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Škrbić T, Giacometti A, Hoang TX, Maritan A, Banavar JR. A Tale of Two Chains: Geometries of a Chain Model and Protein Native State Structures. Polymers (Basel) 2024; 16:502. [PMID: 38399880 PMCID: PMC10892082 DOI: 10.3390/polym16040502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2023] [Revised: 02/06/2024] [Accepted: 02/10/2024] [Indexed: 02/25/2024] Open
Abstract
Linear chain molecules play a central role in polymer physics with innumerable industrial applications. They are also ubiquitous constituents of living cells. Here, we highlight the similarities and differences between two distinct ways of viewing a linear chain. We do this, on the one hand, through the lens of simulations for a standard polymer chain of tethered spheres at low and high temperatures and, on the other hand, through published experimental data on an important class of biopolymers, proteins. We present detailed analyses of their local and non-local structures as well as the maps of their closest contacts. We seek to reconcile the startlingly different behaviors of the two types of chains based on symmetry considerations.
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Affiliation(s)
- Tatjana Škrbić
- Department of Molecular Sciences and Nanosystems, Ca’ Foscari University of Venice, 30170 Venice, Italy;
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, OR 97403, USA;
| | - Achille Giacometti
- Department of Molecular Sciences and Nanosystems, Ca’ Foscari University of Venice, 30170 Venice, Italy;
- European Centre for Living Technology (ECLT), Ca’ Bottacin, Dorsoduro 3911, Calle Crosera, 30123 Venice, Italy
| | - Trinh X. Hoang
- Institute of Physics, Vietnam Academy of Science and Technology, Hanoi 11108, Vietnam;
| | - Amos Maritan
- Department of Physics and Astronomy, University of Padua, 35122 Padua, Italy;
| | - Jayanth R. Banavar
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, OR 97403, USA;
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2
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Polanowski P, Sikorski A. Coil-globule transition in two-dimensional polymer chains in an explicit solvent. SOFT MATTER 2023; 19:7979-7987. [PMID: 37818732 DOI: 10.1039/d3sm00975k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/13/2023]
Abstract
The structure of two-dimensional polymer chains in a solvent at different temperatures is still far from being fully understood. Computer simulations of high-density macromolecular systems require the use of appropriate algorithms, and therefore the simulations were carried out using the Cooperative Motion Algorithm. The polymer model studied was exactly two-dimensional, coarse-grained and based on a triangular lattice. The theta temperature and temperature of coil-to-globule transition, and critical exponents were determined. The differences between the structure of such a disk and that of a chain in a dense polymer liquid were shown.
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Affiliation(s)
- Piotr Polanowski
- Department of Molecular Physics, Łódź University of Technology, Żeromskiego 116, 90-543 Łódź, Poland
| | - Andrzej Sikorski
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland.
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3
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Taklimi NA, Ferrari F, Piątek MR, Tubiana L. Thermal properties of knotted block copolymer rings with charged monomers subjected to short-range interactions. Phys Rev E 2023; 108:034503. [PMID: 37849145 DOI: 10.1103/physreve.108.034503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2022] [Accepted: 08/19/2023] [Indexed: 10/19/2023]
Abstract
The thermal properties of coarse-grained knotted copolymer rings fluctuating in a highly screening solution are investigated on a simple cubic lattice using the Wang-Landau Monte Carlo algorithm. The rings contain two kinds of monomers A and B with opposite charges that are subjected to short-range interactions. In view of possible applications in medicine and the construction of intelligent materials, it is shown that the behavior of copolymer rings can be tuned by changing both their monomer configuration and topology. We find several phase transitions depending on the monomer distribution. They include the expansion and collapse of the knotted polymer as well as rearrangements leading to metastable states. The temperatures at which these phase transitions are occurring and other features can be tuned by changing the topology of the system. The processes underlying the observed transitions are identified. In knots formed by diblock copolymers, two different classes of behaviors are detected depending on whether there is an excess of monomers of one kind or not. Moreover, we find that the most stable compact states are formed by copolymers in which units of two A monomers are alternated by units of two B monomers. Remarkably, these compact states are in a lamellar phase. The transition from the lamellar to the expanded state produces in the specific heat capacity a narrow and high peak that is centered at temperatures that are much higher than those of the peaks observed in all other monomer distributions.
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Affiliation(s)
- Neda Abbasi Taklimi
- CASA* and Institute of Physics, University of Szczecin, 70-453 Szczecin, Poland
| | - Franco Ferrari
- CASA* and Institute of Physics, University of Szczecin, 70-453 Szczecin, Poland
| | | | - Luca Tubiana
- Physics Department, University of Trento, I-38123 Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, I-38123 Trento, Italy
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4
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Banavar JR, Giacometti A, Hoang TX, Maritan A, Škrbić T. A geometrical framework for thinking about proteins. Proteins 2023. [PMID: 37565735 DOI: 10.1002/prot.26567] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2023] [Revised: 07/16/2023] [Accepted: 07/21/2023] [Indexed: 08/12/2023]
Abstract
We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise attraction that assembles these building blocks, while respecting their individual symmetries. Instead of seeking to mimic the complexity of proteins, we look for a simple abstraction of reality that yet captures the essence of proteins. We employ analytic calculations and detailed Monte Carlo simulations to explore some consequences of our theory. The predictions of our approach are in accord with experimental data. Our framework provides a rationalization for understanding the common characteristics of proteins. Our results show that the free energy landscape of a globular protein is pre-sculpted at the backbone level, sequences and functionalities evolve in the fixed backdrop of the folds determined by geometry and symmetry, and that protein structures are unique in being simultaneously characterized by stability, diversity, and sensitivity.
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Affiliation(s)
- Jayanth R Banavar
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, Oregon, USA
| | - Achille Giacometti
- Ca' Foscari University of Venice, Department of Molecular Sciences and Nanosystems, Venice, Italy
- European Centre for Living Technology (ECLT), Venice, Italy
| | - Trinh X Hoang
- Vietnam Academy of Science and Technology, Institute of Physics, Hanoi, Vietnam
| | - Amos Maritan
- University of Padua, Department of Physics and Astronomy, Padua, Italy
| | - Tatjana Škrbić
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, Oregon, USA
- Ca' Foscari University of Venice, Department of Molecular Sciences and Nanosystems, Venice, Italy
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5
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Herranz M, Pedrosa C, Martínez-Fernández D, Foteinopoulou K, Karayiannis NC, Laso M. Fine-tuning of colloidal polymer crystals by molecular simulation. Phys Rev E 2023; 107:064605. [PMID: 37464607 DOI: 10.1103/physreve.107.064605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2022] [Accepted: 06/04/2023] [Indexed: 07/20/2023]
Abstract
Through extensive molecular simulations we determine a phase diagram of attractive, fully flexible polymer chains in two and three dimensions. A rich collection of distinct crystal morphologies appear, which can be finely tuned through the range of attraction. In three dimensions these include the face-centered cubic, hexagonal close packed, simple hexagonal, and body-centered cubic crystals and the Frank-Kasper phase. In two dimensions the dominant structures are the triangular and square crystals. A simple geometric model is proposed, based on the concept of cumulative neighbors of ideal crystals, which can accurately predict most of the observed structures and the corresponding transitions. The attraction range can thus be considered as an adjustable parameter for the design of colloidal polymer crystals with tailored morphologies.
