51
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Škrbić T, Hoang TX, Giacometti A. Effective stiffness and formation of secondary structures in a protein-like model. J Chem Phys 2016; 145:084904. [DOI: 10.1063/1.4961387] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tatjana Škrbić
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca’ Foscari di Venezia, Campus Scientifico, Edificio Alfa, via Torino 155, 30170 Venezia Mestre, Italy
| | - Trinh X. Hoang
- Center for Computational Physics, Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Ba Dinh, Hanoi, Vietnam
| | - Achille Giacometti
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca’ Foscari di Venezia, Campus Scientifico, Edificio Alfa, via Torino 155, 30170 Venezia Mestre, Italy
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52
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Schierz P, Zierenberg J, Janke W. First-order phase transitions in the real microcanonical ensemble. Phys Rev E 2016; 94:021301. [PMID: 27627238 DOI: 10.1103/physreve.94.021301] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2016] [Indexed: 01/30/2023]
Abstract
We present a simulation and data analysis technique to investigate first-order phase transitions and the associated transition barriers. The simulation technique is based on the real microcanonical ensemble where the sum of kinetic and potential energy is kept constant. The method is tested for the droplet condensation-evaporation transition in a Lennard-Jones system with up to 2048 particles at fixed density, using simple Metropolis-like sampling combined with a replica-exchange scheme. Our investigation of the microcanonical ensemble properties reveals that the associated transition barrier is significantly lower than in the canonical counterpart. Along the line of investigating the microcanonical ensemble behavior, we develop a framework for general ensemble evaluations. This framework is based on a clear separation between system-related and ensemble-related properties, which can be exploited to specifically tailor artificial ensembles suitable for first-order phase transitions.
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Affiliation(s)
- Philipp Schierz
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
| | - Johannes Zierenberg
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
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53
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Zablotskiy SV, Martemyanova JA, Ivanov VA, Paul W. Diagram of states and morphologies of flexible-semiflexible copolymer chains: A Monte Carlo simulation. J Chem Phys 2016; 144:244903. [PMID: 27369540 DOI: 10.1063/1.4946035] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
A single copolymer chain consisting of multiple flexible (F) and semiflexible (S) blocks has been studied using a continuum bead-spring model by Stochastic Approximation Monte Carlo simulations, which determine the density of states of the model. The only difference between F and S blocks is the intramolecular bending potential, all non-bonded interactions are equal. The state diagrams for this class of models display multiple nematic phases in the collapsed state, characterized through a demixing of the blocks of different stiffness and orientational ordering of the stiff blocks. We observe dumbbell-like morphologies, lamellar phases, and for the larger block lengths also Saturn-like structures with a core of flexible segments and the stiff segments forming a ring around the core.
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Affiliation(s)
| | | | - Viktor A Ivanov
- Faculty of Physics, Moscow State University, Moscow 119991, Russia
| | - Wolfgang Paul
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, Halle (Saale) 06099, Germany
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54
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Lee J. Microcanonical analysis of a finite-size nonequilibrium system. Phys Rev E 2016; 93:052148. [PMID: 27300870 DOI: 10.1103/physreve.93.052148] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2015] [Indexed: 11/07/2022]
Abstract
Microcanonical analysis is a powerful method that can be used to generalize the concept of phase transitions to finite-size systems. However, microcanonical analysis has only been applied to equilibrium systems. I show that it is possible to conduct the microcanonical analysis of a finite-size nonequilibrium system by generalizing the concept of microcanonical entropy. A one-dimensional asymmetric diffusion process is studied as an example for which such a generalized entropy can be explicitly found, and the microcanonical method is used to define a generalized phase transition for the finite-size nonequilibrium system.
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Affiliation(s)
- Julian Lee
- Department of Bioinformatics and Life Science, Soongsil University, Seoul, Korea
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55
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Yang X, Lu ZY. Control globular structure formation of a copolymer chain through inverse design. J Chem Phys 2016; 144:224902. [PMID: 27306020 DOI: 10.1063/1.4953576] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Abstract
A copolymer chain in dilute solution can exhibit various globular structures with characteristic morphologies, which makes it a potentially useful candidate for artificial materials design. However, the chain has a huge conformation space and may not naturally form the globular structure we desire. An ideal way to control globular structure formation should be inverse design, i.e., starting from the target structure and finding out what kind of polymers can effectively generate it. To accomplish this, we propose an inverse design procedure, which is combined with Wang-Landau Monte Carlo to fully and precisely explore the huge conformation space of the chain. Starting from a desired target structure, all the geometrically possible sequences are exactly enumerated. Interestingly, reasonable interaction strengths are obtained and found to be not specified for only one sequence. Instead, they can be combined with many other sequences and also achieve a relatively high yield for target structure, although these sequences may be rather different. These results confirm the possibility of controlling globular structure formation of a copolymer chain through inverse design and pave the way for targeted materials design.
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Affiliation(s)
- Xi Yang
- State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130021, China
| | - Zhong-Yuan Lu
- State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130021, China
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56
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Williams MJ, Bachmann M. Significance of bending restraints for the stability of helical polymer conformations. Phys Rev E 2016; 93:062501. [PMID: 27415311 DOI: 10.1103/physreve.93.062501] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2016] [Indexed: 01/30/2023]
Abstract
We performed parallel-tempering Monte Carlo simulations to investigate the formation and stability of helical tertiary structures for flexible and semiflexible polymers, employing a generic coarse-grained model. Structural conformations exhibit helical order with tertiary ordering into single helices, multiple helical segments organized into bundles, and disorganized helical arrangements. For both bending-restrained semiflexible and bending-unrestrained flexible helical polymers, the stability of the structural phases is discussed systematically by means of hyperphase diagrams parametrized by suitable order parameters, temperature, and torsion strength. This exploration lends insight into the restricted flexibility of biological polymers such as double-stranded DNA and proteins.
