1
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Maruyama Y, Mitsutake A. Effect of Main and Side Chains on the Folding Mechanism of the Trp-Cage Miniprotein. ACS OMEGA 2023; 8:43827-43835. [PMID: 38027385 PMCID: PMC10666239 DOI: 10.1021/acsomega.3c05809] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/07/2023] [Revised: 09/19/2023] [Accepted: 10/27/2023] [Indexed: 12/01/2023]
Abstract
Proteins that do not fold into their functional native state have been linked to diseases. In this study, the influence of the main and side chains of individual amino acids on the folding of the tryptophan cage (Trp-cage), a designed 20-residue miniprotein, was analyzed. For this purpose, we calculated the solvation free energy (SFE) contributions of individual atoms by using the 3D-reference interaction site model with the atomic decomposition method. The mechanism by which the Trp-cage is stabilized during the folding process was examined by calculating the total energy, which is the sum of the conformational energy and SFE. The folding process of the Trp-cage resulted in a stable native state, with a total energy that was 62.4 kcal/mol lower than that of the unfolded state. The solvation entropy, which is considered to be responsible for the hydrophobic effect, contributed 31.3 kcal/mol to structural stabilization. In other words, the contribution of the solvation entropy accounted for approximately half of the total contribution to Trp-cage folding. The hydrophobic core centered on Trp6 contributed 15.6 kcal/mol to the total energy, whereas the solvation entropy contribution was 6.3 kcal/mol. The salt bridge formed by the hydrophilic side chains of Asp9 and Arg16 contributed 10.9 and 5.0 kcal/mol, respectively. This indicates that not only the hydrophobic core but also the salt bridge of the hydrophilic side chains gain solvation entropy and contribute to stabilizing the native structure of the Trp-cage.
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Affiliation(s)
- Yutaka Maruyama
- Data
Science Center for Creative Design and Manufacturing, The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan
- Department
of Physics, School of Science and Technology, Meiji University, 1-1-1
Higashi-Mita, Tama-ku, Kawasaki-shi, Kanagawa 214-8571, Japan
| | - Ayori Mitsutake
- Department
of Physics, School of Science and Technology, Meiji University, 1-1-1
Higashi-Mita, Tama-ku, Kawasaki-shi, Kanagawa 214-8571, Japan
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2
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Sun Q, He X, Fu Y. The "Beacon" Structural Model of Protein Folding: Application for Trp-Cage in Water. Molecules 2023; 28:5164. [PMID: 37446826 DOI: 10.3390/molecules28135164] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2023] [Revised: 06/30/2023] [Accepted: 06/30/2023] [Indexed: 07/15/2023] Open
Abstract
Protein folding is a process in which a polypeptide must undergo folding process to obtain its three-dimensional structure. Thermodynamically, it is a process of enthalpy to overcome the loss of conformational entropy in folding. Folding is primarily related to hydrophobic interactions and intramolecular hydrogen bondings. During folding, hydrophobic interactions are regarded to be the driving forces, especially in the initial structural collapse of a protein. Additionally, folding is guided by the strong interactions within proteins, such as intramolecular hydrogen bondings related to the α-helices and β-sheets of proteins. Therefore, a protein is divided into the folding key (FK) regions related to intramolecular hydrogen bondings and the non-folding key (non-FK) regions. Various conformations are expected for FK and non-FK regions. Different from non-FK regions, it is necessary for FK regions to form the specific conformations in folding, which are regarded as the necessary folding pathways (or "beacons"). Additionally, sequential folding is expected for the FK regions, and the intermediate state is found during folding. They are reflected on the local basins in the free energy landscape (FEL) of folding. To demonstrate the structural model, molecular dynamics (MD) simulations are conducted on the folding pathway of the TRP-cage in water.
