Figure 3.

Velocity of individual actin (□) and actin–Tm filaments (●) as a function of thin filament length and the predicted relationship if the presence of Tm effectively reduces the number of available XBs (dashed curve). The mean velocity of actin and actin–Tm filaments was 5.0 and 1.8 μm/s, respectively, at a myosin concentration of 22.5 μg/ml. At low myosin surface densities, velocity is a function of the number of XBs that can potentially interact with the filament (22). Under these conditions, the determinants of velocity are filament length (i.e., the total number of myosin heads that can interact with the thin filament) and duty cycle (i.e., the fraction of the XB cycle that myosin is strongly bound to actin). The dependence of velocity on filament length is hyperbolic with the asymptote of the relationship achieved, when a sufficient number of XBs interact with the filament to move it at its maximal velocity (17). For illustrative purposes, the solid curves that depict this relationship for actin and actin–Tm are presented and were generated with a defined relationship (17): v_max = av_o[1 − (1 − f_xb)ⁿ], where v_max is the filament velocity, av_o is the filament velocity when at least one XB is attached to actin at all times and undergoing its power stroke, f_xb is the XB duty cycle, and n is the number of XBs available to interact with the filament. For this model (solid curves), we assumed the av_o to be equal to the mean velocities (see above), with f_xb = 0.038 and n = 20 heads per micrometer of filament length based on previous studies (17). If Tm effectively reduces the number of available XB heads without having any effect on the kinetics of the XB cycle (i.e., no change in f_xb or av_o), then one can create a relationship in which the parameters f_xb and av_o are set at 0.038 and 5.0, respectively, and n is adjusted so that the mean velocity of the fit (over the range of thin filament lengths measured) equals the mean velocity for the actin–Tm data. The dashed curve is this relationship and requires Tm to effectively reduce the number of available XB heads per micrometer of filament length by 92%. If so, then there should have been a profound dependence of velocity on filament length, which was not observed.