Microscopic origin of diffusive dynamics in the context of transition path time distributions for protein folding and unfolding

Dutta, Rajesh; Pollak, Eli

doi:10.1039/d2cp03158b

Phys. Chem. Chem. Phys.

2022

DOI: 10.1039/d2cp03158b

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Microscopic origin of diffusive dynamics in the context of transition path time distributions for protein folding and unfolding

Rajesh Dutta

Eli Pollak

Abstract: Experimentally measured transition path time distributions are usually analyzed theoretically in terms of a diffusion equation over a free energy barrier. It is though well understood that the free energy...

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2024

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Cited by 4 publications

References 69 publications

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Transition Path Dynamics of Non-Markovian Systems across a Rough Potential Barrier

Jangid,

Chaudhury

2024

J. Phys. Chem. A

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Transition paths refer to rare events in physics, chemistry, and biology where the molecules cross barriers separating stable molecular conformations. The conventional analysis of the transition path times employs a diffusive and memoryless transition over a smooth potential barrier. However, it is widely acknowledged that the free energy profile between two minima in biomolecular processes is inherently not smooth. In this article, we discuss a theoretical model with a parabolic rough potential barrier and obtain analytical results of the transition path distribution and mean transition path times by incorporating absorbing boundary conditions across the boundaries under the driving of Gaussian white noise. Further, the influence of anomalous dynamics in rough potential driven by a power-law memory kernel is analyzed by deriving a time-dependent scaled diffusion coefficient that coarse-grains the effects of roughness, and the system's dynamics is reduced to a scaled diffusion on a smooth potential. Our theoretical results are tested and validated against numerical simulations. The findings of our study show the influence of the boundary conditions, barrier height, barrier roughness, and memory effect on the transition path time distributions in a rough potential, and the validity of the scaling diffusion coefficient has been discussed.

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Transition Path Dynamics of Non-Markovian Systems across a Rough Potential Barrier

Jangid,

Chaudhury

2024

J. Phys. Chem. A

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Barrier-crossing transition-path times for non-Markovian systems

Lavacchi,

Netz

2024

The Journal of Chemical Physics

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By simulation and asymptotic theory, we investigate the transition-path time of a one-dimensional finite-mass reaction coordinate crossing a double-well potential in the presence of non-Markovian friction. First, we consider single-exponential memory kernels and demonstrate that memory accelerates transition paths compared to the Markovian case, especially in the low-mass/high-friction limit. Then, we generalize to multi-exponential kernels and construct an asymptotic formula for the transition-path time that compares well with simulation data.

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The significance of fuzzy boundaries of the barrier regions in single-molecule measurements of failed barrier crossing attempts

Berezhkovskii,

Makarov

2024

The Journal of Chemical Physics

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A recent ground-breaking experimental study [Lyons et al., Phys. Rev. X 14(1), 011017 (2024)] reports on measuring the temporal duration and the spatial extent of failed attempts to cross an activation barrier (i.e., “loops”) for a folding transition in a single molecule and for a Brownian particle trapped within a bistable potential. Within the model of diffusive dynamics, however, both of these quantities are, on average, exactly zero because of the recrossings of the barrier region boundary. That is, an observer endowed with infinite spatial and temporal resolution would find that finite loops do not exist (or, more precisely, form a set of measure zero). Here we develop a description of the experiment that takes the “fuzziness” of the boundaries caused by finite experimental resolution into account and show how the experimental uncertainty of localizing the point, in time and space, where the barrier is crossed leads to observable distributions of loop times and sizes. Although these distributions generally depend on the experimental resolution, this dependence, in certain cases, may amount to a simple resolution-dependent factor and, therefore, the experiments do probe inherent properties of barrier crossing dynamics.

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Microscopic origin of diffusive dynamics in the context of transition path time distributions for protein folding and unfolding

Abstract: Experimentally measured transition path time distributions are usually analyzed theoretically in terms of a diffusion equation over a free energy barrier. It is though well understood that the free energy...

Cited by 4 publications

References 69 publications

Transition Path Dynamics of Non-Markovian Systems across a Rough Potential Barrier

Transition Path Dynamics of Non-Markovian Systems across a Rough Potential Barrier

Barrier-crossing transition-path times for non-Markovian systems

The significance of fuzzy boundaries of the barrier regions in single-molecule measurements of failed barrier crossing attempts

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