Simulation of an Ensemble of Conformational Transitions in a United-Residue Model of Calmodulin

Zuckerman, Daniel M.

doi:10.1021/jp0370730

Cited by 82 publications

(124 citation statements)

References 129 publications

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“…23 In the "double native" Gō potential used, both the apo (Ca 2+ -free) 24 and holo (Ca 2+ -bound) 25 structures are stabilized, so that occasional spontaneous transitions are observed between the two states.…”

Section: Calmodulinmentioning

confidence: 99%

On the Structural Convergence of Biomolecular Simulations by Determination of the Effective Sample Size

2007

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Although atomistic simulations of proteins and other biological systems are approaching microsecond timescales, the quality of simulation trajectories has remained difficult to assess. Such assessment is critical not only for establishing the relevance of any individual simulation, but also in the extremely active field of developing computational methods. Here we map the trajectory assessment problem onto a simple statistical calculation of the "effective sample size" -i.e., the number of statistically independent configurations. The mapping is achieved by asking the question, "How much time must elapse between snapshots included in a sample for that sample to exhibit the statistical properties expected for independent and identically distributed configurations?" Our method is more general than standard autocorrelation methods, in that it directly probes the configuration space distribution, without requiring a priori definition of configurational substates, and without any fitting parameters. We show that the method is equally and directly applicable to toy models, peptides, and a 72-residue protein model. Variants of our approach can readily be applied to a wide range of physical and chemical systems.What does convergence mean? The answer is not simply of abstract interest, since many aspects of the biomolecular simulation field depend on it. When parameterizing potential functions, it is essential to know whether inaccuracies are attributable to the potential, rather than undersampling. 1 In the extremely active area of methods development for equilibrium sampling, it is necessary to demonstrate that a novel approach is better than its predecessors, in the sense that it equilibrates the relative populations of different conformers in less CPU time. 2 And in the important area of free energy calculations, under-sampling can result in both systematic error and poor precision. 3To rephrase the basic question, given a simulation trajectory (an ordered set of correlated configurations), what characteristics should be observed if convergence has been achieved? The obvious, if tautological, answer is that all states should have been visited with the correct relative probabilities, as governed by a Boltzmann factor (implicitly, free energy) in most cases of physical interest. Yet given the omnipresence of statistical error, it has long been accepted that such idealizations are of limited value. The more pertinent questions have therefore been taken to be: Does the trajectory give reliable estimates for quantities of interest? What is the statistical uncertainty in these estimates 4-7 ? In other words, convergence is relative, and in principle, it is rarely meaningful to describe a simulation as not converged, in an absolute sense. (An exception is when a priori information indicates the trajectory has failed to visit certain states.)

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Section: Calmodulinmentioning

confidence: 99%

On the Structural Convergence of Biomolecular Simulations by Determination of the Effective Sample Size

2007

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“…54,55 Similar schemes for combining more than one structure-based model have been proposed based on quantum mechanical mixing 56,57 or by combining contacts from different models in a pairwise fashion. 58,59 The advantage of the present formulation is that it does not sacrifice the cooperative formation of folded structures, and allows an arbitrary number of different conformations to be included easily. Multi-Gō models of various flavours have been successfully applied to the study of problems such as conformational transitions in adenylate kinase, 56, 60-62 calmodulin 55,58 and glutaminebinding protein, 57 base-flipping in B-DNA, 63 activation of src-kinase, 64 conformational exchange between different protein folds, 59, 65 structural transitions in motor proteins, 66 and protein binding mechanisms.…”

Section: Model and Methodsmentioning

confidence: 99%

Discriminating binding mechanisms of an intrinsically disordered protein via a multi-state coarse-grained model

Knott

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2014

The Journal of Chemical Physics

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Many proteins undergo a conformational transition upon binding to their cognate binding partner, with intrinsically disordered proteins (IDPs) providing an extreme example in which a folding transition occurs. However, it is often not clear whether this occurs via an "induced fit" or "conformational selection" mechanism, or via some intermediate scenario. In the first case, transient encounters with the binding partner favour transitions to the bound structure before the two proteins dissociate, while in the second the bound structure must be selected from a subset of unbound structures which are in the correct state for binding, because transient encounters of the incorrect conformation with the binding partner are most likely to result in dissociation. A particularly interesting situation involves those intrinsically disordered proteins which can bind to different binding partners in different conformations. We have devised a multi-state coarse-grained simulation model which is able to capture the binding of IDPs in alternate conformations, and by applying it to the binding of nuclear coactivator binding domain (NCBD) to either ACTR or IRF-3 we are able to determine the binding mechanism. By all measures, the binding of NCBD to either binding partner appears to occur via an induced fit mechanism. Nonetheless, we also show how a scenario closer to conformational selection could arise by choosing an alternative non-binding structure for NCBD. © 2014 AIP Publishing LLC.

