arXiv subjects

Daniel M. Zuckerman

Publications and source records attributed to Daniel M. Zuckerman.

At least 37 records · Page 2Linked to original sources

arXiv2010

Extending fragment-based free energy calculations with library Monte Carlo simulation: Annealing in interaction space

Pre-calculated libraries of molecular fragment configurations have previously been used as a basis for both equilibrium sampling (via "library-based Monte Carlo") and for obtaining absolute free energies using a polymer-growth formalism. Here, we combine the two approaches to extend the size of systems for which free energies can be calculated. We study a series of all-atom poly-alanine systems in a simple dielectric "solvent" and find that precise free energies can be obtained rapidly. For instance, for 12 residues, less than an hour of single-processor is required. The combined approach is formally equivalent to the "annealed importance sampling" algorithm; instead of annealing by decreasing temperature, however, interactions among fragments are gradually added as the molecule is "grown." We discuss implications for future binding affinity calculations in which a ligand is grown into a binding site.

q-bio.QM↗

arXiv2010

Steady-state simulations using weighted ensemble path sampling

We extend the weighted ensemble (WE) path sampling method to perform rigorous statistical sampling for systems at steady state. The straightforward steady-state implementation of WE is directly practical for simple landscapes, but not when significant metastable intermediates states are present. We therefore develop an enhanced WE scheme, building on existing ideas, which accelerates attainment of steady state in complex systems. We apply both WE approaches to several model systems confirming their correctness and efficiency by comparison with brute-force results. The enhanced version is significantly faster than the brute force and straightforward WE for systems with WE bins that accurately reflect the reaction coordinate(s). The new WE methods can also be applied to equilibrium sampling, since equilibrium is a steady state.

physics.bio-ph↗

arXiv2010

Heterogeneous path ensembles for conformational transitions in semi-atomistic models of adenylate kinase

We performed "weighted ensemble" path-sampling simulations of adenylate kinase, using several semi-atomistic protein models. Our study investigated both the biophysics of conformational transitions as well as the possibility of increasing model accuracy without sacrificing good sampling. Biophysically, the path ensembles show significant heterogeneity and the explicit possibility of two principle pathways in the Open-Closed transition. We recently showed, under certain conditions, a "symmetry of hetereogeneity" is expected between the forward and the reverse transitions: the fraction of transitions taking a specific pathway/channel will be the same in both the directions. Our path ensembles are analyzed in the light of the symmetry relation and its conditions. In the realm of modeling, we employed an all-atom backbone with various levels of residue interactions. Because reasonable path sampling required only a few weeks of single-processor computing time with these models, the addition of further chemical detail should be feasible.

physics.bio-ph↗

arXiv2010

Automated sampling assessment for molecular simulations using the effective sample size

To quantify the progress in development of algorithms and forcefields used in molecular simulations, a method for the assessment of the sampling quality is needed. We propose a general method to assess the sampling quality through the estimation of the number of independent samples obtained from molecular simulations. This method is applicable to both dynamic and nondynamic methods and utilizes the variance in the populations of physical states to determine the ESS. We test the correctness and robustness of our procedure in a variety of systems--two-state toy model, all-atom butane, coarse-grained calmodulin, all-atom dileucine and Met-enkaphalin. We also introduce an automated procedure to obtain approximate physical states from dynamic trajectories: this procedure allows for sample--size estimation for systems for which physical states are not known in advance.

physics.comp-ph↗

arXiv2010

Symmetry of forward and reverse path populations

In this note, we address formally the issue of symmetry for probabilities of different dynamical pathways in the forward and reverse directions of a conformational transition. Our discussion is based on a decomposition of equilibrium into opposing steady states, and makes clear the conditions necessary for symmetry to apply. From a practical point of view, we also discuss when approximate symmetry is to be expected.

physics.comp-ph↗

arXiv2010

Efficient equilibrium sampling of all-atom peptides using library-based Monte Carlo

We applied our previously developed library-based Monte Carlo (LBMC) to equilibrium sampling of several implicitly solvated all-atom peptides. LBMC can perform equilibrium sampling of molecules using the pre-calculated statistical libraries of molecular-fragment configurations and energies. For this study, we employed residue-based fragments distributed according to the Boltzmann factor of the OPLS-AA forcefield describing the individual fragments. Two solvent models were employed: a simple uniform dielectric and the Generalized Born/Surface Area (GBSA) model. The efficiency of LBMC was compared to standard Langevin dynamics (LD) using three different statistical tools. The statistical analyses indicate that LBMC is more than 100 times faster than LD not only for the simple solvent model but also for GBSA.

physics.bio-ph↗

arXiv2009

The "weighted ensemble" path sampling method is statistically exact for a broad class of stochastic processes and binning procedures