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Affiliation(s)
- Matthew J Williams
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| | - Michael Bachmann
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA.,Instituto de Física, Universidade Federal de Mato Grosso, Cuiabá (MT), Brazil.,Departamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte (MG), Brazil
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57
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Zablotskiy SV, Ivanov VA, Paul W. Multidimensional stochastic approximation Monte Carlo. Phys Rev E 2016; 93:063303. [PMID: 27415383 DOI: 10.1103/physreve.93.063303] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2016] [Indexed: 06/06/2023]
Abstract
Stochastic Approximation Monte Carlo (SAMC) has been established as a mathematically founded powerful flat-histogram Monte Carlo method, used to determine the density of states, g(E), of a model system. We show here how it can be generalized for the determination of multidimensional probability distributions (or equivalently densities of states) of macroscopic or mesoscopic variables defined on the space of microstates of a statistical mechanical system. This establishes this method as a systematic way for coarse graining a model system, or, in other words, for performing a renormalization group step on a model. We discuss the formulation of the Kadanoff block spin transformation and the coarse-graining procedure for polymer models in this language. We also apply it to a standard case in the literature of two-dimensional densities of states, where two competing energetic effects are present g(E_{1},E_{2}). We show when and why care has to be exercised when obtaining the microcanonical density of states g(E_{1}+E_{2}) from g(E_{1},E_{2}).
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Affiliation(s)
| | - Victor A Ivanov
- Faculty of Physics, Moscow State University, Moscow 119991, Russia
| | - Wolfgang Paul
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle (Saale), Germany
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58
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Škrbić T, Badasyan A, Hoang TX, Podgornik R, Giacometti A. From polymers to proteins: the effect of side chains and broken symmetry on the formation of secondary structures within a Wang-Landau approach. SOFT MATTER 2016; 12:4783-4793. [PMID: 27137225 DOI: 10.1039/c6sm00542j] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We use a micro-canonical Wang-Landau technique to study the equilibrium properties of a single flexible homopolymer where consecutive monomers are represented by impenetrable hard spherical beads tangential to each other, and non-consecutive monomers interact via a square-well potential. To mimic the characteristics of a protein-like system, the model is then refined in two different directions. Firstly, by allowing partial overlap between consecutive beads, we break the spherical symmetry and thus provide a severe constraint on the possible conformations of the chain. Alternatively, we introduce additional spherical beads at specific positions in the direction normal to the backbone, to represent the steric hindrance of the side chains in real proteins. Finally, we consider also a combination of these two ingredients. In all three systems, we obtain the full phase diagram in the temperature-interaction range plane and find the presence of helicoidal structures at low temperatures in the intermediate range of interactions. The effect of the range of the square-well attraction is highlighted, and shown to play a role similar to that found in simple liquids and polymers. Perspectives in terms of protein folding are finally discussed.
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Affiliation(s)
- Tatjana Škrbić
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari di Venezia, Campus Scientifico, Edificio Alfa, via Torino 155, 30170 Venezia Mestre, Italy.
| | - Artem Badasyan
- Material Research Laboratory, University of Nova Gorica, SI-5270 Ajdovscina, Slovenia.
| | - Trinh Xuan Hoang
- Center for Computational Physics Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan St., Hanoi, Vietnam.
| | - Rudolf Podgornik
- Department of Theoretical Physics, J. Stefan Institute and Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia.
| | - Achille Giacometti
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari di Venezia, Campus Scientifico, Edificio Alfa, via Torino 155, 30170 Venezia Mestre, Italy.
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59
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Glagoleva AA, Vasilevskaya VV. Formation of a vesicle-like globule under steric restrictions. POLYMER SCIENCE SERIES A 2016. [DOI: 10.1134/s0965545x16020097] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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60
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Janke W, Paul W. Thermodynamics and structure of macromolecules from flat-histogram Monte Carlo simulations. SOFT MATTER 2016; 12:642-657. [PMID: 26574738 DOI: 10.1039/c5sm01919b] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Over the last decade flat-histogram Monte Carlo simulations, especially multi-canonical and Wang-Landau simulations, have emerged as a strong tool to study the statistical mechanics of polymer chains. These investigations have focused on coarse-grained models of polymers on the lattice and in the continuum. Phase diagrams of chains in bulk as well as chains attached to surfaces were studied, for homopolymers as well as for protein-like models. Also, aggregation behavior in solution of these models has been investigated. We will present here the theoretical background for these simulations, explain the algorithms used and discuss their performance and give an overview over the systems studied with these methods in the literature, where we will limit ourselves to studies of coarse-grained model systems. Implementations of these algorithms on parallel computers will be also briefly described. In parallel to the development of these simulation methods, the power of a micro-canonical analysis of such simulations has been recognized, and we present the current state of the art in applying the micro-canonical analysis to phase transitions in nanoscopic polymer systems.
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Affiliation(s)
- Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, 04009 Leipzig, Germany.
