-protein kinase A (cAMP-PKA)-dependent signaling pathway. Here, we employed an in vitro technique called single-molecule force spectroscopy to study the effect of modulation of the cAMP-PKA-dependent pathway on ICAM-4 receptor activation. We quantified the frequency of active ICAM-4 receptors on WT-RBC and SS-RBC membranes, as well as the median unbinding force between ICAM-4 and αvβ3. We showed that the collective frequency of unbinding events in WT-RBCs is not significantly different from that of SS-RBCs. This result was confirmed by confocal microscopy experiments. In addition, we showed that incubation of normal RBCs and SS-RBCs with epinephrine, a catecholamine that binds to the β-adrenergic receptor and activates the cAMP-PKA-dependent pathway, caused a significant increase in the frequency of active ICAM-4 receptors in both normal RBCs and SS-RBCs. However, the unbinding force between ICAM-4 and the corresponding ligand αvβ3 remained the same. Furthermore, we demonstrated that forskolin, an adenylyl cyclase activator, significantly increased the frequency of ICAM-4 receptors in WT-RBCs and SS-RBCs, confirming that the activation of ICAM-4 is regulated by the cAMP-PKA pathway. Finally, we showed that A-kinase anchoring proteins play an essential role in ICAM-4 activation.

The Effect of Thermal Fluctuation on the Receptor-Mediated Adhesion of a Cell Membrane to an Elastic Substrate

Mechanics of the bilayer membrane play an important role in many biological and bioengineering problems such as cell-substrate and cell-nanomaterial interactions. In this work, we study the effect of thermal fluctuation and the substrate elasticity on the cell membrane-substrate adhesion. We model the adhesion of a fluctuating membrane on an elastic substrate as a two-step reaction comprised of the out-of-plane membrane fluctuation and the receptor-ligand binding. The equilibrium closed bond ratio as a function of substrate rigidity was computed by developing a coupled Fourier space Brownian dynamics and Monte Carlo method. The simulation results show that there exists a crossover value of the substrate rigidity at which the closed bond ratio is maximal.

Integrin-mediated mechanotransduction

Sun, Guo, and Fässler review the function and regulation of integrin-mediated mechanotransduction and discuss how its dysregulation impacts cancer progession.

Cells can detect and react to the biophysical properties of the extracellular environment through integrin-based adhesion sites and adapt to the extracellular milieu in a process called mechanotransduction. At these adhesion sites, integrins connect the extracellular matrix (ECM) with the F-actin cytoskeleton and transduce mechanical forces generated by the actin retrograde flow and myosin II to the ECM through mechanosensitive focal adhesion proteins that are collectively termed the “molecular clutch.” The transmission of forces across integrin-based adhesions establishes a mechanical reciprocity between the viscoelasticity of the ECM and the cellular tension. During mechanotransduction, force allosterically alters the functions of mechanosensitive proteins within adhesions to elicit biochemical signals that regulate both rapid responses in cellular mechanics and long-term changes in gene expression. Integrin-mediated mechanotransduction plays important roles in development and tissue homeostasis, and its dysregulation is often associated with diseases.

A viscoelastic-stochastic model of the effects of cytoskeleton remodelling on cell adhesion

Cells can adapt their mechanical properties through cytoskeleton remodelling in response to external stimuli when the cells adhere to the extracellular matrix (ECM). Many studies have investigated the effects of cell and ECM elasticity on cell adhesion. However, experiments determined that cells are viscoelastic and exhibiting stress relaxation, and the mechanism behind the effect of cellular viscoelasticity on the cell adhesion behaviour remains unclear. Therefore, we propose a theoretical model of a cluster of ligand-receptor bonds between two dissimilar viscoelastic media subjected to an applied tensile load. In this model, the distribution of interfacial traction is assumed to follow classical continuum viscoelastic equations, whereas the rupture and rebinding of individual molecular bonds are governed by stochastic equations. On the basis of this model, we determined that viscosity can significantly increase the lifetime, stability and dynamic strength of the adhesion cluster of molecular bonds, because deformation relaxation attributed to the viscoelastic property can increase the rebinding probability of each open bond and reduce the stress concentration in the adhesion area.

