Past–future information bottleneck for sampling molecular reaction coordinate simultaneously with thermodynamics and kinetics

The ability to rapidly learn from high-dimensional data to make reliable bets about the future is crucial in many contexts. This could be a fly avoiding predators, or the retina processing gigabytes of data to guide human actions. In this work we draw parallels between these and the efficient sampling of biomolecules with hundreds of thousands of atoms. For this we use the Predictive Information Bottleneck framework used for the first two problems, and re-formulate it for the sampling of biomolecules, especially when plagued with rare events. Our method uses a deep neural network to learn the minimally complex yet most predictive aspects of a given biomolecular trajectory. This information is used to perform iteratively biased simulations that enhance the sampling and directly obtain associated thermodynamic and kinetic information. We demonstrate the method on two test-pieces, studying processes slower than milliseconds, calculating free energies, kinetics and critical mutations. Efficient sampling of rare events in all-atom molecular dynamics simulations remains a challenge. Here, the authors adapt the Predictive Information Bottleneck framework to sample biomolecular structure and dynamics through iterative rounds of biased simulations and deep learning.

[1]  Massimiliano Bonomi,et al.  PLUMED 2: New feathers for an old bird , 2013, Comput. Phys. Commun..

[2]  Christoph Dellago,et al.  On the calculation of reaction rate constants in the transition path ensemble , 1999 .

[3]  Mohammad M. Sultan,et al.  Transferable Neural Networks for Enhanced Sampling of Protein Dynamics. , 2018, Journal of chemical theory and computation.

[4]  Frank Noé,et al.  Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics , 2017, The Journal of chemical physics.

[5]  R. Dror,et al.  How Fast-Folding Proteins Fold , 2011, Science.

[6]  A. Berezhkovskii,et al.  One-dimensional reaction coordinates for diffusive activated rate processes in many dimensions. , 2005, The Journal of chemical physics.

[7]  D. van der Spoel,et al.  GROMACS: A message-passing parallel molecular dynamics implementation , 1995 .

[8]  Aaron R Dinner,et al.  Automatic method for identifying reaction coordinates in complex systems. , 2005, The journal of physical chemistry. B.

[9]  Hao Wu,et al.  VAMPnets for deep learning of molecular kinetics , 2017, Nature Communications.

[10]  Michele Parrinello,et al.  Enhancing Important Fluctuations: Rare Events and Metadynamics from a Conceptual Viewpoint. , 2016, Annual review of physical chemistry.

[11]  Gerhard Hummer,et al.  Cooperative water filling of a nonpolar protein cavity observed by high-pressure crystallography and simulation. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Jakub Rydzewski,et al.  Promoting transparency and reproducibility in enhanced molecular simulations , 2019, Nature Methods.

[13]  M. Parrinello,et al.  From metadynamics to dynamics. , 2013, Physical review letters.

[14]  Roger B. Grosse,et al.  Isolating Sources of Disentanglement in Variational Autoencoders , 2018, NeurIPS.

[15]  B. Berne,et al.  Spectral gap optimization of order parameters for sampling complex molecular systems , 2015, Proceedings of the National Academy of Sciences.

[16]  Pratyush Tiwary,et al.  Multi-dimensional spectral gap optimization of order parameters (SGOOP) through conditional probability factorization , 2018, bioRxiv.

[17]  Pratyush Tiwary,et al.  Reweighted autoencoded variational Bayes for enhanced sampling (RAVE). , 2018, The Journal of chemical physics.

[18]  Jagannath Mondal,et al.  Atomic resolution mechanism of ligand binding to a solvent inaccessible cavity in T4 lysozyme , 2018, bioRxiv.

[19]  Susanne Still,et al.  Information Bottleneck Approach to Predictive Inference , 2014, Entropy.

[20]  Michael J. Berry,et al.  Predictive information in a sensory population , 2013, Proceedings of the National Academy of Sciences.

[21]  Alexander A. Alemi,et al.  Deep Variational Information Bottleneck , 2017, ICLR.

[22]  John E. Straub,et al.  Classical and modern methods in reaction rate theory , 1988 .

[23]  Oliver F. Lange,et al.  Solution structure of a minor and transiently formed state of a T4 lysozyme mutant , 2011, Nature.

[24]  Berk Hess,et al.  GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers , 2015 .

[25]  John A. Montgomery,et al.  Trajectory analysis of a kinetic theory for isomerization dynamics in condensed phases , 1979 .

[26]  G. Hummer,et al.  Reaction coordinates and rates from transition paths. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[27]  M. Parrinello,et al.  Polymorphic transitions in single crystals: A new molecular dynamics method , 1981 .

[28]  B. Berne,et al.  How wet should be the reaction coordinate for ligand unbinding? , 2016, The Journal of chemical physics.

[29]  Victoria A. Feher,et al.  Access of ligands to cavities within the core of a protein is rapid , 1996, Nature Structural Biology.

[30]  Danna Zhou,et al.  d. , 1934, Microbial pathogenesis.

[31]  Pratyush Tiwary,et al.  Toward Achieving Efficient and Accurate Ligand-Protein Unbinding with Deep Learning and Molecular Dynamics through RAVE. , 2018, Journal of chemical theory and computation.

[32]  L. Goddard Information Theory , 1962, Nature.

[33]  M. Parrinello,et al.  Canonical sampling through velocity rescaling. , 2007, The Journal of chemical physics.

[34]  N. Goldenfeld Lectures On Phase Transitions And The Renormalization Group , 1972 .

[35]  Joshua W. Shaevitz,et al.  Predictability and hierarchy in Drosophila behavior , 2016, Proceedings of the National Academy of Sciences.

[36]  Wei Chen,et al.  Molecular enhanced sampling with autoencoders: On‐the‐fly collective variable discovery and accelerated free energy landscape exploration , 2017, J. Comput. Chem..

[37]  Axel van de Walle,et al.  A Review of Enhanced Sampling Approaches for Accelerated Molecular Dynamics , 2016 .

[38]  B. Matthews,et al.  Response of a protein structure to cavity-creating mutations and its relation to the hydrophobic effect. , 1992, Science.

[39]  K. Lindorff-Larsen,et al.  Biomolecular conformational changes and ligand binding: from kinetics to thermodynamics† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c7sc01627a , 2017, Chemical science.