1
|
Kinugawa K, Takemoto A. Quantum polyamorphism in compressed distinguishable helium-4. J Chem Phys 2021; 154:224503. [PMID: 34241222 DOI: 10.1063/5.0048539] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We demonstrate that two amorphous solid states can exist in 4He consisting of distinguishable Boltzmann atoms under compressed conditions. The isothermal compression of normal or supercritical fluid 4He was conducted at 3-25 K using the isobaric-isothermal path integral centroid molecular dynamics simulation. The compression of fluid first produced the low-dispersion amorphous (LDA) state possessing modest extension of atomic necklaces. Further isothermal compression up to the order of 10 kbar to 1 Mbar or an isobaric cooling of LDA induced the transition to the high-dispersion amorphous (HDA) state. The HDA was characterized by long quantum wavelengths of atoms extended over several Angstroms and the promotion of atomic residual diffusion. They were related to the quantum tunneling of atoms bestriding the potential saddle points in this glass. The change in pressure or temperature induced the LDA-HDA transition reversibly with hysteresis, while it resembled the coil-globule transition of classical polymers. The HDA had lower kinetic and higher Gibbs free energies than the LDA at close temperature. The HDA was absent at T ≥ 13 K, while the LDA-HDA transition pressure significantly decreased with lowering temperature. The LDA and HDA correspond to the trapped and tunneling regimes proposed by Markland et al. [J. Chem. Phys. 136, 074511 (2012)], respectively. The same reentrant behavior as they found was observed for the expansion factor of the quantum wavelength as well as for atomic diffusivity.
Collapse
Affiliation(s)
- Kenichi Kinugawa
- Division of Chemistry, Graduate School of Humanities and Sciences, Nara Women's University, Nara 630-8506, Japan
| | - Ayumi Takemoto
- Division of Chemistry, Graduate School of Humanities and Sciences, Nara Women's University, Nara 630-8506, Japan
| |
Collapse
|
2
|
Ahuja P, Molayem M, Gadre SR. Electrostatics-Assisted Building-Up Procedure for Capturing Energy Minima of Metal Clusters: Test Case of Ag n Clusters. J Phys Chem A 2019; 123:7872-7880. [PMID: 31433180 DOI: 10.1021/acs.jpca.9b05601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Global geometry optimization of metal clusters is an important problem in nanophysics. The starting geometries of the clusters generated with empirical or other model potentials are generally optimized further by density functional theory (DFT)-based energy minimization. For this purpose, several algorithms such as simulated annealing, genetic algorithms, basin hopping, etc. are used. Our building-up procedure generates putative lower-energy structures of metal (M) clusters, Mn+1, Mn+2, etc., by anchoring one or more metal atoms in the vicinity of the minima of the molecular electrostatic potential (MESP) of Mn. Here, we report an application of this method to Agn clusters, for 5 ≤ n ≤ 20, followed up by DFT-based geometry optimization, generating several lower-energy structures than those reported in the literature. New low-energy isomers are obtained by applying the same procedure to the test case of mixed-metal clusters, NinAgm, for n + m = 4 and 5. In conclusion, our MESP-based building-up procedure offers a new general methodology for generating lower-energy geometries of metal clusters.
