F1-ATPase Rotary Mechanism: Interpreting Results of Diverse Experimental Modes With an Elastic Coupling Theory

Abstract

In this chapter, we review single-molecule observations of rotary motors, focusing on the general theme that their mechanical motion proceeds in substeps with each substep described by an angle-dependent rate constant. In the molecular machine F1-ATPase, the stepping rotation is described for individual steps by forward and back reaction rate constants, some of which depend strongly on the rotation angle. The rotation of a central shaft is typically monitored by an optical probe. We review our recent work on the theory for the angle-dependent rate constants built to treat a variety of single-molecule and ensemble experiments on the F1-ATPase, and relating the free energy of activation of a step to the standard free energy of reaction for that step. This theory, an elastic molecular transfer theory, provides a framework for a multistate model and includes the probe used in single-molecule imaging and magnetic manipulation experiments. Several examples of its application are the following: (a) treatment of the angle-dependent rate constants in stalling experiments, (b) use of the model to enhance the time resolution of the single-molecule imaging apparatus and to detect short-lived states with a microsecond lifetime, states hidden by the fluctuations of the imaging probe, (c) treatment of out-of-equilibrium “controlled rotation” experiments, (d) use of the model to predict, without adjustable parameters, the angle-dependent rate constants of nucleotide binding and release, using data from other experiments, and (e) insights obtained from correlation of kinetic and cryo-EM structural data. It is also noted that in the case where the release of ADP would be a bottleneck process, the binding of ATP to another site acts to accelerate the release by 5–6 orders of magnitude. The relation of the present set of studies to previous and current theoretical work in the field is described. An overall goal is to gain mechanistic insight into the biological function in relation to structure.

Beyond binding change: the molecular mechanism of ATP hydrolysis by F1-ATPase and its biochemical consequences

“…These models are incorrect, given that the operative mode of catalysis during steady-state ATP hydrolysis by F 1 -ATPase is trisite. Similarly, physical models ( Mukherjee and Warshel, 2011 ; Nam and Karplus, 2019 ; Volkán-Kacsó and Marcus, 2022 ) proposed for the working of the F 1 motor are not true trisite models and hence are incorrect. Designating an ATPase mechanism as trisite simply because it alternates between having two and three catalytic sites filled with nucleotide at any time is insufficient and constitutes an imperfect criterion.…”

“…Boyer’s binding change mechanism ( Boyer et al, 1973 ; Boyer, 1993 ) and Nath's torsional mechanism of ATP synthesis/hydrolysis ( Nath, 2002 ; Nath, 2008 ; Mehta et al, 2020 ) are two important and detailed theories that have been proposed to explain the functioning of the enzyme during steady-state ATP synthesis/hydrolysis. Other physical models of F 1 -ATPase have been developed by various theory groups ( Wang and Oster, 1998 ; Bai et al, 2020 ; Gerritsma and Gaspard, 2010 ; Lenz et al, 2003 ; Mukherjee and Warshel, 2011 ; Volkán-Kacsó and Marcus, 2017 ; Nam and Karplus, 2019 ; Volkán-Kacsó and Marcus, 2022 ). These latter works, though important in their own right, do not address the biochemical issues of “unisite” catalysis, cold chase, and rate enhancement in multisite catalysis when the substrate binds to additional catalytic sites.…”