PARENT: A Parallel Software Suite for the Calculation of Configurational Entropy in Biomolecular Systems.

Accurate estimation of configurational entropy from the in silico-generated biomolecular ensembles, e.g., from molecular dynamics (MD) trajectories, is dependent strongly on exhaustive sampling for physical reasons. This, however, creates a major computational problem for the subsequent estimation of configurational entropy using the Maximum Information Spanning Tree (MIST) or Mutual Information Expansion (MIE) approaches for internal molecular coordinates. In particular, the available software for such estimation exhibits serious limitations when it comes to molecules with hundreds or thousands of atoms, because of its reliance on a serial program architecture. To overcome this problem, we have developed a parallel, hybrid MPI/openMP C++ implementation of MIST and MIE, called PARENT, which is particularly optimized for high-performance computing and provides efficient estimation of configurational entropy in different biological processes (e.g., protein-protein interactions). In addition, PARENT also allows for a detailed mapping of intramolecular allosteric networks. Here, we benchmark the program on a set of 1-μs-long MD trajectories of 10 different protein complexes and their components, demonstrating robustness and good scalability. A direct comparison between MIST and MIE on the same dataset demonstrates a superior convergence behavior for the former approach, when it comes to total simulation length and configurational-space binning.

[1]  Harold A. Scheraga,et al.  On the Use of Classical Statistical Mechanics in the Treatment of Polymer Chain Conformation , 1976 .

[2]  Matsuda,et al.  Physical nature of higher-order mutual information: intrinsic correlations and frustration , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  M. Karplus,et al.  Method for estimating the configurational entropy of macromolecules , 1981 .

[4]  A. Singer,et al.  Maximum entropy formulation of the Kirkwood superposition approximation. , 2004, The Journal of chemical physics.

[5]  Andrew L. Lee,et al.  Using NMR to study fast dynamics in proteins: methods and applications. , 2010, Current opinion in pharmacology.

[6]  Bruce Tidor,et al.  MIST: Maximum Information Spanning Trees for dimension reduction of biological data sets , 2009, Bioinform..

[7]  Andrew T. Fenley,et al.  Correlation as a Determinant of Configurational Entropy in Supramolecular and Protein Systems , 2014, The journal of physical chemistry. B.

[8]  J. Kirkwood,et al.  The Radial Distribution Function in Liquids , 1942 .

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

[10]  Andrew T. Fenley,et al.  Entropy–enthalpy transduction caused by conformational shifts can obscure the forces driving protein–ligand binding , 2012, Proceedings of the National Academy of Sciences.

[11]  M. Gilson,et al.  Ligand configurational entropy and protein binding , 2007, Proceedings of the National Academy of Sciences.

[12]  M. Gilson,et al.  Calculation of Molecular Configuration Integrals , 2003 .

[13]  M. Gilson,et al.  Free energy, entropy, and induced fit in host-guest recognition: calculations with the second-generation mining minima algorithm. , 2004, Journal of the American Chemical Society.

[14]  Jorge Numata,et al.  Balanced and Bias-Corrected Computation of Conformational Entropy Differences for Molecular Trajectories. , 2012, Journal of chemical theory and computation.

[15]  A. Wand,et al.  Conformational entropy in molecular recognition by proteins , 2007, Nature.

[16]  Ruben Abagyan,et al.  ICM—A new method for protein modeling and design: Applications to docking and structure prediction from the distorted native conformation , 1994, J. Comput. Chem..

[17]  Antonija Kuzmanic,et al.  On the Contribution of Linear Correlations to Quasi-harmonic Conformational Entropy in Proteins. , 2012, Journal of chemical theory and computation.

[18]  W. Ebeling,et al.  Finite sample effects in sequence analysis , 1994 .

[19]  B. Zagrovic,et al.  Estimation of conformational entropy in protein-ligand interactions: a computational perspective. , 2012, Methods in molecular biology.

[20]  A. Wand,et al.  A surprising role for conformational entropy in protein function. , 2013, Topics in current chemistry.

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

[22]  J. Maurice Rojas,et al.  Practical conversion from torsion space to Cartesian space for in silico protein synthesis , 2005, J. Comput. Chem..

[23]  Ioan Andricioaei,et al.  On the calculation of entropy from covariance matrices of the atomic fluctuations , 2001 .

[24]  D. Herschbach,et al.  Molecular Partition Functions in Terms of Local Properties , 1959 .

[25]  Ugo Bastolla,et al.  Torsional network model: normal modes in torsion angle space better correlate with conformation changes in proteins. , 2010, Physical review letters.

[26]  A. Montanari,et al.  How to compute loop corrections to the Bethe approximation , 2005, cond-mat/0506769.

[27]  S. Tzeng,et al.  Protein activity regulation by conformational entropy , 2012, Nature.

[28]  Mark S. Gordon,et al.  Approximate Self‐Consistent Molecular‐Orbital Theory. VI. INDO Calculated Equilibrium Geometries , 1968 .

[29]  A. Joshua Wand,et al.  The role of conformational entropy in molecular recognition by calmodulin , 2010, Nature chemical biology.

[30]  Bruce Tidor,et al.  Efficient calculation of molecular configurational entropies using an information theoretic approximation. , 2012, The journal of physical chemistry. B.

[31]  H. Bethe Statistical Theory of Superlattices , 1935 .

[32]  Michael K Gilson,et al.  Extraction of configurational entropy from molecular simulations via an expansion approximation. , 2007, The Journal of chemical physics.

[33]  L. Dagum,et al.  OpenMP: an industry standard API for shared-memory programming , 1998 .

[34]  Kenneth S. Pitzer,et al.  Energy Levels and Thermodynamic Functions for Molecules with Internal Rotation: II. Unsymmetrical Tops Attached to a Rigid Frame , 1946 .

[35]  E. Freire Do enthalpy and entropy distinguish first in class from best in class? , 2008, Drug discovery today.

[36]  Harshinder Singh,et al.  Nearest‐neighbor nonparametric method for estimating the configurational entropy of complex molecules , 2007, J. Comput. Chem..

[37]  J. Schlitter Estimation of absolute and relative entropies of macromolecules using the covariance matrix , 1993 .

[38]  S. C. O'brien,et al.  C60: Buckminsterfullerene , 1985, Nature.

[39]  M. Gilson,et al.  The statistical-thermodynamic basis for computation of binding affinities: a critical review. , 1997, Biophysical journal.

[40]  R. Prim Shortest connection networks and some generalizations , 1957 .

[41]  Michael K. Gilson,et al.  Thermodynamic and Differential Entropy under a Change of Variables , 2010, Entropy.

[42]  Jun Tan,et al.  Efficient calculation of configurational entropy from molecular simulations by combining the mutual‐information expansion and nearest‐neighbor methods , 2008, J. Comput. Chem..

[43]  J Andrew McCammon,et al.  Statistical mechanics and molecular dynamics in evaluating thermodynamic properties of biomolecular recognition , 2011, Quarterly Reviews of Biophysics.

[44]  Michael K. Gilson,et al.  Theory of free energy and entropy in noncovalent binding. , 2009, Chemical reviews.