| Abstract: | Living matter physics aims to understand the physical principles and behaviors of living systems at various levels of organization, from molecular and cellular to organismal and ecological scales. In this study, we focus on the phenomenon of cell migration on solid substrates using a phenomenological paradigm. Cell migration is crucial to many biological processes, including embryonic morphogenesis, tissue repair, immune response, and cancer progression. One of the main challenges in studying cell motility is understanding how cells respond to external stimuli, such as chemical, geometrical, and physical signals. These responses often involve movement toward or away from a stimulus, which is called a taxis. Several types of taxis are known, including chemotaxis, haptotaxis, curvotaxis, and durotaxis, etc. However, an important feature of the tactic movement of living cells -- non-negligible active random fluctuations -- has not been accounted for properly. In this talk, I will introduce a simple way to account for such active fluctuations by introducing stochastic forces into the equations of motion for individual cells. This phenomenological description of the random motion of living cells dates to Przibram and Furth (1920), who introduced the persistent random walk (PRW) model to describe the random swimming of living microorganisms. We propose that the PRW model and related self-propelled particle models provide a phenomenological paradigm for quantifying cellular taxis, in which the fluctuations or randomness are taken into account by persistent random motion and the taxis is included into some “potentials”. The potential can be either derived from phenomenological physics-based cell models or learned from experimental data (stochastic cell trajectories) using deep learning methods. 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. |