A Variable Neighbourhood Descent Heuristic for Conformational Search Using a Quantum Annealer

Discovering the low-energy conformations of a molecule is of great interest to computational chemists, with applications in in silico materials design and drug discovery. In this paper, we propose a variable neighbourhood search heuristic for the conformational search problem. Using the structure of a molecule, neighbourhoods are chosen to allow for the efficient use of a binary quadratic optimizer for conformational search. The method is flexible with respect to the choice of molecular force field and the number of discretization levels in the search space, and can be further generalized to take advantage of higher-order binary polynomial optimizers. It is well-suited for the use of devices such as quantum annealers. After carefully defining neighbourhoods, the method easily adapts to the size and topology of these devices, allowing for seamless scaling alongside their future improvements.

[1]  Wang,et al.  Replica Monte Carlo simulation of spin glasses. , 1986, Physical review letters.

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

[3]  H. Stoll,et al.  Energy-adjustedab initio pseudopotentials for the second and third row transition elements , 1990 .

[4]  W. Clark Still,et al.  An unbounded systematic search of conformational space , 1991 .

[5]  Stephen R. Wilson,et al.  Applications of simulated annealing to the conformational analysis of flexible molecules , 1991 .

[6]  W. Goddard,et al.  UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations , 1992 .

[7]  P. J. Phillips,et al.  The Science of Polymer Molecules: Contents , 1994 .

[8]  Joseph W. Ziller,et al.  A Series of Well‐Defined Metathesis Catalysts–Synthesis of [RuCl2(CHR′)(PR3)2] and Its Reactions , 1995 .

[9]  William L. Jorgensen,et al.  Monte Carlo vs Molecular Dynamics for Conformational Sampling , 1996 .

[10]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

[11]  New optimization method for conformational energy calculations on polypeptides: Conformational space annealing , 1997 .

[12]  Maurice Brookhart,et al.  Highly Active Iron and Cobalt Catalysts for the Polymerization of Ethylene , 1998 .

[13]  Valerie Daggett,et al.  Conformational search using a molecular dynamics–minimization procedure: Applications to clusters of coulombic charges, Lennard–Jones particles, and waters , 1998 .

[14]  Alexander J. Blake,et al.  Poly-orthophenylenes: Synthesis by suzuki coupling and solid state helical structures , 1998 .

[15]  Gregory A. Solan,et al.  IRON AND COBALT ETHYLENE POLYMERIZATION CATALYSTS BEARING 2,6-BIS(IMINO)PYRIDYL LIGANDS : SYNTHESIS, STRUCTURES, AND POLYMERIZATION STUDIES , 1999 .

[16]  Klaus Müllen,et al.  Polyphenylene Nanostructures. , 1999, Chemical reviews.

[17]  L. B. Morales,et al.  A parallel tabu search for conformational energy optimization of oligopeptides , 2000 .

[18]  J. Skolnick,et al.  Comparison of three Monte Carlo conformational search strategies for a proteinlike homopolymer model: Folding thermodynamics and identification of low-energy structures , 2000 .

[19]  Kengo Katayama,et al.  Performance of simulated annealing-based heuristic for the unconstrained binary quadratic programming problem , 2001, Eur. J. Oper. Res..

[20]  Bernd Freisleben,et al.  Greedy and Local Search Heuristics for Unconstrained Binary Quadratic Programming , 2002, J. Heuristics.

[21]  Florian Weigend,et al.  A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency , 2002 .

[22]  N. Kashiwa,et al.  FI Catalysts: A New Family of High Performance Catalysts for Olefin Polymerization , 2002 .

[23]  R. Car,et al.  Theory of Quantum Annealing of an Ising Spin Glass , 2002, Science.

[24]  V. Pande,et al.  Multiplexed-replica exchange molecular dynamics method for protein folding simulation. , 2003, Biophysical journal.

[25]  Tina Maria Trnka.  Catalysts for olefin metathesis: ruthenium alkylidene complexes with phosphine and N-heterocyclic carbene ligands , 2003 .

[26]  S. Goedecker.  Minima hopping: an efficient search method for the global minimum of the potential energy surface of complex molecular systems. , 2004, The Journal of chemical physics.

