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Mukuta N, Miura S. Potential energy landscape and thermodynamic transitions of coarse-grained protein models revealed by the multicanonical generalized hybrid Monte Carlo method. Biophys Physicobiol 2020; 17:14-24. [PMID: 32509490 PMCID: PMC7246090 DOI: 10.2142/biophysico.bsj-2019051] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2019] [Accepted: 01/23/2020] [Indexed: 12/01/2022] Open
Abstract
In the present study, thermodynamic properties of coarse-grained protein models have been studied by an extended ensemble method. Two types of protein model were analyzed; one is categorized into a fast folder and the other into a slow folder. Both models exhibit the following thermodynamic transitions: the collapse transition between random coil states and spatially compact, but non-native states and the folding transition between the collapsed states and the folded native states. Caloric curve for the fast folder shows strong statistical ensemble dependence, while almost no ensemble dependence is found for the slow folder. Microcanonical caloric curve for the fast folder exhibits S-shaped temperature dependence on the internal energy around the collapse transition which is reminiscent of the van der Waals loop observed for the first order transition; at the transition temperature, the collapsed and random coil states coexist dynamically. The corresponding microcanonical heat capacity is found to have negative region around the transition. This kind of exotic behaviors could be utilized to distinguish fast folding proteins.
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Affiliation(s)
- Natsuki Mukuta
- Division of Mathematical and Physical Sciences, Graduate School of Natural Science and Technology, Kanazawa University, Kakuma, Kanazawa, Ishikawa 920-1192, Japan
| | - Shinichi Miura
- Faculty of Mathematics and Physics, Kanazawa University, Kakuma, Kanazawa, Ishikawa 920-1192, Japan
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2
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Nonnative Energetic Frustrations in Protein Folding at Residual Level: A Simulation Study of Homologous Immunoglobulin-like β-Sandwich Proteins. Int J Mol Sci 2018; 19:ijms19051515. [PMID: 29783701 PMCID: PMC5983731 DOI: 10.3390/ijms19051515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2018] [Revised: 05/08/2018] [Accepted: 05/09/2018] [Indexed: 11/16/2022] Open
Abstract
Nonnative interactions cause energetic frustrations in protein folding and were found to dominate key events in folding intermediates. However, systematically characterizing energetic frustrations that are caused by nonnative intra-residue interactions at residual resolution is still lacking. Recently, we studied the folding of a set of homologous all-α proteins and found that nonnative-contact-based energetic frustrations are highly correlated to topology of the protein native-contact network. Here, we studied the folding of nine homologous immunoglobulin-like (Ig-like) β-sandwich proteins, and examined nonnative-contact-based energetic frustrations Gō-like model. Our calculations showed that nonnative-interaction-based energetic frustrations in β-sandwich proteins are much more complicated than those in all-α proteins, and they exhibit highly heterogeneous effects on the folding of secondary structures. Further, the nonnative interactions introduced distinct correlations in the folding of different folding-patches of β-sandwich proteins. Taken together, a strong interplay might exist between nonnative-interaction energetic frustrations and the protein native-contact networks, which ensures that β-sandwich domains adopt a common folding mechanism.
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Combined effect of confinement and affinity of crowded environment on conformation switching of adenylate kinase. J Mol Model 2014; 20:2530. [DOI: 10.1007/s00894-014-2530-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2014] [Accepted: 11/12/2014] [Indexed: 01/25/2023]
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Smeeton LC, Oakley MT, Johnston RL. Visualizing energy landscapes with metric disconnectivity graphs. J Comput Chem 2014; 35:1481-90. [PMID: 24866379 PMCID: PMC4285870 DOI: 10.1002/jcc.23643] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2013] [Revised: 03/12/2014] [Accepted: 04/14/2014] [Indexed: 11/24/2022]
Abstract
The visualization of multidimensional energy landscapes is important, providing insight into the kinetics and thermodynamics of a system, as well the range of structures a system can adopt. It is, however, highly nontrivial, with the number of dimensions required for a faithful reproduction of the landscape far higher than can be represented in two or three dimensions. Metric disconnectivity graphs provide a possible solution, incorporating the landscape connectivity information present in disconnectivity graphs with structural information in the form of a metric. In this study, we present a new software package, PyConnect, which is capable of producing both disconnectivity graphs and metric disconnectivity graphs in two or three dimensions. We present as a test case the analysis of the 69-bead BLN coarse-grained model protein and show that, by choosing appropriate order parameters, metric disconnectivity graphs can resolve correlations between structural features on the energy landscape with the landscapes energetic and kinetic properties.