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Affiliation(s)
- Qiang Sun
- Key Laboratory of Orogenic Belts and Crustal Evolution, Ministry of Education, The School of Earth and Space Sciences, Peking University, Beijing 100871, China
| | - Xian He
- Key Laboratory of Orogenic Belts and Crustal Evolution, Ministry of Education, The School of Earth and Space Sciences, Peking University, Beijing 100871, China
| | - Yanfang Fu
- Key Laboratory of Orogenic Belts and Crustal Evolution, Ministry of Education, The School of Earth and Space Sciences, Peking University, Beijing 100871, China
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3
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Torrillo PA, Bogetti AT, Chong LT. A Minimal, Adaptive Binning Scheme for Weighted Ensemble Simulations. J Phys Chem A 2021; 125:1642-1649. [PMID: 33577732 PMCID: PMC8091492 DOI: 10.1021/acs.jpca.0c10724] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
A promising approach for simulating rare events with rigorous kinetics is the weighted ensemble path sampling strategy. One challenge of this strategy is the division of configurational space into bins for sampling. Here we present a minimal adaptive binning (MAB) scheme for the automated, adaptive placement of bins along a progress coordinate within the framework of the weighted ensemble strategy. Results reveal that the MAB binning scheme, despite its simplicity, is more efficient than a manual, fixed binning scheme in generating transitions over large free energy barriers, generating a diversity of pathways, estimating rate constants, and sampling conformations. The scheme is general and extensible to any rare-events sampling strategy that employs progress coordinates.
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Affiliation(s)
- Paul A Torrillo
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Anthony T Bogetti
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Lillian T Chong
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
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4
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Sharpe DJ, Wales DJ. Efficient and exact sampling of transition path ensembles on Markovian networks. J Chem Phys 2020; 153:024121. [DOI: 10.1063/5.0012128] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Affiliation(s)
- Daniel J. Sharpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - David J. Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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5
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Swenson DWH, Prinz JH, Noe F, Chodera JD, Bolhuis PG. OpenPathSampling: A Python Framework for Path Sampling Simulations. 1. Basics. J Chem Theory Comput 2018; 15:813-836. [PMID: 30336030 PMCID: PMC6374749 DOI: 10.1021/acs.jctc.8b00626] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
![]()
Transition
path sampling techniques allow molecular dynamics simulations of complex
systems to focus on rare dynamical events, providing
insight into mechanisms and the ability to calculate rates inaccessible
by ordinary dynamics simulations. While path sampling algorithms are
conceptually as simple as importance sampling Monte Carlo, the technical
complexity of their implementation has kept these techniques out of
reach of the broad community. Here, we introduce an easy-to-use Python
framework called OpenPathSampling (OPS) that facilitates path sampling
for (bio)molecular systems with minimal effort and yet is still extensible.
Interfaces to OpenMM and an internal dynamics engine for simple models
are provided in the initial release, but new molecular simulation
packages can easily be added. Multiple ready-to-use transition path
sampling methodologies are implemented, including standard transition
path sampling (TPS) between reactant and product states and transition
interface sampling (TIS) and its replica exchange variant (RETIS),
as well as recent multistate and multiset extensions of transition
interface sampling (MSTIS, MISTIS). In addition, tools are provided
to facilitate the implementation of new path sampling schemes built
on basic path sampling components. In this paper, we give an overview
of the design of this framework and illustrate the simplicity of applying
the available path sampling algorithms to a variety of benchmark problems.