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“…In one approach, dating to the earliest computational studies of proteins [1,2], coarse-grained protein representations are adopted. This strategy continues to be popular [3,4].…”

mentioning

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“…In one approach, dating to the earliest computational studies of proteins[1, 2], coarse-grained protein representations are adopted. This strategy continues to be popular [3,4].A second class of strategies attempts directly to enhance sampling of atomic-resolution models, including multiple time step methods [5,6], replica exchange [7]/parallel tempering [8,9,10], and other generalized ensemble techniques [11]. Parallel tempering (PT), which employs a ladder of replicas simulated at increasing temperatures, is widely used for state-of-the-art molecular dynamics simulations, but presently is limited to small proteins [12], as the resources required increase rapidly with the system size.…”

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Resolution Exchange Simulation

2006

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We extend replica exchange simulation in two ways, and apply our approaches to biomolecules. The first generalization permits exchange simulation between models of differing resolutioni.e., between detailed and coarse-grained models. Such "resolution exchange" can be applied to molecular systems or spin systems. The second extension is to "pseudo-exchange" simulations, which require little CPU usage for most levels of the exchange ladder and also substantially reduces the need for overlap between levels. Pseudo exchanges can be used in either replica or resolution exchange simulations. We perform efficient, converged simulations of a 50-atom peptide to illustrate the new approaches.Accepted for publication in physical review letters. PACS numbers:The simulation of biomolecules with 10 4 − 10 5 degrees of freedom has become routine, thanks to the accessibility of powerful computing resources, the development of reliable simulation software, and standardized empirical potential energy functions. For many biological applications, such as binding free energy estimation, it is desirable to generate an equilibrated ensemble of conformations. In principle, standard Monte Carlo (MC) and molecular dynamics (MD) algorithms are perfectly ergodic, and therefore will eventually generate such ensembles. In practice, the µ sec − sec timescale, which describes biologically relevant fluctuations, is not within reach of computation even for small proteins.Two broad strategies have been developed to address this problem. In one approach, dating to the earliest computational studies of proteins[1, 2], coarse-grained protein representations are adopted. This strategy continues to be popular [3,4].A second class of strategies attempts directly to enhance sampling of atomic-resolution models, including multiple time step methods [5,6], replica exchange [7]/parallel tempering [8,9,10], and other generalized ensemble techniques [11]. Parallel tempering (PT), which employs a ladder of replicas simulated at increasing temperatures, is widely used for state-of-the-art molecular dynamics simulations, but presently is limited to small proteins [12], as the resources required increase rapidly with the system size.This Letter presents two new tools for biomolecular simulation, by extending the PT approach and exploiting the speed of coarse-grained models. The first extension is a "resolution exchange" (res-ex) algorithm whichinstead of using high-temperature simulation to increase sampling, as does PT -uses inexpensive coarse-grained * elyman@ccbb.pitt.edu † dmz@ccbb.pitt.edu models to cross barriers. Boltzmann-weighted ensembles are produced. The algorithm is implemented in close analogy to PT, and can also be applied to magnetic systems (e.g., the Ising model). The res-ex approach is natural for proteins, and indeed the kernel of the idea was suggested in the early days of protein simulation [1]. More recently, the approach has been implemented in an ad hoc way, without proper statistical weighting [3]. A rigorous method to calculate free en...

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Simulation of an Ensemble of Conformational Transitions in a United-Residue Model of Calmodulin

Cited by 82 publications

References 129 publications

On the Structural Convergence of Biomolecular Simulations by Determination of the Effective Sample Size

On the Structural Convergence of Biomolecular Simulations by Determination of the Effective Sample Size

Discriminating binding mechanisms of an intrinsically disordered protein via a multi-state coarse-grained model

Resolution Exchange Simulation

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