1
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Liu Y, Ghosh TK, Lin G, Chen M. Unbiasing Enhanced Sampling on a High-Dimensional Free Energy Surface with a Deep Generative Model. J Phys Chem Lett 2024; 15:3938-3945. [PMID: 38568182 DOI: 10.1021/acs.jpclett.3c03515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/12/2024]
Abstract
Biased enhanced sampling methods that utilize collective variables (CVs) are powerful tools for sampling conformational ensembles. Due to their large intrinsic dimensions, efficiently generating conformational ensembles for complex systems requires enhanced sampling on high-dimensional free energy surfaces. While temperature-accelerated molecular dynamics (TAMD) can trivially adopt many CVs in a simulation, unbiasing the simulation to generate unbiased conformational ensembles requires accurate modeling of a high-dimensional CV probability distribution, which is challenging for traditional density estimation techniques. Here we propose an unbiasing method based on the score-based diffusion model, a deep generative learning method that excels in density estimation across complex data landscapes. We demonstrate that this unbiasing approach, tested on multiple TAMD simulations, significantly outperforms traditional unbiasing methods and can generate accurate unbiased conformational ensembles. With the proposed approach, TAMD can adopt CVs that focus on improving sampling efficiency and the proposed unbiasing method enables accurate evaluation of ensemble averages of important chemical features.
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Affiliation(s)
- Yikai Liu
- Department of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47906, United States
| | - Tushar K Ghosh
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47906, United States
| | - Guang Lin
- Department of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47906, United States
| | - Ming Chen
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47906, United States
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2
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Giese TJ, Ekesan Ş, McCarthy E, Tao Y, York DM. Surface-Accelerated String Method for Locating Minimum Free Energy Paths. J Chem Theory Comput 2024; 20:2058-2073. [PMID: 38367218 PMCID: PMC11059188 DOI: 10.1021/acs.jctc.3c01401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/19/2024]
Abstract
We present a surface-accelerated string method (SASM) to efficiently optimize low-dimensional reaction pathways from the sampling performed with expensive quantum mechanical/molecular mechanical (QM/MM) Hamiltonians. The SASM accelerates the convergence of the path using the aggregate sampling obtained from the current and previous string iterations, whereas approaches like the string method in collective variables (SMCV) or the modified string method in collective variables (MSMCV) update the path only from the sampling obtained from the current iteration. Furthermore, the SASM decouples the number of images used to perform sampling from the number of synthetic images used to represent the path. The path is optimized on the current best estimate of the free energy surface obtained from all available sampling, and the proposed set of new simulations is not restricted to being located along the optimized path. Instead, the umbrella potential placement is chosen to extend the range of the free energy surface and improve the quality of the free energy estimates near the path. In this manner, the SASM is shown to improve the exploration for a minimum free energy pathway in regions where the free energy surface is relatively flat. Furthermore, it improves the quality of the free energy profile when the string is discretized with too few images. We compare the SASM, SMCV, and MSMCV using 3 QM/MM applications: a ribozyme methyltransferase reaction using 2 reaction coordinates, the 2'-O-transphosphorylation reaction of Hammerhead ribozyme using 3 reaction coordinates, and a tautomeric reaction in B-DNA using 5 reaction coordinates. We show that SASM converges the paths using roughly 3 times less sampling than the SMCV and MSMCV methods. All three algorithms have been implemented in the FE-ToolKit package made freely available.
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Affiliation(s)
- Timothy J. Giese
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Şölen Ekesan
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Erika McCarthy
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Yujun Tao
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Darrin M. York
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
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3
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Rydzewski J, Gökdemir T. Learning Markovian dynamics with spectral maps. J Chem Phys 2024; 160:091102. [PMID: 38436438 DOI: 10.1063/5.0189241] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2023] [Accepted: 02/05/2024] [Indexed: 03/05/2024] Open
Abstract
The long-time behavior of many complex molecular systems can often be described by Markovian dynamics in a slow subspace spanned by a few reaction coordinates referred to as collective variables (CVs). However, determining CVs poses a fundamental challenge in chemical physics. Depending on intuition or trial and error to construct CVs can lead to non-Markovian dynamics with long memory effects, hindering analysis. To address this problem, we continue to develop a recently introduced deep-learning technique called spectral map [J. Rydzewski, J. Phys. Chem. Lett. 14, 5216-5220 (2023)]. Spectral map learns slow CVs by maximizing a spectral gap of a Markov transition matrix describing anisotropic diffusion. Here, to represent heterogeneous and multiscale free-energy landscapes with spectral map, we implement an adaptive algorithm to estimate transition probabilities. Through a Markov state model analysis, we validate that spectral map learns slow CVs related to the dominant relaxation timescales and discerns between long-lived metastable states.
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Affiliation(s)
- Jakub Rydzewski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Toruń, Poland
| | - Tuğçe Gökdemir
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Toruń, Poland
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4
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Georgiou A, Vandecasteele H, Bello-Rivas JM, Kevrekidis I. Locating saddle points using gradient extremals on manifolds adaptively revealed as point clouds. CHAOS (WOODBURY, N.Y.) 2023; 33:123108. [PMID: 38048255 PMCID: PMC10697725 DOI: 10.1063/5.0178947] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2023] [Accepted: 11/01/2023] [Indexed: 12/06/2023]
Abstract
Steady states are invaluable in the study of dynamical systems. High-dimensional dynamical systems, due to separation of time scales, often evolve toward a lower dimensional manifold M. We introduce an approach to locate saddle points (and other fixed points) that utilizes gradient extremals on such a priori unknown (Riemannian) manifolds, defined by adaptively sampled point clouds, with local coordinates discovered on-the-fly through manifold learning. The technique, which efficiently biases the dynamical system along a curve (as opposed to exhaustively exploring the state space), requires knowledge of a single minimum and the ability to sample around an arbitrary point. We demonstrate the effectiveness of the technique on the Müller-Brown potential mapped onto an unknown surface (namely, a sphere). Previous work employed a similar algorithmic framework to find saddle points using Newton trajectories and gentlest ascent dynamics; we, therefore, also offer a brief comparison with these methods.
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Affiliation(s)
- A. Georgiou
- Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | | | - J. M. Bello-Rivas
- Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, Maryland 21218, USA
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5
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Ko T, Heindel JP, Guan X, Head-Gordon T, Williams-Young DB, Yang C. Using Diffusion Maps to Analyze Reaction Dynamics for a Hydrogen Combustion Benchmark Dataset. J Chem Theory Comput 2023; 19:5872-5885. [PMID: 37585272 PMCID: PMC10500976 DOI: 10.1021/acs.jctc.3c00426] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2023] [Indexed: 08/18/2023]
Abstract
We use local diffusion maps to assess the quality of two types of collective variables (CVs) for a recently published hydrogen combustion benchmark dataset1 that contains ab initio molecular dynamics (MD) trajectories and normal modes along minimum energy paths. This approach was recently advocated in2 for assessing CVs and analyzing reactions modeled by classical MD simulations. We report the effectiveness of this approach to molecular systems modeled by quantum ab initio MD. In addition to assessing the quality of CVs, we also use global diffusion maps to perform committor analysis as proposed in.2 We show that the committor function obtained from the global diffusion map allows us to identify transition regions of interest in several hydrogen combustion reaction channels.
