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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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Coldstream JG, Camp PJ, Phillips DJ, Dowding PJ. Polymeric surfactants at liquid-liquid interfaces: Dependence of structural and thermodynamic properties on copolymer architecture. J Chem Phys 2024; 160:054902. [PMID: 38341694 DOI: 10.1063/5.0189156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2023] [Accepted: 01/11/2024] [Indexed: 02/13/2024] Open
Abstract
Polymeric surfactants are amphiphilic molecules with two or more different types of monomers. If one type of monomer interacts favorably with a liquid, and another type of monomer interacts favorably with another, immiscible liquid, then polymeric surfactants adsorb at the interface between the two liquids and reduce the interfacial tension. The effects of polymer architecture on the structural and thermodynamic properties of the liquid-liquid interface are studied using molecular simulations. The interface is modeled with a non-additive binary Lennard-Jones fluid in the two-phase region of the phase diagram. Block and gradient copolymer surfactants are represented with coarse-grained, bead-spring models, where each component of the polymer favors one or the other liquid. Gradient copolymers have a greater concentration at the interface than do block copolymers because the gradient copolymers adopt conformations partially aligned with the interface. The interfacial tension is determined as a function of the surface excess of polymeric surfactant. Gradient copolymers are more potent surfactants than block copolymers because the gradient copolymers cross the dividing surface multiple times, effectively acting as multiple individual surfactants. For a given surface excess, the interfacial tension decreases monotonically when changing from a block to a gradient architecture. The coarse-grained simulations are complemented by all-atom simulations of acrylic-acid/styrene copolymers at the chloroform-water interface, which have been studied in experiments. The agreement between the simulations (both coarse-grained and atomistic) and experiments is shown to be excellent, and the molecular-scale structures identified in the simulations help explain the variation of surfactancy with copolymer architecture.
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Affiliation(s)
- Jonathan G Coldstream
- School of Chemistry, University of Edinburgh, David Brewster Road, Edinburgh EH9 3FJ, Scotland
| | - Philip J Camp
- School of Chemistry, University of Edinburgh, David Brewster Road, Edinburgh EH9 3FJ, Scotland
| | - Daniel J Phillips
- Infineum UK Ltd., P.O. Box 1, Milton Hill, Abingdon OX13 6BB, United Kingdom
| | - Peter J Dowding
- Infineum UK Ltd., P.O. Box 1, Milton Hill, Abingdon OX13 6BB, United Kingdom
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3
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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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4
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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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5
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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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6
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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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7
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Yang X, Lu ZY. A method for directly counting and quantitatively comparing aggregated structures during cluster formation. CHINESE J CHEM PHYS 2021. [DOI: 10.1063/1674-0068/cjcp2008139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Xi Yang
- State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130021, China
| | - Zhong-yuan Lu
- State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130021, China
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8
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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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9
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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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10
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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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11
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Affiliation(s)
- Mark P. Taylor
- Department of Physics, Hiram College, Hiram, Ohio 44234, United States
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12
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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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13
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Yang X, Lu ZY. Control globular structure formation of a copolymer chain through inverse design. J Chem Phys 2016; 144:224902. [PMID: 27306020 DOI: 10.1063/1.4953576] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Abstract
A copolymer chain in dilute solution can exhibit various globular structures with characteristic morphologies, which makes it a potentially useful candidate for artificial materials design. However, the chain has a huge conformation space and may not naturally form the globular structure we desire. An ideal way to control globular structure formation should be inverse design, i.e., starting from the target structure and finding out what kind of polymers can effectively generate it. To accomplish this, we propose an inverse design procedure, which is combined with Wang-Landau Monte Carlo to fully and precisely explore the huge conformation space of the chain. Starting from a desired target structure, all the geometrically possible sequences are exactly enumerated. Interestingly, reasonable interaction strengths are obtained and found to be not specified for only one sequence. Instead, they can be combined with many other sequences and also achieve a relatively high yield for target structure, although these sequences may be rather different. These results confirm the possibility of controlling globular structure formation of a copolymer chain through inverse design and pave the way for targeted materials design.