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Affiliation(s)
- Lewis C Smeeton
- School of Chemistry, University of Birmingham, Edgbaston, Birmingham, B15 2TT, United Kingdom
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Hills RD. Balancing bond, nonbond, and gō-like terms in coarse grain simulations of conformational dynamics. Methods Mol Biol 2014; 1084:123-140. [PMID: 24061919 DOI: 10.1007/978-1-62703-658-0_7] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Characterization of the protein conformational landscape remains a challenging problem, whether it concerns elucidating folding mechanisms, predicting native structures or modeling functional transitions. Coarse-grained molecular dynamics simulation methods enable exhaustive sampling of the energetic landscape at resolutions of biological interest. The general utility of structure-based models is reviewed along with their differing levels of approximation. Simple Gō models incorporate attractive native interactions and repulsive nonnative contacts, resulting in an ideal smooth landscape. Non-Gō coarse-grained models reduce the parameter set as needed but do not include bias to any desired native structure. While non-Gō models have achieved limited success in protein coarse-graining, they can be combined with native structured-based potentials to create a balanced and powerful force field. Recent applications of such Gō-like models have yielded insight into complex folding mechanisms and conformational transitions in large macromolecules. The accuracy and usefulness of reduced representations are also revealed to be a function of the mathematical treatment of the intrinsic bonded topology.
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Affiliation(s)
- Ronald D Hills
- Department of Pharmaceutical Sciences, University of New England, Portland, ME, USA
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Kim J, Straub JE, Keyes T. Replica exchange statistical temperature molecular dynamics algorithm. J Phys Chem B 2012; 116:8646-53. [PMID: 22540354 PMCID: PMC11240102 DOI: 10.1021/jp300366j] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
The replica exchange statistical temperature molecular dynamics (RESTMD) algorithm is presented, designed to alleviate an extensive increase of the number of replicas required as system size increases in the conventional temperature replica exchange method (tREM), and to obtain improved sampling in individual replicas. RESTMD optimally integrates multiple STMD (Phys. Rev. Lett. 2006, 97, 050601) runs with replica exchanges, giving rise to a flat energy sampling in each replica with a self-adjusting weight determination. The expanded flat energy dynamic sampling range allows the use of significantly fewer STMD replicas while maintaining the desired acceptance probability for replica exchanges. The computational advantages of RESTMD over conventional REM and single-replica STMD are explicitly demonstrated with an application to a coarse-grained protein model. The effect of two different kinetic temperature control schemes on the sampling efficiency is explored for diverse simulation conditions.
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Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, United States.
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Chen Y, Ding J. Roles of non-native hydrogen-bonding interaction in helix-coil transition of a single polypeptide as revealed by comparison between Gō-like and non-Gō models. Proteins 2010; 78:2090-100. [PMID: 20455265 DOI: 10.1002/prot.22724] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
To explore the role of non-native interactions in the helix-coil transition, a detailed comparison between a Gō-like model and a non-Gō model has been performed via lattice Monte Carlo simulations. Only native hydrogen bonding interactions occur in the Gō-like model, and the non-native ones with sequence interval more than 4 is also included into the non-Gō model. Some significant differences between the results from those two models have been found. The non-native hydrogen bonds were found most populated at temperature around the helix-coil transition. The rearrangement of non-native hydrogen bonds into native ones in the formation of alpha-helix leads to the increase of susceptibility of chain conformation, and even two peaks of susceptibility of radius of gyration versus temperature exist in the case of non-Gō model for a non-short peptide, while just a single peak exists in the case of Gō model for a single polypeptide chain with various chain lengths. The non-native hydrogen bonds have complicated the temperature-dependence of Zimm-Bragg nucleation constant. The increase of relative probability of non-native hydrogen bonding for long polypeptide chains leads to non-monotonous chain length effect on the transition temperature.