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Affiliation(s)
- Taehee Ko
- Department
of Mathematics, Penn State University, University Park, Pennsylvania 16802, United States
| | - Joseph P. Heindel
- Kenneth
S. Pitzer Theory Center and Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - Xingyi Guan
- Kenneth
S. Pitzer Theory Center and Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - Teresa Head-Gordon
- Kenneth
S. Pitzer Theory Center and Department of Chemistry, University of California, Berkeley, California 94720, United States
- Departments
of Bioengineering and Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, United States
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - David B. Williams-Young
- Applied
Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Chao Yang
- Applied
Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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6
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Rydzewski J, Chen M, Ghosh TK, Valsson O. Reweighted Manifold Learning of Collective Variables from Enhanced Sampling Simulations. J Chem Theory Comput 2022; 18:7179-7192. [PMID: 36367826 DOI: 10.1021/acs.jctc.2c00873] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
Enhanced sampling methods are indispensable in computational chemistry and physics, where atomistic simulations cannot exhaustively sample the high-dimensional configuration space of dynamical systems due to the sampling problem. A class of such enhanced sampling methods works by identifying a few slow degrees of freedom, termed collective variables (CVs), and enhancing the sampling along these CVs. Selecting CVs to analyze and drive the sampling is not trivial and often relies on chemical intuition. Despite routinely circumventing this issue using manifold learning to estimate CVs directly from standard simulations, such methods cannot provide mappings to a low-dimensional manifold from enhanced sampling simulations, as the geometry and density of the learned manifold are biased. Here, we address this crucial issue and provide a general reweighting framework based on anisotropic diffusion maps for manifold learning that takes into account that the learning data set is sampled from a biased probability distribution. We consider manifold learning methods based on constructing a Markov chain describing transition probabilities between high-dimensional samples. We show that our framework reverts the biasing effect, yielding CVs that correctly describe the equilibrium density. This advancement enables the construction of low-dimensional CVs using manifold learning directly from the data generated by enhanced sampling simulations. We call our framework reweighted manifold learning. We show that it can be used in many manifold learning techniques on data from both standard and enhanced sampling simulations.
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Affiliation(s)
- Jakub Rydzewski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Toruń, Poland
| | - Ming Chen
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Tushar K Ghosh
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Omar Valsson
- Department of Chemistry, University of North Texas, Denton, Texas 76201, United States
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7
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Evans L, Cameron MK, Tiwary P. Computing committors via Mahalanobis diffusion maps with enhanced sampling data. J Chem Phys 2022; 157:214107. [PMID: 36511548 DOI: 10.1063/5.0122990] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/03/2022] Open
Abstract
The study of phenomena such as protein folding and conformational changes in molecules is a central theme in chemical physics. Molecular dynamics (MD) simulation is the primary tool for the study of transition processes in biomolecules, but it is hampered by a huge timescale gap between the processes of interest and atomic vibrations that dictate the time step size. Therefore, it is imperative to combine MD simulations with other techniques in order to quantify the transition processes taking place on large timescales. In this work, the diffusion map with Mahalanobis kernel, a meshless approach for approximating the Backward Kolmogorov Operator (BKO) in collective variables, is upgraded to incorporate standard enhanced sampling techniques, such as metadynamics. The resulting algorithm, which we call the target measure Mahalanobis diffusion map (tm-mmap), is suitable for a moderate number of collective variables in which one can approximate the diffusion tensor and free energy. Imposing appropriate boundary conditions allows use of the approximated BKO to solve for the committor function and utilization of transition path theory to find the reactive current delineating the transition channels and the transition rate. The proposed algorithm, tm-mmap, is tested on the two-dimensional Moro-Cardin two-well system with position-dependent diffusion coefficient and on alanine dipeptide in two collective variables where the committor, the reactive current, and the transition rate are compared to those computed by the finite element method (FEM). Finally, tm-mmap is applied to alanine dipeptide in four collective variables where the use of finite elements is infeasible.
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Affiliation(s)
- L Evans
- Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA
| | - M K Cameron
- Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA
| | - P Tiwary
- Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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8
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Paul TK, Taraphder S. Nonlinear Reaction Coordinate of an Enzyme Catalyzed Proton Transfer Reaction. J Phys Chem B 2022; 126:1413-1425. [PMID: 35138854 DOI: 10.1021/acs.jpcb.1c08760] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
We present an in-depth study on the theoretical calculation of an optimum reaction coordinate as a linear or nonlinear combination of important collective variables (CVs) sampled from an ensemble of reactive transition paths for an intramolecular proton transfer reaction catalyzed by the enzyme human carbonic anhydrase (HCA) II. The linear models are optimized by likelihood maximization for a given number of CVs. The nonlinear models are based on an artificial neural network with the same number of CVs and optimized by minimizing the root-mean-square error in comparison to a training set of committor estimators generated for the given transition. The nonlinear reaction coordinate thus obtained yields the free energy of activation and rate constant as 9.46 kcal mol-1 and 1.25 × 106 s-1, respectively. These estimates are found to be in quantitative agreement with the known experimental results. We have also used an extended autoencoder model to show that a similar analysis can be carried out using a single CV only. The resultant free energies and kinetics of the reaction slightly overestimate the experimental data. The implications of these results are discussed using a detailed microkinetic scheme of the proton transfer reaction catalyzed by HCA II.
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Affiliation(s)
- Tanmoy Kumar Paul
- Department of Chemistry, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
| | - Srabani Taraphder
- Department of Chemistry, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
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9
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Abstract
We use molecular dynamics simulations to study the thermodynamics and kinetics of alanine dipeptide isomerization at the air-water interface. Thermodynamically, we find an affinity of the dipeptide to the interface. This affinity arises from stabilizing intramolecular interactions that become unshielded as the dipeptide is desolvated. Kinetically, we consider the rate of transitions between the αL and β conformations of alanine dipeptide and evaluate it as a continuous function of the distance from the interface using a recent extension of transition path sampling, TPS+U. The rate of isomerization at the Gibbs dividing surface is suppressed relative to the bulk by a factor of 3. Examination of the ensemble of transition states elucidates the role of solvent degrees of freedom in mediating favorable intramolecular interactions along the reaction pathway of isomerization. Near the air-water interface, water is less effective at mediating these intramolecular interactions.
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Affiliation(s)
- Aditya N Singh
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - David T Limmer
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Kavli Energy Nanoscience Institute at Berkeley, Berkeley, California 94720, United States
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10
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Damjanovic J, Murphy JM, Lin YS. CATBOSS: Cluster Analysis of Trajectories Based on Segment Splitting. J Chem Inf Model 2021; 61:5066-5081. [PMID: 34608796 PMCID: PMC8549068 DOI: 10.1021/acs.jcim.1c00598] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Abstract
![]()
Molecular dynamics
(MD) simulations are an exceedingly and increasingly
potent tool for molecular behavior prediction and analysis. However,
the enormous wealth of data generated by these simulations can be
difficult to process and render in a human-readable fashion. Cluster
analysis is a commonly used way to partition data into structurally
distinct states. We present a method that improves on the state of
the art by taking advantage of the temporal information of MD trajectories
to enable more accurate clustering at a lower memory cost. To date,
cluster analysis of MD simulations has generally treated simulation
snapshots as a mere collection of independent data points and attempted
to separate them into different clusters based on structural similarity.
This new method, cluster analysis of trajectories based on segment
splitting (CATBOSS), applies density-peak-based clustering to classify trajectory segments learned by change detection. Applying
the method to a synthetic toy model as well as four real-life data
sets–trajectories of MD simulations of alanine dipeptide and
valine dipeptide as well as two fast-folding proteins–we find
CATBOSS to be robust and highly performant, yielding natural-looking
cluster boundaries and greatly improving clustering resolution. As
the classification of points into segments emphasizes density gaps
in the data by grouping them close to the state means, CATBOSS applied
to the valine dipeptide system is even able to account for a degree
of freedom deliberately omitted from the input data set. We also demonstrate
the potential utility of CATBOSS in distinguishing metastable states
from transition segments as well as promising application to cases
where there is little or no advance knowledge of intrinsic coordinates,
making for a highly versatile analysis tool.
