1
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Lee SC, Z Y. Interpretation of autoencoder-learned collective variables using Morse-Smale complex and sublevelset persistent homology: An application on molecular trajectories. J Chem Phys 2024; 160:144104. [PMID: 38591676 DOI: 10.1063/5.0191446] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2023] [Accepted: 03/22/2024] [Indexed: 04/10/2024] Open
Abstract
Dimensionality reduction often serves as the first step toward a minimalist understanding of physical systems as well as the accelerated simulations of them. In particular, neural network-based nonlinear dimensionality reduction methods, such as autoencoders, have shown promising outcomes in uncovering collective variables (CVs). However, the physical meaning of these CVs remains largely elusive. In this work, we constructed a framework that (1) determines the optimal number of CVs needed to capture the essential molecular motions using an ensemble of hierarchical autoencoders and (2) provides topology-based interpretations to the autoencoder-learned CVs with Morse-Smale complex and sublevelset persistent homology. This approach was exemplified using a series of n-alkanes and can be regarded as a general, explainable nonlinear dimensionality reduction method.
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Affiliation(s)
- Shao-Chun Lee
- Department of Nuclear, Plasma, and Radiological Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Y Z
- Department of Nuclear, Plasma, and Radiological Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
- Department of Nuclear Engineering and Radiological Sciences, Department of Materials Science and Engineering, Department of Robotics, and Applied Physics Program, University of Michigan, Ann Arbor, Michigan 48105, USA
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2
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Müllender L, Rizzi A, Parrinello M, Carloni P, Mandelli D. Effective data-driven collective variables for free energy calculations from metadynamics of paths. PNAS NEXUS 2024; 3:pgae159. [PMID: 38665160 PMCID: PMC11044970 DOI: 10.1093/pnasnexus/pgae159] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/05/2023] [Accepted: 04/04/2024] [Indexed: 04/28/2024]
Abstract
A variety of enhanced sampling (ES) methods predict multidimensional free energy landscapes associated with biological and other molecular processes as a function of a few selected collective variables (CVs). The accuracy of these methods is crucially dependent on the ability of the chosen CVs to capture the relevant slow degrees of freedom of the system. For complex processes, finding such CVs is the real challenge. Machine learning (ML) CVs offer, in principle, a solution to handle this problem. However, these methods rely on the availability of high-quality datasets-ideally incorporating information about physical pathways and transition states-which are difficult to access, therefore greatly limiting their domain of application. Here, we demonstrate how these datasets can be generated by means of ES simulations in trajectory space via the metadynamics of paths algorithm. The approach is expected to provide a general and efficient way to generate efficient ML-based CVs for the fast prediction of free energy landscapes in ES simulations. We demonstrate our approach with two numerical examples, a 2D model potential and the isomerization of alanine dipeptide, using deep targeted discriminant analysis as our ML-based CV of choice.
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Affiliation(s)
- Lukas Müllender
- Department of Applied Physics, Science for Life Laboratory, KTH Royal Institute of Technology, SE-171 21 Solna, Sweden
- Computational Biomedicine, Institute of Advanced Simulations IAS-5/Institute for Neuroscience and Medicine INM-9, Forschungszentrum Jülich GmbH, 52428 Jülich, Germany
- Department of Physics, RWTH Aachen University, 52062 Aachen, Germany
| | - Andrea Rizzi
- Computational Biomedicine, Institute of Advanced Simulations IAS-5/Institute for Neuroscience and Medicine INM-9, Forschungszentrum Jülich GmbH, 52428 Jülich, Germany
- Atomistic Simulations, Italian Institute of Technology, 16163 Genova, Italy
| | - Michele Parrinello
- Atomistic Simulations, Italian Institute of Technology, 16163 Genova, Italy
| | - Paolo Carloni
- Computational Biomedicine, Institute of Advanced Simulations IAS-5/Institute for Neuroscience and Medicine INM-9, Forschungszentrum Jülich GmbH, 52428 Jülich, Germany
- Department of Physics, RWTH Aachen University, 52062 Aachen, Germany
- Universitätsklinikum, RWTH Aachen University, 52062 Aachen, Germany
| | - Davide Mandelli
- Computational Biomedicine, Institute of Advanced Simulations IAS-5/Institute for Neuroscience and Medicine INM-9, Forschungszentrum Jülich GmbH, 52428 Jülich, Germany
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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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Fu H, Bian H, Shao X, Cai W. Collective Variable-Based Enhanced Sampling: From Human Learning to Machine Learning. J Phys Chem Lett 2024; 15:1774-1783. [PMID: 38329095 DOI: 10.1021/acs.jpclett.3c03542] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2024]
Abstract
Enhanced-sampling algorithms relying on collective variables (CVs) are extensively employed to study complex (bio)chemical processes that are not amenable to brute-force molecular simulations. The selection of appropriate CVs characterizing the slow movement modes is of paramount importance for reliable and efficient enhanced-sampling simulations. In this Perspective, we first review the application and limitations of CVs obtained from chemical and geometrical intuition. We also introduce path-sampling algorithms, which can identify path-like CVs in a high-dimensional free-energy space. Machine-learning algorithms offer a viable approach to finding suitable CVs by analyzing trajectories from preliminary simulations. We discuss both the performance of machine-learning-derived CVs in enhanced-sampling simulations of experimental models and the challenges involved in applying these CVs to realistic, complex molecular assemblies. Moreover, we provide a prospective view of the potential advancements of machine-learning algorithms for the development of CVs in the field of enhanced-sampling simulations.
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Affiliation(s)
- Haohao Fu
- Research Center for Analytical Sciences, Frontiers Science Center for New Organic Matter, College of Chemistry, Nankai University, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
| | - Hengwei Bian
- Research Center for Analytical Sciences, Frontiers Science Center for New Organic Matter, College of Chemistry, Nankai University, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
| | - Xueguang Shao
- Research Center for Analytical Sciences, Frontiers Science Center for New Organic Matter, College of Chemistry, Nankai University, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
| | - Wensheng Cai
- Research Center for Analytical Sciences, Frontiers Science Center for New Organic Matter, College of Chemistry, Nankai University, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
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5
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Herringer NSM, Dasetty S, Gandhi D, Lee J, Ferguson AL. Permutationally Invariant Networks for Enhanced Sampling (PINES): Discovery of Multimolecular and Solvent-Inclusive Collective Variables. J Chem Theory Comput 2024; 20:178-198. [PMID: 38150421 DOI: 10.1021/acs.jctc.3c00923] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2023]
Abstract
The typically rugged nature of molecular free-energy landscapes can frustrate efficient sampling of the thermodynamically relevant phase space due to the presence of high free-energy barriers. Enhanced sampling techniques can improve phase space exploration by accelerating sampling along particular collective variables (CVs). A number of techniques exist for the data-driven discovery of CVs parametrizing the important large-scale motions of the system. A challenge to CV discovery is learning CVs invariant to the symmetries of the molecular system, frequently rigid translation, rigid rotation, and permutational relabeling of identical particles. Of these, permutational invariance has proved a persistent challenge in frustrating the data-driven discovery of multimolecular CVs in systems of self-assembling particles and solvent-inclusive CVs for solvated systems. In this work, we integrate permutation invariant vector (PIV) featurizations with autoencoding neural networks to learn nonlinear CVs invariant to translation, rotation, and permutation and perform interleaved rounds of CV discovery and enhanced sampling to iteratively expand the sampling of configurational phase space and obtain converged CVs and free-energy landscapes. We demonstrate the permutationally invariant network for enhanced sampling (PINES) approach in applications to the self-assembly of a 13-atom argon cluster, association/dissociation of a NaCl ion pair in water, and hydrophobic collapse of a C45H92 n-pentatetracontane polymer chain. We make the approach freely available as a new module within the PLUMED2 enhanced sampling libraries.
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Affiliation(s)
| | - Siva Dasetty
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Diya Gandhi
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Junhee Lee
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Andrew L Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
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6
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Fu H, Liu H, Xing J, Zhao T, Shao X, Cai W. Deep-Learning-Assisted Enhanced Sampling for Exploring Molecular Conformational Changes. J Phys Chem B 2023; 127:9926-9935. [PMID: 37947397 DOI: 10.1021/acs.jpcb.3c05284] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2023]
Abstract
We present a novel strategy to explore conformational changes and identify stable states of molecular objects, eliminating the need for a priori knowledge. The approach applies a deep learning method to extract information about the movement modes of the molecular object from a short, high-dimensional, and parameter-free preliminary enhanced-sampling simulation. The gathered information is described by a small set of deep-learning-based collective variables (dCVs), which steer the production-enhanced-sampling simulation. Considering the challenge of adequately exploring the configurational space using the low-dimensional, suboptimal dCVs, we incorporate a method designed for ergodic sampling, namely, Gaussian-accelerated molecular dynamics (MD), into the framework of CV-based enhanced sampling. MD simulations on both toy models and nontrivial examples demonstrate the remarkable computational efficiency of the strategy in capturing the conformational changes of molecular objects without a priori knowledge. Specifically, we achieved the blind folding of two fast folders, chignolin and villin, within a time scale of hundreds of nanoseconds and successfully reconstructed the free-energy landscapes that characterize their reversible folding. All in all, the presented strategy holds significant promise for investigating conformational changes in macromolecules, and it is anticipated to find extensive applications in the fields of chemistry and biology.