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Affiliation(s)
- David W H Swenson
- van 't Hoff Institute for Molecular Sciences , University of Amsterdam , P.O. Box 94157, 1090 GD Amsterdam , The Netherlands.,Computational and Systems Biology Program , Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center , New York , New York 10065 , United States
| | - Jan-Hendrik Prinz
- Computational and Systems Biology Program , Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center , New York , New York 10065 , United States.,Department of Mathematics and Computer Science, Arnimallee 6 , Freie Universität Berlin , 14195 Berlin , Germany
| | - Frank Noe
- Department of Mathematics and Computer Science, Arnimallee 6 , Freie Universität Berlin , 14195 Berlin , Germany
| | - John D Chodera
- Computational and Systems Biology Program , Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center , New York , New York 10065 , United States
| | - Peter G Bolhuis
- van 't Hoff Institute for Molecular Sciences , University of Amsterdam , P.O. Box 94157, 1090 GD Amsterdam , The Netherlands
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6
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Vijaykumar A, Ten Wolde PR, Bolhuis PG. Rate constants for proteins binding to substrates with multiple binding sites using a generalized forward flux sampling expression. J Chem Phys 2018; 148:124109. [PMID: 29604887 DOI: 10.1063/1.5012854] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
To predict the response of a biochemical system, knowledge of the intrinsic and effective rate constants of proteins is crucial. The experimentally accessible effective rate constant for association can be decomposed in a diffusion-limited rate at which proteins come into contact and an intrinsic association rate at which the proteins in contact truly bind. Reversely, when dissociating, bound proteins first separate into a contact pair with an intrinsic dissociation rate, before moving away by diffusion. While microscopic expressions exist that enable the calculation of the intrinsic and effective rate constants by conducting a single rare event simulation of the protein dissociation reaction, these expressions are only valid when the substrate has just one binding site. If the substrate has multiple binding sites, a bound enzyme can, besides dissociating into the bulk, also hop to another binding site. Calculating transition rate constants between multiple states with forward flux sampling requires a generalized rate expression. We present this expression here and use it to derive explicit expressions for all intrinsic and effective rate constants involving binding to multiple states, including rebinding. We illustrate our approach by computing the intrinsic and effective association, dissociation, and hopping rate constants for a system in which a patchy particle model enzyme binds to a substrate with two binding sites. We find that these rate constants increase as a function of the rotational diffusion constant of the particles. The hopping rate constant decreases as a function of the distance between the binding sites. Finally, we find that blocking one of the binding sites enhances both association and dissociation rate constants. Our approach and results are important for understanding and modeling association reactions in enzyme-substrate systems and other patchy particle systems and open the way for large multiscale simulations of such systems.
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Affiliation(s)
- Adithya Vijaykumar
- FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
| | | | - Peter G Bolhuis
- van't Hoff Institute for Molecular Sciences, University of Amsterdam, P.O. Box 94157, 1090 GD Amsterdam, The Netherlands
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7
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Abstract
Interacting-particle reaction dynamics (iPRD) simulates the spatiotemporal evolution of particles that experience interaction forces and can react with one another. The combination of interaction forces and reactions enables a wide range of complex reactive systems in biology and chemistry to be simulated, but gives rise to new questions such as how to evolve the dynamical equations in a computationally efficient and statistically correct manner. Here we consider reversible reactions such as A + B ⇄ C with interacting particles and derive expressions for the microscopic iPRD simulation parameters such that desired values for the equilibrium constant and the dissociation rate are obtained in the dilute limit. We then introduce a Monte Carlo algorithm that ensures detailed balance in the iPRD time-evolution (iPRD-DB). iPRD-DB guarantees the correct thermodynamics at all concentrations and maintains the desired kinetics in the dilute limit, where chemical rates are well-defined and kinetic measurement experiments usually operate. We show that in dense particle systems, the incorporation of detailed balance is essential to obtain physically realistic solutions. iPRD-DB is implemented in ReaDDy 2.
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Affiliation(s)
- Christoph Fröhner
- Fachbereich Mathematik und Informatik , Freie Universität Berlin , Arnimallee 6 , 14195 Berlin , Germany
| | - Frank Noé
- Fachbereich Mathematik und Informatik , Freie Universität Berlin , Arnimallee 6 , 14195 Berlin , Germany
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8
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Bolhuis PG, Csányi G. Nested Transition Path Sampling. PHYSICAL REVIEW LETTERS 2018; 120:250601. [PMID: 29979082 DOI: 10.1103/physrevlett.120.250601] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2017] [Indexed: 06/08/2023]
Abstract
We introduce a novel transition path (TPS) sampling scheme employing nested sampling. Analogous to how nested sampling explores the entire configurational phase space for atomistic systems, nested TPS samples the entire available trajectory space in one simulation. Thermodynamic and path observables can be constructed a posteriori for all temperatures simultaneously. We exploit this to compute the rate of rare processes at arbitrarily low temperature through the coupling to easily accessible rates at high temperature. We illustrate the method on several model systems.
