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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Umbrella sampling: a powerful method to sample tails of distributions

We present the umbrella sampling (US) technique and show that it can be used to sample extremely low-probability areas of the posterior distribution that may be required in statistical analyses of data. In this approach sampling of the target likelihood is split into sampling of multiple biased likelihoods confined within individual umbrella windows. We show that the US algorithm is efficient and highly parallel and that it can be easily used with other existing Markov Chain Monte Carlo (MCMC) samplers. The method allows the user to capitalize on their intuition and define umbrella windows and increase sampling accuracy along specific directions in the parameter space. Alternatively, one can define umbrella windows using an approach similar to parallel tempering. We provide a public code that implements US as a standalone PYTHON package. We present a number of tests illustrating the power of the US method in sampling low-probability areas of the posterior and show that this ability allows a considerably more robust sampling of multimodal distributions compared to standard sampling methods. We also present an application of the method in a real world example of deriving cosmological constraints using the supernova type Ia data. We show that US can sample the posterior accurately down to the approximate to 15 sigma credible region in the Omega(m) - Omega(Lambda) plane, while for the same computational effort the affine-invariant MCMC sampling implemented in the emcee code samples the posterior reliably only to approximate to 3 sigma.

cosmology: cosmological parameters↗
DOE OSTI2018

Implementation of replica-exchange umbrella sampling in GAMESS

In GAMESS-US quantum chemistry package, both replica-exchange molecular dynamics (REMD) and the umbrella sampling (US) methods are available. However, prior to this work, the replica-exchange umbrella sampling (REUS) method, combining REMD and US, was not implemented. Here, REUS affords a more efficient conformational sampling than the conventional US method and is often used in MD simulations. We implemented REUS in GAMESS-US and improved some routines of the existing REMD code. A density-functional tight-binding REMD (DFTB-REMD) simulation of alanine deca-peptide and a DFTB-MD REUS simulation of proton transfer in malonaldehyde were performed. The results of DFTB-MD REUS simulations performed with three different simulation packages were compared to validate our GAMESS-US implementation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Calculating the free energy of transfer of small solutes into a model lipid membrane: Comparison between metadynamics and umbrella sampling

We compare the performance of two well-established computational algorithms for the calculation of free-energy landscapes of biomolecular systems, umbrella sampling and metadynamics. We look at benchmark systems composed of polyethylene and polypropylene oligomers interacting with lipid (phosphatidylcholine) membranes, aiming at the calculation of the oligomer water-membrane free energy of transfer. We model our test systems at two different levels of description, united-atom and coarse-grained. We provide optimized parameters for the two methods at both resolutions. We devote special attention to the analysis of statistical errors in the two different methods and propose a general procedure for the error estimation in metadynamics simulations. Metadynamics and umbrella sampling yield the same estimates for the water-membrane free energy profile, but metadynamics can be more efficient, providing lower statistical uncertainties within the same simulation time.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Quantum chemical replica-exchange umbrella sampling molecular dynamics simulations reveal the formation mechanism of iron phthalocyanine from iron and phthalonitrile

Phthalocyanine (Pc) and its metal complexes (MPcs) have been used industrially since their discovery in the early 20th century. The phthalonitrile (PN) method is a well-known synthesis method in which Pc or MPc can be afforded by heating a mixture of PN and metal powders over 280 °C with only moderate yield. However, the formation mechanism of the phthalocyanines and the intermediate stages of this seemingly simple reaction have yet to be fully understood. To study this mechanism computationally, we carried out quantum chemical molecular dynamics (MD) simulations based on the density-functional tight-binding (DFTB) method, applying the replica-exchange umbrella sampling (REUS) method, starting from four PN molecules and one iron atom. The DFTB-REUS-MD simulations successfully yielded FePc, and a metastable structure very similar to FePc but with a reactive nitrene unit was also identified that might explain the incomplete conversion of the reactants into FePc. Furthermore, analysis of the MD trajectories reveals a three-step FePc formation mechanism for the PN method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Rare behavior of growth processes via umbrella sampling of trajectories