The glycocalyx promotes cooperative binding and clustering of adhesion receptors

Cell adhesion plays a pivotal role in various biological processes, e.g., immune responses, cancer metastasis, and stem cell differentiation. The adhesion behaviors depend subtly on the binding kinetics of receptors and ligands restricted at the cell-substrate interfaces. Although much effort has been directed toward investigating the kinetics of adhesion molecules, the role of the glycocalyx, anchored on cell surfaces as an exterior layer, is still unclear. In this paper, we propose a theoretical approach to study the collective binding kinetics of a few and a large number of binders in the presence of the glycocalyx, representing the cases of initial and mature adhesions of cells, respectively. The analytical results are validated by finding good agreement with our Monte Carlo simulations. In the force loading case, the on-rate and affinity increase as more bonds form, whereas this cooperative effect is not observed in the displacement loading case. The increased thickness and stiffness of the glycocalyx tend to decrease the affinity for a few bonds, while they have less influence on the affinity for a large number of bonds. Moreover, for a flexible membrane with thermally-excited shape fluctuations, the glycocalyx is exhibited to promote the formation of bond clusters, mainly due to the cooperative binding of binders. This study helps to understand the cooperative kinetics of adhesion receptors under physiologically relevant loading conditions and sheds light on the novel role of the glycocalyx in cell adhesion.

Tension-compression asymmetry in the binding affinity of membrane-anchored receptors and ligands

Cell adhesion plays a crucial role in many biological processes of cells, e.g., immune responses, tissue morphogenesis, and stem cell differentiation. An essential problem in the molecular mechanism of cell adhesion is to characterize the binding affinity of membrane-anchored receptors and ligands under different physiological conditions. In this paper, a theoretical model is presented to study the binding affinity between a large number of anchored receptors and ligands under both tensile and compressive stresses, and corroborated by demonstrating excellent agreement with Monte Carlo simulations. It is shown that the binding affinity becomes lower as the magnitude of the applied stress increases, and drops to zero at a critical tensile or compressive stress. Interestingly, the critical compressive stress is found to be substantially smaller than the critical tensile stress for relatively long and flexible receptor-ligand complexes. This counterintuitive finding is explained by using the Euler instability theory of slender columns under compression. The tension-compression asymmetry in the binding affinity of anchored receptors and ligands depends subtly on the competition between the breaking and instability of their complexes. This study helps in understanding the role of mechanical forces in cell adhesion mediated by specific binding molecules.

Modeling Active Mechanosensing in Cell-Matrix Interactions

Cells actively sense the mechanical properties of the extracellular matrix, such as its rigidity, morphology, and deformation. The cell-matrix interaction influences a range of cellular processes, including cell adhesion, migration, and differentiation, among others. This article aims to review some of the recent progress that has been made in modeling mechanosensing in cell-matrix interactions at different length scales. The issues discussed include specific interactions between proteins, the structure and mechanosensitivity of focal adhesions, the cluster effects of the specific binding, the structure and behavior of stress fibers, cells' sensing of substrate stiffness, and cell reorientation on cyclically stretched substrates. The review concludes by looking toward future opportunities in the field and at the challenges to understanding active cell-matrix interactions.

Effects of cellular viscoelasticity in multiple-bond force spectroscopy

Receptor-ligand bonds are often subjected to forces that regulate their detachment via modulating off-rates. Though the dynamics of detachment is primarily controlled by the physical chemistry of adhesion molecules cellular features such as cell deformability and microvillus viscoelasticity have been shown to have an effect on it as well. In this work, Monte Carlo simulation of the rupture of multiple receptor-ligand bonds between substrate and a polymorphonuclear leukocyte (PMN) cell suspended in a Newtonian fluid is performed. It is demonstrated via various micromechanical models of the PMN cell adhered to the substrate by multiple receptor-ligand bonds that viscous drag caused by relative motion of cell suspended in a Newtonian fluid and cellular viscoelasticity modulate transmission of an applied external load to receptor-ligand bonds. It is demonstrated that due to cellular viscoelasticity the instantaneous intermolecular bond force is lower than the instantaneous applied force. It is also demonstrated that due to cellular viscoelasticity, the mean intermolecular bond rupture forces are lowered while the mean bond lifetime increases.

