From actin waves to mechanism and back: How theory aids biological understanding

Abstract

Actin dynamics in cell motility, division, and phagocytosis is regulated by complex factors with multiple feedback loops, often leading to emergent dynamic patterns in the form of propagating waves of actin polymerization activity that are poorly understood. Many in the actin wave community have attempted to discern the underlying mechanisms using experiments and/or mathematical models and theory. Here, we survey methods and hypotheses for actin waves based on signaling networks, mechano-chemical effects, and transport characteristics, with examples drawn from Dictyostelium discoideum, human neutrophils, Caenorhabditis elegans, and Xenopus laevis oocytes. While experimentalists focus on the details of molecular components, theorists pose a central question of universality: Are there generic, model-independent, underlying principles, or just boundless cell-specific details? We argue that mathematical methods are equally important for understanding the emergence, evolution, and persistence of actin waves and conclude with a few challenges for future studies.

Oscillatory dynamics of Rac1 activity inDictyostelium discoideumamoebae

“…In motile D. discoideum cells, actin and associated signaling proteins spontaneously form traveling waves at the ventral cell border [32]. Analyzing these patterns, as well as patterns induced by external stimuli, can facilitate the understanding of complex signaling networks and form the basis for the development of advanced theoretical models [33,34]. In this study, we show that active Rac1 exhibits a variety of dynamic behaviors in D. discoideum cell plasma membrane.…”

Cell morphogenesis via self-propelled treadmilling actin waves

“…Most of actin wave propagations in cells have been explained by the reactiondiffusion mechanism that involves positive and negative feedback interactions between excitable and inhibitory components [20][21][22][23] . On the other hand, actin waves observed here randomly change the direction of movement in a manner similar to self-propelled particles 25,26,28 .…”

“…Dynamic actin filaments undergo wave-like propagations in various cell types [19][20][21][22] . Many of these propagations have been explained by the reaction-diffusion mechanism [20][21][22][23] .…”

“…Dynamic actin filaments undergo wave-like propagations in various cell types [19][20][21][22] . Many of these propagations have been explained by the reaction-diffusion mechanism [20][21][22][23] . On the other hand, we previously reported that actin treadmilling propels the translocation of actin waves and actin-binding proteins towards the axonal tips of neurons in culture and tissue 24 .…”

Solution of steady state in the model polymer system with rupture and rebinding

“…Stability of the steady states has been actively pursued, for instance, in biology [13][14][15]56], fault dynamics [11,54], friction [31,57,60,61], specifically the propagating solutions between the states [56,58]. There are numerous instances of spatial and temporal patterns in biology [62,63], including traveling waves [64], where mathematical models provide insights [65]. The bulk of the cited work on steady states, for instance, in rupture termination, deals with friction failure with theories in fracture mechanics [55,59].…”