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Liu Y, Ghosh TK, Lin G, Chen M. Unbiasing Enhanced Sampling on a High-Dimensional Free Energy Surface with a Deep Generative Model. J Phys Chem Lett 2024; 15:3938-3945. [PMID: 38568182 DOI: 10.1021/acs.jpclett.3c03515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/12/2024]
Abstract
Biased enhanced sampling methods that utilize collective variables (CVs) are powerful tools for sampling conformational ensembles. Due to their large intrinsic dimensions, efficiently generating conformational ensembles for complex systems requires enhanced sampling on high-dimensional free energy surfaces. While temperature-accelerated molecular dynamics (TAMD) can trivially adopt many CVs in a simulation, unbiasing the simulation to generate unbiased conformational ensembles requires accurate modeling of a high-dimensional CV probability distribution, which is challenging for traditional density estimation techniques. Here we propose an unbiasing method based on the score-based diffusion model, a deep generative learning method that excels in density estimation across complex data landscapes. We demonstrate that this unbiasing approach, tested on multiple TAMD simulations, significantly outperforms traditional unbiasing methods and can generate accurate unbiased conformational ensembles. With the proposed approach, TAMD can adopt CVs that focus on improving sampling efficiency and the proposed unbiasing method enables accurate evaluation of ensemble averages of important chemical features.
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Affiliation(s)
- Yikai Liu
- Department of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47906, United States
| | - Tushar K Ghosh
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47906, United States
| | - Guang Lin
- Department of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47906, United States
| | - Ming Chen
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47906, United States
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Alberini G, Alexis Paz S, Corradi B, Abrams CF, Benfenati F, Maragliano L. Molecular Dynamics Simulations of Ion Permeation in Human Voltage-Gated Sodium Channels. J Chem Theory Comput 2023; 19:2953-2972. [PMID: 37116214 DOI: 10.1021/acs.jctc.2c00990] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/30/2023]
Abstract
The recent determination of cryo-EM structures of voltage-gated sodium (Nav) channels has revealed many details of these proteins. However, knowledge of ionic permeation through the Nav pore remains limited. In this work, we performed atomistic molecular dynamics (MD) simulations to study the structural features of various neuronal Nav channels based on homology modeling of the cryo-EM structure of the human Nav1.4 channel and, in addition, on the recently resolved configuration for Nav1.2. In particular, single Na+ permeation events during standard MD runs suggest that the ion resides in the inner part of the Nav selectivity filter (SF). On-the-fly free energy parametrization (OTFP) temperature-accelerated molecular dynamics (TAMD) was also used to calculate two-dimensional free energy surfaces (FESs) related to single/double Na+ translocation through the SF of the homology-based Nav1.2 model and the cryo-EM Nav1.2 structure, with different realizations of the DEKA filter domain. These additional simulations revealed distinct mechanisms for single and double Na+ permeation through the wild-type SF, which has a charged lysine in the DEKA ring. Moreover, the configurations of the ions in the SF corresponding to the metastable states of the FESs are specific for each SF motif. Overall, the description of these mechanisms gives us new insights into ion conduction in human Nav cryo-EM-based and cryo-EM configurations that could advance understanding of these systems and how they differ from potassium and bacterial Nav channels.
