A computational framework for modeling cell-matrix interactions in soft biological tissues.

Living soft tissues appear to promote the development and maintenance of a preferred mechanical state within a defined tolerance around a so-called set point. This phenomenon is often referred to as mechanical homeostasis. In contradiction to the prominent role of mechanical homeostasis in various (patho)physiological processes, its underlying micromechanical mechanisms acting on the level of individual cells and fibers remain poorly understood, especially how these mechanisms on the microscale lead to what we macroscopically call mechanical homeostasis. Here, we present a novel computational framework based on the finite element method that is constructed bottom up, that is, it models key mechanobiological mechanisms such as actin cytoskeleton contraction and molecular clutch behavior of individual cells interacting with a reconstructed three-dimensional extracellular fiber matrix. The framework reproduces many experimental observations regarding mechanical homeostasis on short time scales (hours), in which the deposition and degradation of extracellular matrix can largely be neglected. This model can serve as a systematic tool for future in silico studies of the origin of the numerous still unexplained experimental observations about mechanical homeostasis.

Topological defects produce kinks in biopolymer filament bundles.

Bundles of stiff filaments are ubiquitous in the living world, found both in the cytoskeleton and in the extracellular medium. These bundles are typically held together by smaller cross-linking molecules. We demonstrate, analytically, numerically, and experimentally, that such bundles can be kinked, that is, have localized regions of high curvature that are long-lived metastable states. We propose three possible mechanisms of kink stabilization: a difference in trapped length of the filament segments between two cross-links, a dislocation where the endpoint of a filament occurs within the bundle, and the braiding of the filaments in the bundle. At a high concentration of cross-links, the last two effects lead to the topologically protected kinked states. Finally, we explore, numerically and analytically, the transition of the metastable kinked state to the stable straight bundle.

Directed force propagation in semiflexible networks.

We consider the propagation of tension along specific filaments of a semiflexible filament network in response to the application of a point force using a combination of numerical simulations and analytic theory. We find the distribution of force within the network is highly heterogeneous, with a small number of fibers supporting a significant fraction of the applied load over distances of multiple mesh sizes surrounding the point of force application. We suggest that these structures may be thought of as tensile force chains, whose structure we explore via simulation. We develop self-consistent calculations of the point-force response function and introduce a transfer matrix approach to explore the decay of tension (into bending) energy and the branching of tensile force chains in the network.

Repulsive Backbone-Backbone Interactions Modulate Access to Specific and Unspecific Binding Sites on Surface-Bound Mucins.

Mucin glycoproteins are the matrix-forming key components of mucus, the innate protective barrier protecting us from pathogenic attack. However, this barrier is constantly challenged by mucin-degrading enzymes, which tend to target anionic glycan chains such as sulfate groups and sialic acid residues. Here, we demonstrate that the efficiency of both unspecific and specific binding of small molecules to mucins is reduced when sulfate groups are enzymatically removed from mucins; this is unexpected because neither of the specific mucin-binding partners tested here targets these sulfate motifs on the mucin glycoprotein. Based on simulation results obtained from a numerical model of the mucin macromolecule, we propose that anionic motifs along the mucin chain establish intramolecular repulsion forces which maintain an elongated mucin conformation. In the absence of these repulsive forces, the mucin seems to adopt a more compacted structure, in which the accessibility of several binding sites is restricted. Our results contribute to a better understanding on how different glycans contribute to the broad spectrum of functions mucin glycoproteins have.

Conformation of a semiflexible filament in a quenched random potential.

Motivated by the observation of the storage of excess elastic free energy, prestress, in cross-linked semiflexible networks, we consider the problem of the conformational statistics of a single semiflexible polymer in a quenched random potential. The random potential, which represents the effect of cross-linking to other filaments, is assumed to have a finite correlation length ξ and mean strength V_{0}. We examine statistical distribution of curvature in filament with thermal persistence length ℓ_{P} and length L_{0} in the limit in which ℓ_{P}≫L_{0}. We compare our theoretical predictions to finite-element Brownian dynamics simulations. Finally, we comment on the validity of replica field techniques in addressing these questions.