Stochastic Model ​of Chemotaxis In Eukaryotic Cells
ABSTRACT :
Cells are capable of sensing chemical gradients in their environment and direct their movement accordingly. Unlike prokaryotic cells, eukaryotic cells measure the spatial gradient of ligands using the asymmetry in the distribution of ligand-bound receptors over the surface of the cell. The binding of ligand to a receptor triggers the internal signaling pathway and generates a "polarity vector", which guides the motion of the cell. The process as a whole consists of many stochastic events such as probabilistic receptor ligand binding and fluctuations in local ligand concentration which leads to fluctuations in the polarity vector. In case of multiple cells, coupling of individual polarity vectors occur due to the interaction of cells mediated by the ligand concentration field. Consequently this phenomenon may give rise to collective motion of cells. Recent studies reveal that even in the absence of external cues, the cells polarise spontaneously and move randomly. Motivated by these observations, we propose a stochastic model for spontaneous migration of a spherical cell which predict that the auto-correlation of the polarity vector decays algebraically at long times. Under some conditions, this may lead to super-diffusive motion of the cell, in agreement with the observations. In the long run, our investigation aims to characterise all the principal sources of extrinsic and intrinsic noise in the chemotaxis process, and to understand how it influences the motion of single cells, as well as interactions between them. We are also in the process of developing the numerical simulations to verify and explain the limitations of the analytical results.