Modeling Robustness Tradeoffs in Yeast Cell Polarization Induced by Spatial Gradients

Abstract

Cells localize (polarize) internal components to specific locations in response to external signals such as spatial gradients. For example, yeast cells form a mating projection toward the source of mating pheromone. There are specific challenges associated with cell polarization including amplification of shallow external gradients of ligand to produce steep internal gradients of protein components (e.g. localized distribution), response over a broad range of ligand concentrations, and tracking of moving signal sources. In this work, we investigated the tradeoffs among these performance objectives using a generic model that captures the basic spatial dynamics of polarization in yeast cells, which are small. We varied the positive feedback, cooperativity, and diffusion coefficients in the model to explore the nature of this tradeoff. Increasing the positive feedback gain resulted in better amplification, but also produced multiple steady-states and hysteresis that prevented the tracking of directional changes of the gradient. Feedforward/feedback coincidence detection in the positive feedback loop and multi-stage amplification both improved tracking with only a modest loss of amplification. Surprisingly, we found that introducing lateral surface diffusion increased the robustness of polarization and collapsed the multiple steady-states to a single steady-state at the cost of a reduction in polarization. Finally, in a more mechanistic model of yeast cell polarization, a surface diffusion coefficient between 0.01 and 0.001 µm2/s produced the best polarization performance, and this range is close to the measured value. The model also showed good gradient-sensitivity and dynamic range. This research is significant because it provides an in-depth analysis of the performance tradeoffs that confront biological systems that sense and respond to chemical spatial gradients, proposes strategies for balancing this tradeoff, highlights the critical role of lateral diffusion of proteins in the membrane on the robustness of polarization, and furnishes a framework for future spatial models of yeast cell polarization.

Spatial Stochastic Dynamics Enable Robust Cell Polarization

“…As has been noted in [11], [45], [46] and is clear from the phase planes in Fig. 6, there is a tradeoff between tight polarization and tracking.…”

“…Previously, it has been hypothesized that there is a tradeoff between the amplified polarization and the ability to follow changes in signal direction [11], [45], [46]. We explored this hypothesis in the context of the polarisome system and investigated the effects of stochastic dynamics on the tradeoff.…”

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

“…From a biology perspective, it is known that the cell polarity behavior is quite robust [3], in the sense that the polarization can be established even under very shallow gradient. In the literature, the focus has been on understanding how a shallow external gradient can be amplified to create a steep internal gradient of cellular components.…”

“…Previously, we constructed both generic and mechanistic models of yeast cell polarization in response to mating pheromone spatial gradients [3], in which we used only numerical simulations of a system of reaction-diffusion equations in continuum version to demonstrate the tradeoff between the amplification necessary to tightly localize proteins at the front of the cell and the tracking necessary to follow a change in the gradient direction. In this paper, we analyze several models with similar structures but in different and simple spatial description: two-compartment,three-compartment, and continuum space.…”

“…In this paper, we analyze several models with similar structures but in different and simple spatial description: two-compartment,three-compartment, and continuum space. Using this approach, we are able to investigate both analytically and numerically on several important characteristics and properties of the system that have not been carefully explored in [3]. One of the key features in the model is the existence of multiple steady state solutions for the system in the absence of membrane diffusion, showing the important role of membrane diffusion in regulating polarity.…”