Differentiable molecular simulation can learn all the parameters in a coarse-grained force field for proteins
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Abstract
Finding optimal parameters for force fields used in molecular simulation is a challenging and time-consuming task, partly due to the difficulty of tuning multiple parameters at once. Automatic differentiation presents a general solution: run a simulation, obtain gradients of a loss function with respect to all the parameters, and use these to improve the force field. This approach takes advantage of the deep learning revolution whilst retaining the interpretability and efficiency of existing force fields. We demonstrate that this is possible by parameterising a simple coarse-grained force field for proteins, based on training simulations of up to 2,000 steps learning to keep the native structure stable. The learned potential matches chemical knowledge and PDB data, can fold and reproduce the dynamics of small proteins, and shows ability in protein design and model scoring applications. Problems in applying differentiable molecular simulation to all-atom models of proteins are discussed along with possible solutions and the variety of available loss functions. The learned potential, simulation scripts and training code are made available at https://github.com/psipred/cgdms .
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The innovation in development and integration of MD simulations with deep learning can reproduce, interpret, predict, and generate data relating to the behavior of biological macromolecules.
“The innovation in the development and integration of MD simulations with deep learning can reproduce, interpret, predict, and generate data relating to the behavior of biological macromolecules.”
From AlphaFold, Artificial Intelligence (AI), and Allostery (2022) · cites this paper as [187]
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Cites
Adam: A Method for Stochastic Optimization
Kingma, D. P., & Ba, J. (2014) · arXiv · doi:10.48550/arxiv.1412.6980 · Cited by 98,946 · see citing works
Berman, H. M. (2000) · Nucleic Acids Research · doi:10.1093/nar/28.1.235 · Cited by 40,196 · see citing works
Matplotlib: a 2D graphics environment
Hunter, J. D. (2007) · Computing in Science & Engineering · doi:10.1109/mcse.2007.55 · Cited by 39,249 · see citing works
PyTorch: An Imperative Style, High-Performance Deep Learning Library
Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., et al. (2019) · arXiv · doi:10.48550/arxiv.1912.01703 · Cited by 31,473 · see citing works
Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems
Darden, T., York, D., & Pedersen, L. (1993) · The Journal of Chemical Physics · doi:10.1063/1.464397 · Cited by 29,588 · see citing works
Molecular dynamics simulations at constant pressure and/or temperature
Andersen, H. C. (1980) · The Journal of Chemical Physics · doi:10.1063/1.439486 · Cited by 5,823 · see citing works
Protein secondary structure prediction based on position-specific scoring matrices.
Jones, D. C. (1999) · Journal of Molecular Biology · doi:10.1006/jmbi.1999.3091 · Cited by 5,741 · see citing works
Self-citationImproved protein structure prediction using potentials from deep learning
Senior, A. W., Evans, R., Jumper, J., Kirkpatrick, J., Sifre, L., Green, T., Qin, C., Žídek, A., Nelson, A. W. R., Bridgland, A., et al. (2020) · Nature · doi:10.1038/s41586-019-1923-7 · Cited by 3,378 · see citing works
Self-citationMolecular Dynamics Simulation for All
Hollingsworth, S. A., & Dror, R. O. (2018) · Neuron · doi:10.1016/j.neuron.2018.08.011 · Cited by 3,313 · see citing works
Dynamic personalities of proteins
Henzler-Wildman, K., & Kern, D. (2007) · Nature · doi:10.1038/nature06522 · Cited by 2,545 · see citing works
Statistical potential for assessment and prediction of protein structures
Shen, M., & Šali, A. (2006) · Protein Science · doi:10.1110/ps.062416606 · Cited by 2,294 · see citing works
Shortcut learning in deep neural networks