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Affiliation(s)
- Peter G Bolhuis
- Van 't Hoff Institute for Molecular Sciences, Universiteit van Amsterdam, Science Park 904, Amsterdam 1098 XH, The Netherlands
| | - Gábor Csányi
- Engineering Laboratory, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, United Kingdom
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9
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Newton AC, Groenewold J, Kegel WK, Bolhuis PG. The role of multivalency in the association kinetics of patchy particle complexes. J Chem Phys 2018. [PMID: 28641424 DOI: 10.1063/1.4984966] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
Association and dissociation of particles are elementary steps in many natural and technological relevant processes. For many such processes, the presence of multiple binding sites is essential. For instance, protein complexes and regular structures such as virus shells are formed from elementary building blocks with multiple binding sites. Here we address a fundamental question concerning the role of multivalency of binding sites in the association kinetics of such complexes. Using single replica transition interface sampling simulations, we investigate the influence of the multivalency on the binding kinetics and the association mechanism of patchy particles that form polyhedral clusters. When the individual bond strength is fixed, the kinetics naturally is very dependent on the multivalency, with dissociation rate constants exponentially decreasing with the number of bonds. In contrast, we find that when the total bond energy per particle is kept constant, association and dissociation rate constants turn out rather independent of multivalency, although of course still very dependent on the total energy. The association and dissociation mechanisms, however, depend on the presence and nature of the intermediate states. For instance, pathways that visit intermediate states are less prevalent for particles with five binding sites compared to the case of particles with only three bonds. The presence of intermediate states can lead to kinetic trapping and malformed aggregates. We discuss implications for natural forming complexes such as virus shells and for the design of artificial colloidal patchy particles.
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Affiliation(s)
- Arthur C Newton
- Van't Hoff Institute for Molecular Sciences, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Jan Groenewold
- Van't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands
| | - Willem K Kegel
- Van't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands
| | - Peter G Bolhuis
- Van't Hoff Institute for Molecular Sciences, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
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10
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Cabriolu R, Skjelbred Refsnes KM, Bolhuis PG, van Erp TS. Foundations and latest advances in replica exchange transition interface sampling. J Chem Phys 2017; 147:152722. [DOI: 10.1063/1.4989844] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Raffaela Cabriolu
- Department of Chemistry, Norwegian University of Science and Technology (NTNU), Høgskoleringen 5, 7491 Trondheim, Norway
| | - Kristin M. Skjelbred Refsnes
- Department of Chemistry, Norwegian University of Science and Technology (NTNU), Høgskoleringen 5, 7491 Trondheim, Norway
| | - Peter G. Bolhuis
- Van ’t Hoff Institute for Molecular Sciences, University of Amsterdam, P.O. Box 94157, 1090 GD Amsterdam, The Netherlands
| | - Titus S. van Erp
- Department of Chemistry, Norwegian University of Science and Technology (NTNU), Høgskoleringen 5, 7491 Trondheim, Norway
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11
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Newton AC, Kools R, Swenson DWH, Bolhuis PG. The opposing effects of isotropic and anisotropic attraction on association kinetics of proteins and colloids. J Chem Phys 2017; 147:155101. [DOI: 10.1063/1.5006485] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Arthur C. Newton
- Van ’t Hoff Institute for Molecular Sciences, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Ramses Kools
- Van ’t Hoff Institute for Molecular Sciences, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - David W. H. Swenson
- Van ’t Hoff Institute for Molecular Sciences, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Peter G. Bolhuis
- Van ’t Hoff Institute for Molecular Sciences, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
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12
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Andryushchenko VA, Chekmarev SF. Temperature evolution of Trp-cage folding pathways: An analysis by dividing the probability flux field into stream tubes. J Biol Phys 2017; 43:565-583. [PMID: 28983809 DOI: 10.1007/s10867-017-9470-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2016] [Accepted: 09/01/2017] [Indexed: 11/25/2022] Open
