Mathematical analysis of steady-state solutions in compartment and continuum models of cell polarization

On the influence of cell shape on dynamic reaction-diffusion polarization patterns

The distribution of signaling molecules following mechanical or chemical stimulation of a cell defines cell polarization, with regions of high active Cdc42 at the front and low active Cdc42 at the rear. As reaction-diffusion phenomena between signaling molecules, such as Rho GTPases, define the gradient dynamics, we hypothesize that the cell shape influences the maintenance of the “front-to-back” cell polarization patterns. We investigated the influence of cell shape on the Cdc42 patterns using an established computational polarization model. Our simulation results showed that not only cell shape but also Cdc42 and Rho-related (in)activation parameter values affected the distribution of active Cdc42. Despite an initial Cdc42 gradient, the in silico results showed that the maximal Cdc42 concentration shifts in the opposite direction, a phenomenon we propose to call “reverse polarization”. Additional in silico analyses indicated that “reverse polarization” only occurred in a particular parameter value space that resulted in a balance between inactivation and activation of Rho GTPases. Future work should focus on a mathematical description of the underpinnings of reverse polarization, in combination with experimental validation using, for example, dedicated FRET-probes to spatiotemporally track Rho GTPase patterns in migrating cells. In summary, the findings of this study enhance our understanding of the role of cell shape in intracellular signaling.

Spatiotemporal dynamics of a reaction-diffusion model of pollen tube tip growth

A reaction-diffusion model is proposed to describe the mechanisms underlying the spatial distributions of ROP1 and calcium on the pollen tube tip. The model assumes that the plasma membrane ROP1 activates itself through positive feedback loop, while the cytosolic calcium ions inhibit ROP1 via a negative feedback loop. Furthermore it is proposed that lateral movement of molecules on the plasma membrane are depicted by diffusion. It is shown that bistable or oscillatory dynamics could exist even in the non-spatial model, and stationary and oscillatory spatiotemporal patterns are found in the full spatial model which resemble the experimental data of pollen tube tip growth.

Computational Modeling of the Dynamics of Spatiotemporal Rho GTPase Signaling: A Systematic Review

The Rho family of GTPases are known to play pivotal roles in the regulation of fundamental cellular processes, ranging from cell migration and polarity to wound healing and regulation of actin cytoskeleton. Over the past decades, accumulating experimental work has increasingly mapped out the mechanistic details and interactions between members of the family and their regulators, establishing detailed interaction circuits within the Rho GTPase signaling network. These circuits have served as a vital foundation based on which a multitude of mathematical models have been developed to explain experimental data, gain deeper insights into the biological phenomenon they describe, as well as make new testable predictions and hypotheses. Due to the diverse nature and purpose of these models, they often vary greatly in size, scope, complexity, and formulation. Here, we provide a systematic, categorical, and comprehensive account of the recent modeling studies of Rho family GTPases, with an aim to offer a broad perspective of the field. The modeling limitations and possible future research directions are also discussed.

Alternative cell polarity behaviours arise from changes in G-protein spatial dynamics

Yeast cells form a single mating projection when exposed to mating pheromone, a classic example of cell polarity. Prolonged treatment with pheromone or specific mutations results in alternative cell polarity behaviours. The authors performed mathematical modelling to investigate these unusual cell morphologies from the perspective of balancing spatial amplification (i.e. positive feedback that localises components) with spatial tracking (i.e. negative feedback that allows sensing of gradient). First, they used generic models of cell polarity to explore different cell polarity behaviours that arose from changes in the model spatial dynamics. By exploring the positive and negative feedback loops in each stage of a two-stage model, they simulated a variety of cell morphologies including single bending projections, single straight projections, periodic multiple projections and simultaneous double projections. In the second half of the study, they used a two-stage mechanistic model of yeast cell polarity focusing on G-protein signalling to integrate the modelling results more closely with the authors' previously published experimental observations. In summary, the combination of modelling and experiments describes how yeast cells exhibit a diversity of cell morphologies arising from two-stage G-protein signalling dynamics modulated by positive and negative feedbacks.

Cell polarity: quantitative modeling as a tool in cell biology

Among a number of innovative approaches that have modernized cell biology, modeling has a prominent yet unusual place. One popular view is that we progress linearly, from conceptual to ever more detailed models. We review recent discoveries of cell polarity mechanisms, in which modeling played an important role, to demonstrate that the experiment-theory feedback loop requires diverse models characterized by varying levels of biological detail and mathematical complexity. We argue that a quantitative model is a tool that has to fit an experimental study, and the model's value should be judged not by how complex and detailed it is, but by what could be learned from it.