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Farris ACK, Seaton DT, Landau DP. Effects of lattice constraints in coarse-grained protein models. J Chem Phys 2021; 154:084903. [PMID: 33639740 DOI: 10.1063/5.0038184] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We compare and contrast folding behavior in several coarse-grained protein models, both on- and off-lattice, in an attempt to uncover the effect of lattice constraints in these kinds of models. Using modern, extended ensemble Monte Carlo methods-Wang-Landau sampling, multicanonical sampling, replica-exchange Wang-Landau sampling, and replica-exchange multicanonical sampling, we investigate the thermodynamic and structural behavior of the protein Crambin within the context of the hydrophobic-polar, hydrophobic-"neutral"-polar (H0P), and semi-flexible H0P model frameworks. We uncover the folding process in all cases; all models undergo, at least, the two major structural transitions observed in nature-the coil-globule collapse and the folding transition. As the complexity of the model increases, these two major transitions begin to split into multi-step processes, wherein the lattice coarse-graining has a significant impact on the details of these processes. The results show that the level of structural coarse-graining is coupled to the level of interaction coarse-graining.
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Affiliation(s)
- Alfred C K Farris
- Department of Physics and Astronomy, Oxford College of Emory University, Oxford, Georgia 30054, USA
| | - Daniel T Seaton
- Open Learning, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - David P Landau
- Center for Simulational Physics, Department of Physics and Astronomy, The University of Georgia, Athens, Georgia 30602, USA
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Farris ACK, Shi G, Wüst T, Landau DP. The role of chain-stiffness in lattice protein models: A replica-exchange Wang-Landau study. J Chem Phys 2018; 149:125101. [PMID: 30278675 DOI: 10.1063/1.5045482] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using Monte Carlo simulations, we investigate simple, physically motivated extensions to the hydrophobic-polar lattice protein model for the small (46 amino acid) protein Crambin. We use two-dimensional replica-exchange Wang-Landau sampling to study the effects of a bond angle stiffness parameter on the folding and uncover a new step in the collapse process for particular values of this stiffness parameter. A physical interpretation of the folding is developed by analysis of changes in structural quantities, and the free energy landscape is explored. For these special values of stiffness, we find non-degenerate ground states, a property that is consistent with behavior of real proteins, and we use these unique ground states to elucidate the formation of native contacts during the folding process. Through this analysis, we conclude that chain-stiffness is particularly influential in the low energy, low temperature regime of the folding process once the lattice protein has partially collapsed.
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Affiliation(s)
- Alfred C K Farris
- Center for Simulational Physics, Department of Physics and Astronomy, The University of Georgia, Athens, Georgia 30602, USA
| | - Guangjie Shi
- Center for Simulational Physics, Department of Physics and Astronomy, The University of Georgia, Athens, Georgia 30602, USA
| | - Thomas Wüst
- Scientific IT Services, ETH Zürich, 8092 Zürich, Switzerland
| | - David P Landau
- Center for Simulational Physics, Department of Physics and Astronomy, The University of Georgia, Athens, Georgia 30602, USA
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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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Martins PHL, Bachmann M. Interlocking order parameter fluctuations in structural transitions between adsorbed polymer phases. Phys Chem Chem Phys 2016; 18:2143-51. [PMID: 26690091 DOI: 10.1039/c5cp05038c] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
By means of contact-density chain-growth simulations of a simple coarse-grained lattice model for a polymer grafted at a solid homogeneous substrate, we investigate the complementary behavior of the numbers of surface-monomer and monomer-monomer contacts under various solvent and thermal conditions. This pair of contact numbers represents an appropriate set of order parameters that enables the distinct discrimination of significantly different compact phases of polymer adsorption. Depending on the transition scenario, these order parameters can interlock in perfect cooperation. The analysis helps understand the transitions from compact filmlike adsorbed polymer conformations into layered morphologies and dissolved adsorbed structures, respectively, in more detail.
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Affiliation(s)
- Paulo H L Martins
- Instituto de Física, Universidade Federal de Mato Grosso, 78060-900 Cuiabá, MT, Brazil.
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Shi G, Vogel T, Wüst T, Li YW, Landau DP. Effect of single-site mutations on hydrophobic-polar lattice proteins. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:033307. [PMID: 25314564 DOI: 10.1103/physreve.90.033307] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2014] [Indexed: 06/04/2023]
Abstract
We developed a heuristic method for determining the ground-state degeneracy of hydrophobic-polar (HP) lattice proteins, based on Wang-Landau and multicanonical sampling. It is applied during comprehensive studies of single-site mutations in specific HP proteins with different sequences. The effects in which we are interested include structural changes in ground states, changes of ground-state energy, degeneracy, and thermodynamic properties of the system. With respect to mutations, both extremely sensitive and insensitive positions in the HP sequence have been found. That is, ground-state energies and degeneracies, as well as other thermodynamic and structural quantities, may be either largely unaffected or may change significantly due to mutation.