Collapse
Affiliation(s)
- Prateek Ahuja
- Department of Chemical Sciences , IISER Mohali , Sector-81, Mohali 140306 , India
| | - Mohammad Molayem
- Physical and Theoretical Chemistry , Saarland University , Saarbrücken 66123 , Germany
| | - Shridhar R Gadre
- Interdisciplinary School of Scientific Computing and Department of Chemistry , Savitribai Phule Pune University , Pune 411007 , India
| |
Collapse
|
3
|
Das S, Shimshi M, Raz K, Nitoker Eliaz N, Mhashal AR, Ansbacher T, Major DT. EnzyDock: Protein–Ligand Docking of Multiple Reactive States along a Reaction Coordinate in Enzymes. J Chem Theory Comput 2019; 15:5116-5134. [DOI: 10.1021/acs.jctc.9b00366] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Susanta Das
- Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Mor Shimshi
- Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Keren Raz
- Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel
| | | | - Anil Ranu Mhashal
- Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Tamar Ansbacher
- Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel
- Hadassah Academic College, 7 Hanevi’im Street, Jerusalem 9101001, Israel
| | - Dan T. Major
- Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel
| |
Collapse
|
4
|
Mukuta N, Miura S. Development of a generalized hybrid Monte Carlo algorithm to generate the multicanonical ensemble with applications to molecular systems. J Chem Phys 2018; 149:072322. [PMID: 30134718 DOI: 10.1063/1.5028466] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
In the present paper, a generalized hybrid Monte Carlo method to generate the multicanonical ensemble has been developed, which is a generalization of the multicanonical hybrid Monte Carlo (HMC) method by Hansmann and co-workers [Chem. Phys. Lett. 259, 321 (1996)]. The generalized hybrid Monte Carlo (GHMC) method is an equations-of-motion guided Monte Carlo combined with partial momentum refreshment. We successfully applied our multicanonical GHMC to dense Lennard-Jones fluids and a coarse grained protein model. It is found that good computational efficiency can be gained in the case of the acceptance ratio around 60% for the models examined. While a large number of molecular dynamics (MD) steps in a single GHMC cycle is needed to yield good computational efficiency at a large mixing ratio of momenta with thermal noise vectors, corresponding to the original multicanonical HMC method, a small number of MD steps are enough to achieve good efficiency at a small mixing ratio. This property is useful to develop a composite algorithm combining the present GHMC method with other Monte Carlo moves.
Collapse
Affiliation(s)
- Natsuki Mukuta
- Graduate School of Natural Science and Technology, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan
| | - Shinichi Miura
- Faculty of Mathematics and Physics, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan
| |
Collapse
|
5
|
Soley MB, Markmann A, Batista VS. Classical Optimal Control for Energy Minimization Based On Diffeomorphic Modulation under Observable-Response-Preserving Homotopy. J Chem Theory Comput 2018; 14:3351-3362. [DOI: 10.1021/acs.jctc.8b00124] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Micheline B. Soley
- Department of Chemistry, Yale University, P.O.
Box 208107, New Haven, Connecticut 06520-8107, United States
- Energy Sciences Institute, Yale University, P.O.
Box 27394, West Haven, Connecticut 06516-7394, United States
| | - Andreas Markmann
- Department of Chemistry, Yale University, P.O.
Box 208107, New Haven, Connecticut 06520-8107, United States
- Energy Sciences Institute, Yale University, P.O.
Box 27394, West Haven, Connecticut 06516-7394, United States
| | - Victor S. Batista
- Department of Chemistry, Yale University, P.O.
Box 208107, New Haven, Connecticut 06520-8107, United States
- Energy Sciences Institute, Yale University, P.O.
Box 27394, West Haven, Connecticut 06516-7394, United States
| |
Collapse
|
6
|
Nigg SE, Lörch N, Tiwari RP. Robust quantum optimizer with full connectivity. SCIENCE ADVANCES 2017; 3:e1602273. [PMID: 28435880 PMCID: PMC5384808 DOI: 10.1126/sciadv.1602273] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2016] [Accepted: 02/10/2017] [Indexed: 05/29/2023]
Abstract
Quantum phenomena have the potential to speed up the solution of hard optimization problems. For example, quantum annealing, based on the quantum tunneling effect, has recently been shown to scale exponentially better with system size than classical simulated annealing. However, current realizations of quantum annealers with superconducting qubits face two major challenges. First, the connectivity between the qubits is limited, excluding many optimization problems from a direct implementation. Second, decoherence degrades the success probability of the optimization. We address both of these shortcomings and propose an architecture in which the qubits are robustly encoded in continuous variable degrees of freedom. By leveraging the phenomenon of flux quantization, all-to-all connectivity with sufficient tunability to implement many relevant optimization problems is obtained without overhead. Furthermore, we demonstrate the robustness of this architecture by simulating the optimal solution of a small instance of the nondeterministic polynomial-time hard (NP-hard) and fully connected number partitioning problem in the presence of dissipation.
