Role of ATP-hydrolysis in the dynamics of a single actin filament

We study the stochastic dynamics of growth and shrinkage of single actin filaments taking into account insertion, removal, and ATP hydrolysis of subunits either according to the vectorial mechanism or to the random mechanism. In a previous work, we developed a model for a single actin or microtubule filament where hydrolysis occurred according to the vectorial mechanism: the filament could grow only from one end, and was in contact with a reservoir of monomers. Here we extend this approach in several ways, by including the dynamics of both ends and by comparing two possible mechanisms of ATP hydrolysis. Our emphasis is mainly on two possible limiting models for the mechanism of hydrolysis within a single filament, namely the vectorial or the random model. We propose a set of experiments to test the nature of the precise mechanism of hydrolysis within actin filaments.

💡 Research Summary

The paper presents a comprehensive stochastic model of actin filament dynamics that explicitly incorporates ATP hydrolysis, comparing two mechanistic hypotheses—vectorial (sequential) hydrolysis and random hydrolysis—while extending previous work to include both filament ends. In the model, each actin monomer can exist in three nucleotide states (ATP‑actin, ADP‑Pi‑actin, ADP‑actin). Growth and shrinkage at the plus and minus ends are governed by distinct on‑ and off‑rates (k_on^+, k_off^+, k_on^-, k_off^-). Hydrolysis is implemented in two ways: (1) vectorial hydrolysis, where a hydrolysis “wave” progresses from the oldest ATP‑actin toward the tip at a constant rate k_h, creating a stabilizing ATP‑cap that can be lost, leading to catastrophic depolymerization; and (2) random hydrolysis, where each ATP‑actin hydrolyzes independently with probability k_h, eliminating a coherent cap and producing a more uniform distribution of ADP‑actin along the filament.

By allowing monomer exchange at both ends, the model naturally reproduces treadmilling—the simultaneous addition at the plus end and loss at the minus end that maintains a steady average length. The relative magnitudes of the kinetic parameters, especially the ratio k_h/k_on^+, determine the dynamical regime. When k_h/k_on^+ is low and k_on^+ is high, the filament exhibits sustained growth with a persistent ATP‑cap. As k_h/k_on^+ increases, the cap becomes unstable, and the system transitions to a regime dominated by frequent catastrophes and occasional rescue events, the latter often initiated at the minus end.

Numerical simulations reveal distinct signatures for the two hydrolysis mechanisms. Vectorial hydrolysis generates highly asymmetric length distributions with long tails reflecting rare but large depolymerization bursts; the filament length fluctuations are also larger. Random hydrolysis yields near‑Gaussian length distributions and smaller fluctuations because the lack of a coherent cap reduces the probability of abrupt catastrophes. The model predicts that the probability of rescue events is higher under random hydrolysis, as the filament is more uniformly “aged” and can re‑stabilize from any point along its length.

Parameter sweeps produce a kinetic phase diagram that maps regions of steady growth, treadmilling, catastrophe‑dominated shrinkage, and rescue‑dominated regimes. The diagram shows that the minus‑end kinetic parameters (k_on^-, k_off^-) modulate the boundaries: a more “unstable” minus end (higher k_off^- relative to k_on^-) shifts the system toward rapid overall shortening.

To discriminate experimentally between the two hydrolysis scenarios, the authors propose several in‑vitro assays: total internal reflection fluorescence (TIRF) microscopy of single filaments under controlled ATP and Mg²⁺ concentrations, optical trapping to measure force‑velocity relationships at both ends, and quantitative analysis of cap length, catastrophe frequency, and length distribution asymmetry. By fitting observed statistics to the model predictions, one can infer whether hydrolysis proceeds vectorially or randomly within actin filaments.

In summary, the study demonstrates that the mechanism of ATP hydrolysis is a decisive factor shaping actin filament dynamics, influencing cap stability, length fluctuations, and the balance between growth, treadmilling, catastrophe, and rescue. The extended two‑end stochastic framework provides a versatile platform for interpreting experimental data and for guiding future investigations into cytoskeletal regulation, drug targeting, and the physical modeling of polymerizing biopolymers.