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.