We compute probability distributions of trajectory observables for reversible and irreversible growth processes. These results reveal a correspondence between reversible and irreversible processes, at particular points in parameter space, in terms of their typical and atypical trajectories. Thus key features of growth processes can be insensitive to the precise form of the rate constants used to generate them, recalling the insensitivity to microscopic details of certain equilibrium behavior. We obtained these results using a sampling method, inspired by the "s-ensemble" large-deviation formalism, that amounts to umbrella sampling in trajectory space. The method is a simple variant of existing approaches, and applies to ensembles of trajectories controlled by the total number of events. It can be used to determine large-deviation rate functions for trajectory observables in or out of equilibrium.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Communication: Estimating the initial biasing potential for λ-local-elevation umbrella-sampling (λ-LEUS) simulations via slow growth

In a recent article [Bieler et al., J. Chem. Theory Comput. 10, 3006–3022 (2014)], we introduced a combination of the λ-dynamics (λD) approach for calculating alchemical free-energy differences and of the local-elevation umbrella-sampling (LEUS) memory-based biasing method to enhance the sampling along the alchemical coordinate. The combined scheme, referred to as λ-LEUS, was applied to the perturbation of hydroquinone to benzene in water as a test system, and found to represent an improvement over thermodynamic integration (TI) in terms of sampling efficiency at equivalent accuracy. However, the preoptimization of the biasing potential required in the λ-LEUS method requires “filling up” all the basins in the potential of mean force. This introduces a non-productive pre-sampling time that is system-dependent, and generally exceeds the corresponding equilibration time in a TI calculation. In this letter, a remedy is proposed to this problem, termed the slow growth memory guessing (SGMG) approach. Instead of initializing the biasing potential to zero at the start of the preoptimization, an approximate potential of mean force is estimated from a short slow growth calculation, and its negative used to construct the initial memory. Considering the same test system as in the preceding article, it is shown that of the application of SGMG in λ-LEUS permits to reduce the preoptimization time by about a factor of four.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Multi-point nonequilibrium umbrella sampling and associated fluctuation relations

We describe a simple method of umbrella trajectory sampling for Markov chains. The method allows the estimation of large-deviation rate functions, for path-extensive dynamic observables, for an arbitrary number of models within a certain family. The general relationship between probability distributions of dynamic observables of members of this family is an extended fluctuation relation. When the dynamic observable is chosen to be entropy production, members of this family include the forward Markov chain and its time reverse, whose probability distributions are related by the expected simple fluctuation relation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Supervised learning and the finite-temperature string method for computing committor functions and reaction rates

A central object in the computational studies of rare events is the committor function. Though costly to compute, the committor function encodes complete mechanistic information of the processes involving rare events, including reaction rates and transition-state ensembles. Under the framework of transition path theory, Rotskoff et al. [Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference, Proceedings of Machine Learning Research (PLMR, 2022), Vol. 145, pp. 757–780] proposes an algorithm where a feedback loop couples a neural network that models the committor function with importance sampling, mainly umbrella sampling, which collects data needed for adaptive training. Here, in this work, we show additional modifications are needed to improve the accuracy of the algorithm. The first modification adds elements of supervised learning, which allows the neural network to improve its prediction by fitting to sample-mean estimates of committor values obtained from short molecular dynamics trajectories. The second modification replaces the committor-based umbrella sampling with the finite-temperature string (FTS) method, which enables homogeneous sampling in regions where transition pathways are located. We test our modifications on low-dimensional systems with non-convex potential energy where reference solutions can be found via analytical or finite element methods, and show how combining supervised learning and the FTS method yields accurate computation of committor functions and reaction rates. We also provide an error analysis for algorithms that use the FTS method, using which reaction rates can be accurately estimated during training with a small number of samples. The methods are then applied to a molecular system in which no reference solution is known, where accurate computations of committor functions and reaction rates can still be obtained.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Computing equilibrium free energies through a nonequilibrium quench

