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Horkay F, Douglas JF. Influence of solvent quality on the swelling and deswelling and the shear modulus of semi-dilute solution cross-linked poly(vinyl acetate) gels. J Chem Phys 2023; 158:244901. [PMID: 37377156 PMCID: PMC10310356 DOI: 10.1063/5.0156604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2023] [Accepted: 06/06/2023] [Indexed: 06/29/2023] Open
Abstract
We systematically examine the influence of varying temperature (T) over a large range in model poly(vinyl acetate) gels swollen in isopropyl alcohol. The theta temperature Θ, at which the second virial coefficient A2 vanishes, is found to be equal to within numerical uncertainty to the corresponding high molecular mass polymer solution value without cross-links, and we quantify the swelling and deswelling of our model gels relative to their size at T = Θ, as customary for individual flexible polymer chains in solutions. We also quantify the "solvent quality" dependence of the shear modulus G relative to G(T = Θ) and compare to the hydrogel swelling factor, α. We find that all our network swelling and deswelling data can be reduced to a scaling equation of the same general form as derived from renormalization group theory for flexible linear polymer chains in solutions so that it is not necessary to invoke either the Flory-Huggins mean field theory or the Flory-Rehner hypothesis that the elastic and mixing contributions to the free energy of network swelling are separable to describe our data. We also find that changes of G relative to G(T = Θ) are directly related to α. At the same time, we find that classical rubber elasticity theory describes many aspects of these semi-dilute solution cross-linked networks, regardless of the solvent quality, although the prefactor clearly reflects the existence of network defects whose concentration depends on the initial polymer concentration of the polymer solution from which the networks were synthesized.
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Affiliation(s)
- Ferenc Horkay
- Section on Quantitative Imaging and Tissue Sciences, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Jack F. Douglas
- Material Measurement Laboratory, Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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2
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Singh TV, Shagolsem LS. Universality and Identity Ordering in Heteropolymer Coil–Globule Transition. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01559] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Thoudam Vilip Singh
- Department of Physics, National Institute of Technology Manipur, Imphal795004, India
| | - Lenin S. Shagolsem
- Department of Physics, National Institute of Technology Manipur, Imphal795004, India
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3
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Majumder S, Marenz M, Paul S, Janke W. Knots are Generic Stable Phases in Semiflexible Polymers. Macromolecules 2021. [DOI: 10.1021/acs.macromol.0c02584] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Martin Marenz
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Subhajit Paul
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
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4
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Okamoto Y. Protein structure predictions by enhanced conformational sampling methods. Biophys Physicobiol 2019; 16:344-366. [PMID: 31984190 PMCID: PMC6976031 DOI: 10.2142/biophysico.16.0_344] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2019] [Accepted: 08/07/2019] [Indexed: 12/01/2022] Open
Abstract
In this Special Festschrift Issue for the celebration of Professor Nobuhiro Gō's 80th birthday, we review enhanced conformational sampling methods for protein structure predictions. We present several generalized-ensemble algorithms such as multicanonical algorithm, replica-exchange method, etc. and parallel Monte Carlo or molecular dynamics method with genetic crossover. Examples of the results of these methods applied to the predictions of protein tertiary structures are also presented.
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Affiliation(s)
- Yuko Okamoto
- Department of Physics, Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan
- Structural Biology Research Center, Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan
- Center for Computational Science, Graduate School of Engineering, Nagoya University, Nagoya, Aichi 464-8603, Japan
- Information Technology Center, Nagoya University, Nagoya, Aichi 464-8601, Japan
- JST-CREST, Nagoya, Aichi 464-8602, Japan
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5
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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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6
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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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7
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Marenz M, Janke W. Knots as a Topological Order Parameter for Semiflexible Polymers. PHYSICAL REVIEW LETTERS 2016; 116:128301. [PMID: 27058105 DOI: 10.1103/physrevlett.116.128301] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2015] [Indexed: 06/05/2023]
Abstract
Using a combination of the multicanonical Monte Carlo algorithm and the replica-exchange method, we investigate the influence of bending stiffness on the conformational phases of a bead-stick homopolymer model and present the pseudophase diagram for the complete range of semiflexible polymers, from flexible to stiff. Although it is a simple model, we observe a rich variety of conformational phases, reminiscent of conformations observed for synthetic polymers or biopolymers. Depending on the bending stiffness, the model exhibits different pseudophases like bent, hairpin, or toroidal. In particular, we find thermodynamically stable knots and unusual transitions into these knotted phases with a clear phase coexistence, but almost constant mean total energy, and hence almost no latent heat.