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Affiliation(s)
- Jovan Damjanovic
- Department of Chemistry, Tufts University, Medford, Massachusetts 02155, United States
| | - James M Murphy
- Department of Mathematics, Tufts University, Medford, Massachusetts 02155, United States
| | - Yu-Shan Lin
- Department of Chemistry, Tufts University, Medford, Massachusetts 02155, United States
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11
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Hooft F, Pérez de Alba Ortíz A, Ensing B. Discovering Collective Variables of Molecular Transitions via Genetic Algorithms and Neural Networks. J Chem Theory Comput 2021; 17:2294-2306. [PMID: 33662202 PMCID: PMC8047796 DOI: 10.1021/acs.jctc.0c00981] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2020] [Indexed: 01/13/2023]
Abstract
With the continual improvement of computing hardware and algorithms, simulations have become a powerful tool for understanding all sorts of (bio)molecular processes. To handle the large simulation data sets and to accelerate slow, activated transitions, a condensed set of descriptors, or collective variables (CVs), is needed to discern the relevant dynamics that describes the molecular process of interest. However, proposing an adequate set of CVs that can capture the intrinsic reaction coordinate of the molecular transition is often extremely difficult. Here, we present a framework to find an optimal set of CVs from a pool of candidates using a combination of artificial neural networks and genetic algorithms. The approach effectively replaces the encoder of an autoencoder network with genes to represent the latent space, i.e., the CVs. Given a selection of CVs as input, the network is trained to recover the atom coordinates underlying the CV values at points along the transition. The network performance is used as an estimator of the fitness of the input CVs. Two genetic algorithms optimize the CV selection and the neural network architecture. The successful retrieval of optimal CVs by this framework is illustrated at the hand of two case studies: the well-known conformational change in the alanine dipeptide molecule and the more intricate transition of a base pair in B-DNA from the classic Watson-Crick pairing to the alternative Hoogsteen pairing. Key advantages of our framework include the following: optimal interpretable CVs, avoiding costly calculation of committor or time-correlation functions, and automatic hyperparameter optimization. In addition, we show that applying a time-delay between the network input and output allows for enhanced selection of slow variables. Moreover, the network can also be used to generate molecular configurations of unexplored microstates, for example, for augmentation of the simulation data.
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Affiliation(s)
- Ferry Hooft
- Van ’t Hoff Institute
for Molecular Sciences, AI4Science Laboratory, and Amsterdam Center
for Multiscale Modeling, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Alberto Pérez de Alba Ortíz
- Van ’t Hoff Institute
for Molecular Sciences, AI4Science Laboratory, and Amsterdam Center
for Multiscale Modeling, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Bernd Ensing
- Van ’t Hoff Institute
for Molecular Sciences, AI4Science Laboratory, and Amsterdam Center
for Multiscale Modeling, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
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12
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Chen M. Collective variable-based enhanced sampling and machine learning. THE EUROPEAN PHYSICAL JOURNAL. B 2021; 94:211. [PMID: 34697536 PMCID: PMC8527828 DOI: 10.1140/epjb/s10051-021-00220-w] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2021] [Accepted: 10/03/2021] [Indexed: 05/14/2023]
Abstract
ABSTRACT Collective variable-based enhanced sampling methods have been widely used to study thermodynamic properties of complex systems. Efficiency and accuracy of these enhanced sampling methods are affected by two factors: constructing appropriate collective variables for enhanced sampling and generating accurate free energy surfaces. Recently, many machine learning techniques have been developed to improve the quality of collective variables and the accuracy of free energy surfaces. Although machine learning has achieved great successes in improving enhanced sampling methods, there are still many challenges and open questions. In this perspective, we shall review recent developments on integrating machine learning techniques and collective variable-based enhanced sampling approaches. We also discuss challenges and future research directions including generating kinetic information, exploring high-dimensional free energy surfaces, and efficiently sampling all-atom configurations.
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Affiliation(s)
- Ming Chen
- Department of Chemistry, Purdue University, West Lafayette, IN 47907 USA
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13
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Chiappini M, Patti A, Dijkstra M. Helicoidal dynamics of biaxial curved rods in twist-bend nematic phases unveiled by unsupervised machine learning techniques. Phys Rev E 2020; 102:040601. [PMID: 33212681 DOI: 10.1103/physreve.102.040601] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2020] [Accepted: 09/08/2020] [Indexed: 06/11/2023]
Abstract
Uniaxial rods in a nematic phase diffuse preferentially in the direction parallel to the nematic director n[over ̂]. The nematic director field n[over ̂](r) of a chiral twist-bend nematic (N_{TB}) phase of achiral banana-shaped particles, recently discovered experimentally, displays a heliconical twist of given handedness and periodicity. Using simulations, we investigate the long-time macroscopic diffusion in N_{TB} phases, and find that the predilection of curved rods to diffuse in the direction of the twisting n[over ̂](r) yields a fascinating chiral dynamics along helices, even though achiral curved rods display Brownian motion with a nontrivial rototranslational coupling. We devise a machine learning protocol to characterize the helicoidal particle trajectories, finding that their pitch and radius are determined by the pitch and conical angle of the N_{TB} phase thereby connecting its structural and dynamical properties.
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Affiliation(s)
- Massimiliano Chiappini
- Department of Physics, Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, Utrecht 3584 CC, The Netherlands
| | - Alessandro Patti
- Department of Chemical Engineering and Analytical Science, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - Marjolein Dijkstra
- Department of Physics, Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, Utrecht 3584 CC, The Netherlands
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14
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Gkeka P, Stoltz G, Barati Farimani A, Belkacemi Z, Ceriotti M, Chodera JD, Dinner AR, Ferguson AL, Maillet JB, Minoux H, Peter C, Pietrucci F, Silveira A, Tkatchenko A, Trstanova Z, Wiewiora R, Lelièvre T. Machine Learning Force Fields and Coarse-Grained Variables in Molecular Dynamics: Application to Materials and Biological Systems. J Chem Theory Comput 2020; 16:4757-4775. [PMID: 32559068 PMCID: PMC8312194 DOI: 10.1021/acs.jctc.0c00355] [Citation(s) in RCA: 82] [Impact Index Per Article: 20.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Machine learning encompasses tools and algorithms that are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems. We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling.
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Affiliation(s)
- Paraskevi Gkeka
- Integrated Drug Discovery, Sanofi R&D, 91385 Chilly-Mazarin, France
| | - Gabriel Stoltz
- CERMICS, Ecole des Ponts, Marne-la-Vallée, France
- Matherials Project-Team, Inria Paris, 75012 Paris, France
| | | | - Zineb Belkacemi
- Integrated Drug Discovery, Sanofi R&D, 91385 Chilly-Mazarin, France
- CERMICS, Ecole des Ponts, Marne-la-Vallée, France
| | - Michele Ceriotti
- Laboratory of Computational Science and Modelling, Institute of Materials, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - John D Chodera
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York 10065, United States
| | - Aaron R Dinner
- Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - Andrew L Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, United States
| | | | - Hervé Minoux
- Integrated Drug Discovery, Sanofi R&D, 94403 Vitry-sur-Seine, France
| | | | - Fabio Pietrucci
- UMR CNRS 7590, MNHN, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Université, 75005 Paris, France
| | - Ana Silveira
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York 10065, United States
| | - Alexandre Tkatchenko
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Zofia Trstanova
- School of Mathematics, The University of Edinburgh, Edinburgh EH9 3FD, U.K
| | - Rafal Wiewiora
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York 10065, United States
| | - Tony Lelièvre
- CERMICS, Ecole des Ponts, Marne-la-Vallée, France
- Matherials Project-Team, Inria Paris, 75012 Paris, France
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15
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Sidky H, Chen W, Ferguson AL. Machine learning for collective variable discovery and enhanced sampling in biomolecular simulation. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1737742] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Hythem Sidky
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA
| | - Wei Chen
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Andrew L. Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA
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16
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Trstanova Z, Leimkuhler B, Lelièvre T. Local and global perspectives on diffusion maps in the analysis of molecular systems. Proc Math Phys Eng Sci 2020; 476:20190036. [PMID: 32082050 PMCID: PMC7016551 DOI: 10.1098/rspa.2019.0036] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2019] [Accepted: 11/04/2019] [Indexed: 01/10/2023] Open
Abstract
Diffusion maps approximate the generator of Langevin dynamics from simulation data. They afford a means of identifying the slowly evolving principal modes of high-dimensional molecular systems. When combined with a biasing mechanism, diffusion maps can accelerate the sampling of the stationary Boltzmann-Gibbs distribution. In this work, we contrast the local and global perspectives on diffusion maps, based on whether or not the data distribution has been fully explored. In the global setting, we use diffusion maps to identify metastable sets and to approximate the corresponding committor functions of transitions between them. We also discuss the use of diffusion maps within the metastable sets, formalizing the locality via the concept of the quasi-stationary distribution and justifying the convergence of diffusion maps within a local equilibrium. This perspective allows us to propose an enhanced sampling algorithm. We demonstrate the practical relevance of these approaches both for simple models and for molecular dynamics problems (alanine dipeptide and deca-alanine).
