Diffusion in a bistable potential: The functional integral approach

Caroli, B.; Caroli, C.; Roulet, B.

doi:10.1007/bf01106788

Cited by 83 publications

(84 citation statements)

References 19 publications

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“…The computed times for the C7ax→C7eq and α L → α R transitions are 12.0 and 11.4 ps, respectively. Notice, that this is the most probable transition time, and not the mean first passage, or Kramers time [17]. An analysis of the residence time along the path shows that in each of the two DFP's, there are two points where the conformation of alanine dipeptide has shortest residence time.…”

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confidence: 95%

Quantitative Protein Dynamics from Dominant Folding Pathways

et al. 2007

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We develop a theoretical approach to the protein folding problem based on out-of-equilibrium stochastic dynamics. Within this framework, the computational difficulties related to the existence of large time scale gaps in the protein folding problem are removed and simulating the entire reaction in atomistic details using existing computers becomes feasible. In addition, this formalism provides a natural framework to investigate the relationships between thermodynamical and kinetic aspects of the folding. For example, it is possible to show that, in order to have a large probability to remain unchanged under Langevin diffusion, the native state has to be characterized by a small conformational entropy. We discuss how to determine the most probable folding pathway, to identify configurations representative of the transition state and to compute the most probable transition time. We perform an illustrative application of these ideas, studying the conformational evolution of alanine di-peptide, within an all-atom model based on the empiric GROMOS96 force field.A critical part of the protein-folding problem is to understand its kinetics and the underlying physical processes. To this aim, several different theoretical methods have been recently developed, spanning from analytical approaches[1, 2, 3] to detailed computer simulations [4,5,6]. A major problem in simulating the folding process using standard molecular dynamics (MD) is the huge gap between the time scale of "elementary moves", of the order of 10-100 ps, and that of the entire folding process, which ranges from a few microseconds for fast-folders [7], up to several seconds or even minutes for more complex proteins. This peculiarity of the folding process makes the brute-force molecular dynamics approach too demanding, and a substantial part of the efforts in the field of protein folding simulation aims at bridging this gap.In a recent paper [8] we have presented a novel theoretical framework for investigating the folding dynamics, named hereafter Dominant Folding Pathways (DFP), which is based on a reformulation in terms of path integrals of the dynamics described by the Langevin equation. The DFP analysis allows to compute rigorously (i.e. without any assumptions other than the validity of the underlying Langevin equation) the most probable conformational pathway connecting an arbitrary initial conformation to an arbitrary final conformation. The major advantage of the method is the possibility of bypassing the computational difficulties associated with the existence of different time scales in the problem, while retaining the ability to recover information on the time evolution of the system. As we shall see, the resulting computational simplification is dramatic and makes it feasible to study the formation pattern of conformational structures along the entire folding process using realistic all-atom force fields, on available computers.In this Letter we further develop our formalism and we present the first DFP simulation performed in full atomistic deta...

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confidence: 95%

Quantitative Protein Dynamics from Dominant Folding Pathways

et al. 2007

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“…In our present work we continue our study [50] and derive an approximation of the instantaneous escape rate that applies to quite general time-dependent potentials, temperatures, and damping coefficients, thus unifying and extending several of the previously known approximations [43][44][45][46][47]15,16,48,49,[51][52][53]. Particular examples are periodic time-dependences, but also single pulses as well as single ''jumps" of some system parameter.…”

Section: Introductionmentioning

confidence: 94%

“…The general path-integral formalism relevant for our present set up is well developed and documented in the physical and mathematical literature [51,61]. In this section we recall some basics, previously derived and discussed in detail e.g.…”

Section: Basic Path-integral Formalism and Its Limitationsmentioning

confidence: 99%

Thermally activated escape far from equilibrium: A unified path-integral approach

Getfert

Reimann

2010

Chemical Physics

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“…[9]). In addition, if the initial configuration x 0 is not completely determined, one needs to perform an average over its probability distribution.…”

Section: Statistically Significant Reaction Pathwaysmentioning

confidence: 99%

Dominant reaction pathways in high-dimensional systems

Autieri

Faccioli

Sega

et al. 2009

The Journal of Chemical Physics

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This paper is devoted to the development of a theoretical and computational framework to efficiently sample the statistically significant thermally activated reaction pathways, in multidimensional systems obeying Langevin dynamics. We show how to obtain the set of most probable reaction pathways and compute the corrections due to quadratic thermal fluctuations around such trajectories. We discuss how to obtain predictions for the evolution of arbitrary observables and how to generate conformations which are representative of the transition state ensemble. We present an illustrative implementation of our method by studying the diffusion of a point particle in a 2-dimensional funneled external potential.

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Diffusion in a bistable potential: The functional integral approach

Cited by 83 publications

References 19 publications

Quantitative Protein Dynamics from Dominant Folding Pathways

Quantitative Protein Dynamics from Dominant Folding Pathways

Thermally activated escape far from equilibrium: A unified path-integral approach

Dominant reaction pathways in high-dimensional systems

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