Many methods to accelerate sampling of molecular configurations are based on the idea that temperature can be used to accelerate rare transitions. These methods typically compute equilibrium properties at a target temperature using reweighting or through Monte Carlo exchanges between replicas at higher temperatures. A recent paper [G. M. Rotskoff and E. Vanden-Eijnden, Phys. Rev. Lett. 122, 150602 (2019)] demonstrated that accurate equilibrium densities of states can also be computed through a nonequilibrium “quench” process, where sampling is performed at a higher temperature to encourage rapid mixing and then quenched to lower energy states with dissipative dynamics. Here, we provide an implementation of the quench dynamics in LAMMPS and evaluate a new formulation of nonequilibrium estimators for the computation of partition functions or free energy surfaces (FESs) of molecular systems. We show that the method is exact for a minimal model of N-independent harmonic springs and use these analytical results to develop heuristics for the amount of quenching required to obtain accurate sampling. We then test the quench approach on alanine dipeptide, where we show that it gives an FES that is accurate near the most stable configurations using the quench approach but disagrees with a reference umbrella sampling calculation in high FE regions. We then show that combining quenching with umbrella sampling allows the efficient calculation of the free energy in all regions. Moreover, by using this combined scheme, we obtain the FES across a range of temperatures at no additional cost, making it much more efficient than standard umbrella sampling if this information is required. Finally, we discuss how this approach can be extended to solute tempering and demonstrate that it is highly accurate for the case of solvated alanine dipeptide without any additional modifications.

Chemistry↗
DOE OSTI2018

Chloride Ion Transport by the E. coli CLC Cl – /H + Antiporter: A Combined Quantum-Mechanical and Molecular-Mechanical Study

We performed steered molecular dynamics (SMD) and umbrella sampling simulations of Cl – ion migration through the transmembrane domain of a prototypical E. coli CLC Cl – /H + antiporter by employing combined quantum-mechanical (QM) and molecular-mechanical (MM) calculations. The SMD simulations revealed interesting conformational changes of the protein. While no large-amplitude motions of the protein were observed during pore opening, the side chain rotation of the protonated external gating residue Glu148 was found to be critical for full access of the channel entrance by Cl – . Moving the anion into the external binding site (S ext ) induced small-amplitude shifting of the protein backbone at the N-terminal end of helix F. As Cl – traveled through the pore, rigid-body swinging motions of helix R separated it from helix D. Helix R returned to its original position once Cl – exited the channel. Population analysis based on polarized wavefunction from QM/MM calculations discovered significant (up to 20%) charge loss for Cl – along the ion translocation pathway inside the pore. The delocalized charge was redistributed onto the pore residues, especially the functional groups containing π bonds (e.g., the Tyr445 side chain), while the charges of the H atoms coordinating Cl – changed almost negligibly. Potentials of mean force computed from umbrella sampling at the QM/MM and MM levels both displayed barriers at the same locations near the pore entrance and exit. However, the QM/MM PMF showed higher barriers (~10 kcal/mol) than the MM PMF (~2 kcal/mol). Binding energy calculations indicated that the interactions between Cl – and certain pore residues were overestimated by the semi-empirical PM 3 Hamiltonian and underestimated by the CHARMM36 force fields, both of which were employed in the umbrella sampling simulations. In particular, CHARMM36 underestimated binding interactions for the functional groups containing π bonds, missing the stabilizations of the Cl – ion due to electron delocalization. The results suggested that it is important to explore these quantum effects for accurate descriptions of the Cl – transport.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Convergence and Efficiency of Adaptive Importance Sampling Techniques with Partial Biasing