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61
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Böker A, Paul W. Wang-Landau simulation of Gō model molecules. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:5. [PMID: 26810395 DOI: 10.1140/epje/i2016-16005-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2015] [Accepted: 01/04/2016] [Indexed: 06/05/2023]
Abstract
Gō-like models are one of the oldest protein modeling concepts in computational physics and have proven their value over and over for forty years. The essence of a Gō model is to define a native contact matrix for a well-defined low-energy polymer configuration, e.g., the native state in the case of proteins or peptides. Many different potential shapes and many different cut-off distances in the definition of this native contact matrix have been proposed and applied. We investigate here the physical consequences of the choice for this cut-off distance in the Gō models derived for a square-well tangent sphere homopolymer chain. For this purpose we are performing flat-histogram Monte Carlo simulations of Wang-Landau type, obtaining the thermodynamic and structural properties of such models over the complete temperature range. Differences and similarities with Gō models for proteins and peptides are discussed.
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Affiliation(s)
- Arne Böker
- Institut für Physik, Martin-Luther-Universität, D-06099, Halle (Saale), Germany
| | - Wolfgang Paul
- Institut für Physik, Martin-Luther-Universität, D-06099, Halle (Saale), Germany.
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62
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Taylor MP, Ye Y, Adhikari SR. Conformation of a flexible polymer in explicit solvent: Accurate solvation potentials for Lennard-Jones chains. J Chem Phys 2015; 143:204901. [DOI: 10.1063/1.4935952] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Mark P. Taylor
- Department of Physics, Hiram College, Hiram, Ohio 44234, USA
| | - Yuting Ye
- Department of Physics, Hiram College, Hiram, Ohio 44234, USA
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63
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Koci T, Bachmann M. Confinement effects upon the separation of structural transitions in linear systems with restricted bond fluctuation ranges. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042142. [PMID: 26565203 DOI: 10.1103/physreve.92.042142] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2015] [Indexed: 06/05/2023]
Abstract
By means of advanced parallel replica-exchange Monte Carlo methods we examine the influence of elasticity and confinement on the structural transitions of linear systems with restricted bonded interaction. For this purpose, we adopt a model for coarse-grained flexible polymers of finite length in the dilute regime. Hyperphase diagrams are constructed using energy-dependent canonical quantities to demonstrate the effects of the changes in the range of the confined interaction on the liquid and solid structural phases. With increasing bonded interaction range we observe the disappearance of the liquid phase and the fusion of the gas-liquid (or Θ) and the liquid-solid transitions. One of the most remarkable features, the liquid-gas transition, changes from second to first order if the confined interaction range exceeds a threshold that separates polymeric from nonpolymeric systems. The notoriously difficult sampling of the entropically suppressed conformations in the region of very strong first-order transitions is improved by using multiple Gaussian modified ensembles.
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Affiliation(s)
- Tomas Koci
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| | - Michael Bachmann
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
- Instituto de Física, Universidade Federal de Mato Grosso, Cuiabá (MT), Brazil
- Departamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte (MG), Brazil
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64
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Leitold C, Lechner W, Dellago C. A string reaction coordinate for the folding of a polymer chain. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:194126. [PMID: 25923377 DOI: 10.1088/0953-8984/27/19/194126] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We investigate the crystallization mechanism of a single, flexible homopolymer chain with short range attractions. For a sufficiently narrow attractive well, the system undergoes a first-order like freezing transition from an expanded disordered coil to a compact crystalline state. Based on a maximum likelihood analysis of committor values computed for configurations obtained by Wang-Landau sampling, we construct a non-linear string reaction coordinate for the coil-to-crystal transition. In contrast to a linear reaction coordinate, the string reaction coordinate captures the effect of different degrees of freedom controlling different stages of the transition. Our analysis indicates that a combination of the energy and the global crystallinity parameter Q6 provide the most accurate measure for the progress of the transition. While the crystallinity paramter Q6 is most relevant in the initial stages of the crystallization, the later stages are dominated by a decrease in the potential energy.
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Affiliation(s)
- Christian Leitold
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
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65
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Leitold C, Dellago C. Folding mechanism of a polymer chain with short-range attractions. J Chem Phys 2014; 141:134901. [DOI: 10.1063/1.4896560] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Christian Leitold
- Faculty of Physics, University of Vienna, Sensengasse 8, 1090 Vienna, Austria
| | - Christoph Dellago
- Faculty of Physics, University of Vienna, Sensengasse 8, 1090 Vienna, Austria
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66
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Luettmer-Strathmann J, Binder K. Transitions of tethered chain molecules under tension. J Chem Phys 2014; 141:114911. [DOI: 10.1063/1.4895729] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Affiliation(s)
- Jutta Luettmer-Strathmann
- Department of Physics and Department of Chemistry, The University of Akron, Akron, Ohio 44325-4001, USA
| | - Kurt Binder
- Institut für Physik, Johannes-Gutenberg-Universität, Staudinger Weg 7, D-55099 Mainz, Germany
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67
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Vogel T, Li YW, Wüst T, Landau DP. Scalable replica-exchange framework for Wang-Landau sampling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:023302. [PMID: 25215846 DOI: 10.1103/physreve.90.023302] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2014] [Indexed: 06/03/2023]
Abstract
We investigate a generic, parallel replica-exchange framework for Monte Carlo simulations based on the Wang-Landau method. To demonstrate its advantages and general applicability for massively parallel simulations of complex systems, we apply it to lattice spin models, the self-assembly process in amphiphilic solutions, and the adsorption of molecules on surfaces. While of general current interest, the latter phenomena are challenging to study computationally because of multiple structural transitions occurring over a broad temperature range. We show how the parallel framework facilitates simulations of such processes and, without any loss of accuracy or precision, gives a significant speedup and allows for the study of much larger systems and much wider temperature ranges than possible with single-walker methods.