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Affiliation(s)
- Z. Trstanova
- School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
| | - B. Leimkuhler
- School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
| | - T. Lelièvre
- CERMICS (ENPC), INRIA, Marne-la-Vallée 77455, France
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17
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Ma Y, Ferguson AL. Inverse design of self-assembling colloidal crystals with omnidirectional photonic bandgaps. SOFT MATTER 2019; 15:8808-8826. [PMID: 31603182 DOI: 10.1039/c9sm01500k] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Open colloidal lattices possessing omnidirectional photonic bandgaps in the visible or near-visible regime are attractive optical materials the realization of which has remained elusive. We report the use of an inverse design strategy termed landscape engineering that rationally sculpts the free energy self-assembly landscape using evolutionary algorithms to discover anisotropic patchy colloids capable of spontaneously assembling pyrochlore and cubic diamond lattices possessing complete photonic bandgaps. We validate the designs in computer simulations to demonstrate the defect-free formation of these lattices via a two-stage hierarchical assembly mechanism. Our approach demonstrates a principled strategy for the inverse design of self-assembling colloids for the bottom-up fabrication of desired crystal lattices.
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Affiliation(s)
- Yutao Ma
- Pritzker School of Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA.
| | - Andrew L Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA.
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18
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Tan Q, Duan M, Li M, Han L, Huo S. Approximating dynamic proximity with a hybrid geometry energy-based kernel for diffusion maps. J Chem Phys 2019; 151:105101. [PMID: 31521094 DOI: 10.1063/1.5100968] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The diffusion map is a dimensionality reduction method. The reduction coordinates are associated with the leading eigenfunctions of the backward Fokker-Planck operator, providing a dynamic meaning for these coordinates. One of the key factors that affect the accuracy of diffusion map embedding is the dynamic measure implemented in the Gaussian kernel. A common practice in diffusion map study of molecular systems is to approximate dynamic proximity with RMSD (root-mean-square deviation). In this paper, we present a hybrid geometry-energy based kernel. Since high energy-barriers may exist between geometrically similar conformations, taking both RMSD and energy difference into account in the kernel can better describe conformational transitions between neighboring conformations and lead to accurate embedding. We applied our diffusion map method to the β-hairpin of the B1 domain of streptococcal protein G and to Trp-cage. Our results in β-hairpin show that the diffusion map embedding achieves better results with the hybrid kernel than that with the RMSD-based kernel in terms of free energy landscape characterization and a new correlation measure between the cluster center Euclidean distances in the reduced-dimension space and the reciprocals of the total net flow between these clusters. In addition, our diffusion map analysis of the ultralong molecular dynamics trajectory of Trp-cage has provided a unified view of its folding mechanism. These promising results demonstrate the effectiveness of our diffusion map approach in the analysis of the dynamics and thermodynamics of molecular systems. The hybrid geometry-energy criterion could be also useful as a general dynamic measure for other purposes.
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Affiliation(s)
- Qingzhe Tan
- Gustaf H. Carlson School of Chemistry and Biochemistry, Clark University, 950 Main Street, Worcester, Massachusetts 01610, USA
| | - Mojie Duan
- Gustaf H. Carlson School of Chemistry and Biochemistry, Clark University, 950 Main Street, Worcester, Massachusetts 01610, USA
| | - Minghai Li
- Gustaf H. Carlson School of Chemistry and Biochemistry, Clark University, 950 Main Street, Worcester, Massachusetts 01610, USA
| | - Li Han
- Department of Math and Computer Science, Clark University, Worcester, Massachusetts 01610, USA
| | - Shuanghong Huo
- Gustaf H. Carlson School of Chemistry and Biochemistry, Clark University, 950 Main Street, Worcester, Massachusetts 01610, USA
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19
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Chen W, Sidky H, Ferguson AL. Nonlinear discovery of slow molecular modes using state-free reversible VAMPnets. J Chem Phys 2019; 150:214114. [PMID: 31176319 DOI: 10.1063/1.5092521] [Citation(s) in RCA: 63] [Impact Index Per Article: 12.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
The success of enhanced sampling molecular simulations that accelerate along collective variables (CVs) is predicated on the availability of variables coincident with the slow collective motions governing the long-time conformational dynamics of a system. It is challenging to intuit these slow CVs for all but the simplest molecular systems, and their data-driven discovery directly from molecular simulation trajectories has been a central focus of the molecular simulation community to both unveil the important physical mechanisms and drive enhanced sampling. In this work, we introduce state-free reversible VAMPnets (SRV) as a deep learning architecture that learns nonlinear CV approximants to the leading slow eigenfunctions of the spectral decomposition of the transfer operator that evolves equilibrium-scaled probability distributions through time. Orthogonality of the learned CVs is naturally imposed within network training without added regularization. The CVs are inherently explicit and differentiable functions of the input coordinates making them well-suited to use in enhanced sampling calculations. We demonstrate the utility of SRVs in capturing parsimonious nonlinear representations of complex system dynamics in applications to 1D and 2D toy systems where the true eigenfunctions are exactly calculable and to molecular dynamics simulations of alanine dipeptide and the WW domain protein.
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Affiliation(s)
- Wei Chen
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
| | - Hythem Sidky
- Institute for Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA
| | - Andrew L Ferguson
- Institute for Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA
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20
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Schöberl M, Zabaras N, Koutsourelakis PS. Predictive collective variable discovery with deep Bayesian models. J Chem Phys 2019; 150:024109. [DOI: 10.1063/1.5058063] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Markus Schöberl
- Center for Informatics and Computational Science, University of Notre Dame, 311 Cushing Hall, Notre Dame, Indiana 46556, USA
- Continuum Mechanics Group, Technical University of Munich, Boltzmannstraße 15, 85748 Garching, Germany
| | - Nicholas Zabaras
- Center for Informatics and Computational Science, University of Notre Dame, 311 Cushing Hall, Notre Dame, Indiana 46556, USA
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21
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Wang J, Ferguson AL. Recovery of Protein Folding Funnels from Single-Molecule Time Series by Delay Embeddings and Manifold Learning. J Phys Chem B 2018; 122:11931-11952. [PMID: 30428261 DOI: 10.1021/acs.jpcb.8b08800] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The stability and folding of proteins is governed by the underlying single-molecule free energy surface (smFES) mapping the free energy of the molecule as a function of configurational state. Ascertaining the smFES is of great value in understanding and engineering protein structure and function. By integrating tools from dynamical systems theory and nonlinear manifold learning, we describe an approach to reconstruct the multidimensional smFES for a protein from a time series in a single experimentally measurable observable. We employ Takens' delay embeddings to project the time series into a high-dimensional space in which the projected dynamics are C1-equivalent to the true system dynamics and employ diffusion maps to recover a low-dimensional reconstruction of the smFES that is equivalent to the true smFES up to a smooth and invertible transformation. We validate the approach in molecular dynamics simulations of Trp-cage, Villin, and BBA to demonstrate that landscapes recovered from univariate time series in the head-to-tail distance are topologically identical-they precisely preserve the metastable states and folding pathways-and topographically approximate-the free energy barrier heights and well depths are approximately preserved-to the true landscapes determined from complete knowledge of all atomic coordinates. We go on to show that the reconstructed landscapes reliably predict temperature denaturation and identify point mutations and groups of mutations critical to folding. These results demonstrate that protein folding funnels can be reconstructed from experimentally measurable time series and used to understand and engineer folding.
