arXiv subjects

Daniel M. Zuckerman

Publications and source records attributed to Daniel M. Zuckerman.

53 records · Page 3Linked to original sources

arXiv2006

Resolution exchange simulation with incremental coarsening

We previously developed an algorithm, called resolution exchange, which improves canonical sampling of atomic resolution models by swapping conformations between high- and low-resolution simulations[1]. Here, we demonstrate a generally applicable incremental coarsening procedure and apply the algorithm to a larger peptide, met-enkephalin. In addition, we demonstrate a combination of resolution and temperature exchange, in which the coarser simulations are also at elevated temperatures. Both simulations are implemented in a ``top-down'' mode, to allow efficient allocation of CPU time among the different replicas.

physics.bio-ph↗

arXiv2006

A Second Look at Canonical Sampling of Biomolecules using Replica Exchange Simulation

Because of growing interest in temperature-based sampling methods like replica exchange, this note aims to make some observations and raise some potentially important questions which we have not seen addressed sufficiently in the literature. Mainly, we wish to call attention to limits on the maximum speed-up to be expected from temperature-based methods, and also note the need for careful quantification of sampling efficiency. Because potentially lengthy studies may be necessary to address these issues, we felt it would be useful to bring them to the attention of the broader community. Here \emph{we are strictly concerned with canonical sampling at a fixed temperature,} and \emph{not} with conformational search.

physics.bio-ph↗

arXiv2006

Simple estimation of absolute free energies for biomolecules

One reason that free energy difference calculations are notoriously difficult in molecular systems is due to insufficient conformational overlap, or similarity, between the two states or systems of interest. The degree of overlap is irrelevant, however, if the absolute free energy of each state can be computed. We present a method for calculating the absolute free energy that employs a simple construction of an exactly computable reference system which possesses high overlap with the state of interest. The approach requires only a physical ensemble of conformations generated via simulation, and an auxiliary calculation of approximately equal central-processing-unit (CPU) cost. Moreover, the calculations can converge to the correct free energy value even when the physical ensemble is incomplete or improperly distributed. As a "proof of principle," we use the approach to correctly predict free energies for test systems where the absolute values can be calculated exactly, and also to predict the conformational equilibrium for leucine dipeptide in implicit solvent.

physics.bio-ph↗

arXiv2005

Resolution exchange simulation

We extend replica exchange simulation in two ways, and apply our approaches to biomolecules. The first generalization permits exchange simulation between models of differing resolution -- i.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.

q-bio.BM↗

arXiv2004

Peptide Conformational Equilibria Computed via a Single-Stage Shifting Protocol

We study the conformational equilibria of two peptides using a novel statistical mechanics approach designed for calculating free energy differences between highly dis-similar conformational states. Our results elucidate the contrasting roles of entropy in implicitly solvated leucine dipeptide and decaglycine. The method extends earlier work by Voter, and overcomes the notorious "overlap" problem in free energy computations by constructing a mathematically equivalent calculation with high conformational similarity. The approach requires only equilibrium simulations of the two states of interest, without the need for sampling transition states. We discuss extensions of the approach to binding affinity estimation and explicitly solvated systems, as well as possible optimizations.

physics.bio-ph↗

arXiv2004

Single-ensemble nonequilibrium path-sampling estimates of free energy differences

We introduce a straightforward, single-ensemble, path sampling approach to calculate free energy differences based on Jarzynski's relation. For a two-dimensional ``toy'' test system, the new (minimally optimized) method performs roughly one hundred times faster than either optimized ``traditional'' Jarzynski calculations or conventional thermodynamic integration. The simplicity of the underlying formalism suggests the approach will find broad applicability in molecular systems.

physics.comp-ph↗

arXiv2004

Efficient use of non-equilibrium measurement to estimate free energy differences for molecular systems

A promising method for calculating free energy differences Delta F is to generate non-equilibrium data via ``fast-growth'' simulations or experiments -- and then use Jarzynski's equality. However, a difficulty with using Jarzynski's equality is that Delta F estimates converge very slowly and unreliably due to the nonlinear nature of the calculation -- thus requiring large, costly data sets. Here, we present new analyses of non-equilibrium data from various simulated molecular systems exploiting statistical properties of Jarzynski's equality. Using a fully automated procedure, with no user-input parameters, our results suggest that good estimates of Delta F can be obtained using 6-15 fold less data than was previously possible. Systematizing and extending previous work [1], the new results exploit the systematic behavior of bias due to finite sample size. A key innovation is better use of the more statistically reliable information available from the raw data.