Collapse
|
7
|
Kamberaj H. Conformational sampling enhancement of replica exchange molecular dynamics simulations using swarm particle intelligence. J Chem Phys 2015; 143:124105. [DOI: 10.1063/1.4931599] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
8
|
Soley M, Markmann A, Batista VS. Steered quantum dynamics for energy minimization. J Phys Chem B 2015; 119:715-27. [PMID: 25122515 DOI: 10.1021/jp5046723] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We introduce a quantum optimal control algorithm for energy minimization that combines the diffeomorphic modulation under observable response preserving homotopy (D-MORPH) gradient and the Broyden Fletcher Goldfarb Shanno (BFGS) iterative scheme for nonlinear optimization. An extended set of controls defining the time-dependent mass, dipole moment, and external perturbational field are optimized to find an effective Hamiltonian that steers the dynamics of the system into the global minimum without getting trapped into local minima. The algorithm is illustrated as applied to energy minimization on rugged surfaces and golf potentials comparable to those previously explored for testing quantum annealing methodologies.
Collapse
Affiliation(s)
- Micheline Soley
- Department of Chemistry, Yale University , P.O. Box 208107, New Haven, Connecticut 06520-8107, United States
| | | | | |
Collapse
|
9
|
Kim J, Straub JE, Keyes T. Replica exchange statistical temperature molecular dynamics algorithm. J Phys Chem B 2012; 116:8646-53. [PMID: 22540354 PMCID: PMC11240102 DOI: 10.1021/jp300366j] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
The replica exchange statistical temperature molecular dynamics (RESTMD) algorithm is presented, designed to alleviate an extensive increase of the number of replicas required as system size increases in the conventional temperature replica exchange method (tREM), and to obtain improved sampling in individual replicas. RESTMD optimally integrates multiple STMD (Phys. Rev. Lett. 2006, 97, 050601) runs with replica exchanges, giving rise to a flat energy sampling in each replica with a self-adjusting weight determination. The expanded flat energy dynamic sampling range allows the use of significantly fewer STMD replicas while maintaining the desired acceptance probability for replica exchanges. The computational advantages of RESTMD over conventional REM and single-replica STMD are explicitly demonstrated with an application to a coarse-grained protein model. The effect of two different kinetic temperature control schemes on the sampling efficiency is explored for diverse simulation conditions.
Collapse
Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, United States.
| | | | | |
Collapse
|
10
|
Wang LC, Xie DQ. Simulated Annealing Study on Structures and Energetics of CO2 in Argon Clusters. CHINESE J CHEM PHYS 2011. [DOI: 10.1088/1674-0068/24/05/620-624] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|
11
|
Pickard CJ, Needs RJ. Ab initio random structure searching. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:053201. [PMID: 21406903 DOI: 10.1088/0953-8984/23/5/053201] [Citation(s) in RCA: 349] [Impact Index Per Article: 26.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
It is essential to know the arrangement of the atoms in a material in order to compute and understand its properties. Searching for stable structures of materials using first-principles electronic structure methods, such as density-functional-theory (DFT), is a rapidly growing field. Here we describe our simple, elegant and powerful approach to searching for structures with DFT, which we call ab initio random structure searching (AIRSS). Applications to discovering the structures of solids, point defects, surfaces, and clusters are reviewed. New results for iron clusters on graphene, silicon clusters, polymeric nitrogen, hydrogen-rich lithium hydrides, and boron are presented.
Collapse
Affiliation(s)
- Chris J Pickard
- Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
| | | |
Collapse
|
12
|
Kim SY. An off-lattice frustrated model protein with a six-stranded β-barrel structure. J Chem Phys 2010; 133:135102. [DOI: 10.1063/1.3494038] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
13
|
Affiliation(s)
- Michele Ceriotti
- Computational Science, Department of Chemistry and Applied Biosciences, ETH Zürich, USI Campus, Via Giuseppe Buffi 13, CH-6900 Lugano, Switzerland and Università di Modena e Reggio Emilia and INFM-CNR-S3, via Campi 213/A, 41100 Modena, Italy
| | - Giovanni Bussi
- Computational Science, Department of Chemistry and Applied Biosciences, ETH Zürich, USI Campus, Via Giuseppe Buffi 13, CH-6900 Lugano, Switzerland and Università di Modena e Reggio Emilia and INFM-CNR-S3, via Campi 213/A, 41100 Modena, Italy
| | - Michele Parrinello
- Computational Science, Department of Chemistry and Applied Biosciences, ETH Zürich, USI Campus, Via Giuseppe Buffi 13, CH-6900 Lugano, Switzerland and Università di Modena e Reggio Emilia and INFM-CNR-S3, via Campi 213/A, 41100 Modena, Italy
| |
Collapse
|
14
|
Morita S, Suzuki S, Nakamura T. Quantum-thermal annealing with a cluster-flip algorithm. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:065701. [PMID: 19658557 DOI: 10.1103/physreve.79.065701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2009] [Indexed: 05/28/2023]
Abstract
A quantum-thermal annealing method using a cluster-flip algorithm is studied in the two-dimensional spin-glass model. The temperature (T) and the transverse field (Gamma) are decreased simultaneously with the same rate along a linear path on the T-Gamma plane. We found that the additional pulse of the transverse field to the frozen local spins produces a good approximate solution with a low computational cost.