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Affiliation(s)
- Yantao Chen
- Key Laboratory of Molecular Engineering of Polymers of Ministry of Education, Department of Macromolecular Science, Laboratory of Advanced Materials, Fudan University, Shanghai 200433, China
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Lintuvuori JS, Wilson MR. Statistical temperature molecular dynamics simulations applied to phase transitions in liquid crystalline systems. J Chem Phys 2010; 132:224902. [DOI: 10.1063/1.3429620] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
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Sangha AK, Keyes T. Proteins Fold by Subdiffusion of the Order Parameter. J Phys Chem B 2009; 113:15886-94. [DOI: 10.1021/jp907009r] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | - T. Keyes
- Department of Chemistry, Boston University, Boston, Massachusetts 02215
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Kim J, Keyes T, Straub JE. Replica exchange statistical temperature Monte Carlo. J Chem Phys 2009; 130:124112. [PMID: 19334813 DOI: 10.1063/1.3095422] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
The replica exchange statistical temperature Monte Carlo algorithm (RESTMC) is presented, extending the single-replica STMC algorithm [J. Kim, J. E. Straub, and T. Keyes, Phys. Rev. Lett. 97, 050601 (2006)] to alleviate the slow convergence of the conventional temperature replica exchange method (t-REM) with increasing system size. In contrast to the Gibbs-Boltzmann sampling at a specific temperature characteristic of the standard t-REM, RESTMC samples a range of temperatures in each replica and achieves a flat energy sampling employing the generalized sampling weight, which is automatically determined via the dynamic modification of the replica-dependent statistical temperature. Faster weight determination, through the dynamic update of the statistical temperature, and the flat energy sampling, maximizing energy overlaps between neighboring replicas, lead to a considerable acceleration in the convergence of simulations even while employing significantly fewer replicas. The performance of RESTMC is demonstrated and quantitatively compared with that of the conventional t-REM under varying simulation conditions for Lennard-Jones 19, 31, and 55 atomic clusters, exhibiting single- and double-funneled energy landscapes.
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Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
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Kim J, Straub JE. Optimal replica exchange method combined with Tsallis weight sampling. J Chem Phys 2009; 130:144114. [PMID: 19368436 PMCID: PMC2736612 DOI: 10.1063/1.3108523] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2009] [Accepted: 03/08/2009] [Indexed: 02/03/2023] Open
Abstract
A unified framework integrating the generalized ensemble sampling associated with the Tsallis weight [C. Tsallis, J. Stat. Phys. 52, 479 (1988)] and the replica exchange method (REM) has been proposed to accelerate the convergence of the conventional temperature REM (t-REM). Using the effective temperature formulation of the Tsallis weight sampling, it is shown that the average acceptance probability for configurational swaps between neighboring replicas in the combination of Tsallis weight sampling and REM (Tsallis-REM) is directly proportional to an overlap integral of the energy distributions of neighboring replicas as in the t-REM. Based on this observation, we suggest a robust method to select optimal Tsallis parameters in the conventional parametrization scheme and present new parametrization schemes for the Tsallis-REM, which significantly improves the acceptance of configurational swaps by systematically modulating energy overlaps between neighboring replicas. The distinguished feature of our method is that all relevant parameters in the Tsallis-REM are automatically determined from the equilibrium phase simulation using the t-REM. The overall performance of our method is explicitly demonstrated for various simulation conditions for the Lennard-Jones 31 atom clusters, exhibiting a double-funneled energy landscape.
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Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
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12
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Kim J, Keyes T, Straub JE. Relationship between protein folding thermodynamics and the energy landscape. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:030902. [PMID: 19391891 PMCID: PMC11234522 DOI: 10.1103/physreve.79.030902] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2008] [Indexed: 05/27/2023]
Abstract
The origin of protein folding thermodynamics is examined in terms of the energy landscape, employing an off-lattice protein model with scaled non-native attractions, which is continuously tunable between a Go-like model and a highly frustrated system. Extensive statistical temperature molecular dynamics simulations, combined with inherent structure analysis, reveal the intimate connection between the global geometric properties of the energy landscape and the statistical temperature. The basin depth of the energy landscape is shown to play a key role in the first-order-like characteristics of the statistical temperature, which are easily identified by the squared modulus of the potential energy gradient in the microcanonical ensemble.
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Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA
| | - Thomas Keyes
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA
| | - John E. Straub
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA
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