There is more than one way to model an elephant. Experiment-driven modeling of the actin cytoskeleton

Abstract

Mathematical modeling has established its value for investigating the interplay of biochemical and mechanical mechanisms underlying actin-based motility. Because of the complex nature of actin dynamics and its regulation, many of these models are phenomenological or conceptual, providing a general understanding of the physics at play. But the wealth of carefully measured kinetic data on the interactions of many of the players in actin biochemistry cries out for the creation of more detailed and accurate models that could permit investigators to dissect interdependent roles of individual molecular components. Moreover, no human mind can assimilate all of the mechanisms underlying complex protein networks; so an additional benefit of a detailed kinetic model is that the numerous binding proteins, signaling mechanisms, and biochemical reactions can be computationally organized in a fully explicit, accessible, visualizable, and reusable structure. In this review, we will focus on how comprehensive and adaptable modeling allows investigators to explain experimental observations and develop testable hypotheses on the intracellular dynamics of the actin cytoskeleton.

Figure 1

Accurate modeling of simple actin treadmilling requires complex mathematical descriptions. The cartoon in the center summarizes the overall process. During actin filament treadmilling, ATP-bound actin monomers (red) bind to the barbed end of the filament; as the filament ages, the ATP on each subunit is hydrolyzed, forming ADP-Pi-bound actin (orange); eventually, the Pi is released, forming ADP-bound actin subunits, which then depolymerize from the pointed end. ADP-bound actin monomers then undergo nucleotide exchange to return to their ATP-bound state. As useful as it may be to summarize the biology, this cartoon hides the details that would be required to model this system. VCell reaction network diagrams for each process (barbed-end turnover, pointed-end turnover, ATP hydrolysis, Pi Release, and profilin-mediated nucleotide exchange) are shown to demonstrate the mathematical complexity required for proper description of actin dynamics. In the Virtual Cell reaction diagrams, green balls represent molecular species (i.e., variables) and yellow squares represent reactions, each with a corresponding rate expression. The figure displays only one example of an infinite number of filament lengths and subunit nucleotide-state arrangements. FA, F-actin; GA, G-actin; BE, barbed end; PE, pointed end; Prof, profilin; Pi, inorganic phosphate.

Figure 2

Comprehensive VCell modeling of the actin cytoskeleton. Because of the open nature of models in the VCell, original models can be simplified and/or adapted at the user’s discretion to investigate previously unstudied aspects of actin regulation without building a new model. These models can then be used in a variety of geometries, i.e., lamellipodia or dendritic spines, or with a variety of experimentally simulatable systems, i.e., CALI or FRAP. (A) In the original Actin Dendritic Nucleation model (80), the actin cytoskeleton is regulated by the Arp2/3 complex, capping protein, cofilin, profilin, and thymosin-β4. (B) Building on the base model in (A), Kapustina and colleagues (89) added VASP regulation of capping protein and modeled the effects of CALI and FRAP on eGFP-capping protein-regulated actin dynamics. (C) Using an optimized version of the model, Ditlev and colleagues (90) created an upstream signaling module that activated Arp2/3 complex. With this reaction scheme, a previously unappreciated mechanism of the Nck/N-WASp/Arp2/3 complex pathway was elucidated.