Effects of surface viscoelasticity on cellular responses of endothelial cells

BACKGROUND

One area of nanoscience deals with nanoscopic interactions between nanostructured materials and biological systems. To elucidate the effects of the substrate surface morphology and viscoelasticity on cell proliferation, fractal analysis was performed on endothelial cells cultured on nanocomposite samples based on silicone rubber (SR) and various concentrations of organomodified nanoclay (OC).

METHODS

The nanoclay/SR ratio was tailored to enhance cell behavior via changes in sample substrate surface roughness and viscoelasticity.

RESULTS

Surface roughness of the cured SR filled with negatively-charged nanosilicate layers had a greater effect than elasticity on cell growth. The surface roughness of SR nanocomposite samples increased with increasing the OC content, leading to enhanced cell growth and extracellular matrix (ECM) remodeling. This was consistent with the decrease in SR segmental motions and damping factor as the primary viscoelastic parameters by the nanosilicate layers with increasing clay concentrations.

CONCLUSIONS

The inclusion of clay nanolayers affected the growth and behavior of endothelial cells on microtextured SR.

USNCTAM perspectives on mechanics in medicine

Over decades, the theoretical and applied mechanics community has developed sophisticated approaches for analysing the behaviour of complex engineering systems. Most of these approaches have targeted systems in the transportation, materials, defence and energy industries. Applying and further developing engineering approaches for understanding, predicting and modulating the response of complicated biomedical processes not only holds great promise in meeting societal needs, but also poses serious challenges. This report, prepared for the US National Committee on Theoretical and Applied Mechanics, aims to identify the most pressing challenges in biological sciences and medicine that can be tackled within the broad field of mechanics. This echoes and complements a number of national and international initiatives aiming at fostering interdisciplinary biomedical research. This report also comments on cultural/educational challenges. Specifically, this report focuses on three major thrusts in which we believe mechanics has and will continue to have a substantial impact. (i) Rationally engineering injectable nano/microdevices for imaging and therapy of disease. Within this context, we discuss nanoparticle carrier design, vascular transport and adhesion, endocytosis and tumour growth in response to therapy, as well as uncertainty quantification techniques to better connect models and experiments. (ii) Design of biomedical devices, including point-of-care diagnostic systems, model organ and multi-organ microdevices, and pulsatile ventricular assistant devices. (iii) Mechanics of cellular processes, including mechanosensing and mechanotransduction, improved characterization of cellular constitutive behaviour, and microfluidic systems for single-cell studies.

Predicted rupture force of a single molecular bond becomes rate independent at ultralow loading rates

We present for the first time a theoretical model of studying the saturation of the rupture force of a single molecular bond that causes the rupture force to be rate independent under an ultralow loading rate. This saturation will obviously bring challenges to understanding the rupture behavior of the molecular bond using conventional methods. This intriguing feature implies that the molecular bond has a nonzero strength at a vanishing loading rate. We find that the saturation behavior is caused by bond rebinding when the loading rate is lower than a limiting value depending on the loading stiffness.

