A stochastic model for cell adhesion to the vascular wall

Abstract

We present here a minimal mathematical model of the interaction between a cell and the blood vessel wall in shear flow. The bond dynamics in cell adhesion is modeled as a non-linear discrete stochastic process. Performing a renormalization in the spirit of [22,11], we obtain a continuous model which predicts the existence of a threshold shear velocity associated with cell rolling and a process of firm adhesion that follows the initial rolling.

The nanocaterpillar's random walk: diffusion with ligand–receptor contacts

“…Furthermore, many systems have a valency of thousands of leg contacts, 31,38,39 too many degrees of freedom to resolve experimentally or computationally. 22,40 To make progress, numerical and analytical models often rely on simplified assumptions, e.g. excluding stochastic relaxation of the legs, 41,42 limiting the analysis to a small number of legs, 41,43,44 or assuming small perturbations.…”

“…22 Such models have given insight into a variety of phenomena, such as how specific parameters could favor rolling over sliding 7,41,43,45,46 or how specific mechanisms could increase overall mobility (with coupling effects such as binding dynamics depending on bond number [47][48][49] or when numerous adhesive sites are available for a single ligand 22,50,51 ). Nevertheless, such modeling assumptions are not always justified; for example stochasticity plays a critical role for mobility, facilitating rolling, 37 targeted arrest, 40 or other walking modes. 52 Furthermore, such models can also not reproduce the order of magnitude decrease of diffusion of DNA-coated colloids.…”

Deciphering circulating tumor cells binding in a microfluidic system thanks to a parameterized mathematical model

“…In this work, we aim to capture the role of adhesion proteins and hydrodynamic forces and to understand their interplay focusing on the first phase of CTCs interaction with the endothelial wall. We use a Poiseuille model for the fluid velocity, and weakly couple it to a modification of the model proposed in [36, 37]. This modeling approach allows its rigorous calibration using the in vitro experiments carried out by Osmani and collaborators, see [14, 41].…”

The Nanocaterpillar's Random Walk: Diffusion With Ligand-Receptor Contacts

“…Investigating how microscopic binding details lead to macroscopic mobility is challenging, as it requires probing time and length scales that can often be quite different [19,38] -legs can be much smaller than the nanocaterpillar they are attached to, while leg dynamics can be orders of magnitude faster than the timescales of macroscopic motion. Furthermore, many systems have a valency of thousands of leg contacts [31,38,39], too many degrees of freedom to resolve experimentally or computationally [22,40]. To make progress, numerical and analytical models often rely on simplified assumptions, e.g.…”

“…Such models have given insight into a variety of phenomena, such as how specific parameters could favor rolling over sliding motions [7,41,43,45,46] or how specific mechanisms could increase overall particle mobility (through leg cooperativity [47,48] or using binding rates with multiple adhesive sites [22,49,50]). Nevertheless, such modeling assumptions are not always justified; for example stochasticity plays a critical role for mobility, facilitating rolling [37], targeted arrest [40], or other walking modes [51]. Finally, a systematic derivation of macroscopic mobility from microscopic details that is valid under a broad range of parameters has not, to the best of our knowledge, been carried out.…”