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Affiliation(s)
- Haohao Fu
- Research Center for Analytical Sciences, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, College of Chemistry, Nankai University, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
| | - Han Liu
- Research Center for Analytical Sciences, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, College of Chemistry, Nankai University, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
| | - Jingya Xing
- Research Center for Analytical Sciences, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, College of Chemistry, Nankai University, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
| | - Tong Zhao
- Research Center for Analytical Sciences, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, College of Chemistry, Nankai University, Tianjin 300071, China
| | - Xueguang Shao
- Research Center for Analytical Sciences, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, College of Chemistry, Nankai University, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
| | - Wensheng Cai
- Research Center for Analytical Sciences, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, College of Chemistry, Nankai University, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
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7
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Bajpai S, Petkov BK, Tong M, Abreu CRA, Nair NN, Tuckerman ME. An interoperable implementation of collective-variable based enhanced sampling methods in extended phase space within the OpenMM package. J Comput Chem 2023; 44:2166-2183. [PMID: 37464902 DOI: 10.1002/jcc.27182] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2023] [Revised: 05/30/2023] [Accepted: 06/06/2023] [Indexed: 07/20/2023]
Abstract
Collective variable (CV)-based enhanced sampling techniques are widely used today for accelerating barrier-crossing events in molecular simulations. A class of these methods, which includes temperature accelerated molecular dynamics (TAMD)/driven-adiabatic free energy dynamics (d-AFED), unified free energy dynamics (UFED), and temperature accelerated sliced sampling (TASS), uses an extended variable formalism to achieve quick exploration of conformational space. These techniques are powerful, as they enhance the sampling of a large number of CVs simultaneously compared to other techniques. Extended variables are kept at a much higher temperature than the physical temperature by ensuring adiabatic separation between the extended and physical subsystems and employing rigorous thermostatting. In this work, we present a computational platform to perform extended phase space enhanced sampling simulations using the open-source molecular dynamics engine OpenMM. The implementation allows users to have interoperability of sampling techniques, as well as employ state-of-the-art thermostats and multiple time-stepping. This work also presents protocols for determining the critical parameters and procedures for reconstructing high-dimensional free energy surfaces. As a demonstration, we present simulation results on the high dimensional conformational landscapes of the alanine tripeptide in vacuo, tetra-N-methylglycine (tetra-sarcosine) peptoid in implicit solvent, and the Trp-cage mini protein in explicit water.
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Affiliation(s)
- Shitanshu Bajpai
- Department of Chemistry, Indian Institute of Technology Kanpur (IITK), Kanpur, India
| | - Brian K Petkov
- Department of Chemistry, New York University (NYU), New York, New York, USA
| | - Muchen Tong
- Department of Chemistry, New York University (NYU), New York, New York, USA
| | - Charlles R A Abreu
- Chemical Engineering Department, Escola de Química, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil
| | - Nisanth N Nair
- Department of Chemistry, Indian Institute of Technology Kanpur (IITK), Kanpur, India
| | - Mark E Tuckerman
- Department of Chemistry, New York University (NYU), New York, New York, USA
- Courant Institute of Mathematical Sciences, New York University (NYU), New York, New York, USA
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai, China
- Simons Center for Computational Physical Chemistry, New York University, New York, New York, USA
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8
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Hendley RS, Zhang L, Bevan MA. Multistate Dynamic Pathways for Anisotropic Colloidal Assembly and Reconfiguration. ACS NANO 2023; 17:20512-20524. [PMID: 37788439 DOI: 10.1021/acsnano.3c07202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/05/2023]
Abstract
We report the controlled interfacial assembly and reconfiguration of rectangular prism colloidal particles between microstructures of varying positional and orientational order including stable, metastable, and transient states. Structurally diverse states are realized by programming time dependent electric fields that mediate dipolar interactions determining particle position, orientation, compression, and chaining. We identify an order parameter set that defines each state as a combination of the positional and orientational order. These metrics are employed as reaction coordinates to capture the microstructure evolution between initial and final states upon field changes. Assembly trajectory manifolds between states in the low-dimensional reaction coordinate space reveal a dynamic pathway map including information about pathway accessibility, reversibility, and kinetics. By navigating the dynamic pathway map, we demonstrate reconfiguration between states on minute time scales, which is practically useful for particle-based materials processing and device responses. Our findings demonstrate a conceptually general approach to discover dynamic pathways as a basis to control assembly and reconfiguration of self-organizing building blocks that respond to global external stimuli.
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Affiliation(s)
- Rachel S Hendley
- Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Lechuan Zhang
- Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Michael A Bevan
- Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, United States
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9
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Nagel D, Sartore S, Stock G. Toward a Benchmark for Markov State Models: The Folding of HP35. J Phys Chem Lett 2023; 14:6956-6967. [PMID: 37504674 DOI: 10.1021/acs.jpclett.3c01561] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/29/2023]
Abstract
Adopting a 300 μs long MD trajectory of the folding of villin headpiece (HP35) by D. E. Shaw Research, we recently constructed a Markov state model (MSM) based on inter-residue contacts. The model reproduces the folding time and predicts that the native basin and unfolded region consist of metastable substates that are structurally well-characterized. Recognizing the need to establish well-defined benchmark problems, we study to what extent and in what sense this MSM can be employed as a reference model. Hence, we test the robustness of the MSM by comparing it to models that use alternative combinations of features, dimensionality reduction methods, and clustering schemes. The study suggests some main characteristics of the folding of HP35 that should be reproduced by other competitive models. Moreover, the discussion reveals which parts of the MSM workflow matter most for the considered problem and illustrates the promises and pitfalls of state-based models for the interpretation of biomolecular simulations.
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Affiliation(s)
- Daniel Nagel
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104 Freiburg, Germany
| | - Sofia Sartore
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104 Freiburg, Germany
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10
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Nagel D, Sartore S, Stock G. Selecting Features for Markov Modeling: A Case Study on HP35. J Chem Theory Comput 2023. [PMID: 37167425 DOI: 10.1021/acs.jctc.3c00240] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
Markov state models represent a popular means to interpret molecular dynamics trajectories in terms of memoryless transitions between metastable conformational states. To provide a mechanistic understanding of the considered biomolecular process, these states should reflect structurally distinct conformations and ensure a time scale separation between fast intrastate and slow interstate dynamics. Adopting the folding of villin headpiece (HP35) as a well-established model problem, here we discuss the selection of suitable input coordinates or "features", such as backbone dihedral angles and interresidue distances. We show that dihedral angles account accurately for the structure of the native energy basin of HP35, while the unfolded region of the free energy landscape and the folding process are best described by tertiary contacts of the protein. To construct a contact-based model, we consider various ways to define and select contact distances and introduce a low-pass filtering of the feature trajectory as well as a correlation-based characterization of states. Relying on input data that faithfully account for the mechanistic origin of the studied process, the states of the resulting Markov model are clearly discriminated by the features, describe consistently the hierarchical structure of the free energy landscape, and─as a consequence─correctly reproduce the slow time scales of the process.
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Affiliation(s)
- Daniel Nagel
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104 Freiburg, Germany
| | - Sofia Sartore
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104 Freiburg, Germany
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11
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Wolf S. Predicting Protein-Ligand Binding and Unbinding Kinetics with Biased MD Simulations and Coarse-Graining of Dynamics: Current State and Challenges. J Chem Inf Model 2023; 63:2902-2910. [PMID: 37133392 DOI: 10.1021/acs.jcim.3c00151] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
The prediction of drug-target binding and unbinding kinetics that occur on time scales between milliseconds and several hours is a prime challenge for biased molecular dynamics simulation approaches. This Perspective gives a concise summary of the theory and the current state-of-the-art of such predictions via biased simulations, of insights into the molecular mechanisms defining binding and unbinding kinetics as well as of the extraordinary challenges predictions of ligand kinetics pose in comparison to binding free energy predictions.