Elastic coupling of nascent apCAM adhesions to flowing actin networks

Adhesions are multi-molecular complexes that transmit forces generated by a cell's acto-myosin networks to external substrates. While the physical properties of some of the individual components of adhesions have been carefully characterized, the mechanics of the coupling between the cytoskeleton and the adhesion site as a whole are just beginning to be revealed. We characterized the mechanics of nascent adhesions mediated by the immunoglobulin-family cell adhesion molecule apCAM, which is known to interact with actin filaments. Using simultaneous visualization of actin flow and quantification of forces transmitted to apCAM-coated beads restrained with an optical trap, we found that adhesions are dynamic structures capable of transmitting a wide range of forces. For forces in the picoNewton scale, the nascent adhesions' mechanical properties are dominated by an elastic structure which can be reversibly deformed by up to 1 µm. Large reversible deformations rule out an interface between substrate and cytoskeleton that is dominated by a number of stiff molecular springs in parallel, and favor a compliant cross-linked network. Such a compliant structure may increase the lifetime of a nascent adhesion, facilitating signaling and reinforcement.

A mechanochemical model of cell reorientation on substrates under cyclic stretch

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.

Effect of viscous drag on multiple receptor-ligand bonds rupture force

Monte Carlo simulation of the rupture of multiple receptor-ligand bonds between two PMN cells suspended in a Newtonian fluid is performed. We demonstrate via micro-mechanical model of two cells adhered by multiple receptor-ligand bonds that viscous drag caused by relative motion of cell suspended in a Newtonian fluid modulates transmission of an applied external load to bonds. Specifically, it is demonstrated that at any time the intermolecular bond force is not equivalent to the instantaneous applied force. The difference in the instantaneous applied force and the intermolecular bond force depends on the viscosity of fluid, the size of cell, the applied loading rate, and the number of bonds at any instant of time. Viscous drag acting on cell reduces average bond rupture forces.

Relationship between cell compatibility and elastic modulus of silicone rubber/organoclay nanobiocomposites

BACKGROUND

Substrates in medical science are hydrophilic polymers undergoing volume expansion when exposed to culture medium that influenced on cell attachment. Although crosslinking by chemical agents could reduce water uptake and promote mechanical properties, these networks would release crosslinking agents. In order to overcome this weakness, silicone rubber is used and reinforced by nanoclay.

OBJECTIVES

Attempts have been made to prepare nanocomposites based on medical grade HTV silicone rubber (SR) and organo-modified montmorillonite (OMMT) nanoclay with varying amounts of clay compositions.

MATERIALS AND METHODS

Incorporation of nanocilica platelets into SR matrix was carried out via melt mixing process taking advantage of a Brabender internal mixer. The tensile elastic modulus of nanocomposites was measured by performing tensile tests on the samples. Produced polydimetylsiloxane (PDMS) composites with different flexibilities and crosslink densities were employed as substrates to investigate biocompatibility, cell compaction, and differential behaviors.

RESULTS

The results presented here revealed successful nanocomposite formation with SR and OMMT, resulting in strong PDMS-based materials. The results showed that viability, proliferation, and spreading of cells are governed by elastic modulus and stiffness of samples. Furthermore, adipose derived stem cells (ADSCs) cultured on PDMS and corresponding nanocomposites could retain differentiation potential of osteocytes in response to soluble factors, indicating that inclusion of OMMT would not prevent osteogenic differentiation. Moreover, better spread out and proliferation of cells was observed in nanocomposite samples.

CONCLUSIONS

Considering cell behavior and mechanical properties of nanobiocomposites it could be concluded that silicone rubber substrate filled by nanoclay are a good choice for further experiments in tissue engineering and medical regeneration due to its cell compatibility and differentiation capacity.

Bond energy effects on strength, cooperativity and robustness of molecular structures

A fundamental challenge in engineering biologically inspired materials and systems is the identification of molecular structures that define fundamental building blocks. Here, we report a systematic study of the effect of the energy of chemical bonds on the mechanical properties of molecular structures, specifically, their strength and robustness. By considering a simple model system of an assembly of bonds in a cluster, we demonstrate that weak bonding, as found for example in H-bonds, results in a highly cooperative behaviour where clusters of bonds operate synergistically to form relatively strong molecular clusters. The cooperative effect of bonding results in an enhanced robustness since the drop of strength owing to the loss of a bond in a larger cluster only results in a marginal reduction of the strength. Strong bonding, as found in covalent interactions such as disulphide bonds or in the backbone of proteins, results in a larger mechanical strength. However, the ability for bonds to interact cooperatively is lost, and, as a result, the overall robustness is lower since the mechanical strength hinges on individual bonds rather than a cluster of bonds. The systematic analysis presented here provides general insight into the interplay of bond energy, robustness and other geometric parameters such as bond spacing. We conclude our analysis with a correlation of structural data of natural protein structures, which confirms the conclusions derived from our study.

