Abstract
We present a simple analytical solution for a kinetic model of motor molecule function with multiple arms. This model has a rate of motion proportional to the probability that all arms in a complex are detached from the cytoskeleton and, therefore, we refer to it as obligate cooperativity. The model has the form: v = Vmax/(1 + q/S)n, where Vmax is the maximum velocity, the product nq is the effective Michaelis constant at high [ATP], and n is the number of arms. Values of n = 2 and n = 1 give good fits to the heavy meromyosin and myosin S1 sliding velocity data, respectively, consistent with the number of active sites. Despite the complexity of the eukaryotic axoneme, beat frequency data from Chlamydomonas wild-type and oda mutants are also fit by this model.