Abstract
Owing to its small size and very fast folding rate, the Trp-cage miniprotein has become a benchmark system to study protein folding. Two folding pathways were found to be characteristic of this protein: pathway I, in which the hydrophobic collapse precedes the formation of α-helix, and pathway II, in which the events occur in the reverse order. At the same time, the relative contribution of these pathways at different temperatures as well as the nature of transition from one pathway to the other remain unclear. To gain insight into this issue, we employ a recently proposed hydrodynamic description of protein folding, in which the process of folding is considered as a motion of a "folding fluid" (Chekmarev et al., Phys. Rev. Lett. 100(1), 018107 2008). Using molecular dynamics simulations, we determine the field of probability fluxes of transitions in a space of collective variables and divide it into stream tubes. Each tube contains a definite fraction of the total folding flow and can be associated with a certain pathway. Specifically, three temperatures were considered, T = 285K, T = 315K, and T = 325K. We have found that as the temperature increases, the contribution of pathway I, which is approximately 90% of the total folding flow at T = 285K, decreases to approximately 10% at T = 325K, i.e., pathway II becomes dominant. At T = 315K, both pathways contribute approximately equally. All these temperatures are found below the calculated melting point, which suggests that the Trp-cage folding mechanism is determined by kinetic factors rather than thermodynamics.
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Affiliation(s)
- Vladimir A Andryushchenko
- Institute of Thermophysics, SB RAS, 630090, Novosibirsk, Russia
- Department of Physics, Novosibirsk State University, 630090, Novosibirsk, Russia
| | - Sergei F Chekmarev
- Institute of Thermophysics, SB RAS, 630090, Novosibirsk, Russia.
- Department of Physics, Novosibirsk State University, 630090, Novosibirsk, Russia.
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13
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Duan L, Zhu T, Ji C, Zhang Q, Zhang JZH. Direct folding simulation of helical proteins using an effective polarizable bond force field. Phys Chem Chem Phys 2017; 19:15273-15284. [DOI: 10.1039/c7cp02101a] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
Snapshots of the intermediate conformation of Trp-cage at various simulation times using AMBER03, EPB03, AMBER12SB, and EPB12SB. Here, the N terminal is always on the top.
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Affiliation(s)
- Lili Duan
- School of Physics and Electronics
- Shandong Normal University
- Jinan 250014
- China
- School of Chemistry and Molecular Engineering
| | - Tong Zhu
- School of Chemistry and Molecular Engineering
- East China Normal University
- Shanghai 200062
- China
| | - Changge Ji
- School of Chemistry and Molecular Engineering
- East China Normal University
- Shanghai 200062
- China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai
| | - Qinggang Zhang
- School of Physics and Electronics
- Shandong Normal University
- Jinan 250014
- China
| | - John Z. H. Zhang
- School of Chemistry and Molecular Engineering
- East China Normal University
- Shanghai 200062
- China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai
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14
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Path-sampling strategies for simulating rare events in biomolecular systems. Curr Opin Struct Biol 2016; 43:88-94. [PMID: 27984811 DOI: 10.1016/j.sbi.2016.11.019] [Citation(s) in RCA: 65] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2016] [Revised: 11/18/2016] [Accepted: 11/21/2016] [Indexed: 12/20/2022]
Abstract
Despite more than three decades of effort with molecular dynamics simulations, long-timescale (ms and beyond) biologically relevant phenomena remain out of reach in most systems of interest. This is largely because important transitions, such as conformational changes and (un)binding events, tend to be rare for conventional simulations (<10μs). That is, conventional simulations will predominantly dwell in metastable states instead of making large transitions in complex biomolecular energy landscapes. In contrast, path sampling approaches focus computing effort specifically on transitions of interest. Such approaches have been in use for nearly 20 years in biomolecular systems and enabled the generation of pathways and calculation of rate constants for ms processes, including large protein conformational changes, protein folding, and protein (un)binding.