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Affiliation(s)
- Miguel Herranz
- Institute for Optoelectronic Systems and Microtechnology (ISOM) and Escuela Técnica Superior de Ingenieros Industriales (ETSII), Universidad Politécnica de Madrid (UPM) C. José Gutiérrez Abascal 2, 28006 Madrid, Spain
| | - Clara Pedrosa
- Institute for Optoelectronic Systems and Microtechnology (ISOM) and Escuela Técnica Superior de Ingenieros Industriales (ETSII), Universidad Politécnica de Madrid (UPM) C. José Gutiérrez Abascal 2, 28006 Madrid, Spain
| | - Daniel Martínez-Fernández
- Institute for Optoelectronic Systems and Microtechnology (ISOM) and Escuela Técnica Superior de Ingenieros Industriales (ETSII), Universidad Politécnica de Madrid (UPM) C. José Gutiérrez Abascal 2, 28006 Madrid, Spain
| | - Katerina Foteinopoulou
- Institute for Optoelectronic Systems and Microtechnology (ISOM) and Escuela Técnica Superior de Ingenieros Industriales (ETSII), Universidad Politécnica de Madrid (UPM) C. José Gutiérrez Abascal 2, 28006 Madrid, Spain
| | - Nikos Ch Karayiannis
- Institute for Optoelectronic Systems and Microtechnology (ISOM) and Escuela Técnica Superior de Ingenieros Industriales (ETSII), Universidad Politécnica de Madrid (UPM) C. José Gutiérrez Abascal 2, 28006 Madrid, Spain
| | - Manuel Laso
- Institute for Optoelectronic Systems and Microtechnology (ISOM) and Escuela Técnica Superior de Ingenieros Industriales (ETSII), Universidad Politécnica de Madrid (UPM) C. José Gutiérrez Abascal 2, 28006 Madrid, Spain
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6
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Zhang P, Wang Z, Wang ZG. Conformation Transition of a Homopolymer Chain in Binary Mixed Solvents. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01896] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Affiliation(s)
- Pengfei Zhang
- State Key Laboratory for Modification of Chemical Fibers and Polymer Materials, Center for Advanced Low-Dimension Materials, College of Material Science and Engineering, Donghua University, Shanghai 201620, China
| | - Zheng Wang
- School of Physics, Nankai University, Tianjin 300071, China
| | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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7
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Taylor MP. Confinement free energy for a polymer chain: Corrections to scaling. J Chem Phys 2022; 157:094902. [PMID: 36075705 DOI: 10.1063/5.0105142] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Spatial confinement of a polymer chain results in a reduction of conformational entropy. For confinement of a flexible N-mer chain in a planar slit or cylindrical pore (confining dimension D), a blob model analysis predicts the asymptotic scaling behavior ΔF/N ∼ D-γ with γ ≈ 1.70, where ΔF is the free energy increase due to confinement. Here, we extend this scaling analysis to include the variation of local monomer density upon confinement giving ΔF/N ∼ D-γ(1 - h(N, D)), where the correction-to-scaling term has the form h ∼ Dy/NΔ with exponents y = 3 - γ ≈ 1.30 and Δ = 3/γ - 1 ≈ 0.76. To test these scaling predictions, we carry out Wang-Landau simulations of confined and unconfined tangent-hard-sphere chains (bead diameter σ) in the presence of a square-well trapping potential. The fully trapped chain provides a common reference state, allowing for an absolute determination of the confinement free energy. Our simulation results for 32 ≤ N ≤ 1024 and 3 ≤ D/σ ≤ 14 are well-described by the extended scaling relation giving exponents of γ = 1.69(1), y = 1.25(2), and Δ = 0.75(6).
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Affiliation(s)
- Mark P Taylor
- Department of Physics, Hiram College, Hiram, Ohio 44234, USA
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8
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Bae Y, Ha MY, Bang KT, Yang S, Kang SY, Kim J, Sung J, Kang S, Kang D, Lee WB, Choi TL, Park J. Conformation Dynamics of Single Polymer Strands in Solution. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022; 34:e2202353. [PMID: 35725274 DOI: 10.1002/adma.202202353] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Revised: 06/16/2022] [Indexed: 06/15/2023]
Abstract
Conformational changes in macromolecules significantly affect their functions and assembly into high-level structures. Despite advances in theoretical and experimental studies, investigations into the intrinsic conformational variations and dynamic motions of single macromolecules remain challenging. Here, liquid-phase transmission electron microscopy enables the real-time tracking of single-chain polymers. Imaging linear polymers, synthetically dendronized with conjugated aromatic groups, in organic solvent confined within graphene liquid cells, directly exhibits chain-resolved conformational dynamics of individual semiflexible polymers. These experimental and theoretical analyses reveal that the dynamic conformational transitions of the single-chain polymer originate from the degree of intrachain interactions. In situ observations also show that such dynamics of the single-chain polymer are significantly affected by environmental factors, including surfaces and interfaces.
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Affiliation(s)
- Yuna Bae
- School of Chemical and Biological Engineering, Seoul National University, Seoul, 08826, Republic of Korea
- Institute of Chemical Processes, Seoul National University, Seoul, 08826, Republic of Korea
- Center for Nanoparticle Research, Institute for Basic Science (IBS), Seoul, 08826, Republic of Korea
| | - Min Young Ha
- School of Chemical and Biological Engineering, Seoul National University, Seoul, 08826, Republic of Korea
| | - Ki-Taek Bang
- Department of Chemistry, Seoul National University, Seoul, 08826, Republic of Korea
| | - Sanghee Yang
- Department of Chemistry, Seoul National University, Seoul, 08826, Republic of Korea
| | - Sung Yun Kang
- Department of Chemistry, Seoul National University, Seoul, 08826, Republic of Korea
| | - Joodeok Kim
- School of Chemical and Biological Engineering, Seoul National University, Seoul, 08826, Republic of Korea
- Institute of Chemical Processes, Seoul National University, Seoul, 08826, Republic of Korea
- Center for Nanoparticle Research, Institute for Basic Science (IBS), Seoul, 08826, Republic of Korea
| | - Jongbaek Sung
- School of Chemical and Biological Engineering, Seoul National University, Seoul, 08826, Republic of Korea
- Institute of Chemical Processes, Seoul National University, Seoul, 08826, Republic of Korea
- Center for Nanoparticle Research, Institute for Basic Science (IBS), Seoul, 08826, Republic of Korea
| | - Sungsu Kang
- School of Chemical and Biological Engineering, Seoul National University, Seoul, 08826, Republic of Korea
- Institute of Chemical Processes, Seoul National University, Seoul, 08826, Republic of Korea
- Center for Nanoparticle Research, Institute for Basic Science (IBS), Seoul, 08826, Republic of Korea
| | - Dohun Kang
- Department of Materials Science and Engineering, Northwestern University, Evanston, IL, 60208, USA
| | - Won Bo Lee
- School of Chemical and Biological Engineering, Seoul National University, Seoul, 08826, Republic of Korea
| | - Tae-Lim Choi
- Department of Chemistry, Seoul National University, Seoul, 08826, Republic of Korea
| | - Jungwon Park
- School of Chemical and Biological Engineering, Seoul National University, Seoul, 08826, Republic of Korea
- Institute of Chemical Processes, Seoul National University, Seoul, 08826, Republic of Korea
- Center for Nanoparticle Research, Institute for Basic Science (IBS), Seoul, 08826, Republic of Korea
- Institute of Engineering Research, Seoul National University, Seoul, 08826, Republic of Korea
- Advanced Institutes of Convergence Technology, Seoul National University, Suwon, Gyeonggi, 16229, Republic of Korea
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9
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Wang S, Venkatesh A, Ramkrishna D, Narsimhan V. Brownian bridges for stochastic chemical processes-An approximation method based on the asymptotic behavior of the backward Fokker-Planck equation. J Chem Phys 2022; 156:184108. [PMID: 35568530 DOI: 10.1063/5.0080540] [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
A Brownian bridge is a continuous random walk conditioned to end in a given region by adding an effective drift to guide paths toward the desired region of phase space. This idea has many applications in chemical science where one wants to control the endpoint of a stochastic process-e.g., polymer physics, chemical reaction pathways, heat/mass transfer, and Brownian dynamics simulations. Despite its broad applicability, the biggest limitation of the Brownian bridge technique is that it is often difficult to determine the effective drift as it comes from a solution of a Backward Fokker-Planck (BFP) equation that is infeasible to compute for complex or high-dimensional systems. This paper introduces a fast approximation method to generate a Brownian bridge process without solving the BFP equation explicitly. Specifically, this paper uses the asymptotic properties of the BFP equation to generate an approximate drift and determine ways to correct (i.e., re-weight) any errors incurred from this approximation. Because such a procedure avoids the solution of the BFP equation, we show that it drastically accelerates the generation of conditioned random walks. We also show that this approach offers reasonable improvement compared to other sampling approaches using simple bias potentials.
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Affiliation(s)
- Shiyan Wang
- Davidson School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - Anirudh Venkatesh
- Davidson School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - Doraiswami Ramkrishna
- Davidson School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - Vivek Narsimhan
- Davidson School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, USA
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10
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Kawak P, Banks DS, Tree DR. Semiflexible oligomers crystallize via a cooperative phase transition. J Chem Phys 2021; 155:214902. [PMID: 34879681 DOI: 10.1063/5.0067788] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Semicrystalline polymers are ubiquitous, yet despite their fundamental and industrial importance, the theory of homogeneous nucleation from a melt remains a subject of debate. A key component of the controversy is that polymer crystallization is a non-equilibrium process, making it difficult to distinguish between effects that are purely kinetic and those that arise from the underlying thermodynamics. Due to computational cost constraints, simulations of polymer crystallization typically employ non-equilibrium molecular dynamics techniques with large degrees of undercooling that further exacerbate the coupling between thermodynamics and kinetics. In a departure from this approach, in this study, we isolate the near-equilibrium nucleation behavior of a simple model of a melt of short, semiflexible oligomers. We employ several Monte Carlo methods and compute a phase diagram in the temperature-density plane along with two-dimensional free energy landscapes (FELs) that characterize the nucleation behavior. The phase diagram shows the existence of ordered nematic and crystalline phases in addition to the disordered melt phase. The minimum free energy path in the FEL for the melt-crystal transition shows a cooperative transition, where nematic order and monomer positional order move in tandem as the system crystallizes. This near-equilibrium phase transition mechanism broadly agrees with recent evidence that polymer stiffness plays an important role in crystallization but differs in the specifics of the mechanism from several recent theories. We conclude that the computation of multidimensional FELs for models that are larger and more fine-grained will be important for evaluating and refining theories of homogeneous nucleation for polymer crystallization.
