We present a simple analytical solution for a kinetic model of motor m
olecule function with multiple arms. This model has a rate of motion p
roportional to the probability that all arms in a complex are detached
from the cytoskeleton and, therefore, we refer to it as obligate coop
erativity. The model has the form: v = V-max/(1 + q/S)(n), where V-max
is the maximum velocity, the product nq is the effective Michaelis co
nstant 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 ve
locity 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 mod
el.