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15
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Rotational diffusion affects the dynamical self-assembly pathways of patchy particles. Proc Natl Acad Sci U S A 2015; 112:15308-13. [PMID: 26621742 DOI: 10.1073/pnas.1513210112] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Predicting the self-assembly kinetics of particles with anisotropic interactions, such as colloidal patchy particles or proteins with multiple binding sites, is important for the design of novel high-tech materials, as well as for understanding biological systems, e.g., viruses or regulatory networks. Often stochastic in nature, such self-assembly processes are fundamentally governed by rotational and translational diffusion. Whereas the rotational diffusion constant of particles is usually considered to be coupled to the translational diffusion via the Stokes-Einstein relation, in the past decade it has become clear that they can be independently altered by molecular crowding agents or via external fields. Because virus capsids naturally assemble in crowded environments such as the cell cytoplasm but also in aqueous solution in vitro, it is important to investigate how varying the rotational diffusion with respect to transitional diffusion alters the kinetic pathways of self-assembly. Kinetic trapping in malformed or intermediate structures often impedes a direct simulation approach of a kinetic network by dramatically slowing down the relaxation to the designed ground state. However, using recently developed path-sampling techniques, we can sample and analyze the entire self-assembly kinetic network of simple patchy particle systems. For assembly of a designed cluster of patchy particles we find that changing the rotational diffusion does not change the equilibrium constants, but significantly affects the dynamical pathways, and enhances (suppresses) the overall relaxation process and the yield of the target structure, by avoiding (encountering) frustrated states. Besides insight, this finding provides a design principle for improved control of nanoparticle self-assembly.
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16
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A hydrodynamic view of the first-passage folding of Trp-cage miniprotein. EUROPEAN BIOPHYSICS JOURNAL: EBJ 2015; 45:229-43. [PMID: 26559408 DOI: 10.1007/s00249-015-1089-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2015] [Revised: 09/27/2015] [Accepted: 10/09/2015] [Indexed: 12/11/2022]
Abstract
We study folding of Trp-cage miniprotein in the conditions when the native state of the protein is stable and unfolding events are improbable, which corresponds to physiological conditions. Using molecular dynamics simulations with an implicit solvent model, an ensemble of folding trajectories from unfolded (practically extended) states of the protein to the native state was generated. To get insight into the folding kinetics, the free energy surface and kinetic network projected on this surface were constructed. This, "conventional" analysis of the folding reaction was followed by a recently proposed hydrodynamic description of protein folding (Chekmarev et al. in Phys Rev Lett 100(1):018107, 2008), in which the process of the first-passage folding is viewed as a stationary flow of a folding "fluid" from the unfolded to native state. This approach is conceptually different from the previously used approaches and thus allows an alternative view of the folding dynamics and kinetics of Trp-cage, the conclusions about which are very diverse. In agreement with most previous studies, we observed two characteristic folding pathways: in one pathway (I), the collapse of the hydrophobic core precedes the formation of the [Formula: see text]-helix, and in the other pathway (II), these events occur in the reverse order. We found that although pathway II is complicated by a repeated partial protein unfolding, it contributes to the total folding flow as little as ≈10%, so that the folding kinetics remain essentially single-exponential.
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17
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Rakers C, Bermudez M, Keller BG, Mortier J, Wolber G. Computational close up on protein-protein interactions: how to unravel the invisible using molecular dynamics simulations? WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2015. [DOI: 10.1002/wcms.1222] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Christin Rakers
- Institute of Pharmacy; Freie Universität Berlin; Berlin Germany
| | - Marcel Bermudez
- Institute of Pharmacy; Freie Universität Berlin; Berlin Germany
| | - Bettina G. Keller
- Institute for Chemistry and Biochemistry; Freie Universität Berlin; Berlin Germany
| | - Jérémie Mortier
- Institute of Pharmacy; Freie Universität Berlin; Berlin Germany
| | - Gerhard Wolber
- Institute of Pharmacy; Freie Universität Berlin; Berlin Germany
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18
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Abaskharon RM, Culik RM, Woolley GA, Gai F. Tuning the Attempt Frequency of Protein Folding Dynamics via Transition-State Rigidification: Application to