A model for intracellular actin waves explored by nonlinear local perturbation analysis

Abstract

Waves and dynamic patterns in chemical and physical systems have long interested experimentalists and theoreticians alike. Here we investigate a recent example within the context of cell biology, where waves of actin (a major component of the cytoskeleton) and its regulators (nucleation promoting factors, NPFs) are observed experimentally. We describe and analyze a minimal reaction diffusion model depicting the feedback between signalling proteins and filamentous actin (F-actin). Using numerical simulation, we show that this model displays a rich variety of patterning regimes. A relatively recent nonlinear stability method, the Local Perturbation Analysis (LPA), is used to map the parameter space of this model and explain the genesis of patterns in various linear and nonlinear patterning regimes. We compare our model for actin waves to others in the literature, and focus on transitions between static polarization, transient waves, periodic wave trains, and reflecting waves. We show, using LPA, that the spatially distributed model gives rise to dynamics that are absent in the kinetics alone. Finally, we show that the width and speed of the waves depend counter-intuitively on parameters such as rates of NPF activation, negative feedback, and the F-actin time scale.

Fronts and waves of actin polymerization in a bistability-based mechanism of circular dorsal ruffles

“…Thus, the insights provided here are important steps towards understanding the differences between actin wave dynamics at the dorsal and ventral cell surfaces. We note that the bistability in our system stems from reaction schemes of proteins that are in or close to the level of direct interaction with actin, which is in contrast to previous works attributing bistability in the actin system to the states of upstream molecular switches, such as Rho-GTPases2551, or feedbacks in the actomyosin system52. While the model focuses on the biochemical components, it currently ignores the actual growth of the vertical, cup-shaped protrusions413294053 that may introduce additional details, such as feedback between membrane shape and actin activity162930.…”

Computational modeling of single‐cell mechanics and cytoskeletal mechanobiology

“…There are significant feedbacks between these regulatory layers that influence cell behavior. Dynamic feedbacks from actin back onto GTPase regulation lead to the generation of dynamic waves of actin polymerization that generate force upon colliding with the cell periphery (see, e.g., Figure (c)). Imaging studies have found that a number of actin binding proteins associate with these waves .…”

“…Furthermore, they exhibit excitable characteristics such as mutual annihilation (two waves converging suppress each other), with interactions between small GTPases and actin being reported to give rise to this excitability (Figure (d) for example depicts a relationship between waves of actin activity and FBP17 activity that are out of phase with FBP17 leading the actin wave). Mata and Bernitt have further suggested that, in some cases, the unique nature of GTPases as a conserved excitable activator produces a global coupling between disparate regions of a wave. This type of ‘conserved excitable system’ has distinct wave propagation characteristics, such as size dependent propagation velocity, as observed in …”

Actin and PIP3 waves in giant cells reveal the inherent length scale of an excited state

“…In the model analyzed by Mata et al (Mata et al, 2013), the GTPase enhances its own activation by positive feedback, and is inactivated by negative feedback from F-actin. It is essential for this model that the concentration of a GTPase, i.e.…”