Utilizing correlation functions to develop a multistate model of P. denitrificans F₁-ATPase and enhance single-molecule imaging resolution

Abstract

F₁-ATPase enzyme is a biological motor which hydrolyzes ATP. The enzyme has been observed via single-molecule imaging experiments wherein the enzyme is allowed to rotate freely while being recorded using a gold nanoparticle. During hydrolysis, the enzyme causes Brownian noise when rotating to new chemical states because of a size difference between the 4 nm enzyme and 40 nm probe. The unconvoluted rotary movement has been revealed using techniques including rotational correction, correlation functions, and comparison of average rotational jumps which contribute to developing a multistate model. Within P. denitrificans F₁, the timestep used in experimentation is limited to 100 μs. After correction for tilting, a method for evaluating all three subunits uniformly was implemented in further evaluations. Using corrected data, the torsional spring constant of the rotary shaft was found to be near 25 pN nM for most subunits with a few subunits at much higher values. Implementation of the time correlation function which was proven to be stationary yielded a viscoelastic relaxation time around unity. The relaxation time provides a method for calculating a diffusion coefficient to develop a multistate model and elucidate hidden kinetic states of the functioning enzyme.

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