Dictyostelium discoideum amoeba is a well-established model organism for studying the crawling locomotion of eukaryotic cells. These amoebae extend pseudopodium - a temporary actin-based protrusion of their body membrane to probe the medium and crawl through it. Experiments show highly-ordered patterns in the growth direction of these pseudopodia, which results in persistence cell motility. Here, we propose a discrete model for studying and investigating the cell locomotion based on the experimental evidences. According to our model, Dictyostelium selects its pseudopodium growth direction based on a second-order Markov chain process, in the absence of external cues. Consequently, compared to a random walk process, our model indicates stronger growth in the mean-square displacement of cells, which is consistent with empirical findings. In the presence of external chemical stimulants, cells tend to align with the gradient of chemoattractant molecules. To quantify this tendency, we define a coupling coefficient between the pseudopodium extension direction and the gradient of an external stimulant, which depends on the local stimulant concentration and its gradient. Additionally, we generalize the model to weak-coupling regime by utilizing perturbation methods.
Orchestrated chemical signaling of single cells sounds to be a linchpin of emerging organization and multicellular life form. The social amoeba Dictyostelium discoideum is a well-studied model organism to explore overall pictures of grouped behavior in developmental biology. The chemical waves secreted by aggregating Dictyostelium is a superb example of pattern formation. The waves are either circular or spiral in shape, according to the incremental population density of a self-aggregating community of individuals. Here, we revisit the spatiotemporal patterns that appear in an excitable medium due to synchronization of randomly firing individuals, but with a more parsimonious attitude. According to our model, a fraction of these individuals are less involved in amplifying external stimulants. Our simulations indicate that the cells enhance the system’s asymmetry and as a result, nucleate early sustainable spiral territory zones, provided that their relative population does not exceed a tolerable threshold.
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 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 over 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 the chemoattractant gradient, we observe a nonlinear dependency of the corresponding variance on 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.
After being exposed to an external chemical attractant, several internal cellular downstream signal transduction pathways control the chemotactic machinery of eukaryotes. The spatial activation of these pathways ultimately leads to some sort of symmetry breaking around the cell eriphery in the form of redistribution of several biochemicals, e.g., polymerized actin at one side of the cell for propulsion and the assembly of myosin II at nearly opposite side for retraction. In this study, we revisit the modeling of this process, which is called directional sensing, with a compartment-based design. In our model, we consider a network of excitable elements around cell circumference which are stimulated occasionally with local colored noise. The exciting elements are capable of sharing information with their close neighbors. We show that the dynamic can distinguish a temporary but enough long-lasting direction, statistically, pointing towards the gradient of external stimulants that can be deemed as the preferred orientation of the cell periphery during the directional sensing process in eukaryotes.
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