Effect of loading conditions on the dissociation behaviour of catch bond clusters

Under increasing tensile load, the lifetime of a single catch bond counterintuitively increases up to a maximum and then decreases exponentially like a slip bond. So far, the characteristics of single catch bond dissociation have been extensively studied. However, it remains unclear how a cluster of catch bonds behaves under tensile load. We perform computational analysis on the following models to examine the characteristics of clustered catch bonds: (i) clusters of catch bonds with equal load sharing, (ii) clusters of catch bonds with linear load sharing, and (iii) clusters of catch bonds in micropipette-manipulated cell detachment. We focus on the differences between the slip and catch bond clusters, identifying the critical factors for exhibiting the characteristics of catch bond mechanism for the multiple-bond system. Our computation reveals that for a multiple-bond cluster, the catch bond behaviour could only manifest itself under relatively uniform loading conditions and at certain stages of decohesion, explaining the difficulties in observing the catch bond mechanism under real biological conditions.

Motor force homeostasis in skeletal muscle contraction

In active biological contractile processes such as skeletal muscle contraction, cellular mitosis, and neuronal growth, an interesting common observation is that multiple motors can perform coordinated and synchronous actions, whereas individual myosin motors appear to randomly attach to and detach from actin filaments. Recent experiment has demonstrated that, during skeletal muscle shortening at a wide range of velocities, individual myosin motors maintain a force of ~6 pN during a working stroke. To understand how such force-homeostasis can be so precisely regulated in an apparently chaotic system, here we develop a molecular model within a coupled stochastic-elastic theoretical framework. The model reveals that the unique force-stretch relation of myosin motor and the stochastic behavior of actin-myosin binding cause the average number of working motors to increase in linear proportion to the filament load, so that the force on each working motor is regulated at ~6 pN, in excellent agreement with experiment. This study suggests that it might be a general principle to use catch bonds together with a force-stretch relation similar to that of myosin motors to regulate force homeostasis in many biological processes.

Probing mechanical principles of focal contacts in cell-matrix adhesion with a coupled stochastic-elastic modelling framework

Cell-matrix adhesion depends on the collective behaviours of clusters of receptor-ligand bonds called focal contacts between cell and extracellular matrix. While the behaviour of a single molecular bond is governed by statistical mechanics at the molecular scale, continuum mechanics should be valid at a larger scale. This paper presents an overview of a series of recent theoretical studies aimed at probing the basic mechanical principles of focal contacts in cell-matrix adhesion via stochastic-elastic models in which stochastic descriptions of molecular bonds and elastic descriptions of interfacial traction-separation are unified in a single modelling framework. The intention here is to illustrate these principles using simple analytical and numerical models. The aim of the discussions is to provide possible clues to the following questions: why does the size of focal adhesions (FAs) fall into a narrow range around the micrometre scale? How can cells sense and respond to substrates of varied stiffness via FAs? How do the magnitude and orientation of mechanical forces affect the binding dynamics of FAs? The effects of cluster size, cell-matrix elastic modulus, loading direction and cytoskeletal pretension on the lifetime of FA clusters have been investigated by theoretical arguments as well as Monte Carlo numerical simulations, with results showing that intermediate adhesion size, stiff substrate, cytoskeleton stiffening, low-angle pulling and moderate cytoskeletal pretension are factors that contribute to stable FAs. From a mechanistic point of view, these results provide possible explanations for a wide range of experimental observations and suggest multiple mechanisms by which cells can actively control adhesion and de-adhesion via cytoskeletal contractile machinery in response to mechanical properties of their surroundings.