  Cell migration is a fundamental process involved in physiological phenomena
such as the immune response and morphogenesis, but also in pathological
processes, such as the development of tumor metastasis. These functions are
effectively ensured because cells are active systems that adapt to their
environment. In this work, we consider a migrating cell as an active particle,
where its intracellular activity is responsible for motion. Such system was
already modeled in a previous model where the protrusion activity of the cell
was described by a stochastic Markovian jump process. The model was proven able
to capture the diversity in observed trajectories. Here, we add a description
of the effect of an external chemical attractive signal on the protrusion
dynamics, that may vary in time. We show that the resulting stochastic model is
a well-posed non-homogeneous Markovian process, and provide cell trajectories
in different settings, illustrating the effects of the signal on long-term
trajectories.
