Development of a new physics‐based internal coordinate mechanics force field and its application to protein loop modeling

We report the development of internal coordinate mechanics force field (ICMFF), new force field parameterized using a combination of experimental data for crystals of small molecules and quantum mechanics calculations. The main features of ICMFF include: (a) parameterization for the dielectric constant relevant to the condensed state (ϵ = 2) instead of vacuum, (b) an improved description of hydrogen‐bond interactions using duplicate sets of van der Waals parameters for heavy atom‐hydrogen interactions, and (c) improved backbone covalent geometry and energetics achieved using novel backbone torsional potentials and inclusion of the bond angles at the Cα atoms into the internal variable set. The performance of ICMFF was evaluated through loop modeling simulations for 4–13 residue loops. ICMFF was combined with a solvent‐accessible surface area solvation model optimized using a large set of loop decoys. Conformational sampling was carried out using the biased probability Monte Carlo method. Average/median backbone root‐mean‐square deviations of the lowest energy conformations from the native structures were 0.25/0.21 Å for four residues loops, 0.84/0.46 Å for eight residue loops, and 1.16/0.73 Å for 12 residue loops. To our knowledge, these results are significantly better than or comparable with those reported to date for any loop modeling method that does not take crystal packing into account. Moreover, the accuracy of our method is on par with the best previously reported results obtained considering the crystal environment. We attribute this success to the high accuracy of the new ICM force field achieved by meticulous parameterization, to the optimized solvent model, and the efficiency of the search method. Proteins 2011. © 2010 Wiley‐Liss, Inc.

[1]  Yaohang Li,et al.  Backbone statistical potential from local sequence-structure interactions in protein loops. , 2010, The journal of physical chemistry. B.

[2]  H. Scheraga,et al.  Energy parameters in polypeptides. 10. Improved geometrical parameters and nonbonded interactions for use in the ECEPP/3 algorithm, with application to proline-containing peptides , 1994 .

[3]  G R Marshall,et al.  Ab initio modeling of small, medium, and large loops in proteins. , 2001, Biopolymers.

[4]  A. Goede,et al.  Loops In Proteins (LIP)--a comprehensive loop database for homology modelling. , 2003, Protein engineering.

[5]  R A Friesner,et al.  Prediction of loop geometries using a generalized born model of solvation effects , 1999, Proteins.

[6]  Ruben Abagyan,et al.  Protein structure prediction by global energy optimization , 1997 .

[7]  H. Scheraga,et al.  Coupling between conformation and proton binding in proteins , 2005, Proteins.

[8]  Harold A. Scheraga,et al.  Protein structure prediction using a combination of sequence homology and global energy minimization I. Global energy minimization of surface loops , 1990 .

[9]  Richard A Friesner,et al.  Prediction of Protein Loop Conformations using the AGBNP Implicit Solvent Model and Torsion Angle Sampling. , 2008, Journal of chemical theory and computation.

[10]  Fred E. Cohen,et al.  Conformational Sampling of Loop Structures Using Genetic Algorithms , 1994 .

[11]  Charles L. Brooks,et al.  Prediction of protein loop conformations using multiscale modeling methods with physical energy scoring functions , 2008, J. Comput. Chem..

[12]  T. N. Bhat,et al.  The Protein Data Bank , 2000, Nucleic Acids Res..

[13]  Anna Jagielska,et al.  A new force field (ECEPP-05) for peptides, proteins, and organic molecules. , 2006, The journal of physical chemistry. B.

[14]  J. Moult,et al.  An algorithm for determining the conformation of polypeptide segments in proteins by systematic search , 1986, Proteins.

[15]  C. Deane,et al.  A novel exhaustive search algorithm for predicting the conformation of polypeptide segments in proteins , 2000, Proteins.

[16]  A. Bondi.  Heat of Siblimation of Molecular Crystals: A Catalog of Molecular Structure Increments. , 1963 .

[17]  J. Wójcik,et al.  New efficient statistical sequence-dependent structure prediction of short to medium-sized protein loops based on an exhaustive loop classification. , 1999, Journal of molecular biology.

[18]  Harold A. Scheraga,et al.  Calculations of Conformations of Polypeptides , 1968 .

[19]  Jacco Van de Streek,et al.  On the irrelevance of electrostatics for the crystal structures and polymorphism of long even n‐alkanes , 2002, J. Comput. Chem..