Geirhos, R., Jacobsen, J.-H., Michaelis, C., Zemel, R., Brendel, W., Bethge, M., & Wichmann, F. A. (2020) · Nature Machine Intelligence · doi:10.1038/s42256-020-00257-z · Cited by 2,224 · see citing works
Wang, H., Zhang, L., Han, J., & Weinan, E. (2018) · Computer Physics Communications · doi:10.1016/j.cpc.2018.03.016 · Cited by 2,153 · see citing works
Neural ordinary differential equations
Chen, R. T. Q., Rubanova, Y., Bettencourt, J., & Duvenaud, D. (2018) · arXiv · doi:10.48550/arxiv.1806.07366 · Cited by 2,097 · see citing works
MDAnalysis: A Python Package for the Rapid Analysis of Molecular Dynamics Simulations
Gowers, R. J., Linke, M., Barnoud, J., Reddy, T. J., Melo, M. N., Seyler, S. L., Domański, J., Dotson, D., Buchoux, S., Kenney, I. M., et al. (2016) · Proceedings of the Python in Science Conferences · doi:10.25080/majora-629e541a-00e · Cited by 2,085 · see citing works
Automatic Differentiation in Machine Learning: a Survey
Baydin, A. G., Pearlmutter, B. A., Radul, A., & Siskind, J. M. (2015) · Maynooth University ePrints and eTheses Archive (Maynooth University) · Cited by 2,055 · see citing works
E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials
Batzner, S., Musaelian, A., Sun, L., Geiger, M., Mailoa, J. P., Kornbluth, M., Molinari, N., Smidt, T., & Kozinsky, B. (2022) · Nature Communications · doi:10.1038/s41467-022-29939-5 · Cited by 1,988 · see citing works
How fast-folding proteins fold
Lindorff-Larsen, K., Piana, S., Dror, R. O., & Shaw, D. E. (2011) · Science · doi:10.1126/science.1208351 · Cited by 1,980 · see citing works
Increasing the precision of comparative models with YASARA NOVA—a self‐parameterizing force field
Krieger, E., Koraimann, G., & Vriend, G. (2002) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.10104 · Cited by 1,519 · see citing works
A Multiscale Coarse-Graining Method for Biomolecular Systems
Izvekov, S., & Voth, G. A. (2005) · The Journal of Physical Chemistry B · doi:10.1021/jp044629q · Cited by 1,192 · see citing works
Machine learning of accurate energy-conserving molecular force fields
Chmiela, S., Tkatchenko, A., Sauceda, H. E., Poltavsky, I., Schütt, K. T., & Müller, K. (2017) · Science Advances · doi:10.1126/sciadv.1603015 · Cited by 1,165 · see citing works
PyEMMA 2: A Software Package for Estimation, Validation, and Analysis of Markov Models.
Scherer, M. K., Trendelkamp-Schroer, B., Paul, F., Pérez-Hernández, G., Hoffmann, M., Plattner, N., Wehmeyer, C., Prinz, J.-H., & Noé, F. (2015) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5b00743 · Cited by 1,148 · see citing works
Waskom, M., Botvinnik, O. B., O'Kane, D., Hobson, P., Ostblom, J., Lukauskas, S., Gemperline, D. C., Augspurger, T., Halchenko, Y., Cole, J. B., et al. (2014) · Zenodo (CERN European Organization for Nuclear Research) · doi:10.5281/zenodo.592845 · Cited by 1,119 · see citing works
Coarse-Grained Protein Models and Their Applications
Kmiecik, S., Gront, D., Koliński, M., Wieteska, Ł., Badaczewska-Dawid, A. E., & Koliński, A. (2016) · Chemical Reviews · doi:10.1021/acs.chemrev.6b00163 · Cited by 1,067 · see citing works
Developing a molecular dynamics force field for both folded and disordered protein states
Robustelli, P., Piana, S., & Shaw, D. E. (2018) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1800690115 · Cited by 1,047 · see citing works
Machine Learning for Molecular Simulation
Noé, F., Tkatchenko, A., Müller, K.-R., & Clementi, C. (2020) · Annual Review of Physical Chemistry · doi:10.1146/annurev-physchem-042018-052331 · Cited by 956 · see citing works
Zhou, H., & Zhou, Y. (2002) · Protein Science · doi:10.1110/ps.0217002 · Cited by 902 · see citing works
Automatic differentiation in machine learning: a surveyPreprint
Baydin, A. G., Pearlmutter, B. A., Radul, A., & Siskind, J. M. (2015) · arXiv (Cornell University) · doi:10.4230/lipics.ecoop.2019.25 · Cited by 845 · see citing works
Protein–Ligand Scoring with Convolutional Neural Networks
Ragoza, M., Hochuli, J. E., Idrobo, E., Sunseri, J., & Koes, D. R. (2017) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.6b00740 · Cited by 835 · see citing works
How Robust Are Protein Folding Simulations with Respect to Force Field Parameterization?
