Aggregation dynamics of molecular bonds between compliant materials

Ligand Mobility-Mediated Cell Adhesion and Spreading

Cells live in a highly dynamic environment where their physical connection and communication with the outside are achieved through receptor-ligands binding. Therefore, a precise knowledge of the interaction between receptors and ligands is critical for our understanding of how cells execute different biological duties. Interestingly, recent evidence has shown that the mobility of ligands at the cell-extracellular matrix (ECM) interface significantly affects the adhesion and spreading of cells, while the underlying mechanism remains unclear. Here, we present a modeling investigation to address this critical issue. Specifically, by adopting the Langevin dynamics, the random movement of ligands was captured by assigning a stochastic force along with a viscous drag on them. After that, the evolution of adhesion and subsequent spreading of cells were analyzed by considering the force-regulated binding/breakage of individual molecular bonds connecting polymerizing actin bundles inside the cell to the ECM. Interestingly, a biphasic relationship between adhesion and ligand diffusivity was predicted, resulting in maximized cell spreading at intermediate mobility of ligand molecules. In addition, this peak position was found to be dictated by the aggregation of ligands, effectively reducing their diffusivity, and how fast bond association/dissociation can occur. These predictions are in excellent agreement with our experimental observations where distinct ligand mobility was introduced by tuning the interactions between the self-assembly polymer coating and the surface.

Active chemo-mechanical feedbacks dictate the collective migration of cells on patterned surfaces

Recent evidence has demonstrated that, when cultured on micro-patterned surfaces, living cells can move in a coordinated manner and form distinct migration patterns, including flowing chain, suspended propagating bridge, rotating vortex, etc. However, the fundamental question of exactly how and why cells migrate in these fashions remains elusive. Here, we present a theoretical investigation to show that the tight interplay between internal cellular activities, such as chemo-mechanical feedbacks and polarization, and external geometrical constraints are behind these intriguing experimental observations. In particular, on narrow strip patterns, strongly force-dependent cellular contractility and intercellular adhesion were found to be critical for reinforcing the leading edge of the migrating cell monolayer and eventually result in the formation of suspended cell bridges flying over nonadhesive regions. On the other hand, a weak force-contractility feedback led to the movement of cells like a flowing chain along the adhesive strip. Finally, we also showed that the random polarity forces generated in migrating cells are responsible for driving them into rotating vortices on strips with width above a threshold value (~10 times the size of the cell).

Adhesion-Induced Instability Regulates Contact Mechanics of Soft Thin Elastic Films

Adhesive contact of soft materials plays an essential role in flexible electronics, soft robots, and biological systems. Classical contact mechanics theories assume that the contact region between a spherical indenter and a flat surface is circular. In this paper, however, we show that fingering instability and inner cavitation may appear and disappear during the loading-unloading process when a soft thin elastic film is indented with a spherical indenter. We further demonstrate that this adhesion-induced instability can enhance the resistance to deformation and thus significantly increase contact force. Finally, we find an important dimensionless number, defined as the ratio of adhesion energy to elastic energy, and thus reveal that the competition between adhesion energy and elastic energy yields the critical condition for adhesion-induced instability. Thus, our findings bridge the gap between contact mechanics and interfacial instabilities of soft materials and may have many important implications for the applications of soft materials.

Maturation of Neural Cells Leads to Enhanced Axon-Extracellular Matrix Adhesion and Altered Injury Response

Although it is known that stronger cell-extracellular matrix interactions will be developed as neurons mature, how such change influences their response against traumatic injury remains largely unknown. In this report, by transecting axons with a sharp atomic force microscope tip, we showed that the injury-induced retracting motion of axon can be temporarily arrested by tight NCAM (neural cell adhesion molecule) mediated adhesion patches, leading to a retraction curve decorated with sudden bursts. Interestingly, although the size of adhesion clusters (~0.5–1 μm) was found to be more or less the same in mature and immature neurons (after 7- and 3-days of culturing, respectively), the areal density of such clusters is three times higher in mature axons resulting in a much reduced retraction in response to injury. A physical model was also adopted to explain the observed retraction trajectories which suggested that apparent adhesion energy between axon and the substrate increases from ~0.12 to 0.39 mJ/m² as neural cell matures, in good agreement with our experiments.

