A modelling framework describing the enzyme regulation of membrane lipids underlying gradient perception in Dictyostelium cells II: input-output analysis

Asymmetric PTEN distribution regulated by spatial heterogeneity in membrane-binding state transitions

The molecular mechanisms that underlie asymmetric PTEN distribution at the posterior of polarized motile cells and regulate anterior pseudopod formation were addressed by novel single-molecule tracking analysis. Heterogeneity in the lateral mobility of PTEN on a membrane indicated the existence of three membrane-binding states with different diffusion coefficients and membrane-binding lifetimes. The stochastic state transition kinetics of PTEN among these three states were suggested to be regulated spatially along the cell polarity such that only the stable binding state is selectively suppressed at the anterior membrane to cause local PTEN depletion. By incorporating experimentally observed kinetic parameters into a simple mathematical model, the asymmetric PTEN distribution can be explained quantitatively to illustrate the regulatory mechanisms for cellular asymmetry based on an essential causal link between individual stochastic reactions and stable localizations of the ensemble.

Chemotaxis: navigating by multiple signaling pathways

During chemotaxis, phosphatidylinositol 3,4,5-trisphosphate (PIP(3)) accumulates at the leading edge of a eukaryotic cell, where it induces the formation of pseudopodia. PIP(3) has been suggested to be the compass of cells navigating in gradients of signaling molecules. Recent observations suggest that chemotaxis is more complex than previously anticipated. Complete inhibition of all PIP(3) signaling has little effect, and alternative pathways have been identified. In addition, selective pseudopod growth and retraction are more important in directing cell movement than is the place where new pseudopodia are formed.

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 [17,18]. 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.

Receptor-mediated and intrinsic polarization and their interaction in chemotaxing cells

Polarization--the clear and persistent localization of different signaling molecules to opposite ends of the cell-is critical for effective chemotaxis in eukaryotic systems. In many systems, polarization can also occur without an externally imposed chemical gradient. We build a modeling framework to study the relationship between the intrinsic capacity for polarization, and that induced by an external gradient. Working within this framework, we analyze different scenarios for the interaction of these pathways. The models are qualitatively simplified, motivated by known properties of the signaling pathways. We also examine the possible role of nonlinear transitions occurring in the polarization pathways. The modeling framework generates testable predictions regarding the relationship between intrinsic polarization and that induced during chemotaxis, and is the first step toward a systematic analysis of the interaction between these pathways.

Spontaneous polarization in eukaryotic gradient sensing: a mathematical model based on mutual inhibition of frontness and backness pathways

A key problem of eukaryotic cell motility is the signaling mechanism of chemoattractant gradient sensing. Recent experiments have revealed the molecular correlate of gradient sensing: Frontness molecules, such as PI3P and Rac, localize at the front end of the cell, and backness molecules, such as Rho and myosin II, accumulate at the back of the cell. Importantly, this frontness-backness polarization occurs spontaneously even if the cells are exposed to uniform chemoattractant profiles. The spontaneous polarization suggests that the gradient sensing machinery undergoes a Turing bifurcation. This has led to several classical activator-inhibitor and activator-substrate models which identify the frontness molecules with the activator. Conspicuously absent from these models is any accounting of the backness molecules. This stands in sharp contrast to experiments which show that the backness pathways inhibit the frontness pathways. Here, we formulate a model based on the mutually inhibitory interaction between the frontness and backness pathways. The model builds upon the mutual inhibition model proposed by Bourne and coworkers [Xu et al., 2003. Divergent signals and cytoskeletal assemblies regulate self-organizing polarity in neutrophils. Cell 114, 201-214.]. We show that mutual inhibition alone, without the help of any positive feedback (autocatalysis), can trigger spontaneous polarization of the frontness and backness pathways. The spatial distribution of the frontness and backness molecules in response to inhibition and activation of the frontness and backness pathways are consistent with those observed in experiments. Furthermore, depending on the parameter values, the model yields spatial distributions corresponding to chemoattraction (frontness pathways in-phase with the external gradient) and chemorepulsion (frontness pathways out-of-phase with the external gradient). Analysis of the model suggests a mechanism for the chemorepulsion-to-chemoattraction transition observed in neurons.