A generalized theoretical framework to investigate multicomponent actin dynamics

The length of actin filaments is regulated by the combined action of hundreds of actin-binding proteins. While the roles of individual proteins are well understood, how they combine to regulate actin dynamics in vivo remains unclear. Recent advances in microscopy have enabled precise, high-throughput measurements of filament lengths over time. However, the absence of a unified theoretical framework has hindered a mechanistic understanding of the multicomponent regulation of actin dynamics. To address this, we propose a general kinetic model that incorporates the combined effects of an arbitrary number of regulatory proteins on actin dynamics. We derive exact closed-form expressions for the moments of (1) the distribution of filament lengths over time and (2) the long-time distribution of changes in filament lengths within a fixed time window. We show that these moments allow us to distinguish between different regulatory mechanisms of multicomponent regulation of actin dynamics. Our theoretical framework provides a powerful tool for interpreting existing data and guiding future experiments.Author summary: Actin filaments are essential components of cells, playing key roles in processes like cell movement, division, wound healing, and shape maintenance. The length of actin filaments inside cells is tightly controlled by the collective action of many actin-binding proteins. While the effects of individual proteins have been studied in great detail, how multiple proteins work together regulate filament dynamics in living cells remains poorly understood. Recent improvements in microscopy allow precise, high-throughput measurements of filament lengths over time, offering new avenues to explore this question. In this work, we present a general mathematical framework that captures the combined effects of multiple regulatory proteins on actin filament dynamics. We derive exact expressions for various statistical properties of filament lengths such as the different moments, including how these properties evolve over time and how filament lengths change within a fixed time window in the long time limit. We show that these mathematical results can help identify and distinguish between different mechanisms of multicomponent regulation. This framework provides a valuable tool for interpreting experimental data and designing future studies on actin dynamics in complex cellular environments.