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Affiliation(s)
- Thomas Vogel
- Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| | - Ying Wai Li
- National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Thomas Wüst
- Scientific IT Services, ETH Zürich IT Services, 8092 Zürich, Switzerland
| | - David P Landau
- Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
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68
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Rocha JCS, Schnabel S, Landau DP, Bachmann M. Identifying transitions in finite systems by means of partition function zeros and microcanonical inflection-point analysis: a comparison for elastic flexible polymers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022601. [PMID: 25215750 DOI: 10.1103/physreve.90.022601] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2014] [Indexed: 06/03/2023]
Abstract
For the estimation of transition points of finite elastic, flexible polymers with chain lengths from 13 to 309 monomers, we compare systematically transition temperatures obtained by the Fisher partition function zeros approach with recent results from microcanonical inflection-point analysis. These methods rely on accurate numerical estimates of the density of states, which have been obtained by advanced multicanonical Monte Carlo sampling techniques. Both the Fisher zeros method and microcanonical inflection-point analysis yield very similar results and enable the unique identification of transition points in finite systems, which is typically impossible in the conventional canonical analysis of thermodynamic quantities.
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Affiliation(s)
- Julio C S Rocha
- Center for Simulational Physics, University of Georgia, Athens, Georgia 30602, USA
| | - Stefan Schnabel
- Institut für Theoretische Physik and Centre for Theoretical Sciences (NTZ), Universität Leipzig, Postfach 100920, D-04009 Leipzig, Germany
| | - David P Landau
- Center for Simulational Physics, University of Georgia, Athens, Georgia 30602, USA
| | - Michael Bachmann
- Center for Simulational Physics, University of Georgia, Athens, Georgia 30602, USA and Instituto de Física, Universidade Federal de Mato Grosso, Cuiabá (MT), Brazil and Departamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte (MG), Brazil
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69
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Thermodynamic and conformational insights into the phase transition of a single flexible homopolymer chain using replica exchange Monte Carlo method. J Mol Model 2014; 20:2296. [PMID: 24961896 DOI: 10.1007/s00894-014-2296-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2014] [Accepted: 05/05/2014] [Indexed: 10/25/2022]
Abstract
The phase transition of a single flexible homopolymer chain in the limit condition of dilute solution is systematically investigated using a coarse-grained model. Replica exchange Monte Carlo method is used to enhance the performance of the conformation space exploration, and thus detailed investigation of phase behavior of the system can be provided. With the designed potentials, the coil-globule transition and the liquid-solid-like transition are identified, and the transition temperatures are measured with the conformational and thermodynamic analyses. Additionally, by extrapolating the coil-globule transition temperature, T Θ , and the liquid-solid-like transition temperature T(L → S) to the thermodynamic limit, N → ∞, we found no "tri-critical" point in the current model.
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70
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Li YW, Vogel T, Wüst T, Landau DP. A new paradigm for petascale Monte Carlo simulation: Replica exchange Wang-Landau sampling. ACTA ACUST UNITED AC 2014. [DOI: 10.1088/1742-6596/510/1/012012] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
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71
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Tian P, Jónsson SÆ, Ferkinghoff-Borg J, Krivov SV, Lindorff-Larsen K, Irbäck A, Boomsma W. Robust Estimation of Diffusion-Optimized Ensembles for Enhanced Sampling. J Chem Theory Comput 2014; 10:543-53. [DOI: 10.1021/ct400844x] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Affiliation(s)
- Pengfei Tian
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark
| | - Sigurdur Æ. Jónsson
- Computational Biology
and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE-223 62 Lund, Sweden
| | | | - Sergei V. Krivov
- Astbury Center for
Structural Molecular Biology, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Kresten Lindorff-Larsen
- Structural
Biology and NMR Laboratory, Department of Biology, University of Copenhagen, Ole Maaløes Vej 5 DK-2200 Copenhagen N, Denmark
| | - Anders Irbäck
- Computational Biology
and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE-223 62 Lund, Sweden
| | - Wouter Boomsma
- Structural
Biology and NMR Laboratory, Department of Biology, University of Copenhagen, Ole Maaløes Vej 5 DK-2200 Copenhagen N, Denmark
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72
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Wang-Landau and Stochastic Approximation Monte Carlo for Semi-flexible Polymer Chains. ACTA ACUST UNITED AC 2014. [DOI: 10.1016/j.phpro.2014.08.137] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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73
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Gross J, Neuhaus T, Vogel T, Bachmann M. Effects of the interaction range on structural phases of flexible polymers. J Chem Phys 2013; 138:074905. [PMID: 23445033 DOI: 10.1063/1.4790615] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We systematically investigate how the range of interaction between non-bonded monomers influences the formation of structural phases of elastic, flexible polymers. Massively parallel replica-exchange simulations of a generic, coarse-grained model, performed partly on graphics processing units and in multiple-gaussian modified ensembles, pave the way for the construction of the structural phase diagram, parametrized by interaction range and temperature. Conformational transitions between gas-like, liquid, and diverse solid (pseudo) phases are identified by microcanonical statistical inflection-point analysis. We find evidence for finite-size effects that cause the crossover of "collapse" and "freezing" transitions for very short interaction ranges.