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Affiliation(s)
- Guangjie Shi
- Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
| | - Thomas Vogel
- Theoretical Division (T-1), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Thomas Wüst
- Scientific IT Services, ETH Zürich IT Services, 8092 Zürich, Switzerland
| | - Ying Wai Li
- National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - David P Landau
- Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA
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Narasimhan SL, Rajarajan AK, Vardharaj L. HP-sequence design for lattice proteins—An exact enumeration study on diamond as well as square lattice. J Chem Phys 2012; 137:115102. [DOI: 10.1063/1.4752479] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
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Lewandowski K, Banaszak M. Intraglobular structures in multiblock copolymer chains from a Monte Carlo simulation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:011806. [PMID: 21867204 DOI: 10.1103/physreve.84.011806] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2011] [Revised: 06/15/2011] [Indexed: 05/31/2023]
Abstract
Multiblock copolymer chains in implicit nonselective solvents are studied by using a Monte Carlo method, which employs a parallel tempering algorithm. Chains consisting of 120 A and 120 B monomers, arranged in three distinct microarchitectures: (10-10)12, (6-6)20, and (3-3)40, collapse to globular states upon cooling, as expected. By varying both the reduced temperature T* and the compatibility between monomers ω, numerous intraglobular structures are obtained: diclusters (handshake, spiral, torus with a core, etc.), triclusters, and n clusters with n>3 (lamellar and other), which are reminiscent of the block copolymer nanophases for spherically confined geometries. Phase diagrams for various chains in the (T*,ω) space are mapped. The structure factor S(k), for a selected microarchitecture and ω, is calculated. Since S(k) can be measured in scattering experiments, it can be used to relate simulation results to an experiment. Self-assembly in those systems is interpreted in terms of competition between minimization of the interfacial area separating different types of monomers and minimization of contacts between chain and solvent. Finally, the relevance of this model to the protein folding is addressed.
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Affiliation(s)
- K Lewandowski
- Faculty of Physics, A. Mickiewicz University ul. Umultowska 85, PL-61-614 Poznan, Poland
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Stochastic protein folding simulation in the three-dimensional HP-model. Comput Biol Chem 2008; 32:248-55. [PMID: 18485827 DOI: 10.1016/j.compbiolchem.2008.03.004] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2007] [Accepted: 03/17/2008] [Indexed: 11/23/2022]
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Patel BA, Debenedetti PG, Stillinger FH, Rossky PJ. The effect of sequence on the conformational stability of a model heteropolymer in explicit water. J Chem Phys 2008; 128:175102. [PMID: 18465941 DOI: 10.1063/1.2909974] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the properties of a two-dimensional lattice heteropolymer model for a protein in which water is explicitly represented. The model protein distinguishes between hydrophobic and polar monomers through the effect of the hydrophobic monomers on the entropy and enthalpy of the hydrogen bonding of solvation shell water molecules. As experimentally observed, model heteropolymer sequences fold into stable native states characterized by a hydrophobic core to avoid unfavorable interactions with the solvent. These native states undergo cold, pressure, and thermal denaturation into distinct configurations for each type of unfolding transition. However, the heteropolymer sequence is an important element, since not all sequences will fold into stable native states at positive pressures. Simulation of a large collection of sequences indicates that these fall into two general groups, those exhibiting highly stable native structures and those that do not. Statistical analysis of important patterns in sequences shows a strong tendency for observing long blocks of hydrophobic or polar monomers in the most stable sequences. Statistical analysis also shows that alternation of hydrophobic and polar monomers appears infrequently among the most stable sequences. These observations are not absolute design rules and, in practice, these are not sufficient to rationally design very stable heteropolymers. We also study the effect of mutations on improving the stability of the model proteins, and demonstrate that it is possible to obtain a very stable heteropolymer from directed evolution of an initially unstable heteropolymer.
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Affiliation(s)
- Bryan A Patel
- Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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Vogel T, Bachmann M, Janke W. Freezing and collapse of flexible polymers on regular lattices in three dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:061803. [PMID: 18233861 DOI: 10.1103/physreve.76.061803] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2007] [Indexed: 05/25/2023]
Abstract
We analyze the crystallization and collapse transition of a simple model for flexible polymer chains on simple-cubic and face-centered-cubic lattices by means of sophisticated chain-growth methods. In contrast to the bond-fluctuation polymer model in certain parameter ranges, where these two conformational transitions were found to merge in the thermodynamic limit, we conclude from our results that the two transitions remain well separated in the limit of infinite chain lengths. The reason for this qualitatively distinct behavior is presumably due to the ultrashort attractive interaction range in the lattice models considered here.
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Affiliation(s)
- Thomas Vogel
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany.
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Ji YY, Li YQ, Mao JW, Tang XW. Model study of prionlike folding behavior in aggregated proteins. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:041912. [PMID: 16383425 DOI: 10.1103/physreve.72.041912] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2005] [Indexed: 05/05/2023]
Abstract
We investigate the folding behavior of protein sequences by numerically studying all sequences with a maximally compact lattice model through exhaustive enumeration. We get the prionlike behavior of protein folding. Individual proteins remaining stable in the isolated native state may change their conformations when they aggregate. We observe the folding properties as the interfacial interaction strength changes and find that the strength must be strong enough before the propagation of the most stable structures happens.
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Affiliation(s)
- Yong-Yun Ji
- Department of Physics, Zhejiang University, Hangzhou 310027, People's Republic of China
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