The kinetics of cooperative cofilin binding reveals two states of the cofilin-actin filament

Abstract

The interaction of cofilin with actin filaments displays positive cooperativity. The equilibrium binding and associated thermodynamic properties of this interaction are well described by a simple, one-dimensional Ising model with nearest neighbor interactions. Here we evaluate the kinetic contributions to cooperative binding and the ability of this model to account for binding across a wide range of cofilin concentrations. A Monte Carlo-based simulation protocol that allows for nearest-neighbor interactions between adjacent binding sites was used to globally fit time courses of human cofilin binding to human nonmuscle (beta-, gamma-) actin filaments. Several extensions of the one-dimensional Ising model were tested, and a mechanism that includes isomerization of the actin filament was found to best account for time courses of association as well as irreversible dissociation from a saturated filament. This model predicts two equilibrium states of the cofilin-actin, or cofilactin, filament, and the resulting set of binding parameters are in agreement with equilibrium thermodynamic parameters. We conclude that despite its simplicity, this one-dimensional Ising model is a reliable model for analyzing and interpreting the energetics and kinetics of cooperative cofilin-actin filament interactions. The model predicts that severing activity associated with boundaries between bare and decorated segments will not be linear, but display a transient burst at short times on cofilin activation then dissipate due to a kinetic competition between severing activity and cofilin binding. A second peak of severing activity is predicted to arise from irreversible cofilin dissociation on inactivation. These behaviors predict what we believe to be novel mechanisms of cofilin severing and spatial regulation of actin filament turnover in cells. The methods developed for this system are generally applicable to the kinetic analysis of cooperative ligand binding to linear polymers.

Figure 1

One-dimensional Ising models with nearest neighbor interactions evaluated in this study. Note that the models differ in the number of cofilactin conformations—isomerized and not—and origin of nearest-neighbor cooperative interactions.

Figure 2

Time courses of cooperative cofilin binding to actin filaments. The colored lines represent the best fits of the experimental data (black lines) to: (a and b) Model A; (c and d) Model B; and (e and f) Model C. The paired left-right panels show the same data but are presented on different timescales for visualization. The model results are averaged over 20 individual runs to smooth out the intrinsic noise.

Figure 3

Time course of cofilin dissociation from actin filaments. The time course of irreversible cofilin dissociation (right, trace with noise) is shown with a simulated time course (left, smooth trace) of dissociation as predicted from the best-fit parameters obtained from analysis of association time courses. The dashed line through each curve represents the best fit to a single exponential with observed rate constants 0.09 s⁻¹ of and 0.07 s⁻¹ for the experimental and simulated data, respectively.

Figure 4

Cofilin binding to actin monomers assayed from inhibition of nucleotide exchange. The observed rate constants of ɛATP (triangles) and ɛADP (circles) dissociation from actin monomers were determined from the best fit of the time courses of exchange to single exponentials. Uncertainties are within the data points. The solid lines represent the best fit of the data to Eq. 2.

Figure 5

Time evolution of boundaries between bare and decorated regions that are associated with cofilactin severing activity on cofilin activation. The number density of boundaries was calculated as the number of singly-contiguous bound cofilins plus two times the number of isolated bound cofilins. Considering an isolated bound cofilin as a single boundary has minor effects on the curves. The curves represent activation of (line a) 30, (line b) 20, (line c) 15, (line d) 10, (line e) 7.5, or (line f) 5 μM cofilin. Both panels contain the same data but are presented on different timescales for visualization.

Figure 6

Time evolution of boundaries between bare and decorated regions that are associated with cofilactin severing activity on cofilin dissociation and inactivation. (a) The number density of boundaries was calculated assuming a fully decorated filament at t = 0. (b) Overlay of the time courses of boundary formation comparing activation of 20 μM cofilin and dissociation from a decorated filament.

Figure 7

Model of cofilin binding and severing in cells. After cofilin activation and ATP hydrolysis/phosphate release from actin, cofilin rapidly binds to filaments resulting in a transient peak in the formation of boundaries and associated severing probability. As cofilin continues to bind, the number of boundaries decreases resulting in stable filaments, but as bound cofilin dissociates and activity decreases, the number of boundaries rises again resulting in an increased severing probability. We do not implicate cofilin binding to actin monomers and associated filament nucleation activity (5) because the affinity of human nonmuscle cofilin I for human nonmuscle MgATP actin monomers is weak (Fig. 4). For simplicity, we assume cofilin does not affect the nucleotide state of actin filaments, although it has been suggested to accelerate P_i release allosterically from nonoccupied sites (10).