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Affiliation(s)
- J Gross
- Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA.
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74
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Ivanov VA, Martemyanova JA, Rodionova AS, Stukan MR. Computer simulation of stiff-chain polymers. POLYMER SCIENCE SERIES C 2013. [DOI: 10.1134/s1811238213060039] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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75
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Taylor MP, Paul W, Binder K. Applications of the Wang-Landau algorithm to phase transitions of a single polymer chain. POLYMER SCIENCE SERIES C 2013. [DOI: 10.1134/s1811238213060040] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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76
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Taylor MP, Aung PP, Paul W. Partition function zeros and phase transitions for a square-well polymer chain. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:012604. [PMID: 23944483 DOI: 10.1103/physreve.88.012604] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2012] [Revised: 05/31/2013] [Indexed: 06/02/2023]
Abstract
The zeros of the canonical partition functions for flexible square-well polymer chains have been approximately computed for chains up to length 256 for a range of square-well diameters. We have previously shown that such chain molecules can undergo a coil-globule and globule-crystal transition as well as a direct coil-crystal transition. Here we show that each of these transitions has a well-defined signature in the complex-plane map of the partition function zeros. The freezing transitions are characterized by nearly circular rings of uniformly spaced roots, indicative of a discontinuous transition. The collapse transition is signaled by the appearance of an elliptical horseshoe segment of roots that pinches down towards the positive real axis and defines a boundary to a root-free region of the complex plane. With increasing chain length, the root density on the circular ring and in the space adjacent to the elliptical boundary increases and the leading roots move towards the positive real axis. For finite-length chains, transition temperatures can be obtained by locating the intersection of the ellipse and/or circle of roots with the positive real axis. A finite-size scaling analysis is used to obtain transition temperatures in the long-chain (thermodynamic) limit. The collapse transition is characterized by crossover and specific-heat exponents of φ≈0.76(2) and α≈0.66(2), respectively, consistent with a second-order phase transition.
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Affiliation(s)
- Mark P Taylor
- Department of Physics, Hiram College, Hiram, Ohio 44234, USA.
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77
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Wang MX. Effect of coil-globule transition on the single-chain crystallization. J Phys Chem B 2013; 117:6541-6. [PMID: 23646890 DOI: 10.1021/jp3120397] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The folding process of a single chain including coil-globule transition and crystallization has been investigated through dynamic Monte Carlo simulations. The results based upon ensemble averaging illustrated three distinct states: coil, molten globule, and globule states. Furthermore, the crystallization process from these collapsed states demonstrated various characteristics and it also verified the thermodynamic partitions. The isothermal crystallization in the three states showed the folding rates, and the final crystallite morphologies strongly depended on the collapsed states. Especially, the onset temperature of crystallization in the intermediate molten globule state demonstrated the strongest sensitivity to the solvent qualities in the three different states. Moreover, the crystallization in this intermediate state illustrated a two-step folding mechanism with the prior dense core serving as a precursor to induce the subsequent crystallization. Our observations would help in understanding the thermodynamics and kinetics of phase transition of a single macromolecule. Possible relations to the protein folding were also discussed.
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Affiliation(s)
- Mao-Xiang Wang
- School of Science, Nanjing University of Science and Technology, Nanjing 210094, China.
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78
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Vogel T, Li YW, Wüst T, Landau DP. Generic, hierarchical framework for massively parallel Wang-Landau sampling. PHYSICAL REVIEW LETTERS 2013; 110:210603. [PMID: 23745852 DOI: 10.1103/physrevlett.110.210603] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2013] [Revised: 03/14/2013] [Indexed: 06/02/2023]
Abstract
We introduce a parallel Wang-Landau method based on the replica-exchange framework for Monte Carlo simulations. To demonstrate its advantages and general applicability for simulations of complex systems, we apply it to different spin models including spin glasses, the Ising model, and the Potts model, lattice protein adsorption, and the self-assembly process in amphiphilic solutions. Without loss of accuracy, the method gives significant speed-up and potentially scales up to petaflop machines.
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Affiliation(s)
- Thomas Vogel
- Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA.
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79
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Olivares-Quiroz L. Thermodynamics of ideal proteinogenic homopolymer chains as a function of the energy spectrum E, helical propensity ω and enthalpic energy barrier. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:155103. [PMID: 23515207 DOI: 10.1088/0953-8984/25/15/155103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
A reformulation and generalization of the Zwanzig model (ZW model) for ideal homopolymer chains poly-X, where X represents any of the twenty naturally occurring proteinogenic amino acid residues is presented. This reformulation and generalization provides a direct connection between coarse-grained parameters originally proposed in the ZW model with variables from the Lifson-Roig (LR) theory, such as the helical propensity per residue ω, and new variables introduced here, such as the energy gap Δ between unfolded and folded structures, as well as the ratio f of the energy scales involved. This enables us to discover the relevance of the energy spectrum E to the onset of configurational phase transitions. From the configurational partition function Q, thermodynamic properties such as the configurational entropy S, specific heat v and average energy <E> are calculated in terms of the number of residues K, temperature T, helical propensity ω and energy barrier ΔH for different poly-X chains in vacuo. Results obtained here provide substantial evidence that configurational phase transitions for ideal poly-X chains correspond to first-order phase transitions. An anomalous behavior of the thermodynamic functions <E>, Cv, S with respect to the number K of residues is also highlighted. On-going methods of solution are outlined.