Collapse
Affiliation(s)
- Satoshi Morita
- International School for Advanced Studies, Trieste 34151, Italy
| | | | | |
Collapse
|
15
|
Morrone JA, Lin L, Car R. Tunneling and delocalization effects in hydrogen bonded systems: A study in position and momentum space. J Chem Phys 2009; 130:204511. [DOI: 10.1063/1.3142828] [Citation(s) in RCA: 62] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
16
|
Kim J, Keyes T. Influence of Go-Like Interactions on Global Shapes of Energy Landscapes in β-Barrel Forming Model Proteins: Inherent Structure Analysis and Statistical Temperature Molecular Dynamics Simulation. J Phys Chem B 2007; 112:954-66. [DOI: 10.1021/jp072872u] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215
| | - Thomas Keyes
- Department of Chemistry, Boston University, Boston, Massachusetts 02215
| |
Collapse
|
17
|
Kim J, Straub JE, Keyes T. Statistical temperature molecular dynamics: Application to coarse-grained β-barrel-forming protein models. J Chem Phys 2007; 126:135101. [PMID: 17430069 DOI: 10.1063/1.2711812] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Recently the authors proposed a novel sampling algorithm, "statistical temperature molecular dynamics" (STMD) [J. Kim et al., Phys. Rev. Lett. 97, 050601 (2006)], which combines ingredients of multicanonical molecular dynamics and Wang-Landau sampling. Exploiting the relation between the statistical temperature and the density of states, STMD generates a flat energy distribution and efficient sampling with a dynamic update of the statistical temperature, transforming an initial constant estimate to the true statistical temperature T(U), with U being the potential energy. Here, the performance of STMD is examined in the Lennard-Jones fluid with diverse simulation conditions, and in the coarse-grained, off-lattice BLN 46-mer and 69-mer protein models, exhibiting rugged potential energy landscapes with a high degree of frustration. STMD simulations combined with inherent structure (IS) analysis allow an accurate determination of protein thermodynamics down to very low temperatures, overcoming quasiergodicity, and illuminate the transitions occurring in folding in terms of the energy landscape. It is found that a thermodynamic signature of folding is significantly suppressed by accurate sampling, due to an incoherent contribution from low-lying non-native IS in multifunneled landscapes. It is also shown that preferred accessibility to such IS during the collapse transition is intimately related to misfolding or poor foldability.
Collapse
Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
| | | | | |
Collapse
|
18
|
Stella L, Santoro GE. Quantum annealing of an Ising spin-glass by Green's function Monte Carlo. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:036703. [PMID: 17500822 DOI: 10.1103/physreve.75.036703] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2006] [Revised: 12/08/2006] [Indexed: 05/15/2023]
Abstract
We present an implementation of quantum annealing (QA) via lattice Green's function Monte Carlo (GFMC), focusing on its application to the Ising spin glass in transverse field. In particular, we study whether or not such a method is more effective than the path-integral Monte Carlo- (PIMC) based QA, as well as classical simulated annealing (CA), previously tested on the same optimization problem. We identify the issue of importance sampling, i.e., the necessity of possessing reasonably good (variational) trial wave functions, as the key point of the algorithm. We performed GFMC-QA runs using such a Boltzmann-type trial wave function, finding results for the residual energies that are qualitatively similar to those of CA (but at a much larger computational cost), and definitely worse than PIMC-QA. We conclude that, at present, without a serious effort in constructing reliable importance sampling variational wave functions for a quantum glass, GFMC-QA is not a true competitor of PIMC-QA.
