Taxis Equations for Amoeboid Cells

The classical macroscopic chemotaxis equations have previously been derived from an individual-based description of the tactic response of cells that use a "run-and-tumble" strategy in response to environmental cues. Here we derive macroscopic equations for the more complex type of behavioral response characteristic of crawling cells, which detect a signal, extract directional information from a scalar concentration field, and change their motile behavior accordingly. We present several models of increasing complexity for which the derivation of population-level equations is possible, and we show how experimentally-measured statistics can be obtained from the transport equation formalism. We also show that amoeboid cells that do not adapt to constant signals can still aggregate in steady gradients, but not in response to periodic waves. This is in contrast to the case of cells that use a "run-and-tumble" strategy, where adaptation is essential.Comment: 35 pages, submitted to the Journal of Mathematical Biolog

Individual and collective dynamics of chemotaxing cells

The study of the dynamics of interacting self-propelled entities is a growing area of physics research. This dissertation investigates individual and collective motion of the eukaryote Dictyostelium discoideum, a system amenable to signal manipulation, mathematical modeling, and quantitative analysis. In the wild, Dictyostelium survive adverse conditions through collective behaviors caused by secreting and responding to chemical signals. We explore this collective behavior on size scales ranging from subcellular biochemistry up to dynamics of thousands of communicating cells. To study how individual cells respond to multiple signals, we perform stability analysis on a previously-developed computational model of signal sensing. Polarized cells are linearly stable to perturbations, with a least stable region at about 60 degrees off the polarization axis. This finding is confirmed through simulations of the model response to additional chemical signals. The off-axis sensitivity suggests a mechanism for previously observed zig-zag motion of real cells randomly migrating or chemotaxing in a linear gradient. Moving up in scale, we experimentally investigate the rules of cell motion and interaction in the context of thousands of cells. Migrating Dictyostelium discoideum cells communicate by sensing and secreting directional signals, and we find that this process leads to an initial signal having an increased spatial range of an order of magnitude. While this process steers cells, measurements indicate that intrinsic cell motility remains unaffected. Additionally, migration of individual cells is unaffected by changing cell-surface adhesion energy by nine orders of magnitude, showing that individual motility is a robust process. In contrast, we find that collective dynamics depend on cell-surface adhesion, with greater adhesion causing cells to form smaller collective structures. Overall, this work suggests that the underlying migration ability of individual Dictyostelium cells operates largely independent of environmental conditions. Our gradient-sensing model shows that polarized cells are stable to small perturbations, and our experiments demonstrate that the motility apparatus is robust to considerable changes in cell-surface adhesion or complex signaling fields. However, we find that environmental factors can dramatically affect the collective behavior of cells, emphasizing that the laws governing cell-cell interaction can change migration patterns without altering intrinsic cell motility

Synthetic spatially graded Rac activation drives directed cell polarization and locomotion

Migrating cells possess intracellular gradients of Rho GTPases, but it is unknown whether these shallow gradients themselves can induce motility. Here we describe a new method to present cells with induced linear gradients of active, endogenous Rac without receptor activation. Gradients as low as 15% were sufficient to not only trigger cell migration up the synthetic gradient, but also to induce both cell polarization and repolarization. Response kinetics were inversely proportional to Rac gradient values, in agreement with a new mathematical model, suggesting a role for natural input gradient amplification upstream of Rac. Increases in Rac levels beyond a well-defined threshold dramatically augmented polarization and decreased sensitivity to the gradient value. The threshold was governed by initial cell polarity and PI3K activity, supporting a role for both in defining responsiveness to natural or synthetic Rac activation. Our methodology suggests a general way to investigate processes regulated by intracellular signaling gradients

Dynamical basis of cellular sensing and responsiveness to spatial-temporal signals

Under physiological conditions, cells continuously sense and migrate in response to chemoattractant signals that are noisy, conflicting, and changing over time and space. This suggests cells exhibit seemingly opposed characteristics, such as robust maintenance of polarized state longer than the signal duration, while still remaining adaptive to novel signals. However, the dynamical mechanism that enables such sensing capabilities is still unclear. In this thesis, I propose a generic dynamical mechanism based on critical positioning of receptor signaling network in the vicinity of saddle-node of a sub-critical pitchfork bifurcation (SubPB mechanism). The critical organization leads to the emergence of a dynamical "ghost" that gives transient memory in the polarized response, as well as the ability to continuously adapt to changes in signal localization. Using weakly nonlinear analysis, an analytical description of the necessary conditions for the existence of this mechanism in a general receptor network is provided. Comparing to three classes of existing mathematical models for polarization that operate on the principle of stable attractors, I demonstrate that the metastability arising from "ghost" in the SubPB mechanism uniquely enables sensing dynamic spatial-temporal signals in a history-dependent manner. By using a physical model that couples signaling to morphology, I demonstrate how this mechanism enables cells to navigate in changing environments. Using the well characterized Epidermal growth factor receptor (EGFR) sensing network in epithelial cells, I demonstrated that the described transient memory in signaling mimics working memory in neurons, enabling cells to process non-stationary signals