Cooperativity in axonemal motion: analysis of a four-state, two-site kinetic model.

A kinetic model for axonemal motion based upon a four-state mechanochemical cycle of dynein with two active sites is described. Our model analysis determines the pseudo-steady-state concentrations of enzyme species for specified rate constants, most of which are experimentally determined, with given substrate and product concentrations. The proportion of enzyme species in which both active sites are detached from the microtubule (denoted as "both detached"), numerically calculated from the model, appears to be proportional to experimental observations of flagellar beat frequency. This correlation between beat frequency and the both-detached enzyme species is maintained over a wide range of substrate concentrations and exhibited an apparent positive cooperativity at low substrate concentrations, which we call "obligate cooperativity." The unusual obligate cooperativity exhibited by flagellar beat frequency parallels that seen in the calculated proportion of the both-detached enzyme species and is interpreted as a requirement for a molecule of substrate to bind to each active site in a multimeric dynein in order to produce oscillatory motion. Furthermore, the proportion of the both-detached enzyme species correlates with experimentally observed changes in beat frequency with a nucleotide analog and with product inhibition.