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Affiliation(s)
- Pierre Kawak
- Department of Chemical Engineering, Brigham Young University, Provo, Utah 84602, USA
| | - Dakota S Banks
- Department of Chemical Engineering, Brigham Young University, Provo, Utah 84602, USA
| | - Douglas R Tree
- Department of Chemical Engineering, Brigham Young University, Provo, Utah 84602, USA
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11
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Taylor MP, Basnet S, Luettmer-Strathmann J. Partition-function-zero analysis of polymer adsorption for a continuum chain model. Phys Rev E 2021; 104:034502. [PMID: 34654113 DOI: 10.1103/physreve.104.034502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Accepted: 09/13/2021] [Indexed: 11/07/2022]
Abstract
Polymer chains undergoing adsorption are expected to show universal critical behavior which may be investigated using partition function zeros. The focus of this work is the adsorption transition for a continuum chain, allowing for investigation of a continuous range of the attractive interaction and comparison with recent high-precision lattice model studies. The partition function (Fisher) zeros for a tangent-hard-sphere N-mer chain (monomer diameter σ) tethered to a flat wall with an attractive square-well potential (range λσ, depth ε) have been computed for chains up to N=1280 with 0.01≤λ≤2.0. In the complex-Boltzmann-factor plane these zeros are concentrated in an annular region, centered on the origin and open about the real axis. With increasing N, the leading zeros, w_{1}(N), approach the positive real axis as described by the asymptotic scaling law w_{1}(N)-y_{c}∼N^{-ϕ}, where y_{c}=e^{ε/k_{B}T_{c}} is the critical point and T_{c} is the critical temperature. In this work, we study the polymer adsorption transition by analyzing the trajectory of the leading zeros as they approach y_{c} in the complex plane. We use finite-size scaling (including corrections to scaling) to determine the critical point and the scaling exponent ϕ as well as the approach angle θ_{c}, between the real axis and the leading-zero trajectory. Variation of the interaction range λ moves the critical point, such that T_{c} decreases with λ, while the results for ϕ and θ_{c} are approximately independent of λ. Our values of ϕ=0.479(9) and θ_{c}=56.8(1.4)^{∘} are in agreement with the best lattice model results for polymer adsorption, further demonstrating the universality of these constants across both lattice and continuum models.
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Affiliation(s)
- Mark P Taylor
- Department of Physics, Hiram College, Hiram, Ohio 44234, USA
| | - Samip Basnet
- Department of Physics, Hiram College, Hiram, Ohio 44234, USA
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12
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Škrbić T, Hoang TX, Giacometti A, Maritan A, Banavar JR. Marginally compact phase and ordered ground states in a model polymer with side spheres. Phys Rev E 2021; 104:L012501. [PMID: 34412214 DOI: 10.1103/physreve.104.l012501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2021] [Accepted: 06/14/2021] [Indexed: 11/07/2022]
Abstract
We present the results of a quantitative study of the phase behavior of a model polymer chain with side spheres using two independent computer simulation techniques. We find that the mere addition of side spheres results in key modifications of standard polymer behavior. One obtains a marginally compact phase at low temperatures; the structures in this phase are reduced in dimensionality and are ordered, they include strands assembled into sheets and a variety of helices, and at least one of the transitions on lowering the temperature to access these ordered states is found to be first order. Our model serves to partially bridge conventional polymer phases with biomolecular phases.
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Affiliation(s)
- Tatjana Škrbić
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, Oregon 97403, USA and Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari di Venezia, Campus Scientifico, Edificio Alfa, Via Torino 155, 30170 Venezia Mestre, Italy
| | - Trinh Xuan Hoang
- Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Ba Dinh, Hanoi 11108, 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 and European Center for Living Technologies, Ca' Bottacin, Dorsoduro 3911, Calle Crosera, 30123 Venezia, Italy
| | - Amos Maritan
- Dipartimento di Fisica e Astronomia, Università di Padova and INFN, Via Marzolo 8, 35131 Padova, Italy
| | - Jayanth R Banavar
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, Oregon 97403, USA
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13
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Škrbić T, Hoang TX, Giacometti A, Maritan A, Banavar JR. Spontaneous dimensional reduction and ground state degeneracy in a simple chain model. Phys Rev E 2021; 104:L012101. [PMID: 34412247 DOI: 10.1103/physreve.104.l012101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2021] [Accepted: 04/08/2021] [Indexed: 11/07/2022]
Abstract
Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new homopolymer model of a linear chain molecule subject to an attractive self-interaction promoting compactness. We analyze the model using simple analytic arguments complemented by extensive computer simulations. We find several striking results: there is a first-order transition from a high-temperature random coil phase to a highly unusual low-temperature phase; the modular ground states exhibit significant degeneracy; the ground state structures exhibit spontaneous dimensional reduction and have a two-layer structure; and the ground states are assembled from secondary motifs of helices and strands connected by tight loops. We discuss the similarities and notable differences between the ground state structures [we call these PoSSuM (Planar Structures with Secondary Motifs)] in the phase and protein native state structures.
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Affiliation(s)
- Tatjana Škrbić
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, Oregon 97403, USA and Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari di Venezia, Campus Scientifico, Edificio Alfa, via Torino 155, 30170 Venezia Mestre, Italy
| | - Trinh Xuan Hoang
- Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Ba Dinh, Hanoi 11108, 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 and European Center for Living Technologies (ECLT), Ca' Bottacin, Dorsoduro 3911 Calle Crosera, 30123 Venezia, Italy
| | - Amos Maritan
- Dipartimento di Fisica e Astronomia, Università di Padova and INFN, via Marzolo 8, 35131 Padova, Italy
| | - Jayanth R Banavar
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, Oregon 97403, USA
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14
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Chae MK, Lee NK, Johner A, Park JM. The Measurement of Information and Free Energy in Mechanical-Force-Driven Coil-Globule Transitions. J Phys Chem B 2021; 125:4987-4997. [PMID: 33973787 DOI: 10.1021/acs.jpcb.1c01119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We study the role of information (the relative entropy) for polymers undergoing coil-globule transitions driven by a time-dependent force. Pulling experiments at various speeds are performed by Brownian dynamics simulations. We obtain the work distributions for the forward and time-reversed backward processes and information stored at the end of the nonequilibrium pulling processes. We present the systematic method to measure the information from the pulling experiments and extract the information by analyzing slowly relaxing modes. When the information is incorporated, the work distributions modified by the information allow access to the proper free energy via the formulation of the generalized fluctuation theorems even if the initial states of the forward and time-reversed backward processes are out of equilibrium. This demonstrates that the work-information conversion works well for a single-molecule system with many degrees of freedom.
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Affiliation(s)
- Min-Kyung Chae
- Department of Physics and Astronomy, Sejong University, Seoul, Korea
| | - Nam-Kyung Lee
- Department of Physics and Astronomy, Sejong University, Seoul, Korea
| | - Albert Johner
- Institute Charles Sadron, CNRS 23 Rue du Loess, 67034 Strasbourg cedex 2, France
| | - Jeong-Man Park
- Department of Physics, The Catholic University of Korea, Bucheon, Korea
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15
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Klochko L, Baschnagel J, Wittmer JP, Semenov AN. General relations to obtain the time-dependent heat capacity from isothermal simulations. J Chem Phys 2021; 154:164501. [PMID: 33940827 DOI: 10.1063/5.0046697] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Abstract
It is well-known that time-dependent correlation functions related to temperature and energy can crucially depend on the thermostatting mechanism used in computer simulations of molecular systems. We argue, however, that linear response functions must be considered as universal properties of physical systems. This implies that the classical fluctuation equation for the transient heat capacity, cv(t), is not applicable to the thermostatted molecular dynamics (apart from long enough times). To improve on this point, we derive a number of exact general expressions for the frequency-dependent heat capacity in terms of energy correlation functions, valid for the Nosé-Hoover and some other thermostats. We also establish a general relation between auto- and cross correlation functions of energy and temperature. Recommendations on how to use these relations to maximize the numerical precision are provided. It is demonstrated that our approach allows us to obtain cv(t) for a supercooled liquid system with high precision and over many decades in time reflecting all pertinent relaxation processes.