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Affiliation(s)
- L Olivares-Quiroz
- Universidad Autónoma de la Ciudad de México, Campus Cuautepec, Av La Corona 320, Col Loma Alta CP 07160 DF, Mexico.
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80
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Chi P, Wang Z, Yin Y, Li B, Shi AC. Finite-length effects on the coil-globule transition of a strongly charged polyelectrolyte chain in a salt-free solvent. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:042608. [PMID: 23679444 DOI: 10.1103/physreve.87.042608] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2012] [Revised: 03/27/2013] [Indexed: 06/02/2023]
Abstract
The nature of coil-globule transition and scaling behavior of a strongly charged polyelectrolyte chain in a solution system with explicit neutralizing counterions and solvent molecules are studied using replica-exchange Monte Carlo simulations, focusing on the effects of finite chain length. The results reveal that at the thermodynamic limit of infinitely long chain length, the coil-globule transition may remain first order. Phase transition temperatures at various ion concentrations are obtained by extrapolating the values obtained at finite chain lengths. Furthermore, it is found that the exponent ν of the radius of gyration, <R(g)(2)> ~ N(2ν), can be slightly larger than 1 under some conditions.
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Affiliation(s)
- Peng Chi
- The MOE Key Laboratory of Weak Light Nonlinear Photonics and School of Physics, Nankai University, Tianjin, 300071, China
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81
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Hoy RS, Harwayne-Gidansky J, O'Hern CS. Minimal energy packings of nearly flexible polymers. J Chem Phys 2013; 138:054905. [PMID: 23406147 DOI: 10.1063/1.4790168] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We extend recent studies of the minimal energy packings of short flexible polymers with hard-core-like repulsions and short-range attractions to include bond-angle interactions with the aim of describing the collapsed conformations of "colloidal" polymers. We find that flexible tangent sticky-hard-sphere (t-SHS) packings provide a useful perturbative basis for analyzing polymer packings with nonzero bending stiffness only for small ratios of the stiffnesses for the bond-angle (k(b)) and pair (k(c)) interactions, i.e., k(b) (crit)/k(c)</~0.01 for N < 10 monomers, and the critical ratio decreases with N. Below k(b) (crit), angular interactions give rise to an exponential (in N) increase in the number of distinct angular energies arising from the diversity of covalent backbone paths through t-SHS packings. As k(b) increases above k(b) (crit), the low-lying energy landscape changes dramatically as finite bending stiffness alters the structure of the polymer packings. This study lays the groundwork for exact-enumeration studies of the collapsed states of t-SHS-like models with larger bending stiffness.
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Affiliation(s)
- Robert S Hoy
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA.
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82
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Fiore CE, da Luz MGE. Exploiting a semi-analytic approach to study first order phase transitions. J Chem Phys 2013; 138:014105. [DOI: 10.1063/1.4772809] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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83
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Maerzke KA, Gai L, Cummings PT, McCabe C. Incorporating configurational-bias Monte Carlo into the Wang-Landau algorithm for continuous molecular systems. J Chem Phys 2012. [DOI: 10.1063/1.4766354] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
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84
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Tito NB, Milner ST, Lipson JEG. Ball-of-Yarn Conformation of a Linear Gradient Copolymer in a Homopolymer Melt. Macromolecules 2012. [DOI: 10.1021/ma3011558] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Nicholas B. Tito
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Scott T. Milner
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
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85
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Caparica AA, Cunha-Netto AG. Wang-Landau sampling: improving accuracy. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:046702. [PMID: 22680601 DOI: 10.1103/physreve.85.046702] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2011] [Revised: 12/19/2011] [Indexed: 06/01/2023]
Abstract
In this work, we investigate the behavior of the microcanonical and canonical averages of the two-dimensional Ising model during the Wang-Landau simulation. The simulations were carried out using conventional Wang-Landau sampling and the 1/t scheme. Our findings reveal that the microcanonical average should not be accumulated during the initial modification factors f, and they outline a criterion to find this limit, which we define as f(micro). We show that updating the density of states only after every L(2) spin-flip trials leads to a much better precision. We present a mechanism to determine for the given model up to what final modification factor f(final) the simulations should be carried out. Altogether these small adjustments lead to an improved procedure for simulations with much more reliable results. We compare our results with 1/t simulations. We also present an application of the procedure to a self-avoiding homopolymer.
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Affiliation(s)
- A A Caparica
- Instituto de Física, Universidade Federal de Goiás, Goiânia, GO, Brazil
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86
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Swetnam A, Brett C, Allen MP. Phase diagrams of knotted and unknotted ring polymers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031804. [PMID: 22587116 DOI: 10.1103/physreve.85.031804] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2012] [Indexed: 05/31/2023]
Abstract
The phase diagram for a lattice ring polymer under applied force, with variable solvent quality, for different topological knot states, is determined for the first time. In addition to eliminating pseudophases where the polymer is flattened into a single layer, it is found that nontrivial knots result in additional pseudophases under tensile force conditions.
