A model of stepping kinetics for rotary enzymes. Application to the F1-ATPase.

Our simple kinetic model, based on the classic "binding change mechanism", describes the stepping kinetics for the rotary enzyme motors. The model shows that the cooperative interactions between active sites in the motor enzyme F1-ATPase induce the stepping product release. This phenomenon results from non-harmonic oscillations in the enzyme forms. The found rate constants, corresponding to the stepping phenomenon, are close to the rate constants known for the F1-ATPase. The duration of dwells during the product release is shown to depend on the ATP concentration in accordance with the known experimental data.

Kinetic model for dynein oscillatory activity.

A kinetic model for dynein, a molecular motor, is considered. This model explains the oscillatory behaviour, observed by Chikako Shingyoji et al. [Ch. Shingyoji, H. Higuchi, M. Yoshimura, E. Katayama, T. Yanagida, Dynein arms are oscillatory force generators, Nature 393 (1998) 711-714.] and by Susumu Aoyama and Ritsu Kamiya [S. Aoyama, R. Kamiya, Cyclical interactions between two outer doublet microtubules in split flagellar axonemes, Biophys. J. 89 (2005) 3261-3268.] in surprisingly simple axonemal fragments. The model shows that sustained oscillations can be generated due to the obligate cooperative interaction of the two dynein heads in the axonemal fragments. No other feedback control interactions are involved in the model to explain oscillations, similar to those observed experimentally, for realistic dynein rate constants. The modified model shows how the ATP hydrolytic exhaustion influences the amplitude and frequency of dynein oscillatory activity.

Oscillatory activity of P-type membrane adenosine triphosphatases: a kinetic model.

A kinetic model for membrane P-type adenosine triphosphatases is considered, the main application being to the erythrocyte Ca2+-ATPase. It is shown that a simple modification of the known catalytic mechanism of the ATPase by addition of a self-inhibition step and the steady calcium influx leads to damped oscillations in the system discussed. In this way, the model can explain the kinetic experimental results obtained for the purified enzyme in solution as well as for the enzyme incorporated into liposome membranes. The estimated kinetic parameters are close to the experimental ones. Alternative changes in time, demonstrated by the kinetic model for the conformational enzyme states, E(1 )and E(2), confirm the model of two alternatively functioning gates in the ion pumping Ca2+-ATPase.

Influence of Ca2+ oscillatory influx on membrane Ca2+-ATPase activity: a kinetic model.

A kinetic model for the membrane Ca2+-ATPase is considered. The catalytic cycle in the model is extended by enzyme auto-inhibition and by oscillatory calcium influx. It is shown that the conductive enzyme activity can be registered as damped or sustained Ca2+ pulses similar to observed experimentally. It is shown that frequency variations in Ca2+ oscillatory influx induce changes of pulsating enzyme activity. Encoding is observed for the signal frequency into a number of fixed levels of sustained pulses in the enzyme activity. At certain calcium signal frequencies, the calculated Ca2+-ATPase conductivity demonstrates chaotic multi-level pulses, similar to those observed experimentally.

Regulation of pyruvate dehydrogenase complex activity in Ehrlich ascites carcinoma cells by Ca2+ and pyruvate.

The dependence of pyruvate dehydrogenase complex (PDC) activity on [Ca2+] was determined in Ehrlich ascites carcinoma cells at different pyruvate concentrations. The resulting family of curves had the following characteristics: a) bell-shaped appearance of all curves with maximum activity at 600 nM Ca2+; b) unchanged position of maxima with changes in pyruvate concentration; c) nonmonotonous changes in PDC activity with increasing pyruvate concentration at fixed [Ca2+]. Feasible mechanisms involving Ca2+-dependent phosphatase and kinase which are consistent with the experimental findings are discussed. To determine the steps in the chain of PDC reactions which determine the observed phenomena, a mathematical model is suggested which is based on the known data on the structural--functional relationships between the complex components--pyruvate dehydrogenase (E1), dihydrolipoyl acetyl transferase (E2), dihydrolipoyl dehydrogenase (E3), protein X, kinase, and phosphatase. To adequately describe the non-trivial dependence of PDC activity on [Ca2+] at different pyruvate concentrations, it was also necessary to consider the interdependence of some steps in the general chain of PDC reactions. Phenomenon (a) is shown to be due only to the involvement of protein X in the PDC reactions, phenomenon (b) to be due to changes in the activity of kinase, and phenomenon (c) to be due to dependence of acetylation and transacetylation rates on pyruvate concentration.