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Affiliation(s)
- Martin Marenz
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
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8
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Electron microscopic visualization of complementary labeled DNA with platinum-containing guanine derivative. Microsc Res Tech 2016; 79:280-4. [DOI: 10.1002/jemt.22628] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2015] [Revised: 01/02/2016] [Accepted: 01/04/2016] [Indexed: 01/28/2023]
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9
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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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10
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Dai L, Renner CB, Yan J, Doyle PS. Coil-globule transition of a single semiflexible chain in slitlike confinement. Sci Rep 2015; 5:18438. [PMID: 26679086 PMCID: PMC4683450 DOI: 10.1038/srep18438] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2015] [Accepted: 11/18/2015] [Indexed: 11/30/2022] Open
Abstract
Single polymer chains undergo a phase transition from coiled conformations to globular conformations as the effective attraction between monomers becomes strong enough. In this work, we investigated the coil-globule transition of a semiflexible chain confined between two parallel plates, i.e. a slit, using the lattice model and Pruned-enriched Rosenbluth method (PERM) algorithm. We find that as the slit height decreases, the critical attraction for the coil-globule transition changes non-monotonically due to the competition of the confinement free energies of the coiled and globular states. In wide (narrow) slits, the coiled state experiences more (less) confinement free energy, and hence the transition becomes easier (more difficult). In addition, we find that the transition becomes less sharp with the decreasing slit height. Here, the sharpness refers to the sensitivity of thermodynamic quantities when varying the attraction around the critical value. The relevant experiments can be performed for DNA condensation in microfluidic devices.
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Affiliation(s)
- Liang Dai
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre, Singapore 138602
| | - C. Benjamin Renner
- Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139
| | - Jie Yan
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre, Singapore 138602
- Department of Physics, National University of Singapore, Singapore, 117551
| | - Patrick S. Doyle
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre, Singapore 138602
- Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139
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11
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Taylor MP, Paul W, Binder K. Applications of the Wang-Landau algorithm to phase transitions of a single polymer chain. POLYMER SCIENCE SERIES C 2013. [DOI: 10.1134/s1811238213060040] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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12
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Abstract
In biomolecular systems (especially all-atom models) with many degrees of freedom such as proteins and nucleic acids, there exist an astronomically large number of local-minimum-energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. Enhanced conformational sampling techniques are thus in great demand. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. From only one simulation run, one can obtain canonical-ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review uses of the generalized-ensemble algorithms in biomolecular systems. Three well-known methods, namely, multicanonical algorithm, simulated tempering, and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present various extensions of these three generalized-ensemble algorithms. The effectiveness of the methods is tested with short peptide and protein systems.
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Affiliation(s)
- Ayori Mitsutake
- Department of Physics, Keio University, Yokohama, Kanagawa, Japan
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13
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The application of condensed matter methods to the study of the conformation and elastic properties of biopolymers and the transport of DNA through cell membranes. Theor Chem Acc 2011. [DOI: 10.1007/s00214-011-1022-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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14
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dell'Erba MG, Zemba GR. Topological phase transition in a RNA model in the de Gennes regime. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:041926. [PMID: 19905361 DOI: 10.1103/physreve.80.041926] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2009] [Indexed: 05/28/2023]
Abstract
We study a simplified model of the RNA molecule proposed by Vernizzi in the regime of strong concentration of positive ions in solution. The model considers a flexible chain of equal bases that can pairwise interact with any other one along the chain while preserving the property of saturation of the interactions. In the regime considered, we observe the emergence of a critical temperature Tc separating two phases that can be characterized by the topology of the predominant configurations: in the large temperature regime, the dominant configurations of the molecule have very large genera (on the order of the size of the molecule), corresponding to a complex topology, whereas in the opposite regime of low temperatures the dominant configurations are simple and have the topology of a sphere. We determine that this topological phase transition is of first order and provide an analytical expression for Tc. The regime studied for this model exhibits analogies with the dense polymer systems studied by de Gennes.
