Title: Modelling of Dictyostelium Discoideum Movement in Linear Gradient of Chemoattractant,
Abstract: Chemotaxis is a ubiquitous biological phenomenon in which cells detect a
spatial gradient of chemoattractant, and then move towards the source. Here we
present a position-dependent advection-diffusion model that quantitatively
describes the statistical features of the chemotactic motion of the social
amoeba {\it Dictyostelium discoideum} in a linear gradient of cAMP (cyclic
adenosine monophosphate). We fit the model to experimental trajectories that
are recorded in a microfluidic setup with stationary cAMP gradients and extract
the diffusion and drift coefficients in the gradient direction. Our analysis
shows that for the majority of gradients, both coefficients decrease in time
and become negative as the cells crawl up the gradient. The extracted model
parameters also show that besides the expected drift in the direction of
chemoattractant gradient, we observe a nonlinear dependency of the
corresponding variance in time, which can be explained by the model.
Furthermore, the results of the model show that the non-linear term in the mean
squared displacement of the cell trajectories can dominate the linear term on
large time scales.