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Register a new userNoise correlation-induced splitting of Kramers escape rate from a metastable state
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Added by
Pulak Kumar Ghosh Dr.
Publication date
2012
fields
Physics
and research's language is
English
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A correlation between two noise processes driving the thermally activated particles in a symmetric triple well potential, may cause a symmetry breaking and a difference in relative stability of the two side wells with respect to the middle one. This leads to an asymmetric localization of population and splitting of Kramers rate of escape from the middle well, ensuring a preferential distribution of the products in the course of a parallel reaction.
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We consider the escape of particles located in the middle well of a symmetric triple well potential driven sinusoidally by two forces such that the potential wells roll as in stochastic resonance and the height of the potential barrier oscillates symmetrically about a mean as in resonant activation. It has been shown that depending on their phase difference the application of these two synchronized signals may lead to a splitting of time averaged Kramers escape rate and a preferential product distribution in a parallel chemical reaction in the steady state.
We study the dynamics of flexible, semiflexible, and self-avoiding polymer chains moving under a Kramers metastable potential. Due to thermal noise, the polymers, initially placed in the metastable well, can cross the potential barrier, but these events are extremely rare if the barrier is much larger than thermal energy. To speed up the slow rate processes in computer simulations, we extend the recently proposed path integral hyperdynamics method to the cases of polymers. We consider the cases where the polymers radii of gyration are comparable to the distance between the well bottom and the barrier top. We find that, for a flexible polymer, the crossing rate ($mathcal{R}$) monotonically decreases with chain contour length ($L$), but with the magnitude much larger than the Kramers rate in the globular limit. For a semiflexible polymer, the crossing rate decreases with $L$ but becomes nearly constant for large $L$. For a fixed $L$, the crossing rate becomes maximum at an intermediate bending stiffness. For a self-avoiding chain, the rate is a nonmonotonic function of $L$, first decreasing with $L$, and then, above certain length, increasing with $L$. These findings can be instrumental for efficient separation of biopolymers.
We have studied the effects of an external sinusoidal force in protein folding kinetics. The externally applied force field acts on the each amino acid residues of polypeptide chains. Our simulation results show that mean protein folding time first increases with driving frequency and then decreases passing through a maximum. With further increase of the driving frequency the mean folding time starts increasing as the noise-induced hoping event (from the denatured state to the native state) begins to experience many oscillations over the mean barrier crossing time period. Thus unlike one-dimensional barrier crossing problems, the external oscillating force field induces both emph{stabilization or destabilization of the denatured state} of a protein. We have also studied the parametric dependence of the folding dynamics on temperature, viscosity, non-Markovian character of bath in presence of the external field.
The linear noise approximation models the random fluctuations from the mean field model of a chemical reaction that unfolds near the thermodynamic limit. Specifically, the fluctuations obey a linear Langevin equation up to order $Omega^{-1/2}$, where $Omega$ is the size of the chemical system (usually the volume). Under the presence of disparate timescales, the linear noise approximation admits a quasi-steady-state reduction referred to as the slow scale linear noise approximation. However, the slow scale linear approximation has only been derived for fast/slow systems that are in Tikhonov standard form. In this work, we derive the slow scale linear noise approximation directly from Fenichel theory, without the need for a priori scaling and dimensional analysis. In so doing, we can apply for the first time the slow scale linear noise approximation to fast/slow systems that are not of standard form. This is important, because often times algorithms are only computationally expensive in parameter ranges where the system is singularly perturbed, but not in standard form. We also comment on the breakdown of the slow scale linear noise approximation near dynamic bifurcation points -- a topic that has remained absent in the chemical kinetics literature, despite the presence of bifurcations in simple biochemical reactions, such the Michaelis--Menten reaction mechanism.
We revisit the interpretation of earlier low temperature experiments on Josephson junctions under the influence of applied microwaves. It was claimed that these experiments unambiguously established a quantum phenomenology with discrete levels in shallow wells of the washboard potential, and macroscopic quantum tunneling. We here apply the previously developed classical theory to a direct comparison with the original experimental observations, and we show that the experimental data can be accurately represented classically. Thus, our analysis questions the necessity of the earlier quantum mechanical interpretation.
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