| Abstract: | Cell migration is essential to many biological processes such as embryonic morphogenesis, wound healing, and cancer progression. The main challenge in the study of cell motility is to understand how cells respond to external stimuli such as chemical, geometrical, and physical signals. The response frequently involves movement toward or away from an external stimulus, and such a response is called a taxis. Many different types of taxis are known, including chemotaxis, haptotaxis, curvotaxis, and durotaxis, etc. Such cellular taxis are characterized, in most biological literature, simply as positive or negative, depending on whether it is toward or away from the external stimulus. However, another important feature in the tactic movement of living cells – the non-negligible active random fluctuations – has not been accounted properly. In this talk, I adopt a simple way to account for such active fluctuations, without resolving the underlying complex molecular mechanisms, by introducing stochastic forces into the equations of motion of individual cells. Such phenomenological description of the random motion of living cells has a long history dating back to Przibram (1913) and Furth (1920), who introduced the notion of persistent random walk (PRW) to the description of random swimming of living microorganisms. However, the PRW model has not been applied to the migration of crawling animal cells until Gail and Boone (1970) for fibroblasts on flat, homogeneous solid substrates. Later on, the PRW model has been found to work also well for many (although not all) cell types such as blood neutrophil leucocytes (Allan and Wilkinson, 1978), microvessel endothelial cells (Stokes et al, 1991), and lung epithelial cells (Wright et al, 2008). I propose that the PRW model and the related self-propelled particle models provide a phenomenological paradigm for the quantification of cellular taxis, in which the fluctuations or randomness is taken into account by persistent random motion and the taxis is included into some “potentials” derived from phenomenological cell models. Based on this simple idea, I will present our theoretical models for some typical cellular taxis such as haptotaxis on substrates with fibronectin gradients, curvotaxis on stiff cylinders, and durotaxis on substrates with stiffness gradients. |