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Affiliation(s)
- Steffen Wolf
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104 Freiburg, Germany
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12
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Shmilovich K, Ferguson AL. Girsanov Reweighting Enhanced Sampling Technique (GREST): On-the-Fly Data-Driven Discovery of and Enhanced Sampling in Slow Collective Variables. J Phys Chem A 2023; 127:3497-3517. [PMID: 37036804 DOI: 10.1021/acs.jpca.3c00505] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
Abstract
Molecular dynamics simulations of microscopic phenomena are limited by the short integration time steps which are required for numerical stability but which limit the practically achievable simulation time scales. Collective variable (CV) enhanced sampling techniques apply biases to predefined collective coordinates to promote barrier crossing, phase space exploration, and sampling of rare events. The efficacy of these techniques is contingent on the selection of good CVs correlated with the molecular motions governing the long-time dynamical evolution of the system. In this work, we introduce Girsanov Reweighting Enhanced Sampling Technique (GREST) as an adaptive sampling scheme that interleaves rounds of data-driven slow CV discovery and enhanced sampling along these coordinates. Since slow CVs are inherently dynamical quantities, a key ingredient in our approach is the use of both thermodynamic and dynamical Girsanov reweighting corrections for rigorous estimation of slow CVs from biased simulation data. We demonstrate our approach on a toy 1D 4-well potential, a simple biomolecular system alanine dipeptide, and the Trp-Leu-Ala-Leu-Leu (WLALL) pentapeptide. In each case GREST learns appropriate slow CVs and drives sampling of all thermally accessible metastable states starting from zero prior knowledge of the system. We make GREST accessible to the community via a publicly available open source Python package.
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Affiliation(s)
- Kirill Shmilovich
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Andrew L Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
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13
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Wolf S, Post M, Stock G. Path separation of dissipation-corrected targeted molecular dynamics simulations of protein-ligand unbinding. J Chem Phys 2023; 158:124106. [PMID: 37003731 DOI: 10.1063/5.0138761] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023] Open
Abstract
Protein-ligand (un)binding simulations are a recent focus of biased molecular dynamics simulations. Such binding and unbinding can occur via different pathways in and out of a binding site. Here, we present a theoretical framework on how to compute kinetics along separate paths and on how to combine the path-specific rates into global binding and unbinding rates for comparison with experimental results. Using dissipation-corrected targeted molecular dynamics in combination with temperature-boosted Langevin equation simulations [S. Wolf et al., Nat. Commun. 11, 2918 (2020)] applied to a two-dimensional model and the trypsin-benzamidine complex as test systems, we assess the robustness of the procedure and discuss the aspects of its practical applicability to predict multisecond kinetics of complex biomolecular systems.
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Affiliation(s)
- Steffen Wolf
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Matthias Post
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
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14
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Rydzewski J. Selecting High-Dimensional Representations of Physical Systems by Reweighted Diffusion Maps. J Phys Chem Lett 2023; 14:2778-2783. [PMID: 36897996 PMCID: PMC10041639 DOI: 10.1021/acs.jpclett.3c00265] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Accepted: 03/08/2023] [Indexed: 06/18/2023]
Abstract
Constructing reduced representations of high-dimensional systems is a fundamental problem in physical chemistry. Many unsupervised machine learning methods can automatically find such low-dimensional representations. However, an often overlooked problem is what high-dimensional representation should be used to describe systems before dimensionality reduction. Here, we address this issue using a recently developed method called the reweighted diffusion map [J. Chem. Theory Comput. 2022, 18, 7179-7192]. We show how high-dimensional representations can be quantitatively selected by exploring the spectral decomposition of Markov transition matrices built from data obtained from standard or enhanced sampling atomistic simulations. We demonstrate the performance of the method in several high-dimensional examples.
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15
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Jin J, Voth GA. Statistical Mechanical Design Principles for Coarse-Grained Interactions across Different Conformational Free Energy Surfaces. J Phys Chem Lett 2023; 14:1354-1362. [PMID: 36728761 PMCID: PMC9940719 DOI: 10.1021/acs.jpclett.2c03844] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2022] [Accepted: 01/27/2023] [Indexed: 06/18/2023]
Abstract
Systematic bottom-up coarse-graining (CG) of molecular systems provides a means to explore different coupled length and time scales while treating the molecular-scale physics at a reduced level. However, the configuration dependence of CG interactions often results in CG models with limited applicability for exploring the parametrized configurations. We propose a statistical mechanical theory to design CG interactions across different configurations and conditions. In order to span wide ranges of conformational space, distinct classical CG free energy surfaces for characteristic configurations are identified using molecular collective variables. The coupling interaction between different CG free energy surfaces can then be systematically determined by analogy to quantum mechanical approaches describing coupled states. The present theory can accurately capture the underlying many-body potentials of mean force in the CG variables for various order parameters applied to liquids, interfaces, and in principle proteins, uncovering the complex nature underlying the coupling interaction and imparting a new protocol for the design of predictive multiscale models.
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Affiliation(s)
| | - Gregory A. Voth
- Department of Chemistry,
Chicago Center for Theoretical Chemistry, Institute for Biophysical
Dynamics, and James Franck Institute, The
University of Chicago, Chicago, Illinois 60637, United States
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16
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Šípka M, Erlebach A, Grajciar L. Constructing Collective Variables Using Invariant Learned Representations. J Chem Theory Comput 2023; 19:887-901. [PMID: 36696574 PMCID: PMC9940718 DOI: 10.1021/acs.jctc.2c00729] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2022] [Indexed: 01/26/2023]
Abstract
On the time scales accessible to atomistic numerical modeling, chemical reactions are considered rare events. Therefore, the atomistic simulations are commonly biased along a low-dimensional representation of a chemical reaction in an atomic structure space, i.e., along the collective variables. However, suitable collective variables are often complicated to guess a priori. We propose a novel method of collective variable discovery based on dimensionality reduction of the atomic representation vectors. These linear-scaling and invariant representations can be either fixed (untrained) or learned by supervised training of the end-to-end machine learning potential. The learned representations are expected to reflect not only the structural but also the energetic features of the system that are transferable to all of the reactive transformation covered by the machine learning potential. We demonstrate our approach on four high-barrier reactions ranging from a simple gas-phase hydrogen jump reaction to complex reactions in periodic models of industrially relevant heterogeneous catalysts. High data efficiency, automatized feature extraction, favorable scaling, and retention of inherent invariances are all properties that are expected to enable fast and largely automatic construction of suitable collective variables even in highly complex reactive scenarios such as reactive/catalytic transformations at solid-liquid interfaces.
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Affiliation(s)
- Martin Šípka
- Department
of Physical and Macromolecular Chemistry, Faculty of Sciences, Charles University, Hlavova 8, 128 43 Prague 2, Czech Republic
- Mathematical
Institute, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague, Czech Republic
| | - Andreas Erlebach
- Department
of Physical and Macromolecular Chemistry, Faculty of Sciences, Charles University, Hlavova 8, 128 43 Prague 2, Czech Republic
| | - Lukáš Grajciar
- Department
of Physical and Macromolecular Chemistry, Faculty of Sciences, Charles University, Hlavova 8, 128 43 Prague 2, Czech Republic
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17
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Lin K, Peng J, Xu C, Gu FL, Lan Z. Trajectory Propagation of Symmetrical Quasi-classical Dynamics with Meyer-Miller Mapping Hamiltonian Using Machine Learning. J Phys Chem Lett 2022; 13:11678-11688. [PMID: 36511563 DOI: 10.1021/acs.jpclett.2c02159] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
The long short-term memory recurrent neural network (LSTM-RNN) approach is applied to realize the trajectory-based nonadiabatic dynamics within the framework of the symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian (MM-SQC). After construction, the LSTM-RNN model allows us to propagate the entire trajectory evolutions of all involved degrees of freedoms (DOFs) from initial conditions. The proposed idea is proven to be reliable and accurate in the simulations of the dynamics of several site-exciton electron-phonon coupling models and three Tully's scattering models. It indicates that the LSTM-RNN model perfectly captures the dynamical information on the trajectory evolution in the MM-SQC dynamics. Our work proposes a novel machine learning approach in the simulation of trajectory-based nonadiabatic dynamic of complex systems with a large number of DOFs.