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Affiliation(s)
- Matías G dell'Erba
- Instituto de Física de Mar del Plata, IFIMAR (CONICET-UNMdP), Funes 3350, 7600 Mar del Plata, Argentina
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15
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The application of quantum chemistry and condensed matter theory in studying amino-acids, protein folding and anticancer drug technology. Theor Chem Acc 2009. [DOI: 10.1007/s00214-009-0558-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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16
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17
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Vasilevskaya VV, Markov VA, ten Brinke G, Khokhlov AR. Self-Organization in Solutions of Stiff-Chain Amphiphilic Macromolecules. Macromolecules 2008. [DOI: 10.1021/ma800465j] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- V. V. Vasilevskaya
- A. N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, Vavilova Ul.28, Moscow 119991, Russia, Physics Department, M. V. Lomonosov Moscow State University, Leninskie Gory, Moscow 119992, Russia, and Department of Polymer Chemistry, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
| | - V. A. Markov
- A. N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, Vavilova Ul.28, Moscow 119991, Russia, Physics Department, M. V. Lomonosov Moscow State University, Leninskie Gory, Moscow 119992, Russia, and Department of Polymer Chemistry, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
| | - G. ten Brinke
- A. N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, Vavilova Ul.28, Moscow 119991, Russia, Physics Department, M. V. Lomonosov Moscow State University, Leninskie Gory, Moscow 119992, Russia, and Department of Polymer Chemistry, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
| | - A. R. Khokhlov
- A. N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, Vavilova Ul.28, Moscow 119991, Russia, Physics Department, M. V. Lomonosov Moscow State University, Leninskie Gory, Moscow 119992, Russia, and Department of Polymer Chemistry, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
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18
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Vanormelingen W, Van den Bergh K, Verbiest T, Koeckelberghs G. Conformational Transitions in Chiral, Gallic Acid-Functionalized Poly(dithienopyrrole): A Comparative UV−vis and CD Study. Macromolecules 2008. [DOI: 10.1021/ma8012114] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Wouter Vanormelingen
- Laboratory for Molecular Electronics and Photonics, Katholieke Universiteit Leuven, Celestijnenlaan 200F, B-3001 Heverlee, Belgium
| | - Karlien Van den Bergh
- Laboratory for Molecular Electronics and Photonics, Katholieke Universiteit Leuven, Celestijnenlaan 200F, B-3001 Heverlee, Belgium
| | - Thierry Verbiest
- Laboratory for Molecular Electronics and Photonics, Katholieke Universiteit Leuven, Celestijnenlaan 200F, B-3001 Heverlee, Belgium
| | - Guy Koeckelberghs
- Laboratory for Molecular Electronics and Photonics, Katholieke Universiteit Leuven, Celestijnenlaan 200F, B-3001 Heverlee, Belgium
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19
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Markov VA, Vasilevskaya VV, Khalatur PG, ten Brinke G, Khokhlov AR. Conformational properties of rigid-chain amphiphilic macromolecules: The phase diagram. POLYMER SCIENCE SERIES A 2008. [DOI: 10.1134/s0965545x08060059] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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20
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Markov VA, Vasilevskaya VV, Khalatur PG, ten Brinke G, Khokhlov AR. Diagram of State of Stiff Amphiphilic Macromolecules. ACTA ACUST UNITED AC 2007. [DOI: 10.1002/masy.200750603] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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21
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Methods for Examining Phase Equilibria. ACTA ACUST UNITED AC 2007. [DOI: 10.1007/978-3-540-38448-9_10] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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22
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KAWAKITA H, MASUBUCHI Y. Observation of Individual DNAs in Concentrated DNA/PEG Blend Solutions. KOBUNSHI RONBUNSHU 2007. [DOI: 10.1295/koron.64.740] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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23
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Sarraguça JMG, Dias RS, Pais AACC. Coil-globule coexistence and compaction of DNA chains. J Biol Phys 2006; 32:421-34. [PMID: 19669448 DOI: 10.1007/s10867-006-9026-8] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2006] [Accepted: 09/27/2006] [Indexed: 10/23/2022] Open
Abstract
In this work we discuss different factors governing coil-globule coexistence in the compaction process of DNA. We initially analyse the role played by fluctuations in the degree of binding of an external compacting agent in the conformational behavior of the chain backbone. The analysis relies both on Monte Carlo simulation results and simple statistical approaches. Compacting agents of various binding characteristics are taken into consideration and the degree of charge neutralization upon the chain is related to conformational indicators. Selected model systems comprising stiff chains in the presence of multivalent ions are employed to assess intrinsic single-chain conformational fluctuation, in the presence of external agents but not resulting from differences in binding. It is shown that trends found for a variety of compacting agents, including the extension of the coil-globule coexistence regions, can be rationalised on the basis of this analysis.
