Complex cooperativity of ATP hydrolysis in the F(1)-ATPase molecular motor

The nonlinear chemo-mechanic coupled dynamics of the F 1 -ATPase molecular motor

The ATP synthase consists of two opposing rotary motors, F0 and F1, coupled to each other. When the F1 motor is not coupled to the F0 motor, it can work in the direction hydrolyzing ATP, as a nanomotor called F1-ATPase. It has been reported that the stiffness of the protein varies nonlinearly with increasing load. The nonlinearity has an important effect on the rotating rate of the F1-ATPase. Here, considering the nonlinearity of the γ shaft stiffness for the F1-ATPase, a nonlinear chemo-mechanical coupled dynamic model of F1 motor is proposed. Nonlinear vibration frequencies of the γ shaft and their changes along with the system parameters are investigated. The nonlinear stochastic response of the elastic γ shaft to thermal excitation is analyzed. The results show that the stiffness nonlinearity of the γ shaft causes an increase of the vibration frequency for the F1 motor, which increases the motor's rotation rate. When the concentration of ATP is relatively high and the load torque is small, the effects of the stiffness nonlinearity on the rotating rates of the F1 motor are obvious and should be considered. These results are useful for improving calculation of the rotating rate for the F1 motor and provide insight about the stochastic wave mechanics of F1-ATPase.

On chemomechanical coupling of the F(1)-ATPase molecular motor

F(1)-ATPase catalyzes ATP hydrolysis to drive the central gamma-shaft rotating inside a hexameric cylinder composed of alternating alpha and beta subunits. Experiments showed that the rotation of gamma-shaft proceeds in steps of 120 degrees and each 120 degrees -rotation is composed of an 80 degrees substep and a 40 degrees substep. Here, based on the previously proposed models, an improved physical model for chemomechanical coupling of F(1)-ATPase is presented, with which the two-substep rotation is well explained. One substep is driven by the power stroke upon ATP binding, while the other one resulted from the passage of gamma-shaft from previous to next adjacent beta subunits via free diffusion. Using the model, the dynamics and kinetics of F(1)-ATPase, such as the rotating time of each substep, the dwell time at each pause and the rotation rate, are analytically studied. The theoretical results obtained with only three adjustable parameters reproduce the available experimental data well.

The coupled chemomechanics of the F(1)-ATPase molecular motor

The enzyme F(1)-ATPase is a rotary nanomotor in which the central gamma subunit rotates inside the cavity made of alpha(3)beta(3) subunits. The experiments showed that the rotation proceeds in steps of 120 degrees and each 120 degrees step consists of 80 degrees and 40 degrees substeps. Here the Author proposes a stochastic wave mechanics of the F(1)-ATPase motor and combines it with the structure-based kinetics of the F(1)-ATPase to form a chemomechanic coupled model. The model can reproduce quantitatively and explain the experimental observations about the F(1) motor. Using the model, several rate-limited situations about gamma subunit rotation are proposed, the effects of the friction and the load on the substeps are investigated and the chemomechanic coupled time during ATP hydrolysis cycle is determined.

The metabolic pH response in Lactococcus lactis: an integrative experimental and modelling approach

Lactococcus lactis is characterised by its ability to convert sugar almost exclusively into lactic acid. This organic acid lowers extracellular pH, thus inhibiting growth of competing bacteria. Although L. lactis is able to survive at low pH, glycolysis is strongly affected at pH values below 5, showing reduced rate of glucose consumption. Therefore, in order to deepen our knowledge on central metabolism of L. lactis in natural or industrial environments, an existing full scale kinetic model of glucose metabolism was extended to simulate the impact of lowering extracellular pH in non-growing cells of L. lactis MG1363. Validation of the model was performed using (13)C NMR, (31)P NMR, and nicotinamide adenine dinucleotide hydride auto-fluorescence data of living cells metabolizing glucose at different pH values. The changes in the rate of glycolysis as well as in the dynamics of intracellular metabolites (NADH, nucleotide triphosphates and fructose-1,6-bisphosphate) observed during glucose pulse experiments were reproduced by model simulations. The model allowed investigation of key enzymes at sub-optimum extracellular pH, simulating their response to changing conditions in the complex network, as opposed to in vitro enzyme studies. The model predicts that a major cause of the decrease in the glycolytic rate, upon lowering the extracellular pH, is the lower pool of phosphoenolpyruvate available to fuel glucose uptake via the phosphoenolpyruvate-dependent transport system.

Dynamic and coordinating domain motions in the active subunits of the F1-ATPase molecular motor

F1-ATPase is a rotary molecular motor crucial for various cellular functions. In F1-ATPase, the rotation of the gammadeltaepsilon subunits against the hexameric alpha(3)beta(3) subunits is highly coordinative, driven by ATP hydrolysis and structural changes at three beta subunits. However, the dynamical and coordinating structural transitions in the beta subunits are not fully understood at the molecular level. Here we examine structural transitions and domain motions in the active subunits of F1-ATPase via dynamical domain analysis of the alpha(3)beta(3)gammadeltaepsilon complex. The domain movement and hinge axes and bending residues have been identified and determined for various conformational changes of the beta-subunits. P-loop and the ATP-binding pocket are for the first time found to play essential mechanical functions additional to the catalytic roles. The cooperative conformational changes pertaining to the rotary mechanism of F1-ATPase appears to be more complex than Boyer's 'bi-site' activity. These findings provide unique molecular insights into dynamic and cooperative domain motions in F1-ATPase.

Cooperativity in the motor activities of the ATP-fueled molecular motors

Kinesin, myosin and F1-ATPase are multi-domain molecular motors with multiple catalytic subunits. The motor mechanochemics are achieved via the conversion of ATP hydrolysis energy into forces and motions. We find that the catalysis of these molecular motors do not follow the simple Michaelis-Menten mechanism. The motor activities, such as the hydrolysis or processive rates, of kinesin, myosin and F1-ATPase have a complex ATP-dependent cooperativity. To understand this complexity in kinetics and mechanochemics, we develop a conformation correlation theory of cooperativity for the ATP-fueled motor proteins. The quantitative analysis and simulations indicate that cooperativity is induced by the conformational coupling of binding states of different subunits and prevails in the motor activities.