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Affiliation(s)
- Jiang Wang
- Department of Physics , University of Illinois at Urbana-Champaign , 1110 West Green Street , Urbana , Illinois 61801 , United States
| | - Andrew L Ferguson
- Institute for Molecular Engineering , University of Chicago , 5640 South Ellis Avenue , Chicago , Illinois 60637 , United States
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22
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Chen W, Ferguson AL. Molecular enhanced sampling with autoencoders: On-the-fly collective variable discovery and accelerated free energy landscape exploration. J Comput Chem 2018; 39:2079-2102. [PMID: 30368832 DOI: 10.1002/jcc.25520] [Citation(s) in RCA: 113] [Impact Index Per Article: 18.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2017] [Accepted: 06/14/2018] [Indexed: 01/08/2023]
Abstract
Macromolecular and biomolecular folding landscapes typically contain high free energy barriers that impede efficient sampling of configurational space by standard molecular dynamics simulation. Biased sampling can artificially drive the simulation along prespecified collective variables (CVs), but success depends critically on the availability of good CVs associated with the important collective dynamical motions. Nonlinear machine learning techniques can identify such CVs but typically do not furnish an explicit relationship with the atomic coordinates necessary to perform biased sampling. In this work, we employ auto-associative artificial neural networks ("autoencoders") to learn nonlinear CVs that are explicit and differentiable functions of the atomic coordinates. Our approach offers substantial speedups in exploration of configurational space, and is distinguished from existing approaches by its capacity to simultaneously discover and directly accelerate along data-driven CVs. We demonstrate the approach in simulations of alanine dipeptide and Trp-cage, and have developed an open-source and freely available implementation within OpenMM. © 2018 Wiley Periodicals, Inc.
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Affiliation(s)
- Wei Chen
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois, 61801
| | - Andrew L Ferguson
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois, 61801.,Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, 1304 W Green Street, Urbana, Illinois, 61801.,Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois, 61801
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23
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Chen W, Tan AR, Ferguson AL. Collective variable discovery and enhanced sampling using autoencoders: Innovations in network architecture and error function design. J Chem Phys 2018; 149:072312. [PMID: 30134681 DOI: 10.1063/1.5023804] [Citation(s) in RCA: 80] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
Auto-associative neural networks ("autoencoders") present a powerful nonlinear dimensionality reduction technique to mine data-driven collective variables from molecular simulation trajectories. This technique furnishes explicit and differentiable expressions for the nonlinear collective variables, making it ideally suited for integration with enhanced sampling techniques for accelerated exploration of configurational space. In this work, we describe a number of sophistications of the neural network architectures to improve and generalize the process of interleaved collective variable discovery and enhanced sampling. We employ circular network nodes to accommodate periodicities in the collective variables, hierarchical network architectures to rank-order the collective variables, and generalized encoder-decoder architectures to support bespoke error functions for network training to incorporate prior knowledge. We demonstrate our approach in blind collective variable discovery and enhanced sampling of the configurational free energy landscapes of alanine dipeptide and Trp-cage using an open-source plugin developed for the OpenMM molecular simulation package.
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Affiliation(s)
- Wei Chen
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
| | - Aik Rui Tan
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, 1304 West Green Street, Urbana, Illinois 61801, USA
| | - Andrew L Ferguson
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
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24
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Wang J, Gayatri M, Ferguson AL. Coarse-Grained Molecular Simulation and Nonlinear Manifold Learning of Archipelago Asphaltene Aggregation and Folding. J Phys Chem B 2018; 122:6627-6647. [DOI: 10.1021/acs.jpcb.8b01634] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jiang Wang
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, United States
| | - Mohit Gayatri
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, United States
| | - Andrew L. Ferguson
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, United States
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, United States
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, 1304 West Green Street, Urbana, Illinois 61801, United States
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25
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Ferguson AL. Machine learning and data science in soft materials engineering. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:043002. [PMID: 29111979 DOI: 10.1088/1361-648x/aa98bd] [Citation(s) in RCA: 67] [Impact Index Per Article: 11.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
In many branches of materials science it is now routine to generate data sets of such large size and dimensionality that conventional methods of analysis fail. Paradigms and tools from data science and machine learning can provide scalable approaches to identify and extract trends and patterns within voluminous data sets, perform guided traversals of high-dimensional phase spaces, and furnish data-driven strategies for inverse materials design. This topical review provides an accessible introduction to machine learning tools in the context of soft and biological materials by 'de-jargonizing' data science terminology, presenting a taxonomy of machine learning techniques, and surveying the mathematical underpinnings and software implementations of popular tools, including principal component analysis, independent component analysis, diffusion maps, support vector machines, and relative entropy. We present illustrative examples of machine learning applications in soft matter, including inverse design of self-assembling materials, nonlinear learning of protein folding landscapes, high-throughput antimicrobial peptide design, and data-driven materials design engines. We close with an outlook on the challenges and opportunities for the field.
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Affiliation(s)
- Andrew L Ferguson
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, 1304 West Green Street, Urbana, IL 61801, United States of America. Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, IL 61801, United States of America. Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801, United States of America. Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, United States of America. Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, United States of America
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26
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Wang J, Ferguson AL. A Study of the Morphology, Dynamics, and Folding Pathways of Ring Polymers with Supramolecular Topological Constraints Using Molecular Simulation and Nonlinear Manifold Learning. Macromolecules 2018. [DOI: 10.1021/acs.macromol.7b01684] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Jiang Wang
- Department
of Physics, ‡Department of Materials Science and Engineering, and §Department of
Chemical and Biomolecular Engineering, University of Illinois Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Andrew L. Ferguson
- Department
of Physics, ‡Department of Materials Science and Engineering, and §Department of
Chemical and Biomolecular Engineering, University of Illinois Urbana−Champaign, Urbana, Illinois 61801, United States
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27
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Wang J, Ferguson AL. Nonlinear machine learning in simulations of soft and biological materials. MOLECULAR SIMULATION 2017. [DOI: 10.1080/08927022.2017.1400164] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Affiliation(s)
- J. Wang
- Department of Physics, University of Illinois Urbana-Champaign , Urbana, IL, USA
| | - A. L. Ferguson
- Department of Physics, University of Illinois Urbana-Champaign , Urbana, IL, USA
- Department of Materials Science and Engineering, University of Illinois Urbana-Champaign , Urbana, IL, USA
- Department of Chemical and Biomolecular Engineering, University of Illinois Urbana-Champaign , Urbana, IL, USA
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28
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Ferguson AL. BayesWHAM: A Bayesian approach for free energy estimation, reweighting, and uncertainty quantification in the weighted histogram analysis method. J Comput Chem 2017; 38:1583-1605. [PMID: 28475830 DOI: 10.1002/jcc.24800] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2016] [Revised: 11/27/2016] [Accepted: 03/19/2017] [Indexed: 01/18/2023]
Abstract
The weighted histogram analysis method (WHAM) is a powerful approach to estimate molecular free energy surfaces (FES) from biased simulation data. Bayesian reformulations of WHAM are valuable in proving statistically optimal use of the data and providing a transparent means to incorporate regularizing priors and estimate statistical uncertainties. In this work, we develop a fully Bayesian treatment of WHAM to generate statistically optimal FES estimates in any number of biasing dimensions under arbitrary choices of the Bayes prior. Rigorous uncertainty estimates are generated by Metropolis-Hastings sampling from the Bayes posterior. We also report a means to project the FES and its uncertainties into arbitrary auxiliary order parameters beyond those in which biased sampling was conducted. We demonstrate the approaches in applications of alanine dipeptide and the unthreading of a synthetic mimic of the astexin-3 lasso peptide. Open-source MATLAB and Python implementations of our codes are available for free public download. © 2017 Wiley Periodicals, Inc.
