On the transition coordinate for protein folding

Du, Rose; Pande, Vijay S.; Grosberg, Alexander Y.; Tanaka, Toyoichi; Shakhnovich, Eugene S.

doi:10.1063/1.475393

Cited by 498 publications

(659 citation statements)

References 26 publications

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“…The main motivation was to develop a method where the numerical results of a typical mechanistic study (a FES exploration with the subsequent committor analysis [22][23][24] ) can be further exploited without additional simulations. The underlying theory has common motifs in general with the Bennett-Chandler formalism 2,3 and in particular with the effective positive flux variant (EPF) 4,[25][26][27][28] .…”

Section: Introductionmentioning

confidence: 99%

Divided Saddle Theory: A New Idea for Rate Constant Calculation

Daru

Stirling

2014

J. Chem. Theory Comput.

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We present a theory of rare events and derive an algorithm to obtain rates from postprocessing the numerical data of a free energy calculation and the corresponding committor analysis. The formalism is based on the division of the saddle region of the free energy profile of the rare event into two adjacent segments called Saddle Domains. The method is built on sampling the dynamics within these regions: auxiliary rate constants are defined for the Saddle Domains and the absolute forward and backward rates are obtained by proper reweighting. We call our approach Divided Saddle Theory (DST). An important advantage of our approach is that it requires only standard computational techniques which are available in most molecular dynamics codes. We demonstrate the potential of DST numerically on two examples: rearrangement of alanine-dipeptide (CH3CO-Ala-NHCH3) conformers and the intramolecular Cope reaction of the fluxional barbaralane molecule.

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Section: Introductionmentioning

confidence: 99%

Divided Saddle Theory: A New Idea for Rate Constant Calculation

Daru

Stirling

2014

J. Chem. Theory Comput.

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“…This result has important practical consequences, because the FEPs are most commonly built by using putative reaction coordinates such as the number of native contacts or p fold (19,22), which are highly nonlinear functions of the Cartesian configuration space through which the kinetics proceeds. On the basis of the F H in terms of such coordinates, the basins on the projected FES are determined, and the lowest pathways connecting them are obtained.…”

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confidence: 99%

Diffusive reaction dynamics on invariant free energy profiles

Krivov

Karplus

2008

Proc. Natl. Acad. Sci. U.S.A.

118

192

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A fundamental problem in the analysis of protein folding and other complex reactions in which the entropy plays an important role is the determination of the activation free energy from experimental measurements or computer simulations. This article shows how to combine minimum-cut-based free energy profiles (F C), obtained from equilibrium molecular dynamics simulations, with conventional histogram-based free energy profiles (F H) to extract the coordinatedependent diffusion coefficient on the F C (i.e., the method determines free energies and a diffusive preexponential factor along an appropriate reaction coordinate). The F C, in contrast to the FH, is shown to be invariant with respect to arbitrary transformations of the reaction coordinate, which makes possible partition of configuration space into basins in an invariant way. A ''natural coordinate,'' for which F H and FC differ by a multiplicative constant (constant diffusion coefficient), is introduced. The approach is illustrated by a model onedimensional system, the alanine dipeptide, and the folding reaction of a double ␤-hairpin miniprotein. It is shown how the results can be used to test whether the putative reaction coordinate is a good reaction coordinate.diffusion ͉ protein folding ͉ one-dimensional free energy surfaces ͉ variable diffusion coefficient F ree energy surface (FES) projected on a few progress variables (usually one or two) is often used to describe the equilibrium and kinetic properties of complex systems with a very large number (100 to 1,000 or more) of degrees of freedom. Studies of protein folding are an important example where this type of projected surface has been introduced and progress variables such as the number of native contacts and radius of gyration have been used (1-3). Most experimental analyses of protein folding have used a related approach; for example, if the distribution of folding times is exponential, it is assumed that there is a single free energy barrier along a generally unknown one-dimensional reaction coordinate. For a few systems that show more complex kinetics, the results have been interpreted in terms of projected FESs in two dimensions (4), although, again, the actual progress variables are not known. However, even when a one-dimensional single-barrier free energy projection seems adequate to describe the kinetics, there is a fundamental difficulty in determining the barrier height, because the measurements provide only one parameter (e.g., in protein folding, the rate constant of the corresponding unimolecular reaction is obtained). In such a standard ''one-dimensional'' analysis, the rate constant, k, is written as k ϭ k 0 e Ϫ⌬F/kT , where k 0 is the preexponential factor and ⌬F is the free energy of activation. Thus, there are two unknowns, k 0 and ⌬F, to be determined from one measurement. For many small-molecule reactions, the entropic contribution to the barrier is negligible (⌬F Ϸ ⌬E, the activation energy), so that a measurement of the temperature dependence of the reaction rate can be used t...

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“…Monte Carlo simulations on lattice models [253] p fold as a reaction coordinate for protein folding.…”

Section: Mechanism Of Folding/ Unfoldingmentioning

confidence: 99%

Protein folding: Then and now

Chen

Ding

Nie

et al. 2008

Archives of Biochemistry and Biophysics

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Over the past three decades the protein folding field has undergone monumental changes. Originally a purely academic question, how a protein folds has now become vital in understanding diseases and our abilities to rationally manipulate cellular life by engineering protein folding pathways. We review and contrast past and recent developments in the protein folding field. Specifically, we discuss the progress in our understanding of protein folding thermodynamics and kinetics, the properties of evasive intermediates, and unfolded states. We also discuss how some abnormalities in protein folding lead to protein aggregation and human diseases.

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On the transition coordinate for protein folding

Cited by 498 publications

References 26 publications

Divided Saddle Theory: A New Idea for Rate Constant Calculation

Divided Saddle Theory: A New Idea for Rate Constant Calculation

Diffusive reaction dynamics on invariant free energy profiles

Protein folding: Then and now

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