The "weighted ensemble" method, introduced by Huber and Kim, [G. A. Huber and S. Kim, Biophys. J. 70, 97 (1996)], is one of a handful of rigorous approaches to path sampling of rare events. Expanding earlier discussions, we show that the technique is statistically exact for a wide class of Markovian and non-Markovian dynamics. The derivation is based on standard path-integral (path probability) ideas, but recasts the weighted-ensemble approach as simple "resampling" in path space. Similar reasoning indicates that arbitrary nonstatic binning procedures, which merely guide the resampling process, are also valid. Numerical examples confirm the claims, including the use of bins which can adaptively find the target state in a simple model.

physics.comp-ph↗

arXiv2009

Thermal Motions of the E. Coli Glucose-Galactose Binding Protein Studied Using Well-Sampled Semi-Atomistic Simulations

The E. coli glucose-galactose chemosensory receptor is a 309 residue, 32 kDa protein consisting of two distinct structural domains. In this computational study, we studied the protein's thermal fluctuations, including both the large scale interdomain movements that contribute to the receptor's mechanism of action, as well as smaller scale motions, using two different computational methods. We employ extremely fast, "semi-atomistic" Library-Based Monte Carlo (LBMC) simulations, which include all backbone atoms but "implicit" side chains. Our results were compared with previous experiments and an all-atom Langevin dynamics simulation. Both LBMC and Langevin dynamics simulations were performed using both the apo and glucose-bound form of the protein, with LBMC exhibiting significantly larger fluctuations. The LBMC simulations are also in general agreement with the disulfide trapping experiments of Careaga & Falke (JMB, 1992; Biophys. J., 1992), which indicate that distant residues in the crystal structure (i.e. beta carbons separated by 10 to 20 angstroms) form spontaneous transient contacts in solution. Our simulations illustrate several possible "mechanisms" (configurational pathways) for these fluctuations. We also observe several discrepancies between our calculations and experiment. Nevertheless, we believe that our semi-atomistic approach could be used to study the fluctuations in other proteins, perhaps for ensemble docking, or other analyses of protein flexibility in virtual screening studies.

physics.bio-ph↗

arXiv2009

Weighted Ensemble Path Sampling for Multiple Reaction Channels

Finding and sampling multiple reaction channels for molecular transitions remains an important challenge in physical chemistry. Here we show that the weighted ensemble (WE) path sampling method can readily sample multiple channels. In a first test, both the WE and transition path sampling methods are applied to two-dimensional model potentials. The comparison explains why the weighted ensemble approach will not be trapped in one channel. The WE approach is then used to sample the full transition path ensemble in implicitly solvated alanine dipeptide at two different temperatures. The ensembles are of sufficient quality to permit quantification of the fractional importance of each channel, even at T=300K when brute-force simulation is prohibitively expensive.

physics.bio-ph↗

arXiv2009

Absolute free energies estimated by combining pre-calculated molecular fragment libraries

The absolute free energy -- or partition function, equivalently -- of a molecule can be estimated computationally using a suitable reference system. Here, we demonstrate a practical method for staging such calculations by growing a molecule based on a series of fragments. Significant computer time is saved by pre-calculating fragment configurations and interactions for re-use in a variety of molecules. We employ such fragment libraries and interaction tables for amino acids and capping groups to estimate free energies for small peptides. Equilibrium ensembles for the molecules are generated at no additional computational cost, and are used to check our results by comparison to standard dynamics simulation.

physics.bio-ph↗

arXiv2008

A library-based Monte Carlo technique enables rapid equilibrium sampling of a protein model with atomistic components

There is significant interest in rapid protein simulations because of the time-scale limitations of all-atom methods. Exploiting the low cost and great availability of computer memory, we report a Monte Carlo technique for incorporating fully flexible atomistic protein components (e.g., peptide planes) into protein models without compromising sampling speed or statistical rigor. Building on existing approximate methods (e.g., Rosetta), the technique uses pre-generated statistical libraries of all-atom components which are swapped with the corresponding protein components during a simulation. The simple model we study consists of the three all-atom backbone residues -- Ala, Gly, and Pro -- with structure-based (Go-like) interactions. For the five different proteins considered in this study, LBMC can generate at least 30 statistically independent configurations in about a month of single CPU time. Minimal additional cost is required to add residue-specific interactions.

physics.bio-ph↗

arXiv2007

A "black-box" re-weighting analysis can correct flawed simulation data, after the fact

There is a great need for improved statistical sampling in a range of physical, chemical and biological systems. Even simulations based on correct algorithms suffer from statistical error, which can be substantial or even dominant when slow processes are involved. Further, in key biomolecular applications, such as the determination of protein structures from NMR data, non-Boltzmann-distributed ensembles are generated. We therefore have developed the "black-box" strategy for re-weighting a set of configurations generated by arbitrary means to produce an ensemble distributed according to any target distribution. In contrast to previous algorithmic efforts, the black-box approach exploits the configuration-space density observed in a simulation, rather than assuming a desired distribution has been generated. Successful implementations of the strategy, which reduce both statistical error and bias, are developed for a one-dimensional system, and a 50-atom peptide, for which the correct 250-to-1 population ratio is recovered from a heavily biased ensemble.

