Thin, mechanically compliant coatings commonly serve as substrata for adherent cells in cell biology and biophysics studies, biological engineering applications, and biomedical device design. The deformation of such a coating at the cell-substratum interface defines the link between cellular traction, substratum stiffness, and the chemomechanical feedback mechanisms responsible for cellular mechanosensitivity. Here we apply elasticity theory to investigate how this deformation is affected by the finite thickness of such a cell substratum. The model idealizes a cellular adhesion site (e.g., a focal adhesion) as a circular area of uniform tangential traction, and compares the deformation of a compliant semi-infinite material to that of a coating of the same material supported by a rigid base. Two parameters are identified and considered: center displacement (as a measure of adhesion site displacement) and normal strain gradient (as a measure of adhesion site distortion). The attenuation of these parameters provides two measures for the influence of a finite coating thickness and underlying rigid base on cell-mediated deformation of the compliant substratum. A dimensionless term in the resulting solutions connects the coating thickness to the characteristic size of the adhesion sites. This relation, and calculations of the minimum thickness at which the rigid base is practically undetectable by an adherent cell, are supported by existing experimental literature and our observations of the projected area of fibroblasts adhered to polyacrylamide hydrogel coatings with various thicknesses atop relatively rigid glass. The model thus provides a tool for estimating the effective stiffness sensed by a cell attached to a compliant coating. We also identify and consider conceptualizations of critical thickness, or minimum suitable thickness for an application, which depend on both the frame of reference and the cell behavior of interest. The appropriate usage of different definitions resolves the disparity in values reported in the literature. Finally, the distinction between adhesion site displacement and distortion noted in this model could be useful in designing substrata to elucidate the controlling mechanisms of cellular mechanosensing.

Forced unbinding of complementary macromolecules such as ligand-receptor complexes can reveal energetic and kinetic details governing physiological processes ranging from cellular adhesion to drug metabolism. Although molecular-level experiments have enabled sampling of individual ligand-receptor complex dissociation events, disparities in measured unbinding force F(R) among these methods lead to marked variation in inferred binding energetics and kinetics at equilibrium. These discrepancies are documented for even the ubiquitous ligand-receptor pair, biotin-streptavidin. We investigated these disparities and examined atomic-level unbinding trajectories via steered molecular dynamics simulations, as well as via molecular force spectroscopy experiments on biotin-streptavidin. In addition to the well-known loading rate dependence of F(R) predicted by Bell's model, we find that experimentally accessible parameters such as the effective stiffness of the force transducer k can significantly perturb the energy landscape and the apparent unbinding force of the complex for sufficiently stiff force transducers. Additionally, at least 20% variation in unbinding force can be attributed to minute differences in initial atomic positions among energetically and structurally comparable complexes. For force transducers typical of molecular force spectroscopy experiments and atomistic simulations, this energy barrier perturbation results in extrapolated energetic and kinetic parameters of the complex that depend strongly on k. We present a model that explicitly includes the effect of k on apparent unbinding force of the ligand-receptor complex, and demonstrate that this correction enables prediction of unbinding distances and dissociation rates that are decoupled from the stiffness of actual or simulated molecular linkers.

Preceding molecular dynamics simulations of biomolecular interactions, the molecule of interest is often equilibrated with respect to an initial configuration. This so-called equilibration stage is required because the input structure is typically not within the equilibrium phase space of the simulation conditions, particularly in systems as complex as proteins, which can lead to artifactual trajectories of protein dynamics. The time at which nonequilibrium effects from the initial configuration are minimized-what we will call the equilibration time-marks the beginning of equilibrium phase-space exploration. Note that the identification of this time does not imply exploration of the entire equilibrium phase space. We have found that current equilibration methodologies contain ambiguities that lead to uncertainty in determining the end of the equilibration stage of the trajectory. This results in equilibration times that are either too long, resulting in wasted computational resources, or too short, resulting in the simulation of molecular trajectories that do not accurately represent the physical system. We outline and demonstrate a protocol for identifying the equilibration time that is based on the physical model of Normal Mode Analysis. We attain the computational efficiency required of large-protein simulations via a stretched exponential approximation that enables an analytically tractable and physically meaningful form of the root-mean-square deviation of atoms comprising the protein. We find that the fitting parameters (which correspond to physical properties of the protein) fluctuate initially but then stabilize for increased simulation time, independently of the simulation duration or sampling frequency. We define the end of the equilibration stage--and thus the equilibration time--as the point in the simulation when these parameters attain constant values. Compared to existing methods, our approach provides the objective identification of the time at which the simulated biomolecule has entered an energetic basin. For the representative protein considered, bovine pancreatic trypsin inhibitor, existing methods indicate a range of 0.2-10 ns of simulation until a local minimum is attained. Our approach identifies a substantially narrower range of 4.5-5.5 ns , which will lead to a much more objective choice of equilibration time.

Chemomechanical characteristics of the extracellular materials with which cells interact can have a profound impact on cell adhesion and migration. To understand and modulate such complex multiscale processes, a detailed understanding of the feedback between a cell and the adjacent microenvironment is crucial. Here, we use computational modeling and simulation to examine the cell-matrix interaction at both the molecular and continuum lengthscales. Using steered molecular dynamics, we consider how extracellular matrix (ECM) stiffness and extracellular pH influence the interaction between cell surface adhesion receptors and extracellular matrix ligands, and we predict potential consequences for focal adhesion formation and dissolution. Using continuum level finite element simulations and analytical methods to model cell-induced ECM deformation as a function of ECM stiffness and thickness, we consider the implications toward design of synthetic substrata for cell biology experiments that intend to decouple chemical and mechanical cues.

The function of tissue cells can be significantly modulated by changes in the local mechanical environment, including the stiffness of the substrata to which these cells adhere. To engineer surfaces that maintain or induce cell functions, it is important to understand the force, length, and timescales over which cell surface receptors probe the local mechanical environment. Here we show how simplified continuum and atomistic simulations of the nanoscale forces between cell surface receptors and extracellular matrix molecules help define the critical features of materials designed to recapitulate the cell's in vivo mechanical environment for tissue engineering applications.