[20]  Yujia Xu,et al.  Ramachandran revisited. DFT energy surfaces of diastereomeric trialanine peptides in the gas phase and aqueous solution. , 2009, The journal of physical chemistry. B.

[21]  Olga Kennard,et al.  Systematic analysis of structural data as a research technique in organic chemistry , 1983 .

[22]  D. Baker,et al.  Modeling structurally variable regions in homologous proteins with rosetta , 2004, Proteins.

[23]  Charles L. Brooks,et al.  Application of torsion angle molecular dynamics for efficient sampling of protein conformations , 2005, J. Comput. Chem..

[24]  Barry Honig,et al.  Loop modeling: Sampling, filtering, and scoring , 2007, Proteins.

[25]  A. Bondi.  van der Waals Volumes and Radii , 1964 .

[26]  G. Day,et al.  Atomistic calculations of phonon frequencies and thermodynamic quantities for crystals of rigid organic molecules , 2003 .

[27]  H. Meirovitch,et al.  Optimization of solvation models for predicting the structure of surface loops in proteins , 2001, Proteins.

[28]  P. Bennema,et al.  On the influence of thermal motion on the crystal structures and polymorphism of even n-alkanes. , 2002, Acta Crystallographica Section B Structural Science.

[29]  Harold A Scheraga,et al.  Folding of the villin headpiece subdomain from random structures. Analysis of the charge distribution as a function of pH. , 2004, Journal of molecular biology.

[30]  R Abagyan,et al.  Flexible protein–ligand docking by global energy optimization in internal coordinates , 1997, Proteins.

[31]  Alexander D. MacKerell,et al.  Extending the treatment of backbone energetics in protein force fields: Limitations of gas‐phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations , 2004, J. Comput. Chem..

[32]  Markus A Lill,et al.  New computational method for prediction of interacting protein loop regions , 2010, Proteins.

[33]  R Abagyan,et al.  High-throughput docking for lead generation. , 2001, Current opinion in chemical biology.

[34]  Cinque S. Soto,et al.  Evaluating conformational free energies: The colony energy and its application to the problem of loop prediction , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[35]  Robert E. Bruccoleri,et al.  Chain closure with bond angle variations , 1985 .

[36]  Kai Zhu,et al.  Toward better refinement of comparative models: Predicting loops in inexact environments , 2008, Proteins.

[37]  R. Friesner,et al.  Long loop prediction using the protein local optimization program , 2006, Proteins.

[38]  L. Schāfer,et al.  Predictions of protein backbone bond distances and angles from first principles , 1995 .

[39]  Sture Forsén,et al.  The barrier to internal rotation in monosubstituted amides , 1971 .

[40]  Sarah L. Price,et al.  Role of electrostatic interactions in determining the crystal structures of polar organic molecules. A distributed multipole study , 1996 .

[41]  B. Honig,et al.  Evaluation of the conformational free energies of loops in proteins , 1994, Proteins.

[42]  M. Karplus,et al.  PDB-based protein loop prediction: parameters for selection and methods for optimization. , 1997, Journal of molecular biology.

[43]  Mark S. Gordon,et al.  Chapter 41 – Advances in electronic structure theory: GAMESS a decade later , 2005 .

[44]  Richard S. Judson,et al.  Analysis of the genetic algorithm method of molecular conformation determination , 1993, J. Comput. Chem..

[45]  A. Lesk,et al.  Conformations of immunoglobulin hypervariable regions , 1989, Nature.

[46]  Ruben Abagyan,et al.  Ab InitioFolding of Peptides by the Optimal-Bias Monte Carlo Minimization Procedure , 1999 .

[47]  Jan Kroon,et al.  Crystal structure predictions for acetic acid , 1998, J. Comput. Chem..

[48]  Harold A. Scheraga,et al.  Exact analytical loop closure in proteins using polynomial equations , 1999, J. Comput. Chem..

[49]  A. Gavezzotti,et al.  Empirical intermolecular potentials for organic crystals: the `6‐exp' approximation revisited , 1993 .

[50]  William H. Press,et al.  Numerical recipes in Fortran 77 : the art of scientificcomputing. , 1992 .

[51]  C. Deane,et al.  CODA: A combined algorithm for predicting the structurally variable regions of protein models , 2001, Protein science : a publication of the Protein Society.