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Affiliation(s)
- Giulio Alberini
- Center for Synaptic Neuroscience and Technology (NSYN@UniGe), Istituto Italiano di Tecnologia, Largo Rosanna Benzi 10, 16132 Genova, Italy
- IRCCS Ospedale Policlinico San Martino, Largo Rosanna Benzi 10, 16132 Genova, Italy
| | - Sergio Alexis Paz
- Departamento de Química Teórica y Computacional, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, X5000HUA Córdoba, Argentina
- Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Instituto de Fisicoquímica de Córdoba (INFIQC), X5000HUA Córdoba, Argentina
| | - Beatrice Corradi
- Center for Synaptic Neuroscience and Technology (NSYN@UniGe), Istituto Italiano di Tecnologia, Largo Rosanna Benzi 10, 16132 Genova, Italy
- Department of Experimental Medicine, Università degli Studi di Genova, Viale Benedetto XV 3, 16132 Genova, Italy
| | - Cameron F Abrams
- Department of Chemical and Biological Engineering, Drexel University, Philadelphia, Pennsylvania 19104, United States
| | - Fabio Benfenati
- Center for Synaptic Neuroscience and Technology (NSYN@UniGe), Istituto Italiano di Tecnologia, Largo Rosanna Benzi 10, 16132 Genova, Italy
- IRCCS Ospedale Policlinico San Martino, Largo Rosanna Benzi 10, 16132 Genova, Italy
| | - Luca Maragliano
- Center for Synaptic Neuroscience and Technology (NSYN@UniGe), Istituto Italiano di Tecnologia, Largo Rosanna Benzi 10, 16132 Genova, Italy
- Department of Life and Environmental Sciences, Polytechnic University of Marche, Via Brecce Bianche, 60131 Ancona, Italy
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Abstract
Enhanced sampling and free energy calculation algorithms of the thermodynamic integration family (such as the adaptive biasing force (ABF) method) are not based on the direct computation of a free energy surface but rather of its gradient. Integrating the free energy surface is nontrivial in dimensions higher than one. Here, the author introduces a flexible, portable implementation of a Poisson equation formalism to integrate free energy surfaces from estimated gradients in dimensions 2 and 3 using any combination of periodic and nonperiodic (Neumann) boundary conditions. The algorithm is implemented in portable C++ and provided as a standalone tool that can be used to integrate multidimensional gradient fields estimated on a grid using any algorithm, such as umbrella integration as a post-treatment of umbrella sampling simulations. It is also included in the implementation of ABF (and its extended-system variant eABF) in the Collective Variables Module, enabling the seamless computation of multidimensional free energy surfaces within ABF and eABF simulations. A Python-based analysis toolchain is provided to easily plot and analyze multidimensional ABF simulation results, including metrics to assess their convergence. The Poisson integration algorithm can also be used to perform Helmholtz decomposition of noisy gradient estimates on the fly, resulting in an efficient implementation of the projected ABF (pABF) method proposed by Leliévre and co-workers. In numerical tests, pABF is found to lead to faster convergence with respect to ABF in simple cases of low intrinsic dimension but seems detrimental to convergence in a more realistic case involving degenerate coordinates and hidden barriers due to slower exploration. This suggests that variance reduction schemes do not always yield convergence improvements when applied to enhanced sampling methods.
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Affiliation(s)
- Jérôme Hénin
- Laboratoire de Biochimie Théorique, UPR 9080, CNRS, Université de Paris, 75005 Paris, France.,Institut de Biologie Physico-Chimique-Fondation Edmond de Rothschild, PSL Research University, 75005 Paris, France
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Fernandez F, Paz SA, Otero M, Barraco D, Leiva EPM. Characterization of amorphous Li xSi structures from ReaxFF via accelerated exploration of local minima. Phys Chem Chem Phys 2021; 23:16776-16784. [PMID: 34319321 DOI: 10.1039/d1cp02216d] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Motivated by the abundant experimental work in the area of Li-ion batteries, in the present work we characterize via computer simulations the structure of Si-Li amorphous alloys in a wide range of compositions. Using a reactive force field we propose a novel accelerated exploration of local minima to obtain amorphous structures close to equilibrium. The features of this system analyzed for different alloy compositions are the partial radial distribution functions g(r), the first and second nearest neighbour coordination numbers and the short-order structure. The complex structure of the second peak of the Si-Li g(r) is elucidated using a cluster-connection analysis.
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Affiliation(s)
- Francisco Fernandez
- Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, Córdoba (X5000HUA), Argentina
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