Evaluation of P. denitrificans F1-ATPase Rotary Motion using Automated Methods to Detect Hidden States

Abstract

F-ATPase is a rotary motor enzyme with the biological function of synthesizing ATP, the "fuel molecule" of cells. A subsystem of F-ATPase, F1-ATPase, functions in reverse: it hydrolyses ATP into ADP and inorganic phosphate. During this process, the rotation of F1-ATPase's shaft-like rotor is driven by chemical free energy. Samples of paracoccus denitrificans F1-ATPase are studied in single-molecule imaging experiments while the enzyme undergoes ATP synthesis. This single-molecule experiment is performed through the use of a 40 nanometer gold nano-probe used to record rotation angles at a microsecond temporal resolution. The biomotor enzyme experiences rotary motion during the hydrolysis of ATP, and periodically transitions between various states (angular dwells) in a step-like manner. The substeps observed in other species of F1-ATPase appear to be absent in the paracoccus denitrificans species, so a goal of our work is to use a previous multi-state theory for the angle-dependent velocity to detect any "hidden" substeps with too short a lifespan to be seen in the experimental trajectories. Additionally, the Brownian motion of the probe prohibits analysis of the possible state configuration of F1-ATPase through direct observation. Due to this, we have developed an automated method utilizing the enzyme's rotary progression as well as likelihood theorems to separate dwell and transitional states within single molecule trajectories. The method thereby allows an analysis of the state model of experimental results using calculations based on the existing theory.

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