physics.comp-ph↗

arXiv2007

Annealed importance sampling of dileucine peptide

Annealed importance sampling is a means to assign equilibrium weights to a nonequilibrium sample that was generated by a simulated annealing protocol. The weights may then be used to calculate equilibrium averages, and also serve as an ``adiabatic signature'' of the chosen cooling schedule. In this paper we demonstrate the method on the 50-atom dileucine peptide, showing that equilibrium distributions are attained for manageable cooling schedules. For this system, as naively implemented here, the method is modestly more efficient than constant temperature simulation. However, the method is worth considering whenever any simulated heating or cooling is performed (as is often done at the beginning of a simulation project, or during an NMR structure calculation), as it is simple to implement and requires minimal additional CPU expense. Furthermore, the naive implementation presented here can be improved.

q-bio.BM↗

arXiv2007

Demonstrated convergence of the equilibrium ensemble for a fast united-residue protein model

Due to the time-scale limitations of all-atom simulation of proteins, there has been substantial interest in coarse-grained approaches. Some methods, like "Resolution Exchange," [E. Lyman et al., Phys. Rev. Lett. 96, 028105 (2006)] can accelerate canonical all-atom sampling, but require properly distributed coarse ensembles. We therefore demonstrate that full sampling can indeed be achieved in a sufficiently simplified protein model, as verified by a recently developed convergence analysis. The model accounts for protein backbone geometry in that rigid peptide planes rotate according to atomistically defined dihedral angles, but there are only two degrees of freedom (phi and psi dihedrals) per residue. Our convergence analysis indicates that small proteins (up to 89 residues in our tests) can be simulated for more than 50 "structural decorrelation times" in less than a week on a single processor. We show that the fluctuation behavior is reasonable, as well as discussing applications, limitations, and extensions of the model.

physics.bio-ph↗

arXiv2007

The structural de-correlation time: A robust statistical measure of convergence of biomolecular simulations

Although atomistic simulations of proteins and other biological systems are approaching microsecond timescales, the quality of 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?'' The resulting ``structural de-correlation time'' is robustly calculated using exact properties deduced from our previously developed ``structural histograms,'' without any fitting parameters. We show 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.

q-bio.QM↗

arXiv2006

Transition-Event Durations in One Dimensional Activated Processes

Despite their importance in activated processes, transition-event durations -- which are much shorter than first passage times -- have not received a complete theoretical treatment. We therefore study the distribution of durations of transition events over a barrier in a one-dimensional system undergoing over-damped Langevin dynamics.

cond-mat.stat-mech↗

arXiv2006

Comparison of free energy methods for molecular systems

We present a detailed comparison of computational efficiency and precision for several free energy difference ($ΔF$) methods. The analysis includes both equilibrium and non-equilibrium approaches, and distinguishes between uni-directional and bi-directional methodologies. We are primarily interested in comparing two recently proposed approaches, adaptive integration and single-ensemble path sampling, to more established methodologies. As test cases, we study relative solvation free energies, of large changes to the size or charge of a Lennard-Jones particle in explicit water. The results show that, for the systems used in this study, both adaptive integration and path sampling offer unique advantages over the more traditional approaches. Specifically, adaptive integration is found to provide very precise long-simulation $ΔF$ estimates as compared to other methods used in this report, while also offering rapid estimation of $ΔF$. The results demonstrate that the adaptive integration approach is the best overall method for the systems studied here. The single-ensemble path sampling approach is found to be superior to ordinary Jarzynski averaging for the uni-directional, ``fast-growth'' non-equilibrium case. Closer examination of the path sampling approach on a two-dimensional system suggests it may be the overall method of choice when conformational sampling barriers are high. However, it appears that the free energy landscapes for the systems used in this study have rather modest configurational sampling barriers.

physics.bio-ph↗

arXiv2006

Ensemble based convergence assessment of biomolecular trajectories

Assessing the convergence of a biomolecular simulation is an essential part of any computational investigation. This is because many important quantities (e.g., free energy differences) depend on the relative populations of different conformers; insufficient convergence translates into systematic errors. Here we present a simple method to self-consistently assess the convergence of a simulation. Standard clustering methods first generate a set of reference structures to any desired precision. The trajectory is then classified by proximity to the reference structures, yielding a one-dimensional histogram of structurally distinct populations. Comparing ensembles of different trajectories (or different parts of the same trajectory) built with the same reference structures provides a sensitive, quantitative measure of convergence. Please note: this is a preliminary manuscript, and should be read as such. Comments are most welcome, especially regarding pertinent prior work.

physics.bio-ph↗