[27]  P. Charifson,et al.  Conformational analysis of drug-like molecules bound to proteins: an extensive study of ligand reorganization upon binding. , 2004, Journal of medicinal chemistry.

[28]  P. Merz,et al.  Memetic algorithms for the unconstrained binary quadratic programming problem. , 2004, Bio Systems.

[29]  Thierry Langer,et al.  Comparative Analysis of Protein-Bound Ligand Conformations with Respect to Catalyst's Conformational Space Subsampling Algorithms , 2005, J. Chem. Inf. Model..

[30]  F. Weigend,et al.  Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. , 2005, Physical chemistry chemical physics : PCCP.

[31]  P. Hustad,et al.  Catalytic Production of Olefin Block Copolymers via Chain Shuttling Polymerization , 2006, Science.

[32]  Sun Choi,et al.  The Effects of Biasing Torsional Mutations in a Conformational GA , 2006, J. Chem. Inf. Model..

[33]  Gintaras Palubeckis,et al.  Iterated Tabu Search for the Unconstrained Binary Quadratic Optimization Problem , 2006, Informatica.

[34]  F. Weigend.  Accurate Coulomb-fitting basis sets for H to Rn. , 2006, Physical chemistry chemical physics : PCCP.

[35]  Hiroshi Terao,et al.  Phenoxycycloalkylimine Ligated Zirconium Complexes for Ethylene Polymerization: Formation of Vinyl-Terminated Low Molecular Weight Polyethylenes with High Efficiency , 2006 .

[36]  H.-G. Meyer,et al.  Adiabatic Quantum Computation With Flux Qubits, First Experimental Results , 2007, IEEE Transactions on Applied Superconductivity.

[37]  Holger H. Hoos,et al.  A replica exchange Monte Carlo algorithm for protein folding in the HP model , 2007, BMC Bioinformatics.

[38]  Ekaterina I Izgorodina,et al.  Energy-directed tree search: an efficient systematic algorithm for finding the lowest energy conformation of molecules. , 2007, Physical chemistry chemical physics : PCCP.

[39]  Mark S. Johnson,et al.  Generating Conformer Ensembles Using a Multiobjective Genetic Algorithm , 2007, J. Chem. Inf. Model..

[40]  A. Leach.  A Survey of Methods for Searching the Conformational Space of Small and Medium-Sized Molecules , 2007 .

[41]  András Aszódi,et al.  Analyzing the performance of conformational search programs on compound databases. , 2007, Journal of molecular graphics & modelling.

[42]  H. Nishimori,et al.  Mathematical foundation of quantum annealing , 2008, 0806.1859.

[43]  Markus Christen,et al.  On searching in, sampling of, and dynamically moving through conformational space of biomolecular systems: A review , 2008, J. Comput. Chem..

[44]  D. Truhlar,et al.  The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals , 2008 .

[45]  Ralf Gehrke,et al.  Assessing the efficiency of first-principles basin-hopping sampling , 2009 .

[46]  F. Neese,et al.  Efficient, approximate and parallel Hartree–Fock and hybrid DFT calculations. A ‘chain-of-spheres’ algorithm for the Hartree–Fock exchange , 2009 .

[47]  Bernd Engels,et al.  Tabu search based strategies for conformational search. , 2009, The journal of physical chemistry. A.

[48]  Olivier Sperandio,et al.  MED-3DMC: a new tool to generate 3D conformation ensembles of small molecules with a Monte Carlo sampling of the conformational space. , 2009, European journal of medicinal chemistry.

[49]  Yan Feng,et al.  Funnel hopping: Searching the cluster potential energy surface over the funnels. , 2009, The Journal of chemical physics.

[50]  Chris Neale,et al.  Simulated Tempering Distributed Replica Sampling, Virtual Replica Exchange, and Other Generalized-Ensemble Methods for Conformational Sampling. , 2009, Journal of chemical theory and computation.

[51]  P. Chen,et al.  Tuning the Steric Properties of a Metathesis Catalyst for Copolymerization of Norbornene and Cyclooctene toward Complete Alternation , 2010 .