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Affiliation(s)
- Andrew L Ferguson
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, 61801.,Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, 61801
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29
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Wang J, Gayatri MA, Ferguson AL. Mesoscale Simulation and Machine Learning of Asphaltene Aggregation Phase Behavior and Molecular Assembly Landscapes. J Phys Chem B 2017; 121:4923-4944. [DOI: 10.1021/acs.jpcb.7b02574] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Affiliation(s)
- Jiang Wang
- Department
of Physics, University of Illinois Urbana−Champaign, 1110 West Green Street, Urbana, Illinois 61801, United States
| | - Mohit A. Gayatri
- Department
of Chemical and Biomolecular Engineering, University of Illinois Urbana−Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, United States
| | - Andrew L. Ferguson
- Department
of Chemical and Biomolecular Engineering, University of Illinois Urbana−Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, United States
- Department
of Materials Science and Engineering, University of Illinois Urbana−Champaign, 1304 West Green Street, Urbana, Illinois 61801, United States
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30
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Hashemian B, Millán D, Arroyo M. Charting molecular free-energy landscapes with an atlas of collective variables. J Chem Phys 2016; 145:174109. [DOI: 10.1063/1.4966262] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Affiliation(s)
- Behrooz Hashemian
- LaCàN, Universitat Politècnica de Catalunya–BarcelonaTech, Barcelona, Spain
| | - Daniel Millán
- LaCàN, Universitat Politècnica de Catalunya–BarcelonaTech, Barcelona, Spain
| | - Marino Arroyo
- LaCàN, Universitat Politècnica de Catalunya–BarcelonaTech, Barcelona, Spain
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31
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Long AW, Phillips CL, Jankowksi E, Ferguson AL. Nonlinear machine learning and design of reconfigurable digital colloids. SOFT MATTER 2016; 12:7119-7135. [PMID: 27498992 DOI: 10.1039/c6sm01156j] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Digital colloids, a cluster of freely rotating "halo" particles tethered to the surface of a central particle, were recently proposed as ultra-high density memory elements for information storage. Rational design of these digital colloids for memory storage applications requires a quantitative understanding of the thermodynamic and kinetic stability of the configurational states within which information is stored. We apply nonlinear machine learning to Brownian dynamics simulations of these digital colloids to extract the low-dimensional intrinsic manifold governing digital colloid morphology, thermodynamics, and kinetics. By modulating the relative size ratio between halo particles and central particles, we investigate the size-dependent configurational stability and transition kinetics for the 2-state tetrahedral (N = 4) and 30-state octahedral (N = 6) digital colloids. We demonstrate the use of this framework to guide the rational design of a memory storage element to hold a block of text that trades off the competing design criteria of memory addressability and volatility.
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Affiliation(s)
- Andrew W Long
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
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32
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Affiliation(s)
- Baron Peters
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106;
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33
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Wang J, Ferguson AL. Nonlinear reconstruction of single-molecule free-energy surfaces from univariate time series. Phys Rev E 2016; 93:032412. [PMID: 27078395 DOI: 10.1103/physreve.93.032412] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2015] [Indexed: 01/27/2023]
Abstract
The stable conformations and dynamical fluctuations of polymers and macromolecules are governed by the underlying single-molecule free energy surface. By integrating ideas from dynamical systems theory with nonlinear manifold learning, we have recovered single-molecule free energy surfaces from univariate time series in a single coarse-grained system observable. Using Takens' Delay Embedding Theorem, we expand the univariate time series into a high dimensional space in which the dynamics are equivalent to those of the molecular motions in real space. We then apply the diffusion map nonlinear manifold learning algorithm to extract a low-dimensional representation of the free energy surface that is diffeomorphic to that computed from a complete knowledge of all system degrees of freedom. We validate our approach in molecular dynamics simulations of a C(24)H(50) n-alkane chain to demonstrate that the two-dimensional free energy surface extracted from the atomistic simulation trajectory is - subject to spatial and temporal symmetries - geometrically and topologically equivalent to that recovered from a knowledge of only the head-to-tail distance of the chain. Our approach lays the foundations to extract empirical single-molecule free energy surfaces directly from experimental measurements.
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Affiliation(s)
- Jiang Wang
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Andrew L Ferguson
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.,Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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34
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Nedialkova LV, Amat MA, Kevrekidis IG, Hummer G. Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions. J Chem Phys 2015; 141:114102. [PMID: 25240340 DOI: 10.1063/1.4893963] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using the helix-coil transitions of alanine pentapeptide as an illustrative example, we demonstrate the use of diffusion maps in the analysis of molecular dynamics simulation trajectories. Diffusion maps and other nonlinear data-mining techniques provide powerful tools to visualize the distribution of structures in conformation space. The resulting low-dimensional representations help in partitioning conformation space, and in constructing Markov state models that capture the conformational dynamics. In an initial step, we use diffusion maps to reduce the dimensionality of the conformational dynamics of Ala5. The resulting pretreated data are then used in a clustering step. The identified clusters show excellent overlap with clusters obtained previously by using the backbone dihedral angles as input, with small--but nontrivial--differences reflecting torsional degrees of freedom ignored in the earlier approach. We then construct a Markov state model describing the conformational dynamics in terms of a discrete-time random walk between the clusters. We show that by combining fuzzy C-means clustering with a transition-based assignment of states, we can construct robust Markov state models. This state-assignment procedure suppresses short-time memory effects that result from the non-Markovianity of the dynamics projected onto the space of clusters. In a comparison with previous work, we demonstrate how manifold learning techniques may complement and enhance informed intuition commonly used to construct reduced descriptions of the dynamics in molecular conformation space.
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Affiliation(s)
- Lilia V Nedialkova
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Miguel A Amat
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Ioannis G Kevrekidis
- Department of Chemical and Biological Engineering and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
| | - Gerhard Hummer
- Department of Theoretical Biophysics, Max Planck Institute of Biophysics, Max-von-Laue-Str. 3, 60438 Frankfurt am Main, Germany
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35
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Atomic-level characterization of transport cycle thermodynamics in the glycerol-3-phosphate:phosphate antiporter. Nat Commun 2015; 6:8393. [PMID: 26417850 PMCID: PMC4598623 DOI: 10.1038/ncomms9393] [Citation(s) in RCA: 68] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2015] [Accepted: 08/18/2015] [Indexed: 01/09/2023] Open
Abstract
Membrane transporters actively translocate their substrate by undergoing large-scale structural transitions between inward- (IF) and outward-facing (OF) states ('alternating-access' mechanism). Despite extensive structural studies, atomic-level mechanistic details of such structural transitions, and as importantly, their coupling to chemical events supplying the energy, remain amongst the most elusive aspects of the function of these proteins. Here we present a quantitative, atomic-level description of the functional thermodynamic cycle for the glycerol-3-phosphate:phosphate antiporter GlpT by using a novel approach in reconstructing the free energy landscape governing the IF↔OF transition along a cyclic transition pathway involving both apo and substrate-bound states. Our results provide a fully atomic description of the complete transport process, offering a structural model for the alternating-access mechanism and substantiating the close coupling between global structural transitions and local chemical events.
