ATP hydrolysis stimulates large length fluctuations in single actin filaments

Abstract

Polymerization dynamics of single actin filaments is investigated theoretically using a stochastic model that takes into account the hydrolysis of ATP-actin subunits, the geometry of actin filament tips, and the lateral interactions between the monomers as well as the processes at both ends of the polymer. Exact analytical expressions are obtained for the mean growth velocity, for the dispersion in the length fluctuations, and the nucleotide composition of the actin filaments. It is found that the ATP hydrolysis has a strong effect on dynamic properties of single actin filaments. At high concentrations of free actin monomers, the mean size of the unhydrolyzed ATP-cap is very large, and the dynamics is governed by association/dissociation of ATP-actin subunits. However, at low concentrations the size of the cap becomes finite, and the dissociation of ADP-actin subunits makes a significant contribution to overall dynamics. Actin filament length fluctuations reach a sharp maximum at the boundary between two dynamic regimes, and this boundary is always larger than the critical concentration for the actin filament's growth at the barbed end, assuming the sequential release of phosphate. Random and sequential mechanisms of hydrolysis are compared, and it is found that they predict qualitatively similar dynamic properties at low and high concentrations of free actin monomers with some deviations near the critical concentration. The possibility of attachment and detachment of oligomers in actin filament's growth is also discussed. Our theoretical approach is successfully applied to analyze the latest experiments on the growth and length fluctuations of individual actin filaments.

FIGURE 1

Schematic picture of polymer configurations and possible transitions in the vectorial model of the single actin filament's growth. The size of the monomer subunit is d, while a is a shift between the parallel protofilaments equal to one-half of the monomer size. Two protofilaments are labeled 1 and 2. The transition rates and labels to some of the configurations are explained in the text.

FIGURE 2

Comparison of the growth velocities for the barbed end of the single actin filament as a function of free monomeric actin concentration for the random and the vectorial ATP hydrolysis mechanisms. A vertical dashed line indicates the transition point c′ (in the vectorial hydrolysis). It separates the dynamic regime I (low concentrations) from regime II (high concentrations). The kinetic rate constants used for calculations of the velocities are taken from Table 1.

FIGURE 3

Dispersion of the length of the single actin filament as a function of free monomer concentration for the barbed end and for the pointed end (the vectorial mechanisms). The kinetic rate constants are taken from Table 1. (Vertical dotted lines indicate the critical concentrations c_crit for the barbed and the pointed ends; thin solid line corresponds to the concentration of the treadmilling, which is also almost the same as the transition point for the barbed end.) The transition point for the pointed end is at 0.85 μM. Total dispersion is a sum of the independent contributions for each end of the filament.

FIGURE 4

The size of ATP cap as a function of free monomer concentration for the barbed end of the single actin filament within the vectorial (a and b) and the random (c and d) mechanisms of ATP hydrolysis. (Thick solid lines describe the vectorial mechanism, while dotted lines correspond to the random mechanism.) The kinetic parameters for constructing curves b and d are taken from Table 1. For the curves a and c, the kinetic rate constants are also taken from Table 1 with the exception of the smaller hydrolysis rate r_h = 0.03 s⁻¹. (Vertical dashed line and thin solid line indicate the transition point c′ and the critical concentration c_crit, respectively, for curve b.)

FIGURE 5

The fractions of the capped configurations q for the barbed end of the single actin filament as a function of free monomer concentration. The results for the vectorial (a and b) and the random (c and d) mechanisms of hydrolysis are presented. (Thick solid lines describe the vectorial mechanism, while dotted lines correspond to the random mechanism.) The kinetic parameters for constructing curves b and d are taken from Table 1. For curves a and c the kinetic rate constants are also taken from Table 1 with the exception of the smaller hydrolysis rate r_h = 0.03 s⁻¹.