Modeling Active Cell Movement With the Potts Model

Abstract

In the last decade, the cellular Potts model has been extensively used to model interacting cell systems at the tissue-level. However, in early applications of this model, cell movement was taken as a consequence of membrane fluctuations due to cell-cell interactions, or as a response to an external chemotactic gradient. Recent findings have shown that eukaryotic cells can exhibit persistent displacements across scales larger than cell size, even in the absence of external signals. Persistent cell motion has been incorporated to the cellular Potts model by many authors in the context of collective motion, chemotaxis and morphogenesis. In this paper, we use the cellular Potts model in combination with a random field applied over each cell. This field promotes a uniform cell motion in a given direction during a certain time interval, after which the movement direction changes. The dynamics of the direction is coupled to a first order autoregressive process. We investigated statistical properties, such as the mean-squared displacement and spatio-temporal correlations, associated to these self-propelled in silico cells in different conditions. The proposed model emulates many properties observed in different experimental setups. By studying low and high density cultures, we find that cell-cell interactions decrease the effective persistent time.

Alternating regimes of motion in cell motility models

“…We used periodic boundary conditions and a square lattice of size 1024 × 1024 sites. More details about initial conditions and thermalization can be found in [15].…”

“…However, when the friction term is present, we found that high density cultures exhibited a double-exponential for the velocity ACF, in contrast to an exponential characterizing the Brownian motion of low density cultures. For both densities the MSD behaves as a persistent random walk model for the time scale studied [15]. These results suggest that the complex behavior of cell motion can be consequence of the intrinsic feature of the movement, but also of cell-cell interactions.…”

“…Further, to consider cell motility preferentially along the direction of a driving field an additional term should be added to the Hamiltonian Eq. (1) [15, 19], as we will see below.…”

“…Recently, we have introduced a reorientation model based on the cellular Potts framework [15]. In this model, cell movement due to a driving field, which direction changes following a discrete version of the OU process, was considered.…”

“…In this paper, we are particularly interested in under-standing the interplay between the neighborhood information gathered by the cell in previous displacement and cell motility over large time scales. To address this question, the cellular Potts model (CPM) introduced in [15] with two types of dynamics for the orientation angle of cell displacements are compared. Firstly, we consider a “naive” implementation where the new orientation is related to the field direction operating in the previous step, regardless the cellular direction of displacement.…”