physics.comp-ph↗

arXiv2003

Systematic Finite-Sampling Inaccuracy in Free Energy Differences and Other Nonlinear Quantities

Systematic inaccuracy is inherent in any computational estimate of a non-linear average, such as the free energy difference (Delta-F) between two states or systems, because of the availability of only a finite number of data values, N. In previous work, we outlined the fundamental statistical description of this ``finite-sampling error.'' We now give a more complete presentation of (i) rigorous general bounds on the free energy and other nonlinear averages, which underscore the universality of the phenomenon; (ii) asymptotic N->infinity expansions of the average behavior of the finite-sampling error in Delta-F estimates; (iii) illustrative examples of large-N behavior, both in free-energy and other calculations; and (iv) the universal, large-N relation between the average finite-sampling error and the fluctuation in the error. An explicit role is played by Levy and Gaussian limiting distributions.

physics.comp-ph↗

arXiv2003

Unbiased simulation of structural transitions in calmodulin

We introduce an approach for performing "very long" computer simulations of the dynamics of simplified, folded proteins. Using an alpha-carbon protein model and a fine grid to mimic continuum computations at increased speed, we perform unbiased simulations which exhibit many large-scale conformational transitions at low cost. In the case of the 72-residue N-terminal domain of calmodulin, the approach yields structural transitions between the calcium-free and calcium-bound structures at a rate of roughly one per day on a single Intel processor. Stable intermediates can be clearly characterized. The model employs Go-like interactions to stabilize two (or more) experimentally-determined structures. The approach is trivially parallelizable and readily generalizes to more complex potentials at minimal cost.

physics.bio-ph↗

arXiv2002

Rapid Determination of Multiple Reaction Pathways in Molecular Systems: The Soft-Ratcheting Algorithm

We discuss the ``soft-ratcheting'' algorithm which generates targeted stochastic trajectories in molecular systems with scores corresponding to their probabilities. The procedure, which requires no initial pathway guess, is capable of rapidly determining multiple pathways between known states. Monotonic progress toward the target state is not required. The soft-ratcheting algorithm is applied to an all-atom model of alanine dipeptide, whose unbiased trajectories are assumed to follow overdamped Langevin dynamics. All possible pathways on the two-dimensional dihedral surface are determined. The associated probability scores, though not optimally distributed at present, may provide a mechanism for estimating reaction rates.

physics.chem-ph↗

arXiv2002

Theory of Systematic Computational Error in Free Energy Differences

Systematic inaccuracy is inherent in any computational estimate of a non-linear average, due to the availability of only a finite number of data values, N. Free energy differences (DF) between two states or systems are critically important examples of such averages in physical, chemical and biological settings. Previous work has demonstrated, empirically, that the ``finite-sampling error'' can be very large -- many times kT -- in DF estimates for simple molecular systems. Here, we present a theoretical description of the inaccuracy, including the exact solution of a sample problem, the precise asymptotic behavior in terms of 1/N for large N, the identification of universal law, and numerical illustrations. The theory relies on corrections to the central and other limit theorems, and thus a role is played by stable (Levy) probability distributions.

physics.comp-ph↗

arXiv2001

Extrapolative Analysis of Fast-Switching Free Energy Estimates in a Molecular System

We perform an extrapolative analysis of "fast-growth" free-energy-difference (DF) estimates of a computer-modeled, fully-solvated ethane<->methanol transformation. The results suggest that extrapolation can greatly reduce the systematic error in DF estimated from a small number of very fast switches. Our extrapolation procedure uses block-averages of finite-data estimates, and appears to be particularly useful for broad, non-Gaussian distributions of data which produce substantial systematic errors with insufficient data. In every tested case, the extrapolative results were better than direct estimates.

physics.chem-ph↗

arXiv2001

Transition Events in Butane Simulations: Similarities Across Models

From a variety of long simulations of all-atom butane using both stochastic and fully-solved molecular dynamics, we have uncovered striking generic behavior which also occurs in one-dimensional systems. We find an apparently universal distribution of transition event durations, as well as a characteristic speed profile along the reaction coordinate. An approximate analytic distribution of event durations, derived from a one-dimensional model, correctly predicts the asymptotic behavior of the universal distribution for both short and long durations.