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Affiliation(s)
- Kunni Lin
- School of Chemistry, South China Normal University, Guangzhou 510006, P. R. China
- MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, P. R. China
| | - Jiawei Peng
- School of Chemistry, South China Normal University, Guangzhou 510006, P. R. China
- MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, P. R. China
| | - Chao Xu
- MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, P. R. China
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety, School of Environment, South China Normal University, Guangzhou 510006, P. R. China
| | - Feng Long Gu
- MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, P. R. China
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety, School of Environment, South China Normal University, Guangzhou 510006, P. R. China
| | - Zhenggang Lan
- MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, P. R. China
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety, School of Environment, South China Normal University, Guangzhou 510006, P. R. China
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18
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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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19
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Lin K, Peng J, Xu C, Gu FL, Lan Z. Automatic Evolution of Machine-Learning-Based Quantum Dynamics with Uncertainty Analysis. J Chem Theory Comput 2022; 18:5837-5855. [DOI: 10.1021/acs.jctc.2c00702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Kunni Lin
- School of Chemistry, South China Normal University, Guangzhou510006, P. R. China
- MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou510006, P. R. China
| | - Jiawei Peng
- School of Chemistry, South China Normal University, Guangzhou510006, P. R. China
- MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou510006, P. R. China
| | - Chao Xu
- MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou510006, P. R. China
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety, School of Environment, South China Normal University, Guangzhou510006, P. R. China
| | - Feng Long Gu
- MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou510006, P. R. China
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety, School of Environment, South China Normal University, Guangzhou510006, P. R. China
| | - Zhenggang Lan
- MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou510006, P. R. China
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety, School of Environment, South China Normal University, Guangzhou510006, P. R. China
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20
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Zhu Y, Peng J, Kang X, Xu C, Lan Z. The principal component analysis of the ring deformation in the nonadiabatic surface hopping dynamics. Phys Chem Chem Phys 2022; 24:24362-24382. [PMID: 36178471 DOI: 10.1039/d2cp03323b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The analysis of the leading active molecular motions in the on-the-fly trajectory surface hopping simulation provides the essential information to understand the geometric evolution in nonadiabatic dynamics. When the ring deformation is involved, the identification of the key active coordinates becomes challenging. A "hierarchical" protocol based on the dimensionality reduction and clustering approaches is proposed for the automatic analysis of the ring deformation in the nonadiabatic molecular dynamics. The representative system keto isocytosine is taken as the prototype to illustrate this protocol. The results indicate that the current hierarchical analysis protocol is a powerful way to clearly clarify both the major and minor active molecular motions of the ring distortion in nonadiabatic dynamics.
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Affiliation(s)
- Yifei Zhu
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety, School of Environment, South China Normal University, Guangzhou 510006, P. R. China. .,MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, P. R. China
| | - Jiawei Peng
- MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, P. R. China.,School of Chemistry, South China Normal University, Guangzhou 510006, P. R. China
| | - Xu Kang
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety, School of Environment, South China Normal University, Guangzhou 510006, P. R. China. .,MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, P. R. China
| | - Chao Xu
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety, School of Environment, South China Normal University, Guangzhou 510006, P. R. China. .,MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, P. R. China
| | - Zhenggang Lan
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety, School of Environment, South China Normal University, Guangzhou 510006, P. R. China. .,MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, P. R. China
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21
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Bray S, Tänzel V, Wolf S. Ligand Unbinding Pathway and Mechanism Analysis Assisted by Machine Learning and Graph Methods. J Chem Inf Model 2022; 62:4591-4604. [PMID: 36176219 DOI: 10.1021/acs.jcim.2c00634] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We present two methods to reveal protein-ligand unbinding mechanisms in biased unbinding simulations by clustering trajectories into ensembles representing unbinding paths. The first approach is based on a contact principal component analysis for reducing the dimensionality of the input data, followed by identification of unbinding paths and training a machine learning model for trajectory clustering. The second approach clusters trajectories according to their pairwise mean Euclidean distance employing the neighbor-net algorithm, which takes into account input data bias in the distances set and is superior to dendrogram construction. Finally, we describe a more complex case where the reaction coordinate relevant for path identification is a single intraligand hydrogen bond, highlighting the challenges involved in unbinding path reaction coordinate detection.
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Affiliation(s)
- Simon Bray
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104Freiburg, Germany.,Bioinformatics Group, Institute of Informatics, University of Freiburg, 79110Freiburg, Germany
| | - Victor Tänzel
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104Freiburg, Germany
| | - Steffen Wolf
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104Freiburg, Germany
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22
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Diez G, Nagel D, Stock G. Correlation-Based Feature Selection to Identify Functional Dynamics in Proteins. J Chem Theory Comput 2022; 18:5079-5088. [PMID: 35793551 DOI: 10.1021/acs.jctc.2c00337] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
To interpret molecular dynamics simulations of biomolecular systems, systematic dimensionality reduction methods are commonly employed. Among others, this includes principal component analysis (PCA) and time-lagged independent component analysis (TICA), which aim to maximize the variance and the time scale of the first components, respectively. A crucial first step of such an analysis is the identification of suitable and relevant input coordinates (the so-called features), such as backbone dihedral angles and interresidue distances. As typically only a small subset of those coordinates is involved in a specific biomolecular process, it is important to discard the remaining uncorrelated motions or weakly correlated noise coordinates. This is because they may exhibit large amplitudes or long time scales and therefore will be erroneously considered important by PCA and TICA, respectively. To discriminate collective motions underlying functional dynamics from uncorrelated motions, the correlation matrix of the input coordinates is block-diagonalized by a clustering method. This strategy avoids possible bias due to presumed functional observables and conformational states or variation principles that maximize variance or time scales. Considering several linear and nonlinear correlation measures and various clustering algorithms, it is shown that the combination of linear correlation and the Leiden community detection algorithm yields excellent results for all considered model systems. These include the functional motion of T4 lysozyme to demonstrate the successful identification of collective motion, as well as the folding of the villin headpiece to highlight the physical interpretation of the correlated motions in terms of a functional mechanism.
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Affiliation(s)
- Georg Diez
- Biomolecular Dynamics, Institute of Physics, Albert-Ludwigs-Universität, 79104 Freiburg, Germany
| | - Daniel Nagel
- Biomolecular Dynamics, Institute of Physics, Albert-Ludwigs-Universität, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, Albert-Ludwigs-Universität, 79104 Freiburg, Germany
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23
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Wang W, Poe D, Yang Y, Hyatt T, Xing J. Epithelial-to-mesenchymal transition proceeds through directional destabilization of multidimensional attractor. eLife 2022; 11:74866. [PMID: 35188459 PMCID: PMC8920502 DOI: 10.7554/elife.74866] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2021] [Accepted: 02/06/2022] [Indexed: 11/13/2022] Open
Abstract
How a cell changes from one stable phenotype to another one is a fundamental problem in developmental and cell biology. Mathematically, a stable phenotype corresponds to a stable attractor in a generally multi-dimensional state space, which needs to be destabilized so the cell relaxes to a new attractor. Two basic mechanisms for destabilizing a stable fixed point, pitchfork and saddle-node bifurcations, have been extensively studied theoretically; however, direct experimental investigation at the single-cell level remains scarce. Here, we performed live cell imaging studies and analyses in the framework of dynamical systems theories on epithelial-to-mesenchymal transition (EMT). While some mechanistic details remain controversial, EMT is a cell phenotypic transition (CPT) process central to development and pathology. Through time-lapse imaging we recorded single cell trajectories of human A549/Vim-RFP cells undergoing EMT induced by different concentrations of exogenous TGF-β in a multi-dimensional cell feature space. The trajectories clustered into two distinct groups, indicating that the transition dynamics proceeds through parallel paths. We then reconstructed the reaction coordinates and the corresponding quasi-potentials from the trajectories. The potentials revealed a plausible mechanism for the emergence of the two paths where the original stable epithelial attractor collides with two saddle points sequentially with increased TGF-β concentration, and relaxes to a new one. Functionally, the directional saddle-node bifurcation ensures a CPT proceeds towards a specific cell type, as a mechanistic realization of the canalization idea proposed by Waddington. Cells with the same genetic code can take on many different formss, or phenotypes, which have distinct roles and appearances. Sometimes cells switch from one phenotype to another as part of healthy growth or during disease. One such change is the epithelial-to-mesenchymal transition (EMT), which is involved in fetal development, wound healing and the spread of cancer cells. During EMT, closely connected epithelial cells detach from one another and change into mesenchymal cells that are able to migrate. Cells undergo a number of changes during this transition; however, the path they take to reach their new form is not entirely clear. For instance, do all cells follow the same route, or are there multiple ways that cells can shift from one state to the next? To address this question, Wang et al. studied individual lung cancer cells that had been treated with a protein that drives EMT. The cells were then imaged at regular intervals over the course of two to three days to see how they changed in response to different concentrations of protein. Using a mathematical analysis designed to study chemical reactions, Wang et al. showed that the cells transform into the mesenchymal phenotype through two main routes. This result suggests that attempts to prevent EMT, in cancer treatment for instance, would require blocking both paths taken by the cells. This information could be useful for biomedical researchers trying to regulate the EMT process. The quantitative approach of this study could also help physicists and mathematicians study other types of transition that occur in biology.