Collapse
Affiliation(s)
- Lorenzo Stella
- International School for Advanced Studies (SISSA) and INFM Democritos National Simulation Center, Via Beirut 2-4, I-34014 Trieste, Italy
| | | |
Collapse
|
19
|
Abstract
An analysis in terms of the inherent structures (IS, local minima) of the multidimensional potential energy landscape is applied to proteins. Detailed calculations are performed for the 46 bead BLN model, which folds into a four-stranded beta-barrel. Enhanced sampling has allowed determination of 239 199 IS states, believed to encompass nearly all the compact, low-energy states, and of well-averaged thermodynamic quantities at low temperature. The density of states shows distinct lobes for compact and extended states, and entropic barriers for the collapse and local ordering transitions. A two-dimensional scatterplot or density of states clearly shows the multifunnel structure of the energy landscape. The anharmonic vibrational free energy is found to play a crucial role in protein folding. The problem of determining the folding transition in a multifunnel system is discussed, and novel indicators of folding are introduced. A particularly clear picture is obtained through the occupation probabilities, pi, of individual low-lying IS, which become finite below the collapse temperature; it is suggested that poor foldability corresponds to a large "misfolding interval" where the excited state pi>0 exceeds that of the native state p0.
Collapse
Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
| | | |
Collapse
|
20
|
|
21
|
Santoro GE, Tosatti E. Optimization using quantum mechanics: quantum annealing through adiabatic evolution. ACTA ACUST UNITED AC 2006. [DOI: 10.1088/0305-4470/39/36/r01] [Citation(s) in RCA: 225] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
22
|
Kim J, Straub JE, Keyes T. Statistical-temperature Monte Carlo and molecular dynamics algorithms. PHYSICAL REVIEW LETTERS 2006; 97:050601. [PMID: 17026089 DOI: 10.1103/physrevlett.97.050601] [Citation(s) in RCA: 70] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2006] [Indexed: 05/12/2023]
Abstract
A simulation method is presented that achieves a flat energy distribution by updating the statistical temperature instead of the density of states in Wang-Landau sampling. A novel molecular dynamics algorithm (STMD) applicable to complex systems and a Monte Carlo algorithm are developed from this point of view. Accelerated convergence for large energy bins, essential for large systems, is demonstrated in tests on the Ising model, the Lennard-Jones fluid, and bead models of proteins. STMD shows a superior ability to find local minima in proteins and new global minima are found for the 55 bead AB model in two and three dimensions. Calculations of the occupation probabilities of individual protein inherent structures provide new insights into folding and misfolding.
Collapse
Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, MA 02215, USA.
| | | | | |
Collapse
|
23
|
Pan PW, Gordon HL, Rothstein SM. Local-structural diversity and protein folding: Application to all-β off-lattice protein models. J Chem Phys 2006; 124:024905. [PMID: 16422646 DOI: 10.1063/1.2151174] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Global measures of structural diversity within a distribution of biopolymers, such as the radius of gyration and percent native contacts, have proven useful in the analysis of simulation data for protein folding. In this paper we describe a statistical-based methodology to quantify the local structural variability of a distribution of biopolymers, applied to 46- and 69-"residue" off-lattice, three-color model proteins. Each folds into beta-barrel structures. First we perform a principal component analysis of all interbead distance variables for a large number of independent, converged Boltzmann-distributed samples of conformations collected at each of a wide range of temperatures. Next, the principal component vectors are subjected to orthogonal (varimax) rotation. The results are displayed on so-called "squared-loading" plots. These provide a quantitative measure of the contribution to the sample variance of the position of each residue relative to the others. Dominant structural elements, those having the largest structural diversity within the sampled distribution, are responsible for peaks and shoulders observed in the specific heat versus temperature curves, generated using the weighted histogram analysis method. The loading plots indicate that the local-structural diversity of these systems changes gradually with temperature through the folding transition but radically changes near the collapse transition temperature. The analysis of the structural overlap order statistic suggests that the 46-mer thermodynamic folding transition involves the native state and at least three other nearly native intermediates. In the case of the 46-mer protein model, data are generated at sufficiently low temperatures that squared-loading plots, coupled with cluster analysis, provide a local and energetic description of its glassy state.