physics.chem-ph↗

arXiv2001

Asymmetric Primitive-Model Electrolytes: Debye-Huckel Theory, Criticality and Energy Bounds

Debye-Huckel (DH) theory is extended to treat two-component size- and charge-asymmetric primitive models, focussing primarily on the 1:1 additive hard-sphere electrolyte with, say, negative ion diameters, a--, larger than the positive ion diameters, a++. The treatment highlights the crucial importance of the charge-unbalanced ``border zones'' around each ion into which other ions of only one species may penetrate. Extensions of the DH approach which describe the border zones in a physically reasonable way are exact at high $T$ and low density, $ρ$, and, furthermore, are also in substantial agreement with recent simulation predictions for \emph{trends} in the critical parameters, $T_c$ and $ρ_c$, with increasing size asymmetry. Conversely, the simplest linear asymmetric DH description, which fails to account for physically expected behavior in the border zones at low $T$, can violate a new lower bound on the energy (which applies generally to models asymmetric in both charge and size). Other recent theories, including those based on the mean spherical approximation, have predicted trends in the critical parameters quite opposite to those established by the simulations.

cond-mat.stat-mech↗

arXiv2000

Efficient Dynamic Importance Sampling of Rare Events in One Dimension

Exploiting stochastic path integral theory, we obtain \emph{by simulation} substantial gains in efficiency for the computation of reaction rates in one-dimensional, bistable, overdamped stochastic systems. Using a well-defined measure of efficiency, we compare implementations of ``Dynamic Importance Sampling'' (DIMS) methods to unbiased simulation. The best DIMS algorithms are shown to increase efficiency by factors of approximately 20 for a $5 k_B T$ barrier height and 300 for $9 k_B T$, compared to unbiased simulation. The gains result from close emulation of natural (unbiased), instanton-like crossing events with artificially decreased waiting times between events that are corrected for in rate calculations. The artificial crossing events are generated using the closed-form solution to the most probable crossing event described by the Onsager-Machlup action. While the best biasing methods require the second derivative of the potential (resulting from the ``Jacobian'' term in the action, which is discussed at length), algorithms employing solely the first derivative do nearly as well. We discuss the importance of one-dimensional models to larger systems, and suggest extensions to higher-dimensional systems.

physics.comp-ph↗

arXiv1998

Chemical Association via Exact Thermodynamic Formulations

It can be fruitful to view two-component physical systems of attractive monomers, A and B, ``chemically'' in terms of a reaction A + B <-> C, where C = AB is an associated pair or complex. We show how to construct free energies in the three-component or chemical picture which, under mass-action equilibration, exactly reproduce any given two-component or ``physical'' thermodynamics. Order-by-order matching conditions and closed-form chemical representations reveal the freedom available to modify the A-C, B-C, and C-C interactions and to adjust the association constant. The theory (in the simpler one-component, i.e., A = B, case) is illustrated by treating a van der Waals fluid.

physics.chem-ph↗

arXiv1997

Critique of Primitive Model Electrolyte Theories

Approximate theories for the restricted primitive model electrolyte are compared in the light of Totsuji's lower bound for the energy (an improvement over Onsager's), Gillan's upper bound for the free energy, and thermal stability requirements. Theories based on the Debye-Hueckel (DH) approach and the mean spherical approximation (MSA), including extensions due to Bjerrum, Ebeling, Fisher and Levin, and Stell, Zhou, and Yeh (PMSA1,2,3) are tested. In the range T* = (k_B T)Da/q^2 \lesssim 10 T*_c \simeq 0.5, all DH-based theories satisfy Totsuji's bound, while the MSA possesses a significant region of violation. Both DH and MSA theories violate Gillan's bound in the critical region and below unless ion pairing and the consequent free-ion depletion are incorporated. However, the PMSA theories, which recognize pairing but not depletion, fail to meet the bound. The inclusion of excluded-volume terms has only small effects in this respect. Finally, all the pairing theories exhibit negative constant-volume specific heats when T* \gtrsim 2T*_c \simeq 0.1; this is attributable to the treatment of the association constant.

cond-mat.stat-mech↗