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Affiliation(s)
- Weikang Wang
- Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, United States
| | - Dante Poe
- Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, United States
| | - Yaxuan Yang
- Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, United States
| | - Thomas Hyatt
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, United States
| | - Jianhua Xing
- Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, United States
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24
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Bonati L, Piccini G, Parrinello M. Deep learning the slow modes for rare events sampling. Proc Natl Acad Sci U S A 2021; 118:e2113533118. [PMID: 34706940 PMCID: PMC8612227 DOI: 10.1073/pnas.2113533118] [Citation(s) in RCA: 76] [Impact Index Per Article: 25.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 09/19/2021] [Indexed: 02/08/2023] Open
Abstract
The development of enhanced sampling methods has greatly extended the scope of atomistic simulations, allowing long-time phenomena to be studied with accessible computational resources. Many such methods rely on the identification of an appropriate set of collective variables. These are meant to describe the system's modes that most slowly approach equilibrium under the action of the sampling algorithm. Once identified, the equilibration of these modes is accelerated by the enhanced sampling method of choice. An attractive way of determining the collective variables is to relate them to the eigenfunctions and eigenvalues of the transfer operator. Unfortunately, this requires knowing the long-term dynamics of the system beforehand, which is generally not available. However, we have recently shown that it is indeed possible to determine efficient collective variables starting from biased simulations. In this paper, we bring the power of machine learning and the efficiency of the recently developed on the fly probability-enhanced sampling method to bear on this approach. The result is a powerful and robust algorithm that, given an initial enhanced sampling simulation performed with trial collective variables or generalized ensembles, extracts transfer operator eigenfunctions using a neural network ansatz and then accelerates them to promote sampling of rare events. To illustrate the generality of this approach, we apply it to several systems, ranging from the conformational transition of a small molecule to the folding of a miniprotein and the study of materials crystallization.
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Affiliation(s)
- Luigi Bonati
- Department of Physics, Eidgenössische Technische Hochschule (ETH) Zürich, 8092 Zürich, Switzerland;
- Atomistic Simulations, Italian Institute of Technology, 16163 Genova, Italy
| | | | - Michele Parrinello
- Atomistic Simulations, Italian Institute of Technology, 16163 Genova, Italy;
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25
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Lin K, Hu D, Peng J, Xu C, Gu FL, Lan Z. Prediction of the excited-state reaction channels in photo-induced processes of nitrofurantoin using first-principle calculations and dynamics simulations. CHEMOSPHERE 2021; 281:130831. [PMID: 34289597 DOI: 10.1016/j.chemosphere.2021.130831] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2021] [Revised: 03/25/2021] [Accepted: 05/06/2021] [Indexed: 06/13/2023]
Abstract
The understanding of the photochemistry of antibiotic compounds is important because it gives the direct information on the possible environmental pollution caused by them. Due to their large size, the theoretical studies of their excited-state reactions are rather challenging. In current work, we combined the on-the-fly trajectory surface-hopping dynamics, conical-intersection optimizations and excited-state pathway calculations to study the photochemistry of the trans-isomer of nitrofurantoin, a widely-used drug to treat the urinary tract infections. The dynamics-then-pathway approach was taken. First the trajectory surface hopping dynamics at the state-averaged complete-active-space self-consistent-field (SA-CASSCF) level with small active space and small basis sets were run. Second, the minimum-energy conical-intersection optimizations were performed. Finally the excited pathways from the Frank-Condon region to different reaction channels were built at the multi-state multi-reference second-order perturbation (MS-CASPT2) level with large active space and large basis set. Several possible channels responsible for the photo-induced reaction mechanism of the trans-nitrofurantoin were obtained, including the cleavage of the NO bond of the NO2 moiety, the photoisomerization at the central CN bond, and other internal conversion channels. Our findings give some preliminary explanations on available experimental observations. It is also demonstrates that the current theoretical approach is a powerful tool to explore the excited-state reactions in the photochemistry of media-sized or large-sized drug compounds.
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Affiliation(s)
- Kunni Lin
- Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education, School of Chemistry, South China Normal University, Guangzhou, 510006, PR China
| | - Deping Hu
- Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety and MOE Key Laboratory of Environmental Theoretical Chemistry, SCNU Environmental Research Institute, School of Environment, South China Normal University, Guangzhou, 510006, PR China
| | - Jiawei Peng
- Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety and MOE Key Laboratory of Environmental Theoretical Chemistry, SCNU Environmental Research Institute, School of Environment, South China Normal University, Guangzhou, 510006, PR China
| | - Chao Xu
- Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education, School of Chemistry, South China Normal University, Guangzhou, 510006, PR China
| | - Feng Long Gu
- Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education, School of Chemistry, South China Normal University, Guangzhou, 510006, PR China.
| | - Zhenggang Lan
- Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety and MOE Key Laboratory of Environmental Theoretical Chemistry, SCNU Environmental Research Institute, School of Environment, South China Normal University, Guangzhou, 510006, PR China.
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26
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Glielmo A, Husic BE, Rodriguez A, Clementi C, Noé F, Laio A. Unsupervised Learning Methods for Molecular Simulation Data. Chem Rev 2021; 121:9722-9758. [PMID: 33945269 PMCID: PMC8391792 DOI: 10.1021/acs.chemrev.0c01195] [Citation(s) in RCA: 116] [Impact Index Per Article: 38.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2020] [Indexed: 12/21/2022]
Abstract
Unsupervised learning is becoming an essential tool to analyze the increasingly large amounts of data produced by atomistic and molecular simulations, in material science, solid state physics, biophysics, and biochemistry. In this Review, we provide a comprehensive overview of the methods of unsupervised learning that have been most commonly used to investigate simulation data and indicate likely directions for further developments in the field. In particular, we discuss feature representation of molecular systems and present state-of-the-art algorithms of dimensionality reduction, density estimation, and clustering, and kinetic models. We divide our discussion into self-contained sections, each discussing a specific method. In each section, we briefly touch upon the mathematical and algorithmic foundations of the method, highlight its strengths and limitations, and describe the specific ways in which it has been used-or can be used-to analyze molecular simulation data.
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Affiliation(s)
- Aldo Glielmo
- International
School for Advanced Studies (SISSA) 34014 Trieste, Italy
| | - Brooke E. Husic
- Freie
Universität Berlin, Department of Mathematics
and Computer Science, 14195 Berlin, Germany
| | - Alex Rodriguez
- International Centre for Theoretical
Physics (ICTP), Condensed Matter and Statistical
Physics Section, 34100 Trieste, Italy
| | - Cecilia Clementi
- Freie
Universität Berlin, Department for
Physics, 14195 Berlin, Germany
- Rice
University Houston, Department of Chemistry, Houston, Texas 77005, United States
| | - Frank Noé
- Freie
Universität Berlin, Department of Mathematics
and Computer Science, 14195 Berlin, Germany
- Freie
Universität Berlin, Department for
Physics, 14195 Berlin, Germany
- Rice
University Houston, Department of Chemistry, Houston, Texas 77005, United States
| | - Alessandro Laio
- International
School for Advanced Studies (SISSA) 34014 Trieste, Italy
- International Centre for Theoretical
Physics (ICTP), Condensed Matter and Statistical
Physics Section, 34100 Trieste, Italy
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27
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Musil F, Grisafi A, Bartók AP, Ortner C, Csányi G, Ceriotti M. Physics-Inspired Structural Representations for Molecules and Materials. Chem Rev 2021; 121:9759-9815. [PMID: 34310133 DOI: 10.1021/acs.chemrev.1c00021] [Citation(s) in RCA: 131] [Impact Index Per Article: 43.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic-scale structure of matter and its properties, involves transforming the Cartesian coordinates of the atoms into a suitable representation. The development of atomic-scale representations has played, and continues to play, a central role in the success of machine-learning methods for chemistry and materials science. This review summarizes the current understanding of the nature and characteristics of the most commonly used structural and chemical descriptions of atomistic structures, highlighting the deep underlying connections between different frameworks and the ideas that lead to computationally efficient and universally applicable models. It emphasizes the link between properties, structures, their physical chemistry, and their mathematical description, provides examples of recent applications to a diverse set of chemical and materials science problems, and outlines the open questions and the most promising research directions in the field.
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Affiliation(s)
- Felix Musil
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.,National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Andrea Grisafi
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Albert P Bartók
- Department of Physics and Warwick Centre for Predictive Modelling, School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Christoph Ortner
- University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
| | - Gábor Csányi
- Engineering Laboratory, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, United Kingdom
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.,National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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28
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Lickert B, Wolf S, Stock G. Data-Driven Langevin Modeling of Nonequilibrium Processes. J Phys Chem B 2021; 125:8125-8136. [PMID: 34270245 DOI: 10.1021/acs.jpcb.1c03828] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Given nonstationary data from molecular dynamics simulations, a Markovian Langevin model is constructed that aims to reproduce the time evolution of the underlying process. While at equilibrium the free energy landscape is sampled, nonequilibrium processes can be associated with a biased energy landscape, which accounts for finite sampling effects and external driving. When the data-driven Langevin equation (dLE) approach [Phys. Rev. Lett. 2015, 115, 050602] is extended to the modeling of nonequilibrium processes, an efficient way to calculate multidimensional Langevin fields is outlined. The dLE is shown to correctly account for various nonequilibrium processes, including the enforced dissociation of sodium chloride in water, the pressure-jump induced nucleation of a liquid of hard spheres, and the conformational dynamics of a helical peptide sampled from nonstationary short trajectories.