We propose a new Monte Carlo method to efficiently sample a multimodal distribution (known up to a normalization constant). We consider a generalization of the discrete-time Self Healing Umbrella Sampling method, which can also be seen as a generalization of well-tempered metadynamics. The dynamics is based on an adaptive importance technique. The importance function relies on the weights (namely the relative probabilities) of disjoint sets which form a partition of the space. These weights are unknown but are learnt on the fly yielding an adaptive algorithm. In the context of computational statistical physics, the logarithm of these weights is, up to an additive constant, the free-energy, and the discrete valued function defining the partition is called the collective variable. The algorithm falls into the general class of Wang–Landau type methods, and is a generalization of the original Self Healing Umbrella Sampling method in two ways: (i) the updating strategy leads to a larger penalization strength of already visited sets in order to escape more quickly from metastable states, and (ii) the target distribution is biased using only a fraction of the free-energy, in order to increase the effective sample size and reduce the variance of importance sampling estimators. We prove the convergence of the algorithm and analyze numerically its efficiency on a toy example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Selectivity trend of gas separation through nanoporous graphene

By means of molecular dynamics (MD) simulations, we demonstrate that porous graphene can efficiently separate gases according to their molecular sizes. The flux sequence from the classical MD simulation is H{sub 2}>CO{sub 2}≫N{sub 2}>Ar>CH{sub 4}, which generally follows the trend in the kinetic diameters. This trend is also confirmed from the fluxes based on the computed free energy barriers for gas permeation using the umbrella sampling method and kinetic theory of gases. Both brute-force MD simulations and free-energy calcualtions lead to the flux trend consistent with experiments. Case studies of two compositions of CO{sub 2}/N{sub 2} mixtures further demonstrate the separation capability of nanoporous graphene. - Graphical abstract: Classical molecular dynamics simulations show the flux trend of H{sub 2}>CO{sub 2}≫N{sub 2}>Ar>CH{sub 4} for their permeation through a porous graphene, in excellent agreement with a recent experiment. - Highlights: • Classical MD simulations show the flux trend of H{sub 2}>CO{sub 2}≫N{sub 2}>Ar>CH{sub 4} for their permeation through a porous graphene. • Free energy calculations yield permeation barriers for those gases. • Selectivities for several gas pairs are estimated from the free-energy barriers and the kinetic theory of gases. • The selectivity trend is in excellent agreement with a recent experiment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Quantitative Prediction of Uranium Speciation and Amidoxime Binding in Seawater from Advanced Simulation Techniques