Piana, S., Lindorff‐Larsen, K., & Shaw, D. E. (2011) · Biophysical Journal · doi:10.1016/j.bpj.2011.03.051 · Cited by 798 · see citing works
Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning
Noé, F., Olsson, S., Köhler, J., & Wu, H. (2019) · Science · doi:10.1126/science.aaw1147 · Cited by 747 · see citing works
Systematic Validation of Protein Force Fields against Experimental Data
Lindorff‐Larsen, K., Maragakis, P., Piana, S., Eastwood, M. P., Dror, R. O., & Shaw, D. E. (2012) · PLoS ONE · doi:10.1371/journal.pone.0032131 · Cited by 648 · see citing works
Universal Differential Equations for Scientific Machine Learning
Rackauckas, C., Ma, Y., Martensen, J., Warner, C., Zubov, K., Supekar, R., Skinner, D., Ramadhan, A., & Edelman, A. (2020) · doi:10.21203/rs.3.rs-55125/v1 · Cited by 643 · see citing works
Building Force Fields: An Automatic, Systematic, and Reproducible Approach
Wang, L., Martı́nez, T. J., & Pande, V. S. (2014) · The Journal of Physical Chemistry Letters · doi:10.1021/jz500737m · Cited by 563 · see citing works
Deep-neural-network solution of the electronic Schrödinger equation
Hermann, J., Schätzle, Z., & Noé, F. (2020) · Nature Chemistry · doi:10.1038/s41557-020-0544-y · Cited by 559 · see citing works
Machine Learning of Coarse-Grained Molecular Dynamics Force Fields
Wang, J., Olsson, S., Wehmeyer, C., Pérez, A., Charron, N. E., Fabritiis, G. D., Noé, F., & Clementi, C. (2019) · ACS Central Science · doi:10.1021/acscentsci.8b00913 · Cited by 519 · see citing works
SchNetPack: A Deep Learning Toolbox For Atomistic Systems
Schütt, K. T., Kessel, P., Gastegger, M., Nicoli, K. A., Tkatchenko, A., & Müller, K. R. (2018) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.8b00908 · Cited by 434 · see citing works
ECOD: an evolutionary classification of protein domains
Cheng, H., Schaeffer, R. D., Liao, Y., Kinch, L. N., Pei, J., Shi, S., Kim, B.-H., & Grishin, N. V. (2014) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1003926 · Cited by 426 · cited 2× · see citing works
“Proteins homologous to those used in the results were removed from the dataset by eliminating overlap at the same ECOD T-level [81] and removing hits when searching the PDB using BLAST with an E-value of 1.”
MethodInfluentialAnalyzing Inverse Problems with Invertible Neural NetworksPreprint
Ardizzone, L., Kruse, J., Wirkert, S., Rahner, D., Pellegrini, E. W., Klessen, R. S., Maier‐Hein, L., Rother, C., & Köthe, U. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1808.04730 · Cited by 402 · see citing works
Fast procedure for reconstruction of full‐atom protein models from reduced representations
Rotkiewicz, P., & Skolnick, J. (2008) · Journal of Computational Chemistry · doi:10.1002/jcc.20906 · Cited by 395 · see citing works
Quantum chemical accuracy from density functional approximations via machine learning
Bogojeski, M., Vogt-Maranto, L., Tuckerman, M. E., Müller, K., & Burke, K. (2020) · Nature Communications · doi:10.1038/s41467-020-19093-1 · Cited by 391 · see citing works
End-to-End Differentiable Learning of Protein Structure
AlQuraishi, M. (2019) · Cell Systems · doi:10.1016/j.cels.2019.03.006 · Cited by 371 · see citing works
Protein modeling and structure prediction with a reduced representation.