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Affiliation(s)
- J M G Sarraguça
- Departamento de Química, Universidade de Coimbra, 3004-535 Coimbra, Portugal
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24
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Stukan MR, An EA, Ivanov VA, Vinogradova OI. Stability of toroid and rodlike globular structures of a single stiff-chain macromolecule for different bending potentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:051804. [PMID: 16802960 DOI: 10.1103/physreve.73.051804] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2005] [Indexed: 05/10/2023]
Abstract
We study the effect of the bending potential on the stability of toroidal and rodlike globules which are typical collapsed conformations of a single stiff-chain macromolecule. We perform numerical calculations in the framework of the bead-stick model of a polymer chain. The intrinsic structure of globules is also analyzed. It was shown that the bending potential affects the packing geometry of bundles in a toroidal globule in the ground state. This potential also influences the bends at the ends of a rodlike globule: both the shape of the loops and the number of bonds in each loop have been investigated numerically as well as by Monte Carlo computer simulations performed for a separate loop. Our main results are (1) the shape of the bending potential could be possibly seen from the geometry of a globule; (2) toroidal globules are always more favorable than the rodlike ones.
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Affiliation(s)
- Mikhail R Stukan
- Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
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25
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Vasilevskaya VV, Markov VA, Khalatur PG, Khokhlov AR. Semiflexible amphiphilic polymers: Cylindrical-shaped, collagenlike, and toroidal structures. J Chem Phys 2006; 124:144914. [PMID: 16626252 DOI: 10.1063/1.2191049] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A coarse-grained model is used to study the conformational properties of semiflexible polymers with amphiphilic monomer units containing both hydrophilic and hydrophobic interaction sites. The hydrophobically driven conformational transitions are studied using molecular dynamics simulations for the chains of varying stiffness, as characterized by intrinsic Kuhn segment lengths that vary over a decade. It is shown that the energy of hydrophobic attraction required for the realization of the coil-to-globule transition increases with increasing chain stiffness. For rather stiff backbone, the coil-to-globule transition corresponds to a first order phase transition. We find that depending on the chain stiffness, a variety of thermodynamically stable anisometric chain morphologies are possible in a solvent selectively poor for hydrophobic sites of amphiphilic monomer units. For flexible chains, the amphiphilic polymer forms a cylindrical globule having blob structure with nearly spherical blobs. With increasing stiffness, the number of blobs composing the globule decreases and the shape of blobs transforms into elongated cylinder. Further increase in stiffness leads to compaction of macromolecules into a collagenlike structure when the chain folds itself several times and different strands wind round each other. In this state, the collagenlike structures coexist with toroidal globules, both conformations having approximately equal energies.
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26
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Single macromolecules: hierarchic thermodynamics, irreversibility and biological function. J Biol Phys 2005; 31:243-8. [PMID: 23345896 DOI: 10.1007/s10867-005-7285-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022] Open
Abstract
Single homo-polymers show two different paths in the folding transition; a liquid-like spherical globule is generated for flexible polymers, whereas a rich variety of ordered structures are formed for semi-flexible polymers. This unique characteristic is discussed in relation to its biological significance.
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Affiliation(s)
- Malek O. Khan
- Particulate Fluids Processing Centre, Department of Mathematics & Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia
| | - Derek Y. C. Chan
- Particulate Fluids Processing Centre, Department of Mathematics & Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia
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29
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Huang L, He X, Wang Y, Chen H, Liang H. Phase transitions of short chains at ultralow temperature. J Chem Phys 2003. [DOI: 10.1063/1.1582842] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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30
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Maurstad G, Danielsen S, Stokke BT. Analysis of Compacted Semiflexible Polyanions Visualized by Atomic Force Microscopy: Influence of Chain Stiffness on the Morphologies of Polyelectrolyte Complexes. J Phys Chem B 2003. [DOI: 10.1021/jp0271965] [Citation(s) in RCA: 62] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Gjertrud Maurstad
- Biophysics and Medical Technology, Department of Physics, The Norwegian University of Science and Technology, NTNU, NO-7491 Trondheim, Norway
| | - Signe Danielsen
- Biophysics and Medical Technology, Department of Physics, The Norwegian University of Science and Technology, NTNU, NO-7491 Trondheim, Norway
| | - Bjørn T. Stokke
- Biophysics and Medical Technology, Department of Physics, The Norwegian University of Science and Technology, NTNU, NO-7491 Trondheim, Norway
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31
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Calvo F, Doye JPK, Wales DJ. Collapse of Lennard-Jones homopolymers: Size effects and energy landscapes. J Chem Phys 2002. [DOI: 10.1063/1.1435572] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Abstract
In complex systems with many degrees of freedom such as peptides and proteins, there exists a huge number of local-minimum-energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. From only one simulation run, one can obtain canonical-ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review uses of the generalized-ensemble algorithms in biomolecular systems. Three well-known methods, namely, multicanonical algorithm, simulated tempering, and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present three new generalized-ensemble algorithms that combine the merits of the above methods. The effectiveness of the methods for molecular simulations in the protein folding problem is tested with short peptide systems.
