Coarse-grained model of monomer and filament (a) actin monomer built up from three particles labeled by , , and and connected into an equilateral triangle. (b) These triangles are tied together into a filament by Hookean springs, which are between adjacent , adjacent , and adjacent particles as well as between all next-nearest neighbors particles within the filament (for clarity, only two next-nearest neighbor bonds are shown).
Schematic illustration of the computational mechanism of ADP-filament growth by attachment and detachment of monomers to its ends. Single actin monomers with a bound ADP molecule are labeled with the letter “.” The conical regions at the filament’s ends are capture zones with independent radius and at the filament’s barbed and pointed ends, whose sizes control the rate of free monomer attachment events. Detachment of the terminal monomers at the filament’s barbed and pointed ends is controlled by two more independent parameters, and . Note that the rates of monomer attachment to the filament ends, and , are not parameters of the model but are determined by the capture zone size and the free monomer concentration.
Time evolution of actin protomer number (black solid line, left axis); positions (right axis) of barbed end (red solid line), pointed end (blue solid line), and the initial center (cyan solid line) in the filament vs simulation time step. The capture sizes are and and the detachment rates are and at the barbed and pointed ends, respectively.
Dependence of kinetic rate constants on monomer concentration for different values of the capture zone size , which is varied from (open squares) to (closed stars). In the inset, the mean kinetic rate constants at each capture zone are plotted logarithmically as a function of height ; the straight line has slope 3. In these simulations, we chose .
(a) Normalized histograms for time intervals between successive monomer attachments at barbed and pointed ends. The width of the bins is 10 000 time steps, the probability of attachment is approximately exponentially distributed, . (b) The inverse mean waiting time , which is equal to the attachment rate as a function of monomer concentration at different capture zone sizes.
Dependence of the ADP filament growth rate (left axis) and the inverse mean waiting time at the barbed end (right axis) on actin monomer concentrations . The intersection point of the square symbol curves with the horizontal dotted line defines the critical concentration . The parameters are the same as in Fig. 3.
The growth rate as a function of . (a) The experimental data are taken from Fig. 5 of Ref. 7 and the simulation data in Fig. 6 are expressed in physical units with the rescaling factors and . (b) The experimental data are taken from Fig. 3 of Ref. 5 and the simulation data in Fig. 6 are expressed in physical units with the rescaling factors and . Note that the critical (or equilibrium) concentration at which the growth rate vanishes is rather different for the two sets of experimental data reflecting the different ionic conditions.
Length diffusion constant (solid squares) as defined in Eq. (39) for ADP-actin polymerization. The solid (red) line represents the analytical expression (41). The parameters are the same as in Fig. 3.
The growth rate (solid squares) as a function of . The solid (red) line is a linear fit. The detachment rate and the capture zone size .
The growth rate (solid squares) as a function of , . The solid (red) line is a linear fit. (a) The capture zone size . (b) The capture zone size .
Attachment rate constants , detachment rates , and equilibrium (or critical) concentration for Mg-ADP-actin (Ref. 12) at barbed and pointed ends of actin filaments.
Rescaled attachment rate constants , detachment rates , and equilibrium (or critical) concentration as used in the simulations.
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