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Affiliation(s)
- L Klochko
- Institut Charles Sadron, CNRS - UPR 22, Université de Strasbourg, 23 rue du Loess, BP 84047, 67034 Strasbourg Cedex 2, France
| | - J Baschnagel
- Institut Charles Sadron, CNRS - UPR 22, Université de Strasbourg, 23 rue du Loess, BP 84047, 67034 Strasbourg Cedex 2, France
| | - J P Wittmer
- Institut Charles Sadron, CNRS - UPR 22, Université de Strasbourg, 23 rue du Loess, BP 84047, 67034 Strasbourg Cedex 2, France
| | - A N Semenov
- Institut Charles Sadron, CNRS - UPR 22, Université de Strasbourg, 23 rue du Loess, BP 84047, 67034 Strasbourg Cedex 2, France
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16
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Cho HW, Shi G, Kirkpatrick TR, Thirumalai D. Random First Order Transition Theory for Glassy Dynamics in a Single Condensed Polymer. PHYSICAL REVIEW LETTERS 2021; 126:137801. [PMID: 33861095 DOI: 10.1103/physrevlett.126.137801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2020] [Revised: 12/21/2020] [Accepted: 03/01/2021] [Indexed: 06/12/2023]
Abstract
The number of compact structures of a single condensed polymer (SCP), with similar free energies, grows exponentially with the degree of polymerization. In analogy with structural glasses (SGs), we expect that at low temperatures chain relaxation should occur by activated transitions between the compact metastable states. By evolving the states of the SCP, linearly coupled to a reference state, we show that, below a dynamical transition temperature (T_{d}), the SCP is trapped in a metastable state leading to slow dynamics. At a lower temperature, T_{K}≠0, the configurational entropy vanishes, resulting in a thermodynamic random first order ideal glass transition. The relaxation time obeys the Vogel-Fulcher-Tamman law, diverging at T=T_{0}≈T_{K}. These findings, accord well with the random first order transition theory, establishing that SCP and SG exhibit similar universal characteristics.
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Affiliation(s)
- Hyun Woo Cho
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, USA
- Department of Fine Chemistry, Seoul National University of Science and Technology, Seoul 01811, Korea
| | - Guang Shi
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, USA
| | - T R Kirkpatrick
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - D Thirumalai
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, USA
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17
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Wicks TJ, Wattis JAD, Graham RS. Monte–Carlo simulation of crystallization in single‐chain square‐well homopolymers. POLYMER CRYSTALLIZATION 2021. [DOI: 10.1002/pcr2.10146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Thomas J. Wicks
- School of Mathematical Sciences University of Nottingham Nottingham UK
| | | | - Richard S. Graham
- School of Mathematical Sciences University of Nottingham Nottingham UK
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18
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Taylor MP, Vinci C, Suzuki R. Effects of macromolecular crowding on the folding of a polymer chain: A Wang-Landau simulation study. J Chem Phys 2020; 153:174901. [PMID: 33167653 DOI: 10.1063/5.0025640] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A flexible polymer chain in the presence of inert macromolecular crowders will experience a loss of configurational entropy due to the crowder excluded volume. This entropy reduction will be most pronounced in good solvent conditions where the chain assumes an expanded coil conformation. For polymers that undergo a folding transition from a coil to a compact ordered state, as is the case for many globular proteins, macromolecular crowding is expected to stabilize the folded state and thereby shift the transition location. Here, we study such entropic stabilization effects for a tangent square-well sphere chain (monomer diameter σ) in the presence of hard-sphere (HS) crowders (diameter D ≥ σ). We use the Wang-Landau simulation algorithm to construct the density of states for this chain in a crowded environment and are thus able to directly compute the reduction in configurational entropy due to crowding. We study both a chain that undergoes all-or-none folding directly from the coil state and a chain that folds via a collapsed-globule intermediate state. In each case, we find an increase in entropic stabilization for the compact states with an increase in crowder density and, for fixed crowder density, with a decrease in crowder size (concentrated, small crowders have the largest effect). The crowder significantly reduces the average size for the unfolded states while having a minimal effect on the size of the folded states. In the athermal limit, our results directly provide the confinement free energy due to crowding for a HS chain in a HS solvent.
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Affiliation(s)
- Mark P Taylor
- Department of Physics, Hiram College, Hiram, Ohio 44234, USA
| | | | - Ryogo Suzuki
- Department of Physics, Hiram College, Hiram, Ohio 44234, USA
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19
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Herranz M, Santiago M, Foteinopoulou K, Karayiannis NC, Laso M. Crystal, Fivefold and Glass Formation in Clusters of Polymers Interacting with the Square Well Potential. Polymers (Basel) 2020; 12:polym12051111. [PMID: 32414038 PMCID: PMC7285265 DOI: 10.3390/polym12051111] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2020] [Revised: 04/25/2020] [Accepted: 05/06/2020] [Indexed: 11/23/2022] Open
Abstract
We present results, from Monte Carlo (MC) simulations, on polymer systems of freely jointed chains with spherical monomers interacting through the square well potential. Starting from athermal packings of chains of tangent hard spheres, we activate the square well potential under constant volume and temperature corresponding effectively to instantaneous quenching. We investigate how the intensity and range of pair-wise interactions affected the final morphologies by fixing polymer characteristics such as average chain length and tolerance in bond gaps. Due to attraction chains are brought closer together and they form clusters with distinct morphologies. A wide variety of structures is obtained as the model parameters are systematically varied: weak interactions lead to purely amorphous clusters followed by well-ordered ones. The latter include the whole spectrum of crystal morphologies: from virtually perfect hexagonal close packed (HCP) and face centered cubic (FCC) crystals, to random hexagonal close packed layers of single stacking direction of alternating HCP and FCC layers, to structures of mixed HCP/FCC character with multiple stacking directions and defects in the form of twins. Once critical values of interaction are met, fivefold-rich glassy clusters are formed. We discuss the similarities and differences between energy-driven crystal nucleation in thermal polymer systems as opposed to entropy-driven phase transition in athermal polymer packings. We further calculate the local density of each site, its dependence on the distance from the center of the cluster and its correlation with the crystallographic characteristics of the local environment. The short- and long-range conformations of chains are analyzed as a function of the established cluster morphologies.
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20
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Chaimovich A, Leitold C, Dellago C. The generic unfolding of a biomimetic polymer during force spectroscopy. SOFT MATTER 2020; 16:3941-3951. [PMID: 32267254 DOI: 10.1039/c9sm02545f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
With the help of force spectroscopy, several analytical theories aim at estimating the rate coefficient of folding for various proteins. Nevertheless, a chief bottleneck lies in the fact that there is still no perfect consensus on how does a force generally perturb the crystal-coil transition. Consequently, the goal of our work is in clarifying the generic behavior of most proteins in force spectroscopy; in other words, what general signature does an arbitrary protein exhibit for its rate coefficient as a function of the applied force? By employing a biomimetic polymer in molecular simulations, we focus on evaluating its respective activation energy for unfolding, while pulling on various pairs of its monomers. Above all, we find that in the vicinity of the force-free scenario, this activation energy possesses a negative slope and a negative curvature as a function of the applied force. Our work is in line with the most recent theories for unfolding, which suggest that such a signature is expected for most proteins, and thus, we further reiterate that many of the classical formulae, that estimate the rate coefficient of the crystal-coil transition, are inadequate. Besides, we also present here an analytical expression which experimentalists can use for approximating the activation energy for unfolding; importantly, it is based on measurements for the mean and variance of the distance between the beads which are being pulled. In summary, our work presents an interesting view for protein folding in force spectroscopy.
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Affiliation(s)
- Aviel Chaimovich
- Department of Chemical and Biological Engineering, Drexel University, Philadelphia, Pennsylvania 19104, USA.
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21
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Taylor MP, Prunty TM, O'Neil CM. All-or-none folding of a flexible polymer chain in cylindrical nanoconfinement. J Chem Phys 2020; 152:094901. [PMID: 33480730 DOI: 10.1063/1.5144818] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
Geometric confinement of a polymer chain results in a loss of conformational entropy. For a chain that can fold into a compact native state via a first-order-like transition, as is the case for many small proteins, confinement typically provides an entropic stabilization of the folded state, thereby shifting the location of the transition. This allows for the possibility of confinement (entropy) driven folding. Here, we investigate such confinement effects for a flexible square-well-sphere N-mer chain (monomer diameter σ) confined within a long cylindrical pore (diameter D) or a closed cylindrical box (height H = D). We carry out Wang-Landau simulations to construct the density of states, which provides access to the complete thermodynamics of the system. For a wide pore, an entropic stabilization of the folded state is observed. However, as the pore diameter approaches the size of the folded chain (D ∼ N1/3σ), we find a destabilization effect. For pore diameters smaller than the native ground-state, the chain folds into a different, higher energy, ground state ensemble and the T vs D phase diagram displays non-monotonic behavior as the system is forced into different ground states for different ranges of D. In this regime, isothermal reduction of the confinement dimension can induce folding, unfolding, or crystallite restructuring. For the cylindrical box, we find a monotonic stabilization effect with decreasing D. Scaling laws for the confinement free energy in the athermal limit are also investigated.