Controlling Cellular Volume via Mechanical and Physical Properties of Substrate

The mechanical and physical properties of substrate play a crucial role in regulating many cell functions and behaviors. However, how these properties affect cell volume is still unclear. Here, we show that an increase in substrate stiffness, available spread area, or effective adhesion energy density results in a remarkable cell volume decrease (up to 50%), and the dynamic cell spreading process is also accompanied by dramatic cell volume decrease. Further, studies of ion channel inhibition and osmotic shock suggest that these volume decreases are due to the efflux of water and ions. We also show that disrupting cortex contractility leads to bigger cell volume. Collectively, these results reveal the "mechanism of adhesion-induced compression of cells," i.e., stronger interaction between cell and substrate leads to higher actomyosin contractility, expels water and ions, and thus decreases cell volume.

Cellular mechanosensing of the biophysical microenvironment: A review of mathematical models of biophysical regulation of cell responses

Cells in vivo reside within complex microenvironments composed of both biochemical and biophysical cues. The dynamic feedback between cells and their microenvironments hinges upon biophysical cues that regulate critical cellular behaviors. Understanding this regulation from sensing to reaction to feedback is therefore critical, and a large effort is afoot to identify and mathematically model the fundamental mechanobiological mechanisms underlying this regulation. This review provides a critical perspective on recent progress in mathematical models for the responses of cells to the biophysical cues in their microenvironments, including dynamic strain, osmotic shock, fluid shear stress, mechanical force, matrix rigidity, porosity, and matrix shape. The review highlights key successes and failings of existing models, and discusses future opportunities and challenges in the field.

Tuning interfacial patterns of molecular bonds via surface morphology

Many studies have demonstrated that the mechanical properties of the extracellular matrix can significantly influence the morphology, strength and lifetime of focal adhesions. However, how the morphology of the contact surface affects the pattern formation of the molecular bonds still remains largely unknown. Here, by simplifying the cell and extracellular matrix to two opposing elastic bodies and considering the lateral diffusion as well as the bonding/debonding of molecular bonds, we study the clustering behavior of receptor-ligand bonds between curved surfaces and the phase diagrams of cluster patterns. We reveal the important role of surface morphology and bond kinetics in regulating the patterns of bond clusters. We further investigate the segregation dynamics of the interfacial bonds under various loading speeds, and we show that the average interfacial stress is rate-dependent while the rupture stress is rate-independent. Finally, we demonstrate that programmable patterning of bond clusters can be achieved through the designed surface morphology.

Mechanochemical mechanism of integrin clustering modulated by nanoscale ligand spacing and rigidity of extracellular substrates

Experimental findings indicate that cell function and behavior such as cell growth, division, migration and differentiation, are subtly regulated via integrin-dependent cell adhesion. Cell adhesion is influenced by nanoscale ligand spacing and rigidity of extracellular substrates, as cell adhesion drops greatly when the ligand spacing is larger than ~60nm, and cell adhesion is stronger on stiff than soft substrates. However, how nanoscale ligand spacing and substrate stiffness jointly affect integrin clustering and hence nascent cell adhesion remains to be elucidated. To quantitatively investigate the phenomena and the underlying mechanochemical mechanism of integrin clustering modulated by ligand spacing and substrate stiffness, we introduced Monte Carlo simulations varying the values of ligand spacing and substrate stiffness. Moreover, the effects of integrin number, integrin binding free energy, integrin association free energy, and local ligand spacing were investigated. The simulation results showed that integrin clustering decreased sharply, when ligand spacing was relatively large such as d_L>60nm in the current simulations, regardless of substrate rigidities, though with close spacing, the clustering increased with the substrate stiffness. The investigation contributes to the goals of understanding and predicting experimental phenomena, directing and optimizing biomaterial design, and manipulating integrin-dependent cell-substrate adhesion in tissue engineering.