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36
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Mansbach RA, Ferguson AL. Machine learning of single molecule free energy surfaces and the impact of chemistry and environment upon structure and dynamics. J Chem Phys 2015; 142:105101. [DOI: 10.1063/1.4914144] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
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37
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Kim SB, Dsilva CJ, Kevrekidis IG, Debenedetti PG. Systematic characterization of protein folding pathways using diffusion maps: Application to Trp-cage miniprotein. J Chem Phys 2015; 142:085101. [DOI: 10.1063/1.4913322] [Citation(s) in RCA: 42] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sang Beom Kim
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Carmeline J. Dsilva
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Ioannis G. Kevrekidis
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
- Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
| | - Pablo G. Debenedetti
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
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38
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Hashemian B, Arroyo M. Topological obstructions in the way of data-driven collective variables. J Chem Phys 2015; 142:044102. [PMID: 25637964 DOI: 10.1063/1.4906425] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Abstract
Nonlinear dimensionality reduction (NLDR) techniques are increasingly used to visualize molecular trajectories and to create data-driven collective variables for enhanced sampling simulations. The success of these methods relies on their ability to identify the essential degrees of freedom characterizing conformational changes. Here, we show that NLDR methods face serious obstacles when the underlying collective variables present periodicities, e.g., arising from proper dihedral angles. As a result, NLDR methods collapse very distant configurations, thus leading to misinterpretations and inefficiencies in enhanced sampling. Here, we identify this largely overlooked problem and discuss possible approaches to overcome it. We also characterize the geometry and topology of conformational changes of alanine dipeptide, a benchmark system for testing new methods to identify collective variables.
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Affiliation(s)
- Behrooz Hashemian
- LaCàN, Universitat Politecnica de Catalunya–BarcelonaTech, Barcelona, Spain
| | - Marino Arroyo
- LaCàN, Universitat Politecnica de Catalunya–BarcelonaTech, Barcelona, Spain
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39
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Abstract
Voltage sensor domains (VSDs) are membrane-bound protein modules that confer voltage sensitivity to membrane proteins. VSDs sense changes in the transmembrane voltage and convert the electrical signal into a conformational change called activation. Activation involves a reorganization of the membrane protein charges that is detected experimentally as transient currents. These so-called gating currents have been investigated extensively within the theoretical framework of so-called discrete-state Markov models (DMMs), whereby activation is conceptualized as a series of transitions across a discrete set of states. Historically, the interpretation of DMM transition rates in terms of transition state theory has been instrumental in shaping our view of the activation process, whose free-energy profile is currently envisioned as composed of a few local minima separated by steep barriers. Here we use atomistic level modeling and well-tempered metadynamics to calculate the configurational free energy along a single transition from first principles. We show that this transition is intrinsically multidimensional and described by a rough free-energy landscape. Remarkably, a coarse-grained description of the system, based on the use of the gating charge as reaction coordinate, reveals a smooth profile with a single barrier, consistent with phenomenological models. Our results bridge the gap between microscopic and macroscopic descriptions of activation dynamics and show that choosing the gating charge as reaction coordinate masks the topological complexity of the network of microstates participating in the transition. Importantly, full characterization of the latter is a prerequisite to rationalize modulation of this process by lipids, toxins, drugs, and genetic mutations.
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40
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Omelyan I, Kovalenko A. Multiple time step molecular dynamics in the optimized isokinetic ensemble steered with the molecular theory of solvation: accelerating with advanced extrapolation of effective solvation forces. J Chem Phys 2014; 139:244106. [PMID: 24387356 DOI: 10.1063/1.4848716] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
We develop efficient handling of solvation forces in the multiscale method of multiple time step molecular dynamics (MTS-MD) of a biomolecule steered by the solvation free energy (effective solvation forces) obtained from the 3D-RISM-KH molecular theory of solvation (three-dimensional reference interaction site model complemented with the Kovalenko-Hirata closure approximation). To reduce the computational expenses, we calculate the effective solvation forces acting on the biomolecule by using advanced solvation force extrapolation (ASFE) at inner time steps while converging the 3D-RISM-KH integral equations only at large outer time steps. The idea of ASFE consists in developing a discrete non-Eckart rotational transformation of atomic coordinates that minimizes the distances between the atomic positions of the biomolecule at different time moments. The effective solvation forces for the biomolecule in a current conformation at an inner time step are then extrapolated in the transformed subspace of those at outer time steps by using a modified least square fit approach applied to a relatively small number of the best force-coordinate pairs. The latter are selected from an extended set collecting the effective solvation forces obtained from 3D-RISM-KH at outer time steps over a broad time interval. The MTS-MD integration with effective solvation forces obtained by converging 3D-RISM-KH at outer time steps and applying ASFE at inner time steps is stabilized by employing the optimized isokinetic Nosé-Hoover chain (OIN) ensemble. Compared to the previous extrapolation schemes used in combination with the Langevin thermostat, the ASFE approach substantially improves the accuracy of evaluation of effective solvation forces and in combination with the OIN thermostat enables a dramatic increase of outer time steps. We demonstrate on a fully flexible model of alanine dipeptide in aqueous solution that the MTS-MD/OIN/ASFE/3D-RISM-KH multiscale method of molecular dynamics steered by effective solvation forces allows huge outer time steps up to tens of picoseconds without affecting the equilibrium and conformational properties, and thus provides a 100- to 500-fold effective speedup in comparison to conventional MD with explicit solvent. With the statistical-mechanical 3D-RISM-KH account for effective solvation forces, the method provides efficient sampling of biomolecular processes with slow and/or rare solvation events such as conformational transitions of hydrated alanine dipeptide with the mean life times ranging from 30 ps up to 10 ns for "flip-flop" conformations, and is particularly beneficial for biomolecular systems with exchange and localization of solvent and ions, ligand binding, and molecular recognition.
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Affiliation(s)
- Igor Omelyan
- National Institute for Nanotechnology, 11421 Saskatchewan Drive, Edmonton, Alberta T6G 2M9, Canada
| | - Andriy Kovalenko
- National Institute for Nanotechnology, 11421 Saskatchewan Drive, Edmonton, Alberta T6G 2M9, Canada
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41
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Hashemian B, Millán D, Arroyo M. Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables. J Chem Phys 2014; 139:214101. [PMID: 24320358 DOI: 10.1063/1.4830403] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes with molecular dynamics simulations. Given their importance, there is need for systematic methods that effectively identify CVs for complex systems. In recent years, nonlinear manifold learning has shown its ability to automatically characterize molecular collective behavior. Unfortunately, these methods fail to provide a differentiable function mapping high-dimensional configurations to their low-dimensional representation, as required in enhanced sampling methods. We introduce a methodology that, starting from an ensemble representative of molecular flexibility, builds smooth and nonlinear data-driven collective variables (SandCV) from the output of nonlinear manifold learning algorithms. We demonstrate the method with a standard benchmark molecule, alanine dipeptide, and show how it can be non-intrusively combined with off-the-shelf enhanced sampling methods, here the adaptive biasing force method. We illustrate how enhanced sampling simulations with SandCV can explore regions that were poorly sampled in the original molecular ensemble. We further explore the transferability of SandCV from a simpler system, alanine dipeptide in vacuum, to a more complex system, alanine dipeptide in explicit water.
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Affiliation(s)
- Behrooz Hashemian
- LaCàN, Universitat Politècnica de Catalunya - BarcelonaTech, Campus Nord, 08034 Barcelona, Spain
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42
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Moradi M, Tajkhorshid E. Computational Recipe for Efficient Description of Large-Scale Conformational Changes in Biomolecular Systems. J Chem Theory Comput 2014; 10:2866-2880. [PMID: 25018675 PMCID: PMC4089915 DOI: 10.1021/ct5002285] [Citation(s) in RCA: 52] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2014] [Indexed: 11/30/2022]
Abstract
Characterizing large-scale structural transitions in biomolecular systems poses major technical challenges to both experimental and computational approaches. On the computational side, efficient sampling of the configuration space along the transition pathway remains the most daunting challenge. Recognizing this issue, we introduce a knowledge-based computational approach toward describing large-scale conformational transitions using (i) nonequilibrium, driven simulations combined with work measurements and (ii) free energy calculations using empirically optimized biasing protocols. The first part is based on designing mechanistically relevant, system-specific reaction coordinates whose usefulness and applicability in inducing the transition of interest are examined using knowledge-based, qualitative assessments along with nonequilirbrium work measurements which provide an empirical framework for optimizing the biasing protocol. The second part employs the optimized biasing protocol resulting from the first part to initiate free energy calculations and characterize the transition quantitatively. Using a biasing protocol fine-tuned to a particular transition not only improves the accuracy of the resulting free energies but also speeds up the convergence. The efficiency of the sampling will be assessed by employing dimensionality reduction techniques to help detect possible flaws and provide potential improvements in the design of the biasing protocol. Structural transition of a membrane transporter will be used as an example to illustrate the workings of the proposed approach.
