Elements of the model. Subunit addition and loss from the fast-growing barbed end (to the right) and slow-growing pointed end (to the left) are modeled, as well as random phosphate hydrolysis and release within each filament. Nucleotide replacement (ATP for ADP or ADP·P_i) is assumed to occur instantaneously once a subunit is in solution. In addition, we model two mechanisms of filament fragmentation (random and stress-induced) as well as end-to-end annealing (see text). Constants for all reactions are listed in Table 1.

Steady state length distributions. Length distributions at steady state (~15–24 hours) are shown for simulations with 3.0 μM total actin both with and without normal annealing and fragmentation (black bars and gray bars, respectively). Distributions were averaged from 50 time points taken at 10 minute intervals from ~15–24 hours.

Nucleotide states of simulated actin filaments. (A) State of barbed end terminal subunit versus imposed free actin concentration, at steady state. Curves are shown for 5 simulations: one with no annealing or fragmentation (solid line), two with normal annealing and fragmentation (dashed lines), and two with 50× increased fragmentation rates (dotted lines). Vertical line (dash-dot) indicates critical concentration (0.14 μM). (B) States of the first 370 barbed end terminal subunits at steady state, for 3.0 μM total actin. The fraction of subunits at each position, averaged across all filaments in the simulation volume, in each nucleotide state is shown: ATP- (solid), ADP·P_i- (dashed), and ADP-actin (dotted).

Length diffusivities calculated from simulations at various random fragmentation rates (no fragmentation or annealing, downwards pointing triangles; normal fragmentation and annealing, diamonds; and normal annealing with increased random fragmentation: 10×, stars; 50×, squares; 100×, circles; 200×, upwards pointing triangles)), analyzed using detectability limits (see text) from 0.5 to 2 micrometers. Data from three runs for each parameter set are shown (open symbols), along with average (solid lines).

Polymerization kinetics. F-actin as a function of time resulting from simulations with 150–300 filaments is shown for total actin concentrations of 0.5 (solid), 1.0 (dashed), and 3.0 μM (dash-dot). Data is averaged from 5 simulations at each concentration. (A) Time series for polymerized fraction for all three total actin concentrations. (B) Average lengths for simulated populations, corresponding to simulations in A.

Simulated polymerization curves for various fragmentation rates. Initial concentration for all simulations is 6 μM. Curves show polymerized actin for simulations in which the random fragmentation rate constant was multiplied by a factor of (from right to left) 1×, 5×, 10×, 50×, 100×, and 200×. Inset: Experimental polymerization curves for pure actin (black), 1:12 TMR-actin to unlabeled actin (8.3% labeled; dark gray), and 1:6 TMR- to unlabeled actin (16.6%; light gray). Horizontal axis is seconds, vertical axis is absorbance. Raw data for inset provided by Dmitri Kudryashov.

Lengths of excursions (repeated loss or gain of subunits) at the barbed ends of filaments. Excursions were measured by tracking the lengths of repeated loss or gain of subunits that were then terminated by subunit gain or loss, respectively. Excursions terminated by annealing or complete depolymerization events were not included in this analysis. Measurements were made during the period of 4000 to 5800 seconds, from simulations of 3.0 μM total actin, beginning when the free actin concentration was close to the critical concentration (for the no fragmentation or annealing case) or had reached the critical concentration (all other cases). Curves are shown for no fragmentation or annealing (solid, filled circles) and 1×, 10×, 50×, 100×, and 200× fragmentation rates with normal annealing (solid/open circles, dashed/closed, dashed/open, dotted/closed, dotted/open, respectively) from simulations in which no concentration was imposed. The maximum variation among these curves is for excursions of length −1 (3.6%) and +1 (4.1%). Also shown are two curves from simulations with normal annealing and fragmentation in which concentrations of 0.10 (solid line, small gray circles) and 0.14 μM (dashed line, asterisks) were imposed starting at 3600 seconds. In the simulations, the most frequent barbed end excursion lengths for imposed concentrations of 0.10 and 0.14 μM were from 1 to 4 subunits, and the most frequent excursion durations were between 0.6 and 0.9 seconds. Excursions at the pointed end were roughly the same magnitude, but slower (longer duration).

Diffusivity versus free actin concentration for 300–600 filament simulations with (A) no annealing or fragmentation, (B) normal annealing and fragmentation, and (C) 50-fold increased fragmentation rate with normal annealing. Curves are plotted for detectability limits of 0.5 μm (solid, filled circles), 1.0 μm (solid, open circles), 2.0 μm (dashed, filled circles).