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Affiliation(s)
- Benjamin Lickert
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Steffen Wolf
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
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29
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Xi K, Hu Z, Wu Q, Wei M, Qian R, Zhu L. Assessing the Performance of Traveling-salesman based Automated Path Searching (TAPS) on Complex Biomolecular Systems. J Chem Theory Comput 2021; 17:5301-5311. [PMID: 34270241 DOI: 10.1021/acs.jctc.1c00182] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Though crucial for understanding the function of large biomolecular systems, locating the minimum free energy paths (MFEPs) between their key conformational states is far from trivial due to their high-dimensional nature. Most existing path-searching methods require a static collective variable space as input, encoding intuition or prior knowledge of the transition mechanism. Such information is, however, hardly available a priori and expensive to validate. To alleviate this issue, we have previously introduced a Traveling-salesman based Automated Path Searching method (TAPS) and demonstrated its efficiency on simple peptide systems. Having implemented a parallel version of this method, here we assess the performance of TAPS on three realistic systems (tens to hundreds of residues) in explicit solvents. We show that TAPS successfully located the MFEP for the ground/excited state transition of the T4 lysozyme L99A variant, consistent with previous findings. TAPS also helped identifying the important role of the two polar contacts in directing the loop-in/loop-out transition of the mitogen-activated protein kinase kinase (MEK1), which explained previous mutant experiments. Remarkably, at a minimal cost of 126 ns sampling, TAPS revealed that the Ltn40/Ltn10 transition of lymphotactin needs no complete unfolding/refolding of its β-sheets and that five polar contacts are sufficient to stabilize the various partially unfolded intermediates along the MFEP. These results present TAPS as a general and promising tool for studying the functional dynamics of complex biomolecular systems.
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Affiliation(s)
- Kun Xi
- Warshel Institute for Computational Biology, School of Life and Health Sciences, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, P. R. China.,School of Chemistry and Materials Science, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China
| | - Zhenquan Hu
- Warshel Institute for Computational Biology, School of Life and Health Sciences, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, P. R. China.,School of Chemistry and Materials Science, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China
| | - Qiang Wu
- School of Science and Engineering, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, P. R. China
| | - Meihan Wei
- Warshel Institute for Computational Biology, School of Life and Health Sciences, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, P. R. China
| | - Runtong Qian
- Warshel Institute for Computational Biology, School of Life and Health Sciences, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, P. R. China
| | - Lizhe Zhu
- Warshel Institute for Computational Biology, School of Life and Health Sciences, The Chinese University of Hong Kong (Shenzhen), Shenzhen, Guangdong 518172, P. R. China
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30
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Computational methods for exploring protein conformations. Biochem Soc Trans 2021; 48:1707-1724. [PMID: 32756904 PMCID: PMC7458412 DOI: 10.1042/bst20200193] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2020] [Revised: 07/07/2020] [Accepted: 07/09/2020] [Indexed: 12/13/2022]
Abstract
Proteins are dynamic molecules that can transition between a potentially wide range of structures comprising their conformational ensemble. The nature of these conformations and their relative probabilities are described by a high-dimensional free energy landscape. While computer simulation techniques such as molecular dynamics simulations allow characterisation of the metastable conformational states and the transitions between them, and thus free energy landscapes, to be characterised, the barriers between states can be high, precluding efficient sampling without substantial computational resources. Over the past decades, a dizzying array of methods have emerged for enhancing conformational sampling, and for projecting the free energy landscape onto a reduced set of dimensions that allow conformational states to be distinguished, known as collective variables (CVs), along which sampling may be directed. Here, a brief description of what biomolecular simulation entails is followed by a more detailed exposition of the nature of CVs and methods for determining these, and, lastly, an overview of the myriad different approaches for enhancing conformational sampling, most of which rely upon CVs, including new advances in both CV determination and conformational sampling due to machine learning.
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31
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Bause M, Bereau T. Reweighting non-equilibrium steady-state dynamics along collective variables. J Chem Phys 2021; 154:134105. [PMID: 33832234 DOI: 10.1063/5.0042972] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
Computer simulations generate microscopic trajectories of complex systems at a single thermodynamic state point. We recently introduced a Maximum Caliber (MaxCal) approach for dynamical reweighting. Our approach mapped these trajectories to a Markovian description on the configurational coordinates and reweighted path probabilities as a function of external forces. Trajectory probabilities can be dynamically reweighted both from and to equilibrium or non-equilibrium steady states. As the system's dimensionality increases, an exhaustive description of the microtrajectories becomes prohibitive-even with a Markovian assumption. Instead, we reduce the dimensionality of the configurational space to collective variables (CVs). Going from configurational to CV space, we define local entropy productions derived from configurationally averaged mean forces. The entropy production is shown to be a suitable constraint on MaxCal for non-equilibrium steady states expressed as a function of CVs. We test the reweighting procedure on two systems: a particle subject to a two-dimensional potential and a coarse-grained peptide. Our CV-based MaxCal approach expands dynamical reweighting to larger systems, for both static and dynamical properties, and across a large range of driving forces.
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Affiliation(s)
- Marius Bause
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
| | - Tristan Bereau
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
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32
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Peng J, Xie Y, Hu D, Lan Z. Analysis of bath motion in MM-SQC dynamics via dimensionality reduction approach: Principal component analysis. J Chem Phys 2021; 154:094122. [PMID: 33685149 DOI: 10.1063/5.0039743] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The system-plus-bath model is an important tool to understand the nonadiabatic dynamics of large molecular systems. Understanding the collective motion of a large number of bath modes is essential for revealing their key roles in the overall dynamics. Here, we applied principal component analysis (PCA) to investigate the bath motion in the basis of a large dataset generated from the symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian nonadiabatic dynamics for the excited-state energy transfer in the Frenkel-exciton model. The PCA method clearly elucidated that two types of bath modes, which either display strong vibronic coupling or have frequencies close to that of the electronic transition, are important to the nonadiabatic dynamics. These observations were fully consistent with the physical insights. The conclusions were based on the PCA of the trajectory data and did not involve significant pre-defined physical knowledge. The results show that the PCA approach, which is one of the simplest unsupervised machine learning dimensionality reduction methods, is a powerful one for analyzing complicated nonadiabatic dynamics in the condensed phase with many degrees of freedom.
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Affiliation(s)
- Jiawei Peng
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety & MOE Key Laboratory of Theoretical Chemistry of Environment, South China Normal University, Guangzhou 510006, China
| | - Yu Xie
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety & MOE Key Laboratory of Theoretical Chemistry of Environment, South China Normal University, Guangzhou 510006, China
| | - Deping Hu
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety & MOE Key Laboratory of Theoretical Chemistry of Environment, South China Normal University, Guangzhou 510006, China
| | - Zhenggang Lan
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety & MOE Key Laboratory of Theoretical Chemistry of Environment, South China Normal University, Guangzhou 510006, China
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33
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Lickert B, Stock G. Modeling non-Markovian data using Markov state and Langevin models. J Chem Phys 2020; 153:244112. [DOI: 10.1063/5.0031979] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Benjamin Lickert
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
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34
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Pant S, Smith Z, Wang Y, Tajkhorshid E, Tiwary P. Confronting pitfalls of AI-augmented molecular dynamics using statistical physics. J Chem Phys 2020; 153:234118. [PMID: 33353347 PMCID: PMC7863682 DOI: 10.1063/5.0030931] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2020] [Accepted: 11/29/2020] [Indexed: 12/31/2022] Open
Abstract
Artificial intelligence (AI)-based approaches have had indubitable impact across the sciences through the ability to extract relevant information from raw data. Recently, AI has also found use in enhancing the efficiency of molecular simulations, wherein AI derived slow modes are used to accelerate the simulation in targeted ways. However, while typical fields where AI is used are characterized by a plethora of data, molecular simulations, per construction, suffer from limited sampling and thus limited data. As such, the use of AI in molecular simulations can suffer from a dangerous situation where the AI-optimization could get stuck in spurious regimes, leading to incorrect characterization of the reaction coordinate (RC) for the problem at hand. When such an incorrect RC is then used to perform additional simulations, one could start to deviate progressively from the ground truth. To deal with this problem of spurious AI-solutions, here, we report a novel and automated algorithm using ideas from statistical mechanics. It is based on the notion that a more reliable AI-solution will be one that maximizes the timescale separation between slow and fast processes. To learn this timescale separation even from limited data, we use a maximum caliber-based framework. We show the applicability of this automatic protocol for three classic benchmark problems, namely, the conformational dynamics of a model peptide, ligand-unbinding from a protein, and folding/unfolding energy landscape of the C-terminal domain of protein G. We believe that our work will lead to increased and robust use of trustworthy AI in molecular simulations of complex systems.