Koliński, A. (2004) · Acta Biochimica Polonica · doi:10.18388/abp.2004_3575 · Cited by 338 · see citing works
Best, R., Zheng, W.-W., & Mittal, J. (2014) · Journal of Chemical Theory and Computation · doi:10.1021/ct500569b · Cited by 312 · see citing works
Liwo, A., Khalili, M., & Scheraga, H. A. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0408885102 · Cited by 274 · see citing works
PDB file parser and structure class implemented in Python
Hamelryck, T., & Manderick, B. (2003) · Bioinformatics · doi:10.1093/bioinformatics/btg299 · Cited by 272 · see citing works
Nguyen, T. H. H., Maier, J., Huang, H., Perrone, V., & Simmerling, C. L. (2014) · Journal of the American Chemical Society · doi:10.1021/ja5032776 · Cited by 244 · see citing works
New developments in force fields for biomolecular simulations
Nerenberg, P. S., & Head-Gordon, T. L. (2018) · Current Opinion in Structural Biology · doi:10.1016/j.sbi.2018.02.002 · Cited by 236 · see citing works
TorchMD: A Deep Learning Framework for Molecular Simulations
Doerr, S., Majewski, M., Pérez, A., Krämer, A., Clementi, C., Noe, F., Giorgino, T., & De Fabritiis, G. (2021) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.0c01343 · Cited by 230 · see citing works
DeePCG: Constructing coarse-grained models via deep neural networks
Zhang, L., Han, J., Wang, H., Car, R., & Weinan, E. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5027645 · Cited by 220 · see citing works
A coarse‐grained protein force field for folding and structure prediction
Maupetit, J., Tufféry, P., & Derreumaux, P. (2007) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.21505 · Cited by 216 · see citing works
Coarse graining molecular dynamics with graph neural networks
Husic, B. E., Charron, N. E., Lemm, D., Wang, J., Pérez, A., Majewski, M., Krämer, A., Chen, Y., Olsson, S., Fabritiis, G. D., et al. (2020) · The Journal of Chemical Physics · doi:10.1063/5.0026133 · Cited by 206 · see citing works
DiffTaichi: Differentiable Programming for Physical SimulationPreprint
Hu, Y., Anderson, L., Li, T., Sun, Q. L., Carr, N., Ragan‐Kelley, J., & Durand, F. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1910.00935 · Cited by 190 · see citing works
Crystal Structure of a Ten-Amino Acid Protein
Honda, S., Akiba, T., Kato, Y. S., Sawada, Y., Sekijima, M., Ishimura, M., Ooishi, A., Watanabe, H., Odahara, T., & Harata, K. (2008) · Journal of the American Chemical Society · doi:10.1021/ja8030533 · Cited by 188 · see citing works
Crucial role of nonspecific interactions in amyloid nucleation
Šarić, A., Chebaro, Y., Knowles, T. P. J., & Frenkel, D. (2014) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1410159111 · Cited by 181 · see citing works
Greener, J. G., Kandathil, S. M., & Jones, D. T. (2019) · Nature Communications · doi:10.1038/s41467-019-11994-0 · Cited by 178 · see citing works
Self-citationCoarse-graining auto-encoders for molecular dynamics
Wang, W., & Gómez‐Bombarelli, R. (2019) · npj Computational Materials · doi:10.1038/s41524-019-0261-5 · Cited by 176 · see citing works
Kohn-Sham Equations as Regularizer: Building Prior Knowledge into Machine-Learned Physics
Li, L., Hoyer, S., Pederson, R. D., Sun, R., Cubuk, E. D., Riley, P., & Burke, K. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.036401 · Cited by 170 · see citing works
Gkeka, P., Stoltz, G., Farimani, A. B., Belkacemi, Z., Ceriotti, M., Chodera, J., Dinner, A., Ferguson, A. L., Maillet, J., Minoux, H., et al. (2020) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.0c00355 · Cited by 169 · see citing works
Coarse-graining auto-encoders for molecular dynamics
Wang, W., & Gómez‐Bombarelli, R. (2019) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 160 · see citing works
Machine learning for protein folding and dynamics.
Noé, F., de Fabritiis, G., & Clementi, C. (2019) · Current Opinion in Structural Biology · doi:10.1016/j.sbi.2019.12.005 · Cited by 159 · see citing works
Coarse graining molecular dynamics with graph neural networks
Husic, B. E., Charron, N. E., Lemm, D., Wang, J., Pérez, A., Majewski, M., Krämer, A., Chen, Y., Olsson, S., Fabritiis, G. D., et al. (2020) · Refubium (Universitätsbibliothek der Freien Universität Berlin) · doi:10.17169/refubium-29706 · Cited by 151 · see citing works
ZeRO-Offload: Democratizing Billion-Scale Model Training
Ren, J., Rajbhandari, S., Aminabadi, R. Y., Ruwase, O., Yang, S., Zhang, M., Li, D., & He, Y. (2021) · arXiv · doi:10.48550/arxiv.2101.06840 · Cited by 151 · see citing works