Collapse
Affiliation(s)
- Patricia Wang Pan
- Department of Chemistry, Brock University, St. Catharines, Ontario L2S 3A1, Canada
| | | | | |
Collapse
|
24
|
Gregor T, Car R. Minimization of the potential energy surface of Lennard–Jones clusters by quantum optimization. Chem Phys Lett 2005. [DOI: 10.1016/j.cplett.2005.06.075] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
25
|
Battaglia DA, Santoro GE, Tosatti E. Optimization by quantum annealing: lessons from hard satisfiability problems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:066707. [PMID: 16089911 DOI: 10.1103/physreve.71.066707] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2005] [Indexed: 05/03/2023]
Abstract
The path integral Monte Carlo simulated quantum annealing algorithm is applied to the optimization of a large hard instance of the random satisfiability problem (N = 10,000). The dynamical behavior of the quantum and the classical annealing are compared, showing important qualitative differences in the way of exploring the complex energy landscape of the combinatorial optimization problem. At variance with the results obtained for the Ising spin glass and for the traveling salesman problem, in the present case the linear-schedule quantum annealing performance is definitely worse than classical annealing. Nevertheless, a quantum cooling protocol based on field-cycling and able to outperform standard classical simulated annealing over short time scales is introduced.
Collapse
Affiliation(s)
- Demian A Battaglia
- International School for Advanced Studies (SISSA), and INFM Democritos National Simulation Center, Via Beirut 2-4, I-34014 Trieste, Italy.
| | | | | |
Collapse
|
26
|
Abstract
Molecular simulations and an energy landscape analysis are used to examine the stretching of a model protein. A mapping of the energy landscape shows that stretching the protein causes energy minima and energy barriers to flatten out and disappear, and new energy minima to be created. The implications of these landscape distortions depend on the timescale regime under which the protein is stretched. When the timescale for thermally activated processes is longer than the timescale of stretching, the disappearances of energy barriers provide the mechanism for protein unfolding. When the timescale for thermally activated processes is shorter than the timescale of stretching, the landscape distortions influence the stretching process by changing the number and types of energy minima in which the system can exist.
Collapse
Affiliation(s)
- Daniel J Lacks
- Department of Chemical Engineering, Case Western Reserve University, Cleveland, Ohio, USA.
| |
Collapse
|
27
|
Martonák R, Santoro GE, Tosatti E. Quantum annealing of the traveling-salesman problem. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:057701. [PMID: 15600807 DOI: 10.1103/physreve.70.057701] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2004] [Indexed: 05/24/2023]
Abstract
We propose a path-integral Monte Carlo quantum annealing scheme for the symmetric traveling-salesman problem, based on a highly constrained Ising-like representation, and we compare its performance against standard thermal simulated annealing. The Monte Carlo moves implemented are standard, and consist in restructuring a tour by exchanging two links (two-opt moves). The quantum annealing scheme, even with a drastically simple form of kinetic energy, appears definitely superior to the classical one, when tested on a 1002-city instance of the standard TSPLIB.
Collapse
Affiliation(s)
- Roman Martonák
- Computational Science, Department of Chemistry and Applied Biosciences, ETH Zürich, USI Campus, Via Giuseppe Buffi 13, CH-6900 Lugano, Switzerland
| | | | | |
Collapse
|
28
|
Minary P, Tuckerman ME, Martyna GJ. Long time molecular dynamics for enhanced conformational sampling in biomolecular systems. PHYSICAL REVIEW LETTERS 2004; 93:150201. [PMID: 15524853 DOI: 10.1103/physrevlett.93.150201] [Citation(s) in RCA: 65] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2004] [Indexed: 05/24/2023]
Abstract
Although molecular dynamics methods are commonly used to drive biomolecular simulations, the technique provides insufficient sampling to impact studies of the 200-300 residue proteins of greatest interest. One severe limitation of molecular dynamics is that the integrators are restricted by resonance phenomena to small time steps (Delta t<8 fs) much slower then the time scales of important structural and solvent rearrangements. Here, a novel set of equations of motion and a reversible, resonance-free, integrator are designed which permit step sizes on the order of 100 fs to be used.