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Affiliation(s)
- A Mitsutake
- Department of Theoretical Studies, Institute for Molecular Science, Okazaki, Aichi, Japan
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Fujiwara S, Sato T. Structure formation of a single polymer chain. I. Growth of trans domains. J Chem Phys 2001. [DOI: 10.1063/1.1356440] [Citation(s) in RCA: 54] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Sugita Y, Kitao A, Okamoto Y. Multidimensional replica-exchange method for free-energy calculations. J Chem Phys 2000. [DOI: 10.1063/1.1308516] [Citation(s) in RCA: 680] [Impact Index Per Article: 28.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Iwataki T, Yoshikawa K, Kidoaki S, Umeno D, Kiji M, Maeda M. Cooperativity vs. Phase Transition in a Giant Single DNA Molecule. J Am Chem Soc 2000. [DOI: 10.1021/ja000230d] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Toshio Iwataki
- Contribution from the Division of Informatics for Natural Sciences, Graduate School of Human Informatics, Nagoya University, Nagoya 464-8601, Japan, Department of Physics, Graduate School of Science, Kyoto University & CREST (Core Research for Evolutional Science and Technology) of Japan Sciences and Technology Corporation, Kyoto 606-8502, Japan, and Department of Materials Physics and Chemistry, Graduate School of Engineering, Kyushu University, 6-10-1, Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan
| | - Kenichi Yoshikawa
- Contribution from the Division of Informatics for Natural Sciences, Graduate School of Human Informatics, Nagoya University, Nagoya 464-8601, Japan, Department of Physics, Graduate School of Science, Kyoto University & CREST (Core Research for Evolutional Science and Technology) of Japan Sciences and Technology Corporation, Kyoto 606-8502, Japan, and Department of Materials Physics and Chemistry, Graduate School of Engineering, Kyushu University, 6-10-1, Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan
| | - Satoru Kidoaki
- Contribution from the Division of Informatics for Natural Sciences, Graduate School of Human Informatics, Nagoya University, Nagoya 464-8601, Japan, Department of Physics, Graduate School of Science, Kyoto University & CREST (Core Research for Evolutional Science and Technology) of Japan Sciences and Technology Corporation, Kyoto 606-8502, Japan, and Department of Materials Physics and Chemistry, Graduate School of Engineering, Kyushu University, 6-10-1, Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan
| | - Daisuke Umeno
- Contribution from the Division of Informatics for Natural Sciences, Graduate School of Human Informatics, Nagoya University, Nagoya 464-8601, Japan, Department of Physics, Graduate School of Science, Kyoto University & CREST (Core Research for Evolutional Science and Technology) of Japan Sciences and Technology Corporation, Kyoto 606-8502, Japan, and Department of Materials Physics and Chemistry, Graduate School of Engineering, Kyushu University, 6-10-1, Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan
| | - Masami Kiji
- Contribution from the Division of Informatics for Natural Sciences, Graduate School of Human Informatics, Nagoya University, Nagoya 464-8601, Japan, Department of Physics, Graduate School of Science, Kyoto University & CREST (Core Research for Evolutional Science and Technology) of Japan Sciences and Technology Corporation, Kyoto 606-8502, Japan, and Department of Materials Physics and Chemistry, Graduate School of Engineering, Kyushu University, 6-10-1, Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan
| | - Mizuo Maeda
- Contribution from the Division of Informatics for Natural Sciences, Graduate School of Human Informatics, Nagoya University, Nagoya 464-8601, Japan, Department of Physics, Graduate School of Science, Kyoto University & CREST (Core Research for Evolutional Science and Technology) of Japan Sciences and Technology Corporation, Kyoto 606-8502, Japan, and Department of Materials Physics and Chemistry, Graduate School of Engineering, Kyushu University, 6-10-1, Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan
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Noguchi H, Yoshikawa K. Folding path in a semiflexible homopolymer chain: A Brownian dynamics simulation. J Chem Phys 2000. [DOI: 10.1063/1.481861] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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39