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Affiliation(s)
- Xi Yang
- State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130021, China
| | - Zhong-Yuan Lu
- State Key Laboratory of Supramolecular Structure and Materials, Institute of Theoretical Chemistry, Jilin University, Changchun 130021, China
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14
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Zablotskiy SV, Ivanov VA, Paul W. Multidimensional stochastic approximation Monte Carlo. Phys Rev E 2016; 93:063303. [PMID: 27415383 DOI: 10.1103/physreve.93.063303] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2016] [Indexed: 06/06/2023]
Abstract
Stochastic Approximation Monte Carlo (SAMC) has been established as a mathematically founded powerful flat-histogram Monte Carlo method, used to determine the density of states, g(E), of a model system. We show here how it can be generalized for the determination of multidimensional probability distributions (or equivalently densities of states) of macroscopic or mesoscopic variables defined on the space of microstates of a statistical mechanical system. This establishes this method as a systematic way for coarse graining a model system, or, in other words, for performing a renormalization group step on a model. We discuss the formulation of the Kadanoff block spin transformation and the coarse-graining procedure for polymer models in this language. We also apply it to a standard case in the literature of two-dimensional densities of states, where two competing energetic effects are present g(E_{1},E_{2}). We show when and why care has to be exercised when obtaining the microcanonical density of states g(E_{1}+E_{2}) from g(E_{1},E_{2}).
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Affiliation(s)
| | - Victor A Ivanov
- Faculty of Physics, Moscow State University, Moscow 119991, Russia
| | - Wolfgang Paul
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle (Saale), Germany
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15
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Janke W, Paul W. Thermodynamics and structure of macromolecules from flat-histogram Monte Carlo simulations. SOFT MATTER 2016; 12:642-657. [PMID: 26574738 DOI: 10.1039/c5sm01919b] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Over the last decade flat-histogram Monte Carlo simulations, especially multi-canonical and Wang-Landau simulations, have emerged as a strong tool to study the statistical mechanics of polymer chains. These investigations have focused on coarse-grained models of polymers on the lattice and in the continuum. Phase diagrams of chains in bulk as well as chains attached to surfaces were studied, for homopolymers as well as for protein-like models. Also, aggregation behavior in solution of these models has been investigated. We will present here the theoretical background for these simulations, explain the algorithms used and discuss their performance and give an overview over the systems studied with these methods in the literature, where we will limit ourselves to studies of coarse-grained model systems. Implementations of these algorithms on parallel computers will be also briefly described. In parallel to the development of these simulation methods, the power of a micro-canonical analysis of such simulations has been recognized, and we present the current state of the art in applying the micro-canonical analysis to phase transitions in nanoscopic polymer systems.
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Affiliation(s)
- Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, 04009 Leipzig, Germany.
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16
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Taylor MP, Ye Y, Adhikari SR. Conformation of a flexible polymer in explicit solvent: Accurate solvation potentials for Lennard-Jones chains. J Chem Phys 2015; 143:204901. [DOI: 10.1063/1.4935952] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Mark P. Taylor
- Department of Physics, Hiram College, Hiram, Ohio 44234, USA
| | - Yuting Ye
- Department of Physics, Hiram College, Hiram, Ohio 44234, USA
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17
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Leitold C, Lechner W, Dellago C. A string reaction coordinate for the folding of a polymer chain. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:194126. [PMID: 25923377 DOI: 10.1088/0953-8984/27/19/194126] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We investigate the crystallization mechanism of a single, flexible homopolymer chain with short range attractions. For a sufficiently narrow attractive well, the system undergoes a first-order like freezing transition from an expanded disordered coil to a compact crystalline state. Based on a maximum likelihood analysis of committor values computed for configurations obtained by Wang-Landau sampling, we construct a non-linear string reaction coordinate for the coil-to-crystal transition. In contrast to a linear reaction coordinate, the string reaction coordinate captures the effect of different degrees of freedom controlling different stages of the transition. Our analysis indicates that a combination of the energy and the global crystallinity parameter Q6 provide the most accurate measure for the progress of the transition. While the crystallinity paramter Q6 is most relevant in the initial stages of the crystallization, the later stages are dominated by a decrease in the potential energy.
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Affiliation(s)
- Christian Leitold
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
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18
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Wang-Landau and Stochastic Approximation Monte Carlo for Semi-flexible Polymer Chains. ACTA ACUST UNITED AC 2014. [DOI: 10.1016/j.phpro.2014.08.137] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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