EvoEF2: accurate and fast energy function for computational protein design
Huang, X., Pearce, R., & Zhang, Y. (2019) · Bioinformatics · doi:10.1093/bioinformatics/btz740 · Cited by 119 · see citing works
PeptideBuilder: A simple Python library to generate model peptides
Tien, M. Z., Sydykova, D. K., Meyer, A. G., & Wilke, C. O. (2013) · PeerJ · doi:10.7717/peerj.80 · Cited by 116 · see citing works
Park, H., Zhou, G., Baek, M., Baker, D. A., & DiMaio, F. (2021) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.0c01184 · Cited by 100 · see citing works
CABS-fold: server for the de novo and consensus-based prediction of protein structure
Błaszczyk, M., Jamróz, M. H., Kmiecik, S., & Koliński, A. (2013) · Nucleic Acids Research · doi:10.1093/nar/gkt462 · Cited by 94 · see citing works
Rufa, D. A., Macdonald, H. E. B., Fass, J., Wieder, M., Grinaway, P., Roitberg, A. E., Isayev, O., & Chodera, J. D. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.07.29.227959 · Cited by 94 · see citing works
(2018) · International Conference on Learning Representations · Cited by 92 · see citing works
Optimizing physical energy functions for protein folding
Fujitsuka, Y., Takada, S., Luthey-Schulten, Z. A., & Wolynes, P. G. (2003) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.10429 · Cited by 91 · see citing works
End-to-end differentiable construction of molecular mechanics force fields
Wang, Y., Fass, J., Kaminow, B., Herr, J. E., Rufa, D. A., Zhang, I., Pulido, I., Henry, M. M., Macdonald, H. E. B., Takaba, K., et al. (2022) · Chemical Science · doi:10.1039/d2sc02739a · Cited by 88 · see citing works
3DRobot: automated generation of diverse and well-packed protein structure decoys
Deng, H., Jia, Y., & Zhang, Y. (2015) · Bioinformatics · doi:10.1093/bioinformatics/btv601 · Cited by 77 · see citing works
Czaplewski, C. R., Karczyńska, A. S., Sieradzan, A. K., & Liwo, A. (2018) · Nucleic Acids Research · doi:10.1093/nar/gky328 · Cited by 76 · see citing works
Protein storytelling through physics
Brini, E., Simmerling, C., & Dill, K. (2020) · Science · doi:10.1126/science.aaz3041 · Cited by 72 · see citing works
Designing self-assembling kinetics with differentiable statistical physics models
Goodrich, C. P., King, E. M., Schoenholz, S. S., Cubuk, E. D., & Brenner, M. P. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2024083118 · Cited by 67 · see citing works
Don't Unroll Adjoint: Differentiating SSA-Form ProgramsPreprint
Innes, M. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1810.07951 · Cited by 61 · see citing works
Zygote: A Differentiable Programming System to Bridge Machine Learning and Scientific ComputingPreprint
Innes, M. J., Edelman, A. S., Fischer, K., Rackauckas, C., Saba, E., Shah, V. B., & Tebbutt, W. (2019) · arXiv (Cornell University) · Cited by 61 · see citing works
A 1.8 Å resolution potential function for protein folding
Crippen, G. M., & Snow, M. E. (1990) · Biopolymers · doi:10.1002/bip.360291014 · Cited by 53 · see citing works
High-resolution protein folding with a transferable potential
Hubner, I. A., Deeds, E. J., & Shakhnovich, E. I. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0502181102 · Cited by 50 · see citing works
Krupa, P., Hałabis, A., Żmudzińska, W., Ołdziej, S., Scheraga, H. A., & Liwo, A. (2017) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.7b00254 · Cited by 47 · see citing works
Jumper, J., Faruk, N. F., Freed, K. F., & Sosnick, T. R. (2018) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1006578 · Cited by 44 · see citing works
A Maximum-Likelihood Approach to Force-Field Calibration
Zaborowski, B., Jagieła, D., Czaplewski, C. R., Hałabis, A., Lewandowska, A., Żmudzińska, W., Ołdziej, S., Karczyńska, A. S., Omieczynski, C., Wirecki, T. K., et al. (2015) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.5b00395 · Cited by 40 · see citing works
Funnel sculpting for in silico assembly of secondary structure elements of proteins
Fain, B., & Levitt, M. (2003) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1732312100 · Cited by 38 · see citing works
Differentiable Molecular Simulations for Control and LearningPreprint
Wang, W., Axelrod, S., & Gómez‐Bombarelli, R. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2003.00868 · Cited by 38 · see citing works
Learning to Control PDEs with Differentiable PhysicsPreprint
Holl, P., Koltun, V., & Thuerey, N. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2001.07457 · Cited by 37 · see citing works
