Conformational sampling via a self-regulating effective energy surface.

The difficulty of efficiently sampling the phase space of complex systems with rough energy surfaces is well known. Typical solutions to the problem involve accelerating the crossing of barriers, but such methods often have the secondary problem that the low-energy states of interest are inadequately sampled, unless the parameters of the search algorithm are modified as the system evolves. A method is presented to improve the sampling with particular emphasis on the low-energy conformations, which make the most important contributions to the thermodynamics of the system. The algorithm proposed here samples the details of the minima, while easily surmounting barriers. This is achieved by introducing a self-regulating sampling variable which depends on the current state of the system. Two replicas of the system are introduced and the sampling variable is treated as a particle coupled to the physical system. The method is illustrated with a simple model system and is applied to the realistic example of barrier crossing in a protein-ligand complex.

[1]  H. Scheraga,et al.  On the multiple-minima problem in the conformational analysis of molecules: deformation of the potential energy hypersurface by the diffusion equation method , 1989 .

[2]  Amedeo Caflisch,et al.  Computational combinatorial chemistry for de novo ligand design: Review and assessment , 1995 .

[3]  S. Nosé A molecular dynamics method for simulations in the canonical ensemble , 1984 .

[4]  A. Voter,et al.  Extending the Time Scale in Atomistic Simulation of Materials Annual Re-views in Materials Research , 2002 .

[5]  Christian Bartels,et al.  Multidimensional adaptive umbrella sampling: Applications to main chain and side chain peptide conformations , 1997 .

[6]  U. Hansmann Parallel tempering algorithm for conformational studies of biological molecules , 1997, physics/9710041.

[7]  P A Kollman,et al.  Prediction of the binding free energies of new TIBO-like HIV-1 reverse transcriptase inhibitors using a combination of PROFEC, PB/SA, CMC/MD, and free energy calculations. , 1999, Journal of medicinal chemistry.

[8]  Hoover,et al.  Canonical dynamics: Equilibrium phase-space distributions. , 1985, Physical review. A, General physics.

[9]  M. Karplus,et al.  Proteins: A Theoretical Perspective of Dynamics, Structure, and Thermodynamics , 1988 .

[10]  Charles L. Brooks,et al.  Rapid Screening of Binding Affinities: Application of the λ-Dynamics Method to a Trypsin-Inhibitor System , 1998 .

[11]  E. Bauer Method of Calculating Cross Sections for Molecular Collisions , 1955 .

[12]  Martin Karplus,et al.  Probability Distributions for Complex Systems: Adaptive Umbrella Sampling of the Potential Energy , 1998 .

[13]  M. Karplus,et al.  The topology of multidimensional potential energy surfaces: Theory and application to peptide structure and kinetics , 1997 .

[14]  Charles L. Brooks,et al.  λ‐dynamics: A new approach to free energy calculations , 1996 .

[15]  M. Karplus,et al.  Self-guided enhanced sampling methods for thermodynamic averages , 2003 .

[16]  M. Karplus,et al.  Enhanced sampling in molecular dynamics: use of the time-dependent Hartree approximation for a simulation of carbon monoxide diffusion through myoglobin , 1990 .

[17]  G Stolovitzky,et al.  Catalytic tempering: A method for sampling rough energy landscapes by Monte Carlo. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[18]  M. Karplus,et al.  CHARMM: A program for macromolecular energy, minimization, and dynamics calculations , 1983 .

[19]  Bruce J. Berne,et al.  Method for accelerating chain folding and mixing , 1993 .

[20]  Aaron R. Dinner,et al.  Monte Carlo simulations of biomolecules: The MC module in CHARMM , 2006, J. Comput. Chem..

[21]  Straub,et al.  Generalized simulated annealing algorithms using Tsallis statistics: Application to conformational optimization of a tetrapeptide. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[22]  I. Andricioaei,et al.  On Monte Carlo and molecular dynamics methods inspired by Tsallis statistics: Methodology, optimization, and application to atomic clusters , 1997 .

[23]  M. Karplus,et al.  Simulation of activation free energies in molecular systems , 1996 .

[24]  Charles L. Brooks,et al.  Efficient and Flexible Algorithm for Free Energy Calculations Using the λ-Dynamics Approach , 1998 .

[25]  J.-P. Wery,et al.  Structure-based design of the first potent and selective inhibitor of human non-pancreatic secretory phospholipase A2 , 1995, Nature Structural Biology.

[26]  Christian Bartels,et al.  Determination of equilibrium properties of biomolecular systems using multidimensional adaptive umbrella sampling , 1999 .

[27]  J. J. Rosa,et al.  Structures of free and inhibited human secretory phospholipase A2 from inflammatory exudate. , 1993, Science.

[28]  Lee,et al.  New Monte Carlo algorithm: Entropic sampling. , 1993, Physical review letters.

[29]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[30]  Charles L. Brooks,et al.  Application of Multiple Topology λ-Dynamics to a Host−Guest System: β-Cyclodextrin with Substituted Benzenes , 2001 .

[31]  Bruce Tidor,et al.  Simulated annealing on free energy surfaces by a combined molecular dynamics and Monte Carlo approach , 1993 .

[32]  Berg,et al.  Multicanonical ensemble: A new approach to simulate first-order phase transitions. , 1992, Physical review letters.

[33]  D. L. Freeman,et al.  Reducing Quasi-Ergodic Behavior in Monte Carlo Simulations by J-Walking: Applications to Atomic Clusters , 1990 .

[34]  Charles L. Brooks,et al.  Free energy screening of small ligands binding to an artificial protein cavity , 2000 .

[35]  B. Brooks,et al.  Self-guided Langevin dynamics simulation method , 2003 .

[36]  M. Karplus,et al.  Functionality maps of binding sites: A multiple copy simultaneous search method , 1991, Proteins.

[37]  R. Elber,et al.  Modeling side chains in peptides and proteins: Application of the locally enhanced sampling and the simulated annealing methods to find minimum energy conformations , 1991 .

[38]  Peter A. Kollman,et al.  Designing an Optimum Guest for a Host Using Multimolecule Free Energy Calculations: Predicting the Best Ligand for Rebek's “Tennis Ball” , 1998 .

[39]  M. Karplus,et al.  Advances in chemical physics, volume 71: Proteins: A theoretical perspective of dynamics, structure, and thermodynamics , 2006 .

[40]  Sidney Yip,et al.  Optimized free-energy evaluation using a single reversible-scaling simulation , 1999 .

[41]  Alan E. Mark,et al.  Calculation of Relative Free-Energy Via Indirect Pathways , 1991 .

[42]  Bruce J. Berne,et al.  Multicanonical jump walking: A method for efficiently sampling rough energy landscapes , 1999 .

[43]  Xiongwu Wu,et al.  Enhancing systematic motion in molecular dynamics simulation , 1999 .