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Affiliation(s)
- Shashank Pant
- NIH Center for Macromolecular Modeling and Bioinformatics, Beckman Institute for Advanced Science and Technology, Department of Biochemistry, Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | | | | | - Emad Tajkhorshid
- NIH Center for Macromolecular Modeling and Bioinformatics, Beckman Institute for Advanced Science and Technology, Department of Biochemistry, Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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35
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Prebiotic chemistry and origins of life research with atomistic computer simulations. Phys Life Rev 2020; 34-35:105-135. [DOI: 10.1016/j.plrev.2018.09.004] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2018] [Accepted: 09/10/2018] [Indexed: 02/02/2023]
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36
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Deciphering collaborative sidechain motions in proteins during molecular dynamics simulations. Sci Rep 2020; 10:15901. [PMID: 32985550 PMCID: PMC7522237 DOI: 10.1038/s41598-020-72766-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2020] [Accepted: 06/25/2020] [Indexed: 12/15/2022] Open
Abstract
The dynamic structure of proteins is essential for their functions and may include large conformational transitions which can be studied by molecular dynamics (MD) simulations. However, details of these transitions are difficult to automatically track. To facilitate their analysis, we developed two scores of correlation between sidechain dihedral angles. The CIRCULAR and OMES scores are computed from, respectively, dihedral angle values and rotamer distributions. As a case study, we applied our methods to an activation-like transition of the chemokine receptor CXCR4, observed during accelerated MD simulations. The principal component analysis of the correlation matrices was consistent with the networking structure of the top ranking pairs. Both scores identify a set of residues whose “collaborative” sidechain rotamerization immediately preceded or accompanied the conformational transition of CXCR4. Detailed analysis of the sequential order of these rotamerizations suggests that an allosteric mechanism, involving the outward motion of an asparagine residue in transmembrane helix 3, might be a prerequisite to the large scale conformational transition of CXCR4. This case study provides the proof-of-concept that the correlation methods developed here are valuable exploratory techniques to help decipher complex reactional pathways.
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37
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Bernetti M, Bertazzo M, Masetti M. Data-Driven Molecular Dynamics: A Multifaceted Challenge. Pharmaceuticals (Basel) 2020; 13:E253. [PMID: 32961909 PMCID: PMC7557855 DOI: 10.3390/ph13090253] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2020] [Revised: 09/14/2020] [Accepted: 09/16/2020] [Indexed: 12/18/2022] Open
Abstract
The big data concept is currently revolutionizing several fields of science including drug discovery and development. While opening up new perspectives for better drug design and related strategies, big data analysis strongly challenges our current ability to manage and exploit an extraordinarily large and possibly diverse amount of information. The recent renewal of machine learning (ML)-based algorithms is key in providing the proper framework for addressing this issue. In this respect, the impact on the exploitation of molecular dynamics (MD) simulations, which have recently reached mainstream status in computational drug discovery, can be remarkable. Here, we review the recent progress in the use of ML methods coupled to biomolecular simulations with potentially relevant implications for drug design. Specifically, we show how different ML-based strategies can be applied to the outcome of MD simulations for gaining knowledge and enhancing sampling. Finally, we discuss how intrinsic limitations of MD in accurately modeling biomolecular systems can be alleviated by including information coming from experimental data.
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Affiliation(s)
- Mattia Bernetti
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), via Bonomea 265, I-34136 Trieste, Italy;
| | - Martina Bertazzo
- Computational Sciences, Istituto Italiano di Tecnologia, via Morego 30, I-16163 Genova, Italy;
| | - Matteo Masetti
- Department of Pharmacy and Biotechnology, Alma Mater Studiorum—Università di Bologna, via Belmeloro 6, I-40126 Bologna, Italy
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38
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Bailleul S, Dedecker K, Cnudde P, Vanduyfhuys L, Waroquier M, Van Speybroeck V. Ab initio enhanced sampling kinetic study on MTO ethene methylation reaction. J Catal 2020. [DOI: 10.1016/j.jcat.2020.04.015] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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39
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Wang J, Chmiela S, Müller KR, Noé F, Clementi C. Ensemble learning of coarse-grained molecular dynamics force fields with a kernel approach. J Chem Phys 2020; 152:194106. [DOI: 10.1063/5.0007276] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Affiliation(s)
- Jiang Wang
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Stefan Chmiela
- Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany
| | - Klaus-Robert Müller
- Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany
- Department of Brain and Cognitive Engineering, Korea University, Seoul 02841, South Korea
- Max Planck Institute for Informatics, Saarbrücken 66123, Germany
| | - Frank Noé
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
- Department of Physics, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Cecilia Clementi
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
- Department of Physics, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
- Department of Physics, Rice University, Houston, Texas 77005, USA
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40
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Schilling M, Cunha RA, Luber S. Zooming in on the O–O Bond Formation—An Ab Initio Molecular Dynamics Study Applying Enhanced Sampling Techniques. J Chem Theory Comput 2020; 16:2436-2449. [DOI: 10.1021/acs.jctc.9b01207] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Mauro Schilling
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Richard A. Cunha
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Sandra Luber
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
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41
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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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42
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Alam FF, Rahman T, Shehu A. Evaluating Autoencoder-Based Featurization and Supervised Learning for Protein Decoy Selection. Molecules 2020; 25:E1146. [PMID: 32143444 PMCID: PMC7179114 DOI: 10.3390/molecules25051146] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2020] [Revised: 02/18/2020] [Accepted: 02/25/2020] [Indexed: 11/24/2022] Open
Abstract
Rapid growth in molecular structure data is renewing interest in featurizing structure. Featurizations that retain information on biological activity are particularly sought for protein molecules, where decades of research have shown that indeed structure encodes function. Research on featurization of protein structure is active, but here we assess the promise of autoencoders. Motivated by rapid progress in neural network research, we investigate and evaluate autoencoders on yielding linear and nonlinear featurizations of protein tertiary structures. An additional reason we focus on autoencoders as the engine to obtain featurizations is the versatility of their architectures and the ease with which changes to architecture yield linear versus nonlinear features. While open-source neural network libraries, such as Keras, which we employ here, greatly facilitate constructing, training, and evaluating autoencoder architectures and conducting model search, autoencoders have not yet gained popularity in the structure biology community. Here we demonstrate their utility in a practical context. Employing autoencoder-based featurizations, we address the classic problem of decoy selection in protein structure prediction. Utilizing off-the-shelf supervised learning methods, we demonstrate that the featurizations are indeed meaningful and allow detecting active tertiary structures, thus opening the way for further avenues of research.
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Affiliation(s)
- Fardina Fathmiul Alam
- Department of Computer Science, George Mason University, Fairfax, VA 22030, USA; (F.F.A.); (T.R.)
| | - Taseef Rahman
- Department of Computer Science, George Mason University, Fairfax, VA 22030, USA; (F.F.A.); (T.R.)
| | - Amarda Shehu
- Department of Computer Science, George Mason University, Fairfax, VA 22030, USA; (F.F.A.); (T.R.)
- Center for Advancing Human-Machine Partnerships, George Mason University, Fairfax, VA 22030, USA
- Department of Bioengineering, George Mason University, Fairfax, VA 22030, USA
- School of Systems Biology, George Mason University, Fairfax, VA 22030, USA
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43
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Wolfe DK, Persichetti JR, Sharma AK, Hudson PS, Woodcock HL, O'Brien EP. Hierarchical Markov State Model Building to Describe Molecular Processes. J Chem Theory Comput 2020; 16:1816-1826. [PMID: 32011146 DOI: 10.1021/acs.jctc.9b00955] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
Markov state models can describe ensembles of pathways via kinetic networks but are difficult to create when large free-energy barriers limit unbiased sampling. Chain-of-states simulations allow sampling over large free-energy barriers but are often constructed using a single pathway that is unlikely to thermodynamically average over orthogonal degrees of freedom in complex systems. Here, we combine the advantages of these two approaches in the form of a Markov state model of Markov state models, which we call a Hierarchical Markov state model. In this approach, independent Markov models are constructed in regions of configuration space that are locally well sampled but are separated by large free-energy barriers from other regions. A string method is used to construct an ensemble of pathways connecting the states of these different local Markov models, and the rate through each pathway is then estimated. These rates are then combined with the rate information from the local Markov models in a master equation to predict global rates, fluxes, and populations. By applying this hierarchical approach to tractable systems, a toy potential and dipeptides, we demonstrate that it is more accurate than the conventional single-pathway description. The advantages of this approach are that it (i) is more realistic than the conventional chain-of-states approach, as an ensemble of pathways rather than a single pathway is used to describe processes in high-dimensional systems, and (ii) it resolves the issue of poor sampling in Markov State model building when large free-energy barriers are present. The divide-and-conquer strategy inherent to this approach should make this procedure straightforward to apply to more complex systems.