Topological mirror images in protein structure computation: An underestimated problem
Pastore, A., Atkinson, R. A., Saudek, V., & Williams, R. J. P. (1991) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.340100104 · Cited by 33 · see citing works
Kento, S., Tran, D. P., Takemura, K., Kitao, A., Terayama, K., & Tsuda, K. (2019) · ACS Omega · doi:10.1021/acsomega.9b01480 · Cited by 32 · see citing works
Demerdash, O., Shrestha, U. R., Petridis, L., Smith, J. C., Mitchell, J. C., & Ramanathan, A. (2019) · Frontiers in Molecular Biosciences · doi:10.3389/fmolb.2019.00064 · Cited by 30 · see citing works
De novo protein structure prediction using ultra-fast molecular dynamics simulation
Cheung, N. J., & Yu, W. (2018) · PLoS ONE · doi:10.1371/journal.pone.0205819 · Cited by 26 · see citing works
Configurational Entropy of Folded Proteins and Its Importance for Intrinsically Disordered Proteins
Liu, M., Das, A. K., Lincoff, J., Sasmal, S., Cheng, S. Y., Vernon, R. M., Forman-Kay, J. D., & Head-Gordon, T. L. (2021) · International Journal of Molecular Sciences · doi:10.3390/ijms22073420 · Cited by 17 · see citing works
Teaching computers to fold proteins
Winther, O., & Krogh, A. (2004) · Physical Review E · doi:10.1103/physreve.70.030903 · Cited by 15 · see citing works
Várnai, C., Burkoff, N. S., & Wild, D. L. (2013) · Journal of Chemical Theory and Computation · doi:10.1021/ct400628h · Cited by 15 · see citing works
BioStructures.jl: read, write and manipulate macromolecular structures in Julia
Greener, J. G., Selvaraj, J., & Ward, B. J. (2020) · Bioinformatics · doi:10.1093/bioinformatics/btaa502 · Cited by 14 · see citing works
Self-citationLearning about protein hydrogen bonding by minimizing contrastive divergence
Podtelezhnikov, A. A., Zoubin Ghahramani, A., & Wild, D. L. (2006) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.21247 · Cited by 13 · see citing works
End-to-End Differentiable Molecular Mechanics Force Field ConstructionPreprint
Wang, Y., Fass, J., Kaminow, B., Herr, J. E., Rufa, D., Zhang, I., Pulido, I., Henry, M., & Chodera, J. D. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2010.01196 · Cited by 7 · see citing works
Determination of Forces from a Potential in Molecular DynamicsPreprint
Monasse, B., & Boussinot, F. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1401.1181 · Cited by 3 · see citing works
Configurational Entropy of Folded Proteins and its Importance for Intrinsically Disordered ProteinsPreprint
Liu, M., Das, A. K., Lincoff, J., et al. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2007.06150 · Cited by 3 · see citing works
Self-assembling kinetics: Accessing a new design space via differentiable statistical-physics modelsPreprint
Goodrich, C. P., King, E. M., Schoenholz, S. S., Cubuk, E. D., & Brenner, M. P. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2010.15175 · Cited by 2 · see citing works
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Research works printed but not linked: 1
- [72]Schoenholz SS, Cubuk ED. JAX, M.D.: A Framework for Differentiable Physics. arXiv. 2019;1912.04232.
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- Authors
- Greener, J. G., & Jones, D. T.
- Affiliations
- University College London (GB)
- Corresponding author
- Greener, Joe G.
- Venue
- PLOS ONE
- Publisher
- Public Library of Science (PLoS)
- Published
- 2021-09-02
- Volume
- 16
- Issue
- 9
- Pages
- e0256990
- ISSN
- 1932-6203 (ISSN-L)
- PMC
- PMC8412298
- OpenAlex
- W3198230876
- Cited by
- 29
- References
- 101
- Citations by year
- 2026: 1 · 2025: 9 · 2024: 6 · 2023: 7 · 2022: 4 · 2021: 2
- FWCI
- 1.48
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- PLoS ONE (publishedVersion, cc-by)
- bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- UCL Discovery (University College London) (submittedVersion)
- Funders
- H2020 European Research Council (695558)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Computational Drug Discovery Methods
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Keywords
- force field optimization, coarse-grained force field, proteins, automatic differentiation, protein folding, protein design, model scoring, all-atom force field, loss functions
- MeSH terms
- Protein Conformation, alpha-Helical, Protein Conformation, beta-Strand, Deep Learning, Crystallization, Nuclear Energy, Proteins, Temperature, Protein Structure, Tertiary, Molecular Dynamics Simulation
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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