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Mitsutake A, Okamoto Y. Helix-coil transitions of amino-acid homo-oligomers in aqueous solution studied by multicanonical simulations. J Chem Phys 2000. [DOI: 10.1063/1.481697] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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40
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Piçarra S, Gomes PT, Martinho JMG. Fluorescence Study of the Coil−Globule Transition of a Poly(ε-caprolactone) Chain Labeled with Pyrenes at Both Ends. Macromolecules 2000. [DOI: 10.1021/ma992106o] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Susana Piçarra
- Centro de Química-Física Molecular, Instituto Superior Técnico, 1049-001 Lisboa, Portugal, and Centro de Química Estrutural, Instituto Superior Técnico, 1049-001 Lisboa, Portugal
| | - Pedro T. Gomes
- Centro de Química-Física Molecular, Instituto Superior Técnico, 1049-001 Lisboa, Portugal, and Centro de Química Estrutural, Instituto Superior Técnico, 1049-001 Lisboa, Portugal
| | - J. M. G. Martinho
- Centro de Química-Física Molecular, Instituto Superior Técnico, 1049-001 Lisboa, Portugal, and Centro de Química Estrutural, Instituto Superior Técnico, 1049-001 Lisboa, Portugal
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41
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Khan MO, Mel'nikov SM, Jönsson B. Anomalous Salt Effects on DNA Conformation: Experiment and Theory. Macromolecules 1999. [DOI: 10.1021/ma9905627] [Citation(s) in RCA: 58] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Malek O. Khan
- Theoretical Chemistry and Physical Chemistry 1, Lund University, P. O. Box 124, S-22100 Lund, Sweden
| | - Sergey M. Mel'nikov
- Theoretical Chemistry and Physical Chemistry 1, Lund University, P. O. Box 124, S-22100 Lund, Sweden
| | - Bo Jönsson
- Theoretical Chemistry and Physical Chemistry 1, Lund University, P. O. Box 124, S-22100 Lund, Sweden
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Prince RB, Saven JG, Wolynes PG, Moore JS. Cooperative Conformational Transitions in Phenylene Ethynylene Oligomers: Chain-Length Dependence. J Am Chem Soc 1999. [DOI: 10.1021/ja983995i] [Citation(s) in RCA: 313] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Ryan B. Prince
- Contribution from the School of Chemical Sciences and the Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana, Illinois 61801, and Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104
| | - Jeffery G. Saven
- Contribution from the School of Chemical Sciences and the Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana, Illinois 61801, and Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104
| | - Peter G. Wolynes
- Contribution from the School of Chemical Sciences and the Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana, Illinois 61801, and Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104
| | - Jeffrey S. Moore
- Contribution from the School of Chemical Sciences and the Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana, Illinois 61801, and Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104
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Mel'nikov SM, Khan MO, Lindman B, Jönsson B. Phase Behavior of Single DNA in Mixed Solvents. J Am Chem Soc 1999. [DOI: 10.1021/ja981491e] [Citation(s) in RCA: 110] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Sergey M. Mel'nikov
- Contribution from the Department of Physical Chemistry 1 and Department of Physical Chemistry 2, Center for Chemistry and Chemical Engineering, Lund University, Box 124, S-221 00 Lund, Sweden
| | - Malek O. Khan
- Contribution from the Department of Physical Chemistry 1 and Department of Physical Chemistry 2, Center for Chemistry and Chemical Engineering, Lund University, Box 124, S-221 00 Lund, Sweden
| | - Björn Lindman
- Contribution from the Department of Physical Chemistry 1 and Department of Physical Chemistry 2, Center for Chemistry and Chemical Engineering, Lund University, Box 124, S-221 00 Lund, Sweden
| | - Bo Jönsson
- Contribution from the Department of Physical Chemistry 1 and Department of Physical Chemistry 2, Center for Chemistry and Chemical Engineering, Lund University, Box 124, S-221 00 Lund, Sweden
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Noguchi H, Yoshikawa K. Morphological variation in a collapsed single homopolymer chain. J Chem Phys 1998. [DOI: 10.1063/1.477121] [Citation(s) in RCA: 182] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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