Rotational Mechanism Model of the Bacterial V ₁ Motor Based on Structural and Computational Analyses

The ATP synthases are multiprotein complexes found in the energy-transducing membranes of bacteria, chloroplasts and mitochondria. They employ a transmembrane protonmotive force, Δp, as a source of energy to drive a mechanical rotary mechanism that leads to the chemical synthesis of ATP from ADP and Pi. Their overall architecture, organization and mechanistic principles are mostly well established, but other features are less well understood. For example, ATP synthases from bacteria, mitochondria and chloroplasts differ in the mechanisms of regulation of their activity, and the molecular bases of these different mechanisms and their physiological roles are only just beginning to emerge. Another crucial feature lacking a molecular description is how rotation driven by Δp is generated, and how rotation transmits energy into the catalytic sites of the enzyme to produce the stepping action during rotation. One surprising and incompletely explained deduction based on the symmetries of c-rings in the rotor of the enzyme is that the amount of energy required by the ATP synthase to make an ATP molecule does not have a universal value. ATP synthases from multicellular organisms require the least energy, whereas the energy required to make an ATP molecule in unicellular organisms and chloroplasts is higher, and a range of values has been calculated. Finally, evidence is growing for other roles of ATP synthases in the inner membranes of mitochondria. Here the enzymes form supermolecular complexes, possibly with specific lipids, and these complexes probably contribute to, or even determine, the formation of the cristae.

Allostery, the coupling between ligand binding and protein conformational change, is the heart of biological network and it has often been explained by two representative models, the induced-fit and the population-shift models. Here, we clarified for what systems one model fits better than the other by performing molecular simulations of coupled binding and conformational change. Based on the dynamic energy landscape view, we developed an implicit ligand-binding model combined with the double-basin Hamiltonian that describes conformational change. From model simulations performed for a broad range of parameters, we uncovered that each of the two models has its own range of applicability, stronger and longer-ranged interaction between ligand and protein favors the induced-fit model, and weaker and shorter-ranged interaction leads to the population-shift model. We further postulate that the protein binding to small ligand tends to proceed via the population-shift model, whereas the protein docking to macromolecules such as DNA tends to fit the induced-fit model.

An approach to find transition pathways in complex systems is presented. The method, which is related to the string method in collective variables of Maragliano et al. (J. Chem. Phys. 2006, 125, 024106), is conceptually simple and straightforward to implement. It consists of refining a putative transition path in the multidimensional space supported by a set of collective variables using the average dynamic drift of those variables. This drift is estimated on-the-fly via swarms of short unbiased trajectories started at different points along the path. Successive iterations of this algorithm, which can be naturally distributed over many computer nodes with negligible interprocessor communication, refine an initial trial path toward the most probable transition path (MPTP) between two stable basins. The method is first tested by determining the pathway for the C7eq to C7ax transition in an all-atom model of the alanine dipeptide in vacuum, which has been studied previously with the string method in collective variables. A transition path is found with a committor distribution peaked at 1/2 near the free energy maximum, in accord with previous results. Last, the method is applied to the allosteric conformational change in the nitrogen regulatory protein C (NtrC), represented here with a two-state elastic network model. Even though more than 550 collective variables are used to describe the conformational change, the path converges rapidly. Again, the committor distribution is found to be peaked around 1/2 near the free energy maximum between the two stable states, confirming that a genuine transition state has been localized in this complex multidimensional system.