Collective durotaxis of cohesive cell clusters on a stiffness gradient

Effect of contact inhibition locomotion on confined cellular organization

Experiments performed using micro-patterned one dimensional collision assays have allowed a precise quantitative analysis of the collective manifestation of contact inhibition locomotion (CIL) wherein, individual migrating cells reorient their direction of motion when they come in contact with other cells. Inspired by these experiments, we present a discrete, minimal 1D Active spin model that mimics the CIL interaction between cells in one dimensional channels. We analyze the emergent collective behaviour of migrating cells in such confined geometries, as well as the sensitivity of the emergent patterns to driving forces that couple to cell motion. In the absence of vacancies, akin to dense cell packing, the translation dynamics is arrested and the model reduces to an equilibrium spin model which can be solved exactly. In the presence of vacancies, the interplay of activity-driven translation, cell polarity switching, and CIL results in an exponential steady cluster size distribution. We define a dimensionless Péclet number Q-the ratio of the translation rate and directional switching rate of particles in the absence of CIL. While the average cluster size increases monotonically as a function of Q, it exhibits a non-monotonic dependence on CIL strength, when the Q is sufficiently high. In the high Q limit, an analytical form of average cluster size can be obtained approximately by effectively mapping the system to an equivalent equilibrium process involving clusters of different sizes wherein the cluster size distribution is obtained by minimizing an effective Helmholtz free energy for the system. The resultant prediction of exponential dependence on CIL strength of the average cluster size and [Formula: see text] dependence of the average cluster size is borne out to reasonable accuracy as long as the CIL strength is not very large. The consequent prediction of a single scaling function of Q, particle density and CIL interaction strength, characterizing the distribution function of the cluster sizes and resultant data collapse is observed for a range of parameters.

Matching mechanical heterogeneity of the native spinal cord augments axon infiltration in 3D-printed scaffolds

Scaffolds delivered to injured spinal cords to stimulate axon connectivity often match the anisotropy of native tissue using guidance cues along the rostral-caudal axis, but current approaches do not mimic the heterogeneity of host tissue mechanics. Although white and gray matter have different mechanical properties, it remains unclear whether tissue mechanics also vary along the length of the cord. Mechanical testing performed in this study indicates that bulk spinal cord mechanics do differ along anatomical level and that these differences are caused by variations in the ratio of white and gray matter. These results suggest that scaffolds recreating the heterogeneity of spinal cord tissue mechanics must account for the disparity between gray and white matter. Digital light processing (DLP) provides a means to mimic spinal cord topology, but has previously been limited to printing homogeneous mechanical properties. We describe a means to modify DLP to print scaffolds that mimic spinal cord mechanical heterogeneity caused by variation in the ratio of white and gray matter, which improves axon infiltration compared to controls exhibiting homogeneous mechanical properties. These results demonstrate that scaffolds matching the mechanical heterogeneity of white and gray matter improve the effectiveness of biomaterials transplanted within the injured spinal cord.

Temperature dependent model for the quasi-static stick-slip process on a soft substrate

The classical Prandtl-Tomlinson model is the most famous and efficient method to describe the stick-slip phenomenon and the resulting friction between a slider and a corrugated substrate. It is widely used in all studies of frictional physics and notably in nanotribology. However, it considers a rigid or undeformable substrate and therefore is hardly applicable for investigating the physics of soft matter and in particular biophysics. For this reason, we introduce here a modified model that is capable of taking into consideration a soft or deformable substrate. It is realized by a sequence of elastically bound quadratic energy wells, which represent the corrugated substrate. We study the quasi-static behavior of the system through the equilibrium statistical mechanics. We thus determine the static friction and the deformation of the substrate as a function of temperature and substrate stiffness. The results are of interest for the study of cell motion in biophysics and for haptic and tactile systems in microtechnology.