Cell motility in Dictyostelium

Eukaryotic cells are large enough to detect signals and then orient to them by averaging signal strength over the length and breadth of the cell. Amoebae, fibroblasts, neutrophils and growth cones all behave in this way. Little is known however about cell motion and searching behavior in the absence of a signal. Could the detailed trajectories of individual cells be mathematically modeled as random walks? How is the transition from the freely moving ground state to directed motion achieved? Is the ground state in any sense functional---do individual cells have a search strategy when they are beyond the range of the signal they would otherwise move toward?;To address the second and third questions, we first studied single, isolated, Dictyostelium and Polysphondylium amoebae motion in the absence of external cues. We find that their behavior is well described by a special random walk. Two characteristic time scales are found. Amoebae show a long persistence time (30 min) beyond which they start to lose their direction; they move forward in a zig-zag manner; and they make turns every 1.5 min on average. They bias their motion by remembering the last turn and turning away from it. We demonstrate that this strategy improves their chances of finding a target ∼2X more efficiently than a Brownian search. Also, this system is found independent of one major chemotactic apparatus, because a sextuple knockout of the five endogenous PI3 kinases and PTEN exhibit very similar motion in the absence of chemotactic signals, as well as wild-type amoebae when crawling on agar surfaces containing the homogenous chemoattractant cAMP. This suggests that the motion we have documented is a ground state that runs independently of a well characterized chemotactic system. This special behavior may be contrasted with the well-studied strategy of many chemotactic bacteria, where it is the chemotactic run length that is biased, and turning angles occur at random, driven by Brownian motion. We believe that other eukaryotic cells may employ a strategy similar to Dictyostelium when seeking conditions or signal sources not yet within range of their detection system.;To address the first question, we modeled the motility of Dictyostelium cells in a systematic, data-driven manner with a special set of stochastic integro-differential equations. The experimental trajectories tracked the centroid of the cell's perimeter, which is more sensitive to pseudopod activities than a tracking by centroid or nucleus. Also, with very fine spatial and temporal resolution, our richer data demonstrate individuality of cells and our model captures such individuality. From the pertinent statistics of individual trajectories, we deduce the minimal dynamical model that produces trajectories, which reproduce those statistics. Two generalized Langevin equations are used to describe the stochastic periodic pseudopod activities of cells in a two dimensional plane. This activity propels the amoebae with a random periodic waddle in a direction that has a long persistent time. The pseudopod dynamics is linear by construction, apart from multiplicative noise which is consistent with the observed non-Gaussian distributions of velocities. The model we developed reproduces the statistics of all trajectories we considered, including power spectra, velocity distributions and multiplicative noise. It also captures the individuality of cells as different parameter values in the same model.