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Affiliation(s)
- Adam Swetnam
- Department of Physics, University of Warwick, Coventry, United Kingdom
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87
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88
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Einert TR, Sing CE, Alexander-Katz A, Netz RR. Conformational dynamics and internal friction in homopolymer globules: equilibrium vs. non-equilibrium simulations. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2011; 34:1-16. [PMID: 22167584 DOI: 10.1140/epje/i2011-11130-8] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2011] [Accepted: 11/03/2011] [Indexed: 05/31/2023]
Abstract
We study the conformational dynamics within homopolymer globules by solvent-implicit Brownian dynamics simulations. A strong dependence of the internal chain dynamics on the Lennard-Jones cohesion strength ε and the globule size N (G) is observed. We find two distinct dynamical regimes: a liquid-like regime (for ε < ε(s) with fast internal dynamics and a solid-like regime (for ε > ε(s) with slow internal dynamics. The cohesion strength ε(s) of this freezing transition depends on N (G) . Equilibrium simulations, where we investigate the diffusional chain dynamics within the globule, are compared with non-equilibrium simulations, where we unfold the globule by pulling the chain ends with prescribed velocity (encompassing low enough velocities so that the linear-response, viscous regime is reached). From both simulation protocols we derive the internal viscosity within the globule. In the liquid-like regime the internal friction increases continuously with ε and scales extensive in N (G) . This suggests an internal friction scenario where the entire chain (or an extensive fraction thereof) takes part in conformational reorganization of the globular structure.
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Affiliation(s)
- T R Einert
- Physik Department, Technische Universität München, James-Franck-Straße, Garching, Germany.
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89
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Jónsson SÆ, Mohanty S, Irbäck A. Accelerating atomic-level protein simulations by flat-histogram techniques. J Chem Phys 2011; 135:125102. [DOI: 10.1063/1.3643328] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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90
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Wang Z, He X. Phase transition of a single star polymer: A Wang-Landau sampling study. J Chem Phys 2011; 135:094902. [DOI: 10.1063/1.3629849] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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91
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Binder K, Müller M, Vink RLC. Phase Behavior of Polymer-Containing Systems: Recent Advances Through Computer Simulation. MACROMOL THEOR SIMUL 2011. [DOI: 10.1002/mats.201100046] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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92
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Chi P, Li B, Shi AC. Conformation transitions of a polyelectrolyte chain: a replica-exchange Monte-Carlo study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:021804. [PMID: 21929012 DOI: 10.1103/physreve.84.021804] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2011] [Revised: 06/03/2011] [Indexed: 05/31/2023]
Abstract
The thermodynamic behavior of a strongly charged polyelectrolyte chain immersed in a salt-free solution is studied using replica-exchange Monte-Carlo simulations. The results reveal that the chain can assume a variety of conformations, and it undergoes two phase transitions upon cooling. The first transition is identified as a continuous counterion condensation transition while the second one as a first-order coil-globule transition. In the globular state, the counterions and the charged chain segments are densely packed forming a three-dimensional Wigner crystal.
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Affiliation(s)
- Peng Chi
- The MOE Key Laboratory of Weak Light Nonlinear Photonics and School of Physics, Nankai University, 300071 Tianjin, China
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93
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Schnabel S, Seaton DT, Landau DP, Bachmann M. Microcanonical entropy inflection points: key to systematic understanding of transitions in finite systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:011127. [PMID: 21867133 DOI: 10.1103/physreve.84.011127] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2010] [Revised: 05/31/2011] [Indexed: 05/31/2023]
Abstract
We introduce a systematic classification method for the analogs of phase transitions in finite systems. This completely general analysis, which is applicable to any physical system and extends toward the thermodynamic limit, is based on the microcanonical entropy and its energetic derivative, the inverse caloric temperature. Inflection points of this quantity signal cooperative activity and thus serve as distinct indicators of transitions. We demonstrate the power of this method through application to the long-standing problem of liquid-solid transitions in elastic, flexible homopolymers.
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Affiliation(s)
- Stefan Schnabel
- Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA.
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94
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Siretskiy A, Elvingson C, Vorontsov-Velyaminov P, Khan MO. Method for sampling compact configurations for semistiff polymers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:016702. [PMID: 21867338 DOI: 10.1103/physreve.84.016702] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2011] [Revised: 04/06/2011] [Indexed: 05/31/2023]
Abstract
The sampling of compact configurations is crucial when investigating structural properties of semistiff polymers, like proteins and DNA, using Monte Carlo methods. A sampling scheme for a continuous model based on configuration biasing is introduced, tested, and compared with conventional methods. The proposed configuration biased Monte Carlo method, used together with the Wang-Landau sampling scheme, enables us to obtain any thermodynamic property within the statistical ensemble in use. Using the proposed method, it is possible to collect statistical data of interest for a wide range of compactions (from stretched up to several toroid loops) in a single computer experiment. A second-order-like stretched-toroid phase transition is observed for a semistiff polymer, and the critical temperature is estimated.
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Affiliation(s)
- Alexey Siretskiy
- Department of Physical and Analytical Chemistry, Uppsala University, Uppsala, Sweden.
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95
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Abstract
The collapse of a homopolymer gaussian chain into a globule is represented as a transition between two states, viz., extended and collapsed. Appropriately, this model has been labeled as the all-or-none view of chain collapse. In the collapsed state, the single polymer partition function is expressed by a single Mayer diagram with the maximum number of f-bonds arising from nonbonded square well interactions. Our target is the dependence of the transition temperature on chain length and the interaction range of the square well, as indicated through the behavior of the radius of gyration and the constant volume heat capacity. Properties of the collapse transition are calculated exactly for chains with three to six backbone atoms and heuristically for long chains using arguments derived from the small chains and from conditions of integrability. Comparison with simulation studies is made.
