Abstract
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.