[52]  M. DePristo,et al.  Ab initio construction of polypeptide fragments: Efficient generation of accurate, representative ensembles , 2003, Proteins.

[53]  Harold A. Scheraga,et al.  Standard‐geometry chains fitted to X‐ray derived structures: Validation of the rigid‐geometry approximation. II. Systematic searches for short loops in proteins: Applications to bovine pancreatic ribonuclease A and human lysozyme , 1992 .

[54]  Harold A Scheraga,et al.  Atomically detailed folding simulation of the B domain of staphylococcal protein A from random structures , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[55]  R Abagyan,et al.  Homology modeling by the ICM method , 1995, Proteins.

[56]  Song Liu,et al.  Accurate and efficient loop selections by the DFIRE‐based all‐atom statistical potential , 2004, Protein science : a publication of the Protein Society.

[57]  Alexander D. MacKerell,et al.  Improved treatment of the protein backbone in empirical force fields. , 2004, Journal of the American Chemical Society.

[58]  Gautam R. Desiraju,et al.  The Weak Hydrogen Bond: In Structural Chemistry and Biology , 1999 .

[59]  Roland L. Dunbrack,et al.  Conformation dependence of backbone geometry in proteins. , 2009, Structure.

[60]  Michael J. Frisch,et al.  MP2 energy evaluation by direct methods , 1988 .

[61]  B. Honig,et al.  A hierarchical approach to all‐atom protein loop prediction , 2004, Proteins.

[62]  R Abagyan,et al.  Homology modeling with internal coordinate mechanics: Deformation zone mapping and improvements of models via conformational search , 1997, Proteins.

[63]  Hagai Meirovitch,et al.  Solvation parameters for predicting the structure of surface loops in proteins: Transferability and entropic effects , 2003, Proteins.

[64]  C. Levinthal,et al.  Predicting antibody hypervariable loop conformation. I. Ensembles of random conformations for ringlike structures , 1987, Biopolymers.

[65]  H. Scheraga,et al.  Identifying native‐like protein structures with scoring functions based on all‐atom ECEPP force fields, implicit solvent models and structure relaxation , 2009, Proteins.

[66]  Michael J. Frisch,et al.  A direct MP2 gradient method , 1990 .

[67]  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..

[68]  Luhua Lai,et al.  A fast and efficient program for modeling protein loops , 1997 .

[69]  N. Go,et al.  Ring Closure and Local Conformational Deformations of Chain Molecules , 1970 .

[70]  J. Richardson,et al.  The penultimate rotamer library , 2000, Proteins.

[71]  S. Price,et al.  A Systematic Nonempirical Method of Deriving Model Intermolecular Potentials for Organic Molecules: Application To Amides , 2000 .

[72]  A. Lesk,et al.  Canonical structures for the hypervariable regions of immunoglobulins. , 1987, Journal of molecular biology.

[73]  M. Karplus,et al.  Prediction of the folding of short polypeptide segments by uniform conformational sampling , 1987, Biopolymers.

[74]  P. Karplus.  Experimentally observed conformation‐dependent geometry and hidden strain in proteins , 1996, Protein science : a publication of the Protein Society.

[75]  M. DePristo,et al.  Ab initio construction of polypeptide fragments: Accuracy of loop decoy discrimination by an all‐atom statistical potential and the AMBER force field with the Generalized Born solvation model , 2003, Proteins.

[76]  Jaroslaw Pillardy,et al.  Conformation-family Monte Carlo: A new method for crystal structure prediction , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[77]  Mark S. Gordon,et al.  General atomic and molecular electronic structure system , 1993, J. Comput. Chem..

[78]  Alexander D. MacKerell,et al.  Force field influence on the observation of π-helical protein structures in molecular dynamics simulations , 2003 .

[79]  R. Abagyan,et al.  Biased probability Monte Carlo conformational searches and electrostatic calculations for peptides and proteins. , 1994, Journal of molecular biology.

[80]  A. Sali,et al.  Modeling of loops in protein structures , 2000, Protein science : a publication of the Protein Society.

[81]  H. Scheraga,et al.  Derivation of a new force field for crystal-structure prediction using global optimization: Nonbonded potential parameters for amines, imidazoles, amides, and carboxylic acids , 2004 .