The goal of this project was to quantitatively predict stability of uranium species and thermochemistry of uranium binding with amidoxime ligands in realistic seawater conditions. The specific aims of the project were: (i) determine the stable species of uranium and its solvation structure in realistic seawater conditions; also speciation and solvation of uranium's major competing species in seawater, vanadium; (ii) accurately predict the free energies (and thereby stability constants) of binding between uranium and amidoxime; (iii) accurately predict the reaction enthalpies and entropies of binding between uranium and amidoxime as well as between vanadium and amidoxime. Main results and conclusions are as follows. First-principles molecular dynamic simulations found that the structure of the Ca 2 UO 2 (CO 3 ) 3 complex is very stable and that one Ca ion binds to the center UO 2 (CO 3 ) 3 4- anion stronger than the other Ca ion. This finding suggests that using time-resolved EXAFS spectra may confirm the asymmetry in binding of the two Ca ions in the aqueous Ca 2 UO 2 (CO 3 ) 3 complex. To consider the common ions, solvation of the Ca 2 UO 2 (CO 3 ) 3 complex in seawater was simulated by classical molecular dynamics simulation. It was found that the structure of the Ca 2 UO 2 (CO 3 ) 3 complex is very stable in the model seawater. A Na+ ion was found to be closely associated with the Ca 2 UO 2 (CO 3 ) 3 complex by indirectly interacting with one axial oxygen atom of the UO 2 group bridged by a water molecule. In addition, the Na + ion interacts closely with one Ca 2+ ion than the other. The present simulations revealed the key role of common ions such as Na + in impacting the solvation, structure, and apparent charge of the Ca 2 UO 2 (CO 3 ) 3 complex in seawater. The sequential processes of UO 2 2+ binding with the three CO 3 2- groups and the two Ca 2+ ions in pure water and in 0.1 M NaCl were simulated by classical molecular dynamics with both the non-constrained brute-force approach and umbrella sampling. The simulated free energies show excellent agreement with the experiment. The coordination structures of UO 2 (CO 3 ) 3 4- and CaUO 2 (CO 3 ) 3 2- were found to be significantly affected by the presence of Na + ions, leading to a monodentate binding of a carbonate group to U and a water molecule entering the first coordination shell of U. To shed light on the binding between uranyl and glutardiamidoxime (H 2 B), an important model and state-of-the-art ligand for seawater uranium extraction, a suite of computational methods was employed. From molecular dynamics (MD) simulations, it was found that the binding configurations of B 2- with uranyl favor the twofold distorted η 2 binding between the oximate ends (C=N-O-) and U, while HB - prefers the chelating mode for the oximate end with the neutral end being solvated by water. The free energies of sequential ligand binding to form UO 2 B, [UO 2 B 2 ] 2- , and [UO 2 (HB)B] - were simulated with umbrella sampling and very good agreement with the experimental values was achieved, which corroborates the structural insights into the binding mode. State-of-the-art polymeric sorbents employ both amidoximate and carboxylate groups on the side chains to achieve optimal U uptake and selectivity, so we simulated the binding of a model amidoximate–carboxylate bifunctional ligand with uranyl. Classical MD and free-energy simulations in 0.5 M NaCl showed that the carboxylate group binds first to uranyl, leading to a loose intermediate state, and then, the amidoximate group binds, resulting in a more stable and tight chelate state. Binding of the second bifunctional ligand follows a similar process, and the two ligands prefer a trans configuration around the uranyl group. The simulated free energies indicate that the two bifunctional ligands bind with uranyl 14 kcal/mol stronger than the two ligands with only amidoximate groups, confirming an important synergy between amidoximate and carboxylate groups in binding uranyl.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Towards the Accurate Thermodynamic Characterization of Enzyme Reaction Mechanisms

We employed QM/MM molecular dynamics (MD) simulations to characterize the rate-limiting step of the glycosylation reaction of pancreatic α-amylase with combined DFT/molecular dynamics methods (PBE/def2-SVP : AMBER). Upon careful choice of four starting active site conformations based on thorough reactivity criteria, Gibbs energy profiles were calculated with umbrella sampling simulations within a statistical convergence of 1 -2 kcal · mol -1 . Nevertheless, Gibbs activation barriers and reaction energies still varied from 11.0 to 16.8 kcal · mol -1 and -6.3 to +3.8 kcal · mol -1 depending on the starting conformations, showing that despite significant state-of-the-art QM/MM MD sampling (0.5 ns/profile) the result still depends on the starting structure. In conclusion, the results supported the one step dissociative mechanism of Asp197 glycosylation preceded by an acid-base reaction by the Glu233, which are qualitatively similar to those from multi-PES QM/MM studies, and thus support the use of the latter to determine enzyme reaction mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Computing Potential of the Mean Force Profiles for Ion Permeation Through Channelrhodopsin Chimera, C1C2

Umbrella sampling, coupled with a weighted histogram analysis method (US-WHAM), can be used to construct potentials of mean force (PMFs) for studying the complex ion permeation pathways of membrane transport proteins. Despite the widespread use of US-WHAM, obtaining a physically meaningful PMF can be challenging. Here, we provide a protocol to resolve that issue. Then, we apply that protocol to compute a meaningful PMF for sodium ion permeation through channelrhodopsin chimera, C1C2, for illustration.

59 BASIC BIOLOGICAL SCIENCES↗