Pande, Vijay S., Grosberg, Alexander Yu, and Tanaka, Toyoichi
Reviews of Modern Physics. Jan 2000, Vol. 72 Issue 1, p259, 56 p.
Protein folding -- Models, Polymers -- Thermal properties, Amino acid sequence -- Analysis, and Structure-activity relationships (Biochemistry) -- Testing
The paper discusses the relevance of using heteropolymers, containing monomers in irregular sequences, to understand dynamics of protein folding. Random elements in protein sequences give rise to unique conformational patterns in the folded state, similar to the behavior of heteropolymers.
OSCILLATIONS, COMPUTER simulation, CYTOLOGY, MARKOV random fields, and PHASE transformations (Physics)
The development of tractable nonequilibrium simulation methods represents a bottleneck for efforts to describe the functional dynamics that occur within living cells. We here employ a nonequilibrium approach called the λ ensemble to characterize the dissipative dynamics of a simple Markovian network driven by an external potential. In the highly dissipative regime brought about by the λ bias, we observe a dynamical structure characteristic of cellular architectures: The entropy production drives a damped oscillator over state populations in the network. We illustrate the properties of such oscillations in weakly and strongly driven regimes, and we discuss how control structures associated with the "dynamical phase transition" in the system can be related to switches and oscillators in cellular dynamics. [ABSTRACT FROM AUTHOR]
BIOMOLECULES, DNA, MOLECULAR biology, MOLECULAR dynamics, and SPECTRUM analysis
To explain the observed dynamics in equilibrium single-molecule measurements of biomolecules, the experimental observable is often chosen as a putative reaction coordinate along which kinetic behavior is presumed to be governed by diffusive dynamics. Here, we invoke the splitting probability as a test of the suitability of such a proposed reaction coordinate. Comparison of the observed splitting probability with that computed from the kinetic model provides a simple test to reject poor reaction coordinates. We demonstrate this test for a force spectroscopy measurement of a DNA hairpin. [ABSTRACT FROM AUTHOR]
Hernández CX, Wayment-Steele HK, Sultan MM, Husic BE, and Pande VS
Physical Review. E [Phys Rev E] 2018 Jun; Vol. 97 (6-1), pp. 062412.
Often the analysis of time-dependent chemical and biophysical systems produces high-dimensional time-series data for which it can be difficult to interpret which individual features are most salient. While recent work from our group and others has demonstrated the utility of time-lagged covariate models to study such systems, linearity assumptions can limit the compression of inherently nonlinear dynamics into just a few characteristic components. Recent work in the field of deep learning has led to the development of the variational autoencoder (VAE), which is able to compress complex datasets into simpler manifolds. We present the use of a time-lagged VAE, or variational dynamics encoder (VDE), to reduce complex, nonlinear processes to a single embedding with high fidelity to the underlying dynamics. We demonstrate how the VDE is able to capture nontrivial dynamics in a variety of examples, including Brownian dynamics and atomistic protein folding. Additionally, we demonstrate a method for analyzing the VDE model, inspired by saliency mapping, to determine what features are selected by the VDE model to describe dynamics. The VDE presents an important step in applying techniques from deep learning to more accurately model and interpret complex biophysics.
Physical Review Letters [Phys Rev Lett] 2010 Nov 05; Vol. 105 (19), pp. 198101. Date of Electronic Publication: 2010 Nov 05.
Markov Chains, Models, Molecular, Protein Folding, and Proteins chemistry
We present a simple model of protein folding dynamics that captures key qualitative elements recently seen in all-atom simulations. The goals of this theory are to serve as a simple formalism for gaining deeper insight into the physical properties seen in detailed simulations as well as to serve as a model to easily compare why these simulations suggest a different kinetic mechanism than previous simple models. Specifically, we find that non-native contacts play a key role in determining the mechanism, which can shift dramatically as the energetic strength of non-native interactions is changed. For proteinlike non-native interactions, our model finds that the native state is a kinetic hub, connecting the strength of relevant interactions directly to the nature of folding kinetics.
Physical Review. E, Statistical, Nonlinear, And Soft Matter Physics [Phys Rev E Stat Nonlin Soft Matter Phys] 2010 Jul; Vol. 82 (1 Pt 2), pp. 016705. Date of Electronic Publication: 2010 Jul 19.
We present a Bayesian method for inferring the potential energy experienced by a particle subject to Brownian dynamics. Assuming polynomial potentials, the best polynomial order can be determined by analytical computation of a series of Bayes factors. The coefficients can be estimated from marginal posterior distributions. The method is applicable not only for the motion of an actual Brownian particle but to many kinds of single degree-of-freedom trajectories with Gaussian noise and short, nonzero correlation times.
Physical Review. E, Statistical, Nonlinear, And Soft Matter Physics [Phys Rev E Stat Nonlin Soft Matter Phys] 2007 Jul; Vol. 76 (1 Pt 2), pp. 016703. Date of Electronic Publication: 2007 Jul 16.
Simulated tempering is a method to enhance simulations of complex systems by periodically raising and lowering the temperature. Despite its advantages, simulated tempering has been overshadowed by its parallel counterpart, replica exchange (also known as parallel tempering), due to the difficulty of weight determination in simulated tempering. Here we propose a simple and fast method to obtain near-optimal weights for simulated tempering, and demonstrate its effectiveness in a molecular dynamics simulation of Ala(10) polypeptide in explicit solvent. We believe simulated tempering now deserves another look.
Physical Review. E, Statistical, Nonlinear, And Soft Matter Physics [Phys Rev E Stat Nonlin Soft Matter Phys] 2006 Dec; Vol. 74 (6 Pt 2), pp. 066703. Date of Electronic Publication: 2006 Dec 27.
Exploring conformational spaces is still a challenging task for simulations of complex systems. One way to enhance such a task is weighted sampling, e.g., by assigning high weights to regions that are rarely sampled. It is, however, difficult to estimate adequate weights beforehand, and therefore adaptive methods are desired. Here we present a method for adaptive weighted sampling based on Bayesian inference. Within the framework of Bayesian inference, we develop an update scheme in which the information from previous data is stored in a prior distribution which is then updated to a posterior distribution according to new data. The method proposed here is particularly well suited for distributed computing, in which one must deal with rapid influxes of large amounts of data.
Physical Review Letters [Phys Rev Lett] 2003 Oct 03; Vol. 91 (14), pp. 140601. Date of Electronic Publication: 2003 Oct 02.
We present a maximum likelihood argument for the Bennett acceptance ratio method, and derive a simple formula for the variance of free energy estimates generated using this method. This derivation of the acceptance ratio method, using a form of logistic regression, a common statistical technique, allows us to shed additional light on the underlying physical and statistical properties of the method. For example, we demonstrate that the acceptance ratio method yields the lowest variance for any estimator of the free energy which is unbiased in the limit of large numbers of measurements.