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Affiliation(s)
| | | | - Ajeet K Sharma
- Department of Physics, Indian Institute of Technology, Jammu 181221, India
| | - Phillip S Hudson
- Department of Chemistry, University of South Florida, Tampa, Florida 33620, United States
| | - H Lee Woodcock
- Department of Chemistry, University of South Florida, Tampa, Florida 33620, United States
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44
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Meyer H, Pelagejcev P, Schilling T. Non-Markovian out-of-equilibrium dynamics: A general numerical procedure to construct time-dependent memory kernels for coarse-grained observables. ACTA ACUST UNITED AC 2020. [DOI: 10.1209/0295-5075/128/40001] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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45
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Shi W, Jia T, Li A. Quasi-classical trajectory analysis with isometric feature mapping and locally linear embedding: deep insights into the multichannel reaction on an NH3+(4A) potential energy surface. Phys Chem Chem Phys 2020; 22:17460-17471. [DOI: 10.1039/d0cp01941k] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Two manifold learning methods, isometric feature mapping and locally linear embedding, are applied to the analysis of quasi-classical trajectories for multi-channel reaction NH+ + H2 → N + H3+/NH2+ + H.
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Affiliation(s)
- Weiliang Shi
- Key Laboratory of Synthetic and Natural Functional Molecule of the Ministry of Education
- College of Chemistry and Materials Science
- Northwest University
- Xi’an
- P. R. China
| | - Tian Jia
- Key Laboratory of Synthetic and Natural Functional Molecule of the Ministry of Education
- College of Chemistry and Materials Science
- Northwest University
- Xi’an
- P. R. China
| | - Anyang Li
- Key Laboratory of Synthetic and Natural Functional Molecule of the Ministry of Education
- College of Chemistry and Materials Science
- Northwest University
- Xi’an
- P. R. China
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46
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Mai S, González L. Identification of important normal modes in nonadiabatic dynamics simulations by coherence, correlation, and frequency analyses. J Chem Phys 2019; 151:244115. [DOI: 10.1063/1.5129335] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Affiliation(s)
- Sebastian Mai
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Str. 17, 1090 Vienna, Austria
| | - Leticia González
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Str. 17, 1090 Vienna, Austria
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47
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Pearce P, Woodhouse FG, Forrow A, Kelly A, Kusumaatmaja H, Dunkel J. Learning dynamical information from static protein and sequencing data. Nat Commun 2019; 10:5368. [PMID: 31772168 PMCID: PMC6879630 DOI: 10.1038/s41467-019-13307-x] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2018] [Accepted: 10/24/2019] [Indexed: 11/09/2022] Open
Abstract
Many complex processes, from protein folding to neuronal network dynamics, can be described as stochastic exploration of a high-dimensional energy landscape. Although efficient algorithms for cluster detection in high-dimensional spaces have been developed over the last two decades, considerably less is known about the reliable inference of state transition dynamics in such settings. Here we introduce a flexible and robust numerical framework to infer Markovian transition networks directly from time-independent data sampled from stationary equilibrium distributions. We demonstrate the practical potential of the inference scheme by reconstructing the network dynamics for several protein-folding transitions, gene-regulatory network motifs, and HIV evolution pathways. The predicted network topologies and relative transition time scales agree well with direct estimates from time-dependent molecular dynamics data, stochastic simulations, and phylogenetic trees, respectively. Owing to its generic structure, the framework introduced here will be applicable to high-throughput RNA and protein-sequencing datasets, and future cryo-electron microscopy (cryo-EM) data.
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Affiliation(s)
- Philip Pearce
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139-4307, USA
| | - Francis G Woodhouse
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG, UK
| | - Aden Forrow
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139-4307, USA.,Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG, UK
| | - Ashley Kelly
- Department of Physics, Durham University, South Road, Durham, DH1 3LE, UK
| | - Halim Kusumaatmaja
- Department of Physics, Durham University, South Road, Durham, DH1 3LE, UK.
| | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139-4307, USA.
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48
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Copperman J, Aristoff D, Makarov DE, Simpson G, Zuckerman DM. Transient probability currents provide upper and lower bounds on non-equilibrium steady-state currents in the Smoluchowski picture. J Chem Phys 2019; 151:174108. [PMID: 31703496 PMCID: PMC7043855 DOI: 10.1063/1.5120511] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2019] [Accepted: 10/14/2019] [Indexed: 01/04/2023] Open
Abstract
Probability currents are fundamental in characterizing the kinetics of nonequilibrium processes. Notably, the steady-state current Jss for a source-sink system can provide the exact mean-first-passage time (MFPT) for the transition from the source to sink. Because transient nonequilibrium behavior is quantified in some modern path sampling approaches, such as the "weighted ensemble" strategy, there is strong motivation to determine bounds on Jss-and hence on the MFPT-as the system evolves in time. Here, we show that Jss is bounded from above and below by the maximum and minimum, respectively, of the current as a function of the spatial coordinate at any time t for one-dimensional systems undergoing overdamped Langevin (i.e., Smoluchowski) dynamics and for higher-dimensional Smoluchowski systems satisfying certain assumptions when projected onto a single dimension. These bounds become tighter with time, making them of potential practical utility in a scheme for estimating Jss and the long time scale kinetics of complex systems. Conceptually, the bounds result from the fact that extrema of the transient currents relax toward the steady-state current.
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Affiliation(s)
- Jeremy Copperman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, Oregon 97239, USA
| | - David Aristoff
- Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523, USA
| | - Dmitrii E Makarov
- Department of Chemistry and Oden Institute for Computational Engineering and Sciences, University of Texas, Austin, Texas 78712, USA
| | - Gideon Simpson
- Department of Mathematics, Drexel University, Philadelphia, Pennsylvania 19104, USA
| | - Daniel M Zuckerman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, Oregon 97239, USA
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Eberhardt J, Stote RH, Dejaegere A. Unrolr: Structural analysis of protein conformations using stochastic proximity embedding. J Comput Chem 2019; 39:2551-2557. [PMID: 30447084 DOI: 10.1002/jcc.25599] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2018] [Revised: 08/24/2018] [Accepted: 08/24/2018] [Indexed: 01/29/2023]
Abstract
Molecular dynamics (MD) simulations are widely used to explore the conformational space of biological macromolecules. Advances in hardware, as well as in methods, make the generation of large and complex MD datasets much more common. Although different clustering and dimensionality reduction methods have been applied to MD simulations, there remains a need for improved strategies that handle nonlinear data and/or can be applied to very large datasets. We present an original implementation of the pivot-based version of the stochastic proximity embedding method aimed at large MD datasets using the dihedral distance as a metric. The advantages of the algorithm in terms of data storage and computational efficiency are presented, as well as the implementation realized. Application and testing through the analysis of a 200 ns accelerated MD simulation of a 35-residue villin headpiece is discussed. Analysis of the simulation shows the promise of this method to organize large conformational ensembles. © 2018 Wiley Periodicals, Inc.
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Affiliation(s)
- Jérôme Eberhardt
- Biologie structurale intégrative Institut de Génétique et de Biologie Moléculaire et Cellulaire (IGBMC), Institut National de La Santé et de La Recherche Médicale (INSERM), U1258/Centre National de Recherche Scientifique (CNRS), UMR7104/Université de Strasbourg, Illkirch, France
| | - Roland H Stote
- Biologie structurale intégrative Institut de Génétique et de Biologie Moléculaire et Cellulaire (IGBMC), Institut National de La Santé et de La Recherche Médicale (INSERM), U1258/Centre National de Recherche Scientifique (CNRS), UMR7104/Université de Strasbourg, Illkirch, France
| | - Annick Dejaegere
- Biologie structurale intégrative Institut de Génétique et de Biologie Moléculaire et Cellulaire (IGBMC), Institut National de La Santé et de La Recherche Médicale (INSERM), U1258/Centre National de Recherche Scientifique (CNRS), UMR7104/Université de Strasbourg, Illkirch, France
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Paul S, Nair NN, Vashisth H. Phase space and collective variable based simulation methods for studies of rare events. MOLECULAR SIMULATION 2019. [DOI: 10.1080/08927022.2019.1634268] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Sanjib Paul
- Department of Chemical Engineering, University of New Hampshire, Durham, NH, USA
| | - Nisanth N. Nair
- Department of Chemistry, Indian Institute of Technology, Kanpur, India
| | - Harish Vashisth
- Department of Chemical Engineering, University of New Hampshire, Durham, NH, USA
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