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Affiliation(s)
- Mark P Taylor
- Department of Physics, Hiram College, Hiram, Ohio 44234, USA
| | - Troy M Prunty
- Department of Physics, Hiram College, Hiram, Ohio 44234, USA
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22
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Dai C, Liu JS. Wang-Landau algorithm as stochastic optimization and its acceleration. Phys Rev E 2020; 101:033301. [PMID: 32289991 DOI: 10.1103/physreve.101.033301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2019] [Accepted: 01/31/2020] [Indexed: 06/11/2023]
Abstract
We show that the Wang-Landau algorithm can be formulated as a stochastic gradient descent algorithm minimizing a smooth and convex objective function, of which the gradient is estimated using Markov chain Monte Carlo iterations. The optimization formulation provides us another way to establish the convergence rate of the Wang-Landau algorithm, by exploiting the fact that almost surely the density estimates (on the logarithmic scale) remain in a compact set, upon which the objective function is strongly convex. The optimization viewpoint motivates us to improve the efficiency of the Wang-Landau algorithm using popular tools including the momentum method and the adaptive learning rate method. We demonstrate the accelerated Wang-Landau algorithm on a two-dimensional Ising model and a two-dimensional ten-state Potts model.
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Affiliation(s)
- Chenguang Dai
- Department of Statistics, Harvard University, Cambridge, Massachusetts, USA
| | - Jun S Liu
- Department of Statistics, Harvard University, Cambridge, Massachusetts, USA
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23
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Hussain S, Haji-Akbari A. Studying rare events using forward-flux sampling: Recent breakthroughs and future outlook. J Chem Phys 2020; 152:060901. [DOI: 10.1063/1.5127780] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Sarwar Hussain
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520, USA
| | - Amir Haji-Akbari
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520, USA
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24
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Škrbić T, Banavar JR, Giacometti A. Chain stiffness bridges conventional polymer and bio-molecular phases. J Chem Phys 2019; 151:174901. [PMID: 31703491 DOI: 10.1063/1.5123720] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
Chain molecules play important roles in industry and in living cells. Our focus here is on distinct ways of modeling the stiffness inherent in a chain molecule. We consider three types of stiffnesses-one yielding an energy penalty for local bends (energetic stiffness) and the other two forbidding certain classes of chain conformations (entropic stiffness). Using detailed Wang-Landau microcanonical Monte Carlo simulations, we study the interplay between the nature of the stiffness and the ground state conformation of a self-attracting chain. We find a wide range of ground state conformations, including a coil, a globule, a toroid, rods, helices, and zig-zag strands resembling β-sheets, as well as knotted conformations allowing us to bridge conventional polymer phases and biomolecular phases. An analytical mapping is derived between the persistence lengths stemming from energetic and entropic stiffness. Our study shows unambiguously that different stiffnesses play different physical roles and have very distinct effects on the nature of the ground state of the conformation of a chain, even if they lead to identical persistence lengths.
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Affiliation(s)
- Tatjana Škrbić
- Department of Physics and Institute for Theoretical Science, 1274 University of Oregon, Eugene, Oregon 97403-1274, USA
| | - Jayanth R Banavar
- Department of Physics and Institute for Theoretical Science, 1274 University of Oregon, Eugene, Oregon 97403-1274, USA
| | - 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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25
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Crystallisation in Melts of Short, Semi-Flexible Hard-Sphere Polymer Chains: The Role of the Non-Bonded Interaction Range. ENTROPY 2019; 21:856. [PMCID: PMC7515385 DOI: 10.3390/e21090856] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2019] [Accepted: 08/29/2019] [Indexed: 07/20/2023]
Abstract
A melt of short semi-flexible polymers with hard-sphere-type non-bonded interaction undergoes a first-order crystallisation transition at lower density than a melt of hard-sphere monomers or a flexible hard-sphere chain. In contrast to the flexible hard-sphere chains, the semi-flexible ones have an intrinsic stiffness energy scale, which determines the natural temperature scale of the system. In this paper, we investigate the effect of weak additional non-bonded interaction on the phase transition temperature. We study the system using the stochastic approximation Monte Carlo (SAMC) method to estimate the micro-canonical entropy of the system. Since the density of states in the purely hard-sphere non-bonded interaction case already covers 5600 orders of magnitude, we consider the effect of weak interactions as a perturbation. In this case, the system undergoes the same ordering transition with a temperature shift non-uniformly depending on the additional interaction. Short-range attractions impede ordering of the melt of semi-flexible polymers and decrease the transition temperature, whereas relatively long-range attractions assist ordering and shift the transition temperature to higher values, whereas weak repulsive interactions demonstrate an opposite effect on the transition temperature.
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26
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Škrbić T, Hoang TX, Maritan A, Banavar JR, Giacometti A. Local symmetry determines the phases of linear chains: a simple model for the self-assembly of peptides. SOFT MATTER 2019; 15:5596-5613. [PMID: 31259346 DOI: 10.1039/c9sm00851a] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We discuss the relation between the emergence of new phases with broken symmetry within the framework of simple models of biopolymers. We start with a classic model for a chain molecule of spherical beads tethered together, with the steric constraint that non-consecutive beads cannot overlap, and with a pairwise attractive square well potential accounting for the hydrophobic effect and promoting compaction. We then discuss the consequences of the successive breaking of spurious symmetries. First, we allow the partial interpenetration of consecutive beads. In addition to the standard high temperature coil phase and the low temperature collapsed phase, this results in a new class of marginally compact ground states comprising conformations reminiscent of α-helices and β-sheets, the building blocks of the native states of globular proteins. We then discuss the effect of a further symmetry breaking of the cylindrical symmetry on attaching a side-sphere to the backbone beads along the negative normal of the chain, to mimic the presence of side chains in real proteins. This leads to the emergence of a novel phase within the previously obtained marginally compact phase, with the appearance of more complex secondary structure assemblies. The potential importance of this new phase in the de novo design of self-assembled peptides is highlighted.
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Affiliation(s)
- Tatjana Škrbić
- Department of Physics and Institute for Theoretical Science, 1274 University of Oregon, Eugene, OR 97403-1274, USA. and Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari di Venezia, Campus Scientifico, Edificio Alfa, via Torino 155, 30170 Venezia Mestre, Italy.
| | - Trinh Xuan Hoang
- Center for Computational Physics Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan St., Hanoi, Vietnam.
| | - Amos Maritan
- Dipartimento di Fisica e Astronomia, Università di Padova, and INFN, via Marzolo 8, I-35131 Padova, Italy.
| | - Jayanth R Banavar
- Department of Physics and Institute for Theoretical Science, 1274 University of Oregon, Eugene, OR 97403-1274, USA.
| | - 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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27
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Luettmer-Strathmann J. Configurational contribution to the Soret effect of a protein ligand system : An investigation with density-of-states simulations. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:77. [PMID: 31222556 DOI: 10.1140/epje/i2019-11840-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2019] [Accepted: 05/13/2019] [Indexed: 06/09/2023]
Abstract
Many of the biological functions of proteins are closely associated with their ability to bind ligands and change conformations in response to changing conditions. Since binding state and conformation of a protein affect its response to a temperature gradient, they may be probed with thermophoresis. In recent years, thermophoretic techniques to investigate biomolecular interactions, quantify ligand binding, and probe conformational changes have become established. To develop a better understanding of the mechanisms underlying the thermophoretic behavior of proteins and ligands, we employ a simple, off-lattice model for a protein and ligand in explicit solvent. To investigate the partitioning of the particles in a temperature gradient, we perform Wang-Landau-type simulations in a divided simulation box and construct the density of states over a two-dimensional state space. This method gives us access to the entropy and energy of the divided system and allows us to estimate the configurational contribution to the Soret coefficient. In this work, we focus on dilute solutions of hydrophobic proteins and investigate the effect of ligand binding on their thermophoretic behavior. We find that our simple model captures important aspects of protein-ligand interactions and allows us to relate the binding energy to the change in Soret coefficient upon ligand binding.
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Affiliation(s)
- Jutta Luettmer-Strathmann
- Department of Physics and Department of Chemistry, The University of Akron, 44325-4001, Akron, OH, USA.