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Affiliation(s)
- Mahmoud Moradi
- Department of Biochemistry,
Center for Biophysics and Computational Biology, and Beckman Institute
for Advanced Science and Technology, University
of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Emad Tajkhorshid
- Department of Biochemistry,
Center for Biophysics and Computational Biology, and Beckman Institute
for Advanced Science and Technology, University
of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
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43
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Zheng W, Vargiu AV, Vargiu AV, Rohrdanz MA, Carloni P, Clementi C. Molecular recognition of DNA by ligands: roughness and complexity of the free energy profile. J Chem Phys 2014; 139:145102. [PMID: 24116648 DOI: 10.1063/1.4824106] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Understanding the molecular mechanism by which probes and chemotherapeutic agents bind to nucleic acids is a fundamental issue in modern drug design. From a computational perspective, valuable insights are gained by the estimation of free energy landscapes as a function of some collective variables (CVs), which are associated with the molecular recognition event. Unfortunately the choice of CVs is highly non-trivial because of DNA's high flexibility and the presence of multiple association-dissociation events at different locations and/or sliding within the grooves. Here we have applied a modified version of Locally-Scaled Diffusion Map (LSDMap), a nonlinear dimensionality reduction technique for decoupling multiple-timescale dynamics in macromolecular systems, to a metadynamics-based free energy landscape calculated using a set of intuitive CVs. We investigated the binding of the organic drug anthramycin to a DNA 14-mer duplex. By performing an extensive set of metadynamics simulations, we observed sliding of anthramycin along the full-length DNA minor groove, as well as several detachments from multiple sites, including the one identified by X-ray crystallography. As in the case of equilibrium processes, the LSDMap analysis is able to extract the most relevant collective motions, which are associated with the slow processes within the system, i.e., ligand diffusion along the minor groove and dissociation from it. Thus, LSDMap in combination with metadynamics (and possibly every equivalent method) emerges as a powerful method to describe the energetics of ligand binding to DNA without resorting to intuitive ad hoc reaction coordinates.
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Affiliation(s)
- Wenwei Zheng
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
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44
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Sehgal RM, Maroudas D, Ford DM. Phase behavior of the 38-atom Lennard-Jones cluster. J Chem Phys 2014; 140:104312. [DOI: 10.1063/1.4866810] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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45
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Dsilva CJ, Talmon R, Rabin N, Coifman RR, Kevrekidis IG. Nonlinear intrinsic variables and state reconstruction in multiscale simulations. J Chem Phys 2013; 139:184109. [DOI: 10.1063/1.4828457] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
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46
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Zheng W, Rohrdanz MA, Clementi C. Rapid exploration of configuration space with diffusion-map-directed molecular dynamics. J Phys Chem B 2013; 117:12769-76. [PMID: 23865517 PMCID: PMC3808479 DOI: 10.1021/jp401911h] [Citation(s) in RCA: 62] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
The gap between the time scale of interesting behavior in macromolecular systems and that which our computational resources can afford often limits molecular dynamics (MD) from understanding experimental results and predicting what is inaccessible in experiments. In this paper, we introduce a new sampling scheme, named diffusion-map-directed MD (DM-d-MD), to rapidly explore molecular configuration space. The method uses a diffusion map to guide MD on the fly. DM-d-MD can be combined with other methods to reconstruct the equilibrium free energy, and here, we used umbrella sampling as an example. We present results from two systems: alanine dipeptide and alanine-12. In both systems, we gain tremendous speedup with respect to standard MD both in exploring the configuration space and reconstructing the equilibrium distribution. In particular, we obtain 3 orders of magnitude of speedup over standard MD in the exploration of the configurational space of alanine-12 at 300 K with DM-d-MD. The method is reaction coordinate free and minimally dependent on a priori knowledge of the system. We expect wide applications of DM-d-MD to other macromolecular systems in which equilibrium sampling is not affordable by standard MD.
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Affiliation(s)
- Wenwei Zheng
- Department of Chemistry, Rice University, Houston TX 77005
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47
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Sinko W, Miao Y, de Oliveira CAF, McCammon JA. Population based reweighting of scaled molecular dynamics. J Phys Chem B 2013; 117:12759-68. [PMID: 23721224 PMCID: PMC3808002 DOI: 10.1021/jp401587e] [Citation(s) in RCA: 80] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Molecular dynamics simulation using enhanced sampling methods is one of the powerful computational tools used to explore protein conformations and free energy landscapes. Enhanced sampling methods often employ either an increase in temperature or a flattening of the potential energy surface to rapidly sample phase space, and a corresponding reweighting algorithm is used to recover the Boltzmann statistics. However, potential energies of complex biomolecules usually involve large fluctuations on a magnitude of hundreds of kcal/mol despite minimal structural changes during simulation. This leads to noisy reweighting statistics and complicates the obtainment of accurate final results. To overcome this common issue in enhanced conformational sampling, we propose a scaled molecular dynamics method, which modifies the biomolecular potential energy surface and employs a reweighting scheme based on configurational populations. Statistical mechanical theory is applied to derive the reweighting formula, and the canonical ensemble of simulated structures is recovered accordingly. Test simulations on alanine dipeptide and the fast folding polypeptide Chignolin exhibit sufficiently enhanced conformational sampling and accurate recovery of free energy surfaces and thermodynamic properties. The results are comparable to long conventional molecular dynamics simulations and exhibit better recovery of canonical statistics over methods which employ a potential energy term in reweighting.
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Affiliation(s)
- William Sinko
- Biomedical Sciences Program, Department of Pharmacology, University of California San Diego , La Jolla, California 92093-0365, United States
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48
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Duan M, Fan J, Li M, Han L, Huo S. Evaluation of Dimensionality-reduction Methods from Peptide Folding-unfolding Simulations. J Chem Theory Comput 2013; 9:2490-2497. [PMID: 23772182 DOI: 10.1021/ct400052y] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Dimensionality reduction methods have been widely used to study the free energy landscapes and low-free energy pathways of molecular systems. It was shown that the non-linear dimensionality-reduction methods gave better embedding results than the linear methods, such as principal component analysis, in some simple systems. In this study, we have evaluated several non linear methods, locally linear embedding, Isomap, and diffusion maps, as well as principal component analysis from the equilibrium folding/unfolding trajectory of the second β-hairpin of the B1 domain of streptococcal protein G. The CHARMM parm19 polar hydrogen potential function was used. A series of criteria which reflects different aspects of the embedding qualities were employed in the evaluation. Our results show that principal component analysis is not worse than the non-linear ones on this complex system. There is no clear winner in all aspects of the evaluation. Each dimensionality-reduction method has its limitations in a certain aspect. We emphasize that a fair, informative assessment of an embedding result requires a combination of multiple evaluation criteria rather than any single one. Caution should be used when dimensionality-reduction methods are employed, especially when only a few of top embedding dimensions are used to describe the free energy landscape.
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Affiliation(s)
- Mojie Duan
- Gustaf H. Carlson School of Chemistry and Biochemistry, Clark University, Worcester, MA 01610 USA
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49
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50
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Rohrdanz MA, Zheng W, Clementi C. Discovering Mountain Passes via Torchlight: Methods for the Definition of Reaction Coordinates and Pathways in Complex Macromolecular Reactions. Annu Rev Phys Chem 2013; 64:295-316. [DOI: 10.1146/annurev-physchem-040412-110006] [Citation(s) in RCA: 150] [Impact Index Per Article: 13.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
| | - Wenwei Zheng
- Department of Chemistry, Rice University, Houston, Texas 77005;
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