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Affiliation(s)
- Glenn T Evans
- Department of Chemistry, Oregon State University, Corvallis, Oregon 97331, USA.
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96
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Li T, Yang X, Nies E. A Replica Exchange Molecular Dynamics Simulation of a Single Polyethylene Chain: Temperature Dependence of Structural Properties and Chain Conformational Study at the Equilibrium Melting Temperature. J Chem Theory Comput 2011; 7:188-202. [PMID: 26606232 DOI: 10.1021/ct100513y] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The conformational properties of a finite length polyethylene chain were explored over a wide range of temperatures using a replica exchange molecular dynamics simulation providing high quality simulation data representative for the equilibrium behavior of the chain molecule. The radial distribution function (RDF) and the structure factor S(q) of the chain as a function of temperature are analyzed in detail. The different characteristic peaks in the RDF and S(q) were assigned to specific distances in the chain and structural changes occurring with the temperature. In S(q), a peak characteristic for the order in the solid state was found and used to determine the equilibrium melting temperature. A detailed scaling analysis of the structure factor covering the full q range was performed according to the work of Hammouda. In the Θ region, a quantitative analysis of the full structure factor was done using the equivalent Kuhn chain, which enabled us to assign the Θ region of our chain and to demonstrate, in our particular case, the failure of the Gaussian chain approach. The chain conformational properties at the equilibrium melting temperature are discussed using conformational distribution functions, using the largest principal component of the radius of gyration and shape parameters as order parameters. We demonstrate that for the system studied here, the Landau free energy expression based on this conformational distribution information leads to erroneous conclusions concerning the thermodynamic transition behavior. Finally, we focus on the instantaneous conformational properties at the equilibrium melting temperature and give a detailed analysis of the conformational shapes using different shape parameters and a simulation snapshot. We show that the chain does not only take the lamellar rod-like and globular conformational shapes, typical of the solid and liquid states, but can also explore many other conformational states, including the toroidal conformational state. It is the first demonstration that a flexible molecule like PE can also take a toroidal conformational state, which is normally linked to stiffer chains.
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Affiliation(s)
- Ting Li
- Polymer Research Division, Department of Chemistry, The Leuven Mathematical Modeling and Computational Science Centre (LMCC) and the Leuven Materials Research Centre (LMRC), Katholieke Universiteit Leuven, Celestijnenlaan 200F, B-3001 Heverlee, Belgium, State Key Laboratory of Polymer Physics & Chemistry, Center for Molecular Science, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100080, Peoples' Republic of China, Laboratory of Polymer Technology, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
| | - Xiaozhen Yang
- Polymer Research Division, Department of Chemistry, The Leuven Mathematical Modeling and Computational Science Centre (LMCC) and the Leuven Materials Research Centre (LMRC), Katholieke Universiteit Leuven, Celestijnenlaan 200F, B-3001 Heverlee, Belgium, State Key Laboratory of Polymer Physics & Chemistry, Center for Molecular Science, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100080, Peoples' Republic of China, Laboratory of Polymer Technology, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
| | - Erik Nies
- Polymer Research Division, Department of Chemistry, The Leuven Mathematical Modeling and Computational Science Centre (LMCC) and the Leuven Materials Research Centre (LMRC), Katholieke Universiteit Leuven, Celestijnenlaan 200F, B-3001 Heverlee, Belgium, State Key Laboratory of Polymer Physics & Chemistry, Center for Molecular Science, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100080, Peoples' Republic of China, Laboratory of Polymer Technology, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands
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97
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Li T, Jiang Z, Yan D, Nies E. A polyethylene chain investigated with replica exchange molecular dynamics simulation: Equilibrium lamellar thickness and melting point, ordering and free energy. POLYMER 2010. [DOI: 10.1016/j.polymer.2010.09.019] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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98
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Hoy RS, O'Hern CS. Minimal energy packings and collapse of sticky tangent hard-sphere polymers. PHYSICAL REVIEW LETTERS 2010; 105:068001. [PMID: 20868016 DOI: 10.1103/physrevlett.105.068001] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2010] [Revised: 06/28/2010] [Indexed: 05/29/2023]
Abstract
We enumerate all minimal energy packings (MEPs) for small single linear and ring polymers composed of spherical monomers with contact attractions and hard-core repulsions and compare them to corresponding results for monomer packings. We define and identify "dividing surfaces" in polymer packings, which reduce the number of arrangements that satisfy hard-sphere and covalent-bond constraints. Compared to monomer MEPs, polymer MEPs favor intermediate structural symmetry. We also examine the packing-preparation dependence for longer single chains using molecular dynamics simulations. For slow temperature quenches, chains form crystallites with close-packed cores. As the quench rate increases, the core size decreases and the exterior becomes more disordered. By examining the contact number, we connect the suppression of crystallization to the onset of isostaticity in disordered packings.
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Affiliation(s)
- Robert S Hoy
- Department of Mechanical Engineering, Yale University, New Haven, Connecticut 06520-8286, USA
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99
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Ye X, Ding Y, Li J. Scaling of the molecular weight-dependent thermal volume transition of poly(N-isopropylacrylamide). ACTA ACUST UNITED AC 2010. [DOI: 10.1002/polb.22018] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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100
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