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28
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Xu X, Wei Q, Li H, Wang Y, Chen Y, Jiang Y. Recognition of polymer configurations by unsupervised learning. Phys Rev E 2019; 99:043307. [PMID: 31108670 DOI: 10.1103/physreve.99.043307] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2019] [Indexed: 12/30/2022]
Abstract
Unsupervised learning as an important branch of machine learning is commonly adopted to discover patterns, with the purpose of conducting data clustering without being labeled in advance. In this study, we elucidate the striking ability of unsupervised learning techniques in exploring the phase transitions of polymer configurations. In order to extract the low-dimensional representation of polymer configurations, principal component analysis and diffusion map are applied to distinguish the coiled state and collapsed states and further detect the delicate distinction among collapsed states, respectively. These dimensionality reduction techniques not only identify the distinct states in the feature space, but also offer significant insights to understand the relation between salient features and order parameters in physics. In addition, a hybrid neural network scheme combining the supervised learning and unsupervised learning is utilized to precisely detect the critical point of phase transition between polymer configurations. Our study demonstrates a promising strategy based on the unsupervised learning, particularly in the exploration of phase transition in polymeric systems.
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Affiliation(s)
- Xin Xu
- School of Chemistry & Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education & Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China
| | - Qianshi Wei
- School of Chemistry & Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education & Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China.,Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
| | - Huaping Li
- School of Chemistry & Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education & Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China
| | - Yuzhang Wang
- School of Chemistry & Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education & Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China
| | - Yuguo Chen
- School of Chemistry & Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education & Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China
| | - Ying Jiang
- School of Chemistry & Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education & Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China.,Beijing Advanced Innovation Center for Biomedical Engineering, Beihang University, Beijing 100191, China
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29
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Diagrams of States of Single Flexible-Semiflexible Multi-Block Copolymer Chains: A Flat-Histogram Monte Carlo Study. Polymers (Basel) 2019; 11:polym11050757. [PMID: 31052227 PMCID: PMC6571722 DOI: 10.3390/polym11050757] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2019] [Revised: 04/24/2019] [Accepted: 04/26/2019] [Indexed: 01/16/2023] Open
Abstract
The combination of flexibility and semiflexibility in a single molecule is a powerful design principle both in nature and in materials science. We present results on the conformational behavior of a single multiblock-copolymer chain, consisting of equal amounts of Flexible (F) and Semiflexible (S) blocks with different affinity to an implicit solvent. We consider a manifold of macrostates defined by two terms in the total energy: intermonomer interaction energy and stiffness energy. To obtain diagrams of states (pseudo-phase diagrams), we performed flat-histogram Monte Carlo simulations using the Stochastic Approximation Monte Carlo algorithm (SAMC). We have accumulated two-Dimensional Density of States (2D DoS) functions (defined on the 2D manifold of macrostates) for a SF-multiblock-copolymer chain of length N=64 with block lengths b = 4, 8, 16, and 32 in two different selective solvents. In an analysis of the canonical ensemble, we calculated the heat capacity and determined its maxima and the most probable morphologies in different regions of the state diagrams. These are rich in various, non-trivial morphologies, which are formed without any specific interactions, and depend on the block length and the type of solvent selectivity (preferring S or F blocks, respectively). We compared the diagrams with those for the non-selective solvent and reveal essential changes in some cases. Additionally, we implemented microcanonical analysis in the “conformational” microcanonical (NVU, where U is the potential energy) and the true microcanonical (NVE, where E is the total energy) ensembles with the aim to reveal and classify pseudo-phase transitions, occurring under the change of temperature.
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30
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Qi K, Liewehr B, Koci T, Pattanasiri B, Williams MJ, Bachmann M. Influence of bonded interactions on structural phases of flexible polymers. J Chem Phys 2019; 150:054904. [PMID: 30736671 DOI: 10.1063/1.5081831] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Abstract
We introduce a novel coarse-grained bead-spring model for flexible polymers to systematically examine the effects of an adjusted bonded potential on the formation and stability of structural macrostates in a thermal environment. The density of states obtained in advanced replica-exchange Monte Carlo simulations is analyzed by employing the recently developed generalized microcanonical inflection-point analysis method, which enables the identification of diverse structural phases and the construction of a suitably parameterized hyperphase diagram. It reveals that icosahedral phases dominate for polymers with asymmetric and narrow bond potentials, whereas polymers with symmetric and more elastic bonds tend to form amorphous structures with non-icosahedral cores. We also observe a hierarchy in the freezing transition behavior associated with the formation of the surface layer after nucleation.
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Affiliation(s)
- Kai Qi
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Benjamin Liewehr
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| | - Tomas Koci
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| | - Busara Pattanasiri
- Soft Matter Systems Research Group, Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| | - 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
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31
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32
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Desgranges C, Delhommelle J. Prediction of the phase equilibria for island-type asphaltenes via HMC-WL simulations. J Chem Phys 2018; 149:072307. [DOI: 10.1063/1.5023810] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Caroline Desgranges
- Department of Chemistry, University of North Dakota, Grand Forks, North Dakota 58202, USA
| | - Jerome Delhommelle
- Department of Chemistry, University of North Dakota, Grand Forks, North Dakota 58202, USA
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33
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Shakirov T, Paul W. Crystallization in melts of short, semiflexible hard polymer chains: An interplay of entropies and dimensions. Phys Rev E 2018; 97:042501. [PMID: 29758595 DOI: 10.1103/physreve.97.042501] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2017] [Indexed: 12/19/2022]
Abstract
What is the thermodynamic driving force for the crystallization of melts of semiflexible polymers? We try to answer this question by employing stochastic approximation Monte Carlo simulations to obtain the complete thermodynamic equilibrium information for a melt of short, semiflexible polymer chains with purely repulsive nonbonded interactions. The thermodynamics is obtained based on the density of states of our coarse-grained model, which varies by up to 5600 orders of magnitude. We show that our polymer melt undergoes a first-order crystallization transition upon increasing the chain stiffness at fixed density. This crystallization can be understood by the interplay of the maximization of different entropy contributions in different spatial dimensions. At sufficient stiffness and density, the three-dimensional orientational interactions drive the orientational ordering transition, which is accompanied by a two-dimensional translational ordering transition in the plane perpendicular to the chains resulting in a hexagonal crystal structure. While the three-dimensional ordering can be understood in terms of Onsager theory, the two-dimensional transition can be understood in terms of the liquid-hexatic transition of hard disks. Due to the domination of lateral two-dimensional translational entropy over the one-dimensional translational entropy connected with columnar displacements, the chains form a lamellar phase. Based on this physical understanding, orientational ordering and translational ordering should be separable for polymer melts. A phenomenological theory based on this understanding predicts a qualitative phase diagram as a function of volume fraction and stiffness in good agreement with results from the literature.
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Affiliation(s)
- T Shakirov
- Institute of Physics, Martin-Luther-University, 06099 Halle, Germany
| | - W Paul
- Institute of Physics, Martin-Luther-University, 06099 Halle, Germany
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34
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Wu J, Cheng C, Liu G, Zhang P, Chen T. The folding pathways and thermodynamics of semiflexible polymers. J Chem Phys 2018; 148:184901. [PMID: 29764123 DOI: 10.1063/1.5018114] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
Inspired by the protein folding and DNA packing, we have systematically studied the thermodynamic and kinetic behaviors of single semiflexible homopolymers by Langevin dynamics simulations. In line with experiments, a rich variety of folding products, such as rod-like bundles, hairpins, toroids, and a mixture of them, are observed in the complete diagram of states. Moreover, knotted structures with a significant population are found in a certain range of bending stiffness in thermal equilibrium. As the solvent quality becomes poorer, the population of the intermediate occurring in the folding process increases, which leads to a severe chevron rollover for the folding arm. However, the population of the intermediates in the unfolding process is very low, insufficient to induce unfolding arm rollover. The total types of folding pathways from the coil state to the toroidal state for a semiflexible polymer chain remain unchanged by varying the solvent quality or temperature, whereas the kinetic partitioning into different folding events can be tuned significantly. In the process of knotting, three types of mechanisms, namely, plugging, slipknotting, and sliding, are discovered. Along the folding evolution, a semiflexible homopolymer chain can knot at any stage of folding upon leaving the extended coil state, and the probability to find a knot increases with chain compactness. In addition, we find rich types of knotted topologies during the folding of a semiflexible homopolymer chain. This study should be helpful in gaining insight into the general principles of biopolymer folding.