[52]  Xicheng Wang,et al.  Bioactive conformational generation of small molecules: A comparative analysis between force-field and multiple empirical criteria based methods , 2010, BMC Bioinformatics.

[53]  Michel Gendreau,et al.  Handbook of Metaheuristics , 2010 .

[54]  Fred W. Glover,et al.  A hybrid metaheuristic approach to solving the UBQP problem , 2010, Eur. J. Oper. Res..

[55]  Reza Sandaroos,et al.  A New Family of High‐Performance Ti Catalysts for Olefin Polymerization , 2010 .

[56]  Shouzhong Zou,et al.  ortho-Phenylenes: unusual conjugated oligomers with a surprisingly long effective conjugation length. , 2010, Journal of the American Chemical Society.

[57]  R. Copeland.  Conformational adaptation in drug-target interactions and residence time. , 2011, Future medicinal chemistry.

[58]  M. W. Johnson,et al.  Quantum annealing with manufactured spins , 2011, Nature.

[59]  Koichi Yamashita,et al.  Redox-responsive molecular helices with highly condensed π-clouds. , 2011, Nature chemistry.

[60]  Fred W. Glover,et al.  Path relinking for unconstrained binary quadratic programming , 2012, Eur. J. Oper. Res..

[61]  K. Dill,et al.  The Protein-Folding Problem, 50 Years On , 2012, Science.

[62]  Frank Neese,et al.  The ORCA program system , 2012 .

[63]  G. Rose,et al.  Finding low-energy conformations of lattice protein models by quantum annealing , 2012, Scientific Reports.

[64]  Kenji Shoji,et al.  An iterated greedy algorithm for the binary quadratic programming problem , 2012, The 6th International Conference on Soft Computing and Intelligent Systems, and The 13th International Symposium on Advanced Intelligence Systems.

[65]  Fred W. Glover,et al.  Backbone guided tabu search for solving the UBQP problem , 2011, Journal of Heuristics.

[66]  C. Ziegler,et al.  The role of arene-arene interactions in the folding of ortho-phenylenes. , 2013, Journal of the American Chemical Society.

[67]  Sándor Lovas,et al.  Conformational sampling techniques. , 2014, Current pharmaceutical design.

[68]  C. Ziegler,et al.  Enhanced helical folding of ortho-phenylenes through the control of aromatic stacking interactions. , 2014, Journal of the American Chemical Society.

[69]  Fred W. Glover,et al.  The unconstrained binary quadratic programming problem: a survey , 2014, Journal of Combinatorial Optimization.

[70]  Donald Hamelberg,et al.  Towards fast, rigorous and efficient conformational sampling of biomolecules: Advances in accelerated molecular dynamics. , 2015, Biochimica et biophysica acta.

[71]  Carsten Baldauf,et al.  First-Principles Molecular Structure Search with a Genetic Algorithm , 2015, J. Chem. Inf. Model..

[72]  Shingo Ito,et al.  Iron-catalysed homo- and copolymerisation of propylene: steric influence of bis(imino)pyridine ligands. , 2015, Dalton transactions.

[73]  Aidan Roy,et al.  Fast clique minor generation in Chimera qubit connectivity graphs , 2015, Quantum Inf. Process..

[74]  I. Bruno,et al.  Cambridge Structural Database , 2002 .

[75]  J. Andrew McCammon,et al.  Unconstrained enhanced sampling for free energy calculations of biomolecules: a review , 2016, Molecular simulation.

[76]  Mark A. Spalding,et al.  Handbook of Industrial Polyethylene and Technology: Definitive Guide to Manufacturing, Properties, Processing, Applications and Markets , 2017 .

[77]  Keehyoung Joo,et al.  Protein Loop Structure Prediction Using Conformational Space Annealing , 2017, J. Chem. Inf. Model..

[78]  Rupak Biswas,et al.  A NASA perspective on quantum computing: Opportunities and challenges , 2017, Parallel Comput..

[79]  Qingfu Zhang,et al.  A Parallel Tabu Search for the Unconstrained Binary Quadratic Programming problem , 2017, 2017 IEEE Congress on Evolutionary Computation (CEC).

[80]  P. Hawkins.  Conformation Generation: The State of the Art , 2017, J. Chem. Inf. Model..