Collapse
Affiliation(s)
- P Minary
- Department of Chemistry, New York University, New York, New York 10003, USA
| | | | | |
Collapse
|
29
|
Mancera RL, Källblad P, Todorov NP. Ligand-protein docking using a quantum stochastic tunneling optimization method. J Comput Chem 2004; 25:858-64. [PMID: 15011257 DOI: 10.1002/jcc.20022] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
A novel hybrid optimization method called quantum stochastic tunneling has been recently introduced. Here, we report its implementation within a new docking program called EasyDock and a validation with the CCDC/Astex data set of ligand-protein complexes using the PLP score to represent the ligand-protein potential energy surface and ScreenScore to score the ligand-protein binding energies. When taking the top energy-ranked ligand binding mode pose, we were able to predict the correct crystallographic ligand binding mode in up to 75% of the cases. By using this novel optimization method run times for typical docking simulations are significantly shortened.
Collapse
Affiliation(s)
- Ricardo L Mancera
- De Novo Pharmaceuticals, Compass House, Vision Park, Histon, Cambridge CB4 9ZR, United Kingdom.
| | | | | |
Collapse
|
30
|
Larrass SA, Pegram LM, Gordon HL, Rothstein SM. Efficient generation of low-energy folded states of a model protein. II. Automated histogram filtering. J Chem Phys 2003. [DOI: 10.1063/1.1628671] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
31
|
Kim SY, Lee SJ, Lee J. Conformational space annealing and an off-lattice frustrated model protein. J Chem Phys 2003. [DOI: 10.1063/1.1616917] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
32
|
Liu P, Berne BJ. Quantum path minimization: An efficient method for global optimization. J Chem Phys 2003. [DOI: 10.1063/1.1527919] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
33
|
Todorov N, Mancera R, Monthoux P. A new quantum stochastic tunnelling optimisation method for protein–ligand docking. Chem Phys Lett 2003. [DOI: 10.1016/s0009-2614(02)01925-5] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
|
34
|
Gordon HL, Kwan WK, Gong C, Larrass S, Rothstein SM. Efficient generation of low-energy folded states of a model protein. J Chem Phys 2003. [DOI: 10.1063/1.1530579] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
35
|
Sabo D, Doll JD, Freeman DL. Taming the rugged landscape: Techniques for the production, reordering, and stabilization of selected cluster inherent structures. J Chem Phys 2003. [DOI: 10.1063/1.1562621] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
36
|
Gorse D. Application of a chaperone-based refolding method to two- and three-dimensional off-lattice protein models. Biopolymers 2002; 64:146-60. [PMID: 12012350 DOI: 10.1002/bip.10148] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
A model of protein-chaperone interaction as a two-phase (unfolding/refolding) iterative annealing mechanism able to promote structural segregation of hydrophobic and hydrophilic monomers and thereby facilitate access to nativelike states has recently been applied successfully to two 22-mers of the Honeycutt and Thirumalai BLN (hydrophobic, hydrophilic, neutral) heteropolymer model. This technique is here applied to a much wider data set: 94 8-mers of the off-lattice protein model originally presented in two dimensions by Stillinger and Head-Gordon, and later extended into three dimensions by Irbäck and Potthast; the model chaperone is shown to be equally successful, and by progressive elaboration of the chaperone model as in the earlier BLN model work, to be utilizing very similar underlying mechanisms. It is demonstrated that on average, contacts with the model chaperone give rise to a consistent movement in structure space in the direction of more nativelike structures; this method of global minimization does not therefore rely fundamentally on random search. Insofar as the responses to the chaperone of the two- and three-dimensional forms of the substrate model do differ, this can be interpreted as reflecting the different handling of hydrophilic monomers in the models-in particular, whether there is active repulsion between these and monomers of hydrophobic character. The chaperone-induced refolding method is also tested on a set of 220 9-mer chains of each version of the substrate model, where it is seen that the two-dimensional model, with its more clearly distinguished roles for the hydrophobic and hydrophilic monomers, shows a more favorable scaling behavior.
Collapse
Affiliation(s)
- Denise Gorse
- Department of Computer Science, University College, Gower Street, London WC1E 6BT, UK.
| |
Collapse
|
37
|
Santoro GE, Martonák R, Tosatti E, Car R. Theory of quantum annealing of an Ising spin glass. Science 2002; 295:2427-30. [PMID: 11923532 DOI: 10.1126/science.1068774] [Citation(s) in RCA: 438] [Impact Index Per Article: 19.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Probing the lowest energy configuration of a complex system by quantum annealing was recently found to be more effective than its classical, thermal counterpart. By comparing classical and quantum Monte Carlo annealing protocols on the two-dimensional random Ising model (a prototype spin glass), we confirm the superiority of quantum annealing relative to classical annealing. We also propose a theory of quantum annealing based on a cascade of Landau-Zener tunneling events. For both classical and quantum annealing, the residual energy after annealing is inversely proportional to a power of the logarithm of the annealing time, but the quantum case has a larger power that makes it faster.
Collapse
Affiliation(s)
- Giuseppe E Santoro
- Scuola Internazionale Superiore di Studi Avanzati (SISSA) and Istituto Nazionale per la Fisica della Materia (INFM) (Unità di Ricerca SISSA), I-34014 Trieste, Italy
| | | | | | | |
Collapse
|
38
|
Zhu Z, Tuckerman ME, Samuelson SO, Martyna GJ. Using novel variable transformations to enhance conformational sampling in molecular dynamics. PHYSICAL REVIEW LETTERS 2002; 88:100201. [PMID: 11909330 DOI: 10.1103/physrevlett.88.100201] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2001] [Indexed: 05/23/2023]
Abstract
One of the computational "grand challenges" is to develop methodology capable of sampling conformational equilibria in systems with rough energy landscapes. Here, a significant step forward is made by combining molecular dynamics with a novel variable transformation designed to enhance sampling by reducing barriers without introducing bias and, thus, to preserve, perfectly, equilibrium properties.
Collapse
Affiliation(s)
- Zhongwei Zhu
- Department of Chemistry, New York University, New York, New York 10003, USA
| | | | | | | |
Collapse
|
39
|
Miller TF, Clary DC. Torsional path integral Monte Carlo method for the quantum simulation of large molecules. J Chem Phys 2002. [DOI: 10.1063/1.1467342] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
|
40
|
Abstract
A global energy minimization method based on what is known about the mechanisms of the GroEL/GroES chaperonin system is applied to two 22-mers of an off-lattice protein model whose native states are beta-hairpins and which have structural similarity to short peptides known to interact strongly with the GroEL substrate binding domain. These model substrates have been used by other workers to test the effectiveness of a number of global minimization techniques, and are regarded as providing a significant challenge. The minimization method developed here is progressively elaborated from an initial simple form that targets exposed hydrophobic regions for unfolding to include a refolding phase that encourages the later recompactification of partly unfolded substrate; this refolding phase is seen to be crucial in the successful application of the method. The optimal handling of hydrophilic monomers within the model is also systematically explored, and it is seen that the best interpretation of their role is one that allows the chaperonin model to operate in "proofreading" mode whereby misfolded substrates are recognized by their surface exposure of a large proportion of hydrophobic monomers. The final version of the model allows native-like structures to be found quickly, on average for the two 22-mer substrates after 6 or 7 chaperone contacts. These results compare very favorably with those that have been obtained elsewhere using generic global minimization methods such as those based on thermal annealing. The paper concludes with a discussion of the place of the technique within the general category of hypersurface deformation methods for global minimization, and with suggestions as to how the chaperone-based method developed here could be elaborated so as to be effective on longer substrate chains that give rise to more complex tertiary structures in their native states.
Collapse
Affiliation(s)
- D Gorse
- Department of Computer Science, University College, Gower Street, London WC1E 6BT, UK.
| |
Collapse
|
41
|
Venkatesh PK. On the treatment of thermal and quantum annealing by stochastic variational means. Proc Math Phys Eng Sci 2001. [DOI: 10.1098/rspa.2001.0814] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
|
42
|
Clary DC. Torsional diffusion Monte Carlo: A method for quantum simulations of proteins. J Chem Phys 2001. [DOI: 10.1063/1.1368402] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
|
43
|
Lee YH, Berne BJ. Quantum Thermal Annealing with Renormalization: Application to a Frustrated Model Protein. J Phys Chem A 2000. [DOI: 10.1021/jp002589u] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Yong-Han Lee
- Department of Chemistry and Center for Biomolecular Simulation, Columbia University, 3000 Broadway, New York, New York 10027
| | - B. J. Berne
- Department of Chemistry and Center for Biomolecular Simulation, Columbia University, 3000 Broadway, New York, New York 10027
| |
Collapse
|