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Affiliation(s)
- Jing Wu
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Chenqian Cheng
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Gaoyuan Liu
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Ping Zhang
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Tao Chen
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
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35
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Affiliation(s)
- Yani Zhao
- Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
| | - Marek Cieplak
- Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
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36
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Baldock RJN, Bernstein N, Salerno KM, Pártay LB, Csányi G. Constant-pressure nested sampling with atomistic dynamics. Phys Rev E 2017; 96:043311. [PMID: 29347557 DOI: 10.1103/physreve.96.043311] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2017] [Indexed: 11/07/2022]
Abstract
The nested sampling algorithm has been shown to be a general method for calculating the pressure-temperature-composition phase diagrams of materials. While the previous implementation used single-particle Monte Carlo moves, these are inefficient for condensed systems with general interactions where single-particle moves cannot be evaluated faster than the energy of the whole system. Here we enhance the method by using all-particle moves: either Galilean Monte Carlo or the total enthalpy Hamiltonian Monte Carlo algorithm, introduced in this paper. We show that these algorithms enable the determination of phase transition temperatures with equivalent accuracy to the previous method at 1/N of the cost for an N-particle system with general interactions, or at equal cost when single-particle moves can be done in 1/N of the cost of a full N-particle energy evaluation. We demonstrate this speed-up for the freezing and condensation transitions of the Lennard-Jones system and show the utility of the algorithms by calculating the order-disorder phase transition of a binary Lennard-Jones model alloy, the eutectic of copper-gold, the density anomaly of water, and the condensation and solidification of bead-spring polymers. The nested sampling method with all three algorithms is implemented in the pymatnest software.
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Affiliation(s)
- Robert J N Baldock
- Theory and Simulation of Materials (THEOS), and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - Noam Bernstein
- Center for Materials Physics and Technology, Naval Research Laboratory, Washington, DC 20375, USA
| | - K Michael Salerno
- National Research Council Associateship Program, resident at the US Naval Research Laboratory, Washington, DC 20375, USA
| | - Lívia B Pártay
- Department of Chemistry, University of Reading, Reading, United Kingdom
| | - Gábor Csányi
- Engineering Laboratory, University of Cambridge, Cambridge, United Kingdom
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37
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Taylor MP. Note: Rigorous results for the partition function of a square-well chain in hard-sphere solvent. J Chem Phys 2017; 147:166101. [DOI: 10.1063/1.5001082] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [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
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38
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Barash LY, Fadeeva MA, Shchur LN. Control of accuracy in the Wang-Landau algorithm. Phys Rev E 2017; 96:043307. [PMID: 29347602 DOI: 10.1103/physreve.96.043307] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2017] [Indexed: 01/31/2023]
Abstract
The Wang-Landau (WL) algorithm has been widely used for simulations in many areas of physics. Our analysis of the WL algorithm explains its properties and shows that the difference of the largest eigenvalue of the transition matrix in the energy space from unity can be used to control the accuracy of estimating the density of states. Analytic expressions for the matrix elements are given in the case of the one-dimensional Ising model. The proposed method is further confirmed by numerical results for the one-dimensional and two-dimensional Ising models and also the two-dimensional Potts model.
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Affiliation(s)
- L Yu Barash
- Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia.,Science Center in Chernogolovka, 142432 Chernogolovka, Russia.,National Research University Higher School of Economics, 101000 Moscow, Russia
| | - M A Fadeeva
- Science Center in Chernogolovka, 142432 Chernogolovka, Russia.,National Research University Higher School of Economics, 101000 Moscow, Russia
| | - L N Shchur
- Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia.,Science Center in Chernogolovka, 142432 Chernogolovka, Russia.,National Research University Higher School of Economics, 101000 Moscow, Russia
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39
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Affiliation(s)
- Mark P. Taylor
- Department of Physics, Hiram College, Hiram, Ohio 44234, United States
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40
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Williams MJ, Bachmann M. The effect of surface adsorption on tertiary structure formation in helical polymers. J Chem Phys 2017; 147:024902. [DOI: 10.1063/1.4991564] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Matthew J. Williams
- Institute of Engineering, Murray State University, Murray, Kentucky 42071, USA
- 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
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41
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Koci T, Bachmann M. Subphase transitions in first-order aggregation processes. Phys Rev E 2017; 95:032502. [PMID: 28415362 DOI: 10.1103/physreve.95.032502] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2016] [Indexed: 11/07/2022]
Abstract
In this paper, we investigate the properties of aggregation transitions in the context of generic coarse-grained homopolymer systems. By means of parallel replica-exchange Monte Carlo methods, we perform extensive simulations of systems consisting of up to 20 individual oligomer chains with five monomers each. Using the tools of the versatile microcanonical inflection-point analysis, we show that the aggregation transition is a first-order process consisting of a sequence of subtransitions between intermediate structural phases. We unravel the properties of these intermediate phases by collecting and analyzing their individual contributions towards the density of states of the system. The central theme of this systematic study revolves around translational entropy and its role in the striking phenomena of missing intermediate phases. We conclude with a brief discussion of the scaling properties of the transition temperature and the latent heat.
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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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42
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Wang L, Wang Z, Jiang R, Yin Y, Li B. Conformation transitions of a single polyelectrolyte chain in a poor solvent: a replica-exchange lattice Monte-Carlo study. SOFT MATTER 2017; 13:2216-2227. [PMID: 28247878 DOI: 10.1039/c6sm02540d] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The thermodynamic behaviors of a strongly charged polyelectrolyte chain in a poor solvent are studied using replica-exchange Monte-Carlo simulations on a lattice model, focusing on the effects of finite chain length and the solvent quality on the chain conformation and conformation transitions. The neutralizing counterions and solvent molecules are considered explicitly. The thermodynamic quantities that vary continuously with temperature over a wide range are computed using the multiple histogram reweighting method. Our results suggest that the strength of the short-range hydrophobic interaction, the chain length, and the temperature of the system, characterized by ε, N, and T, respectively, are important parameters that control the conformations of a charged chain. When ε is moderate, the competition between the electrostatic energy and the short-range hydrophobic interaction leads to rich conformations and conformation transitions for a longer chain with a fixed length. Our results have unambiguously demonstrated the stability of the n-pearl-necklace structures, where n has a maximum value and decreases with decreasing temperature. The maximum n value increases with increasing chain length. Our results have also demonstrated the first-order nature of the conformation transitions between the m-pearl and the (m-1)-pearl necklaces. With the increase of ε, the transition temperature increases and the first-order feature becomes more pronounced. It is deduced that at the thermodynamic limit of infinitely long chain length, the conformational transitions between the m-pearl and the (m-1)-pearl necklaces may remain first order when ε > 0 and m = 2 or 3. Pearl-necklace conformations cannot be observed when either ε is too large or N is too small. To observe a pearl-necklace conformation, the T value needs to be carefully chosen for simulations performed at only a single temperature.
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Affiliation(s)
- Lang Wang
- The MOE Key Laboratory of Weak Light Nonlinear Photonics and School of Physics, Nankai University, Tianjin, 300071, China.
| | - Zheng Wang
- The MOE Key Laboratory of Weak Light Nonlinear Photonics and School of Physics, Nankai University, Tianjin, 300071, China.
| | - Run Jiang
- The MOE Key Laboratory of Weak Light Nonlinear Photonics and School of Physics, Nankai University, Tianjin, 300071, China.
| | - Yuhua Yin
- The MOE Key Laboratory of Weak Light Nonlinear Photonics and School of Physics, Nankai University, Tianjin, 300071, China.
| | - Baohui Li
- The MOE Key Laboratory of Weak Light Nonlinear Photonics and School of Physics, Nankai University, Tianjin, 300071, China.
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43
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Taylor MP, Paul W, Binder K. On the polymer physics origins of protein folding thermodynamics. J Chem Phys 2017; 145:174903. [PMID: 27825238 DOI: 10.1063/1.4966645] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
A remarkable feature of the spontaneous folding of many small proteins is the striking similarity in the thermodynamics of the folding process. This process is characterized by simple two-state thermodynamics with large and compensating changes in entropy and enthalpy and a funnel-like free energy landscape with a free-energy barrier that varies linearly with temperature. One might attribute the commonality of this two-state folding behavior to features particular to these proteins (e.g., chain length, hydrophobic/hydrophilic balance, attributes of the native state) or one might suspect that this similarity in behavior has a more general polymer-physics origin. Here we show that this behavior is also typical for flexible homopolymer chains with sufficiently short range interactions. Two-state behavior arises from the presence of a low entropy ground (folded) state separated from a set of high entropy disordered (unfolded) states by a free energy barrier. This homopolymer model exhibits a funneled free energy landscape that reveals a complex underlying dynamics involving competition between folding and non-folding pathways. Despite the presence of multiple pathways, this simple physics model gives the robust result of two-state thermodynamics for both the cases of folding from a basin of expanded coil states and from a basin of compact globule states.
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Affiliation(s)
- Mark P Taylor
- Department of Physics, Hiram College, Hiram, Ohio 44234, USA
| | - Wolfgang Paul
- Institut für Physik, Martin-Luther-Universität, D-06099 Halle (Saale), Germany
| | - Kurt Binder
- Institut für Physik, Johannes-Gutenberg-Universität, Staudinger Weg 7, D-55099 Mainz, Germany
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44
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Schweizerhof S, Demco DE, Mourran A, Keul H, Fechete R, Möller M. Temperature-Induced Phase Transition Characterization of Responsive Polymer Brushes Grafted onto Nanoparticles. MACROMOL CHEM PHYS 2017. [DOI: 10.1002/macp.201600495] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Sjören Schweizerhof
- DWI-Leibniz-Institute for Interactive Materials, e.V.; RWTH-Aachen University; Forckenbeckstraße 50 52074 Aachen Germany
| | - Dan Eugen Demco
- DWI-Leibniz-Institute for Interactive Materials, e.V.; RWTH-Aachen University; Forckenbeckstraße 50 52074 Aachen Germany
- Technical University of Cluj-Napoca; Department of Physics and Chemistry; 25 G. Baritiu Str. 400027 Cluj-Napoca Romania
| | - Ahmed Mourran
- DWI-Leibniz-Institute for Interactive Materials, e.V.; RWTH-Aachen University; Forckenbeckstraße 50 52074 Aachen Germany
| | - Helmut Keul
- DWI-Leibniz-Institute for Interactive Materials, e.V.; RWTH-Aachen University; Forckenbeckstraße 50 52074 Aachen Germany
| | - Radu Fechete
- Technical University of Cluj-Napoca; Department of Physics and Chemistry; 25 G. Baritiu Str. 400027 Cluj-Napoca Romania
| | - Martin Möller
- DWI-Leibniz-Institute for Interactive Materials, e.V.; RWTH-Aachen University; Forckenbeckstraße 50 52074 Aachen Germany
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45
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Werlich B, Taylor MP, Shakirov T, Paul W. On the Pseudo Phase Diagram of Single Semi-Flexible Polymer Chains: A Flat-Histogram Monte Carlo Study. Polymers (Basel) 2017; 9:E38. [PMID: 30970714 PMCID: PMC6432196 DOI: 10.3390/polym9020038] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2016] [Revised: 01/17/2017] [Accepted: 01/19/2017] [Indexed: 01/10/2023] Open
Abstract
Local stiffness of polymer chains is instrumental in all structure formation processes of polymers, from crystallization of synthetic polymers to protein folding and DNA compactification. We present Stochastic Approximation Monte Carlo simulations-a type of flat-histogram Monte Carlo method-determining the density of states of a model class of single semi-flexible polymer chains, and, from this, their complete thermodynamic behavior. The chains possess a rich pseudo phase diagram as a function of stiffness and temperature, displaying non-trivial ground-state morphologies. This pseudo phase diagram also depends on chain length. Differences to existing pseudo phase diagrams of semi-flexible chains in the literature emphasize the fact that the mechanism of stiffness creation matters.
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Affiliation(s)
- Benno Werlich
- Institut für Physik, Martin-Luther-Universität, 06099 Halle, Germany.
| | - Mark P Taylor
- Department of Physics, Hiram College, Hiram, OH 44234, USA.
| | - Timur Shakirov
- Institut für Physik, Martin-Luther-Universität, 06099 Halle, Germany.
| | - Wolfgang Paul
- Institut für Physik, Martin-Luther-Universität, 06099 Halle, Germany.
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46
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Landsgesell J, Holm C, Smiatek J. Wang-Landau Reaction Ensemble Method: Simulation of Weak Polyelectrolytes and General Acid-Base Reactions. J Chem Theory Comput 2017; 13:852-862. [PMID: 28029786 DOI: 10.1021/acs.jctc.6b00791] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
We present a novel method for the study of weak polyelectrolytes and general acid-base reactions in molecular dynamics and Monte Carlo simulations. The approach combines the advantages of the reaction ensemble and the Wang-Landau sampling method. Deprotonation and protonation reactions are simulated explicitly with the help of the reaction ensemble method, while the accurate sampling of the corresponding phase space is achieved by the Wang-Landau approach. The combination of both techniques provides a sufficient statistical accuracy such that meaningful estimates for the density of states and the partition sum can be obtained. With regard to these estimates, several thermodynamic observables like the heat capacity or reaction free energies can be calculated. We demonstrate that the computation times for the calculation of titration curves with a high statistical accuracy can be significantly decreased when compared to the original reaction ensemble method. The applicability of our approach is validated by the study of weak polyelectrolytes and their thermodynamic properties.
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Affiliation(s)
- Jonas Landsgesell
- Institute for Computational Physics, University of Stuttgart , D-70569 Stuttgart, Germany
| | - Christian Holm
- Institute for Computational Physics, University of Stuttgart , D-70569 Stuttgart, Germany
| | - Jens Smiatek
- Institute for Computational Physics, University of Stuttgart , D-70569 Stuttgart, Germany
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47
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Vorselaars B, Růžička Š, Quigley D, Allen MP. Correction: Folding kinetics of a polymer. Phys Chem Chem Phys 2017; 19:5674-5676. [DOI: 10.1039/c7cp90027a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Correction for ‘Folding kinetics of a polymer’ by Štěpán Růžička et al., Phys. Chem. Chem. Phys., 2012, 14, 6044–6053.
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Affiliation(s)
- Bart Vorselaars
- Department of Physics
- University of Warwick
- Coventry CV4 7AL
- UK
| | - Štěpán Růžička
- Department of Physics
- University of Warwick
- Coventry CV4 7AL
- UK
| | - David Quigley
- Department of Physics
- University of Warwick
- Coventry CV4 7AL
- UK
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48
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Zablotskiy SV, Martemyanova JA, Ivanov VA, Paul W. Stochastic approximation Monte Carlo algorithm for calculation of diagram of states of a single flexible-semiflexible copolymer chain. POLYMER SCIENCE SERIES A 2016. [DOI: 10.1134/s0965545x1606016x] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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49
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Perera D, Vogel T, Landau DP. Magnetic phase transition in coupled spin-lattice systems: A replica-exchange Wang-Landau study. Phys Rev E 2016; 94:043308. [PMID: 27841592 DOI: 10.1103/physreve.94.043308] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2016] [Indexed: 11/07/2022]
Abstract
Coupled, dynamical spin-lattice models provide a unique test ground for simulations investigating the finite-temperature magnetic properties of materials under the direct influence of the lattice vibrations. These models are constructed by combining a coordinate-dependent interatomic potential with a Heisenberg-like spin Hamiltonian, facilitating the treatment of both the atomic coordinates and the spins as explicit phase variables. Using a model parameterized for bcc iron, we study the magnetic phase transition in these complex systems via the recently introduced, massively parallel replica-exchange Wang-Landau Monte Carlo method. Comparison with the results obtained from rigid lattice (spin-only) simulations shows that the transition temperature as well as the amplitude of the peak in the specific heat curve is marginally affected by the lattice vibrations. Moreover, the results were found to be sensitive to the particular choice of interatomic potential.
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Affiliation(s)
- Dilina Perera
- Center for Simulational Physics, The University of Georgia, Georgia 30602, USA.,Department of Physics and Astronomy, Mississippi State University, Mississippi State, Mississippi 39762, USA
| | - Thomas Vogel
- Department of Physics, Stetson University, DeLand, Florida 32723, USA
| | - David P Landau
- Center for Simulational Physics, The University of Georgia, Georgia 30602, USA
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50
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Zierenberg J, Marenz M, Janke W. Dilute Semiflexible Polymers with Attraction: Collapse, Folding and Aggregation. Polymers (Basel) 2016; 8:E333. [PMID: 30974608 PMCID: PMC6432187 DOI: 10.3390/polym8090333] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2016] [Revised: 08/12/2016] [Accepted: 08/15/2016] [Indexed: 02/06/2023] Open
Abstract
We review the current state on the thermodynamic behavior and structural phases of self- and mutually-attractive dilute semiflexible polymers that undergo temperature-driven transitions. In extreme dilution, polymers may be considered isolated, and this single polymer undergoes a collapse or folding transition depending on the internal structure. This may go as far as to stable knot phases. Adding polymers results in aggregation, where structural motifs again depend on the internal structure. We discuss in detail the effect of semiflexibility on the collapse and aggregation transition and provide perspectives for interesting future investigations.
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Affiliation(s)
- Johannes Zierenberg
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, Leipzig D-04009, Germany.
| | - Martin Marenz
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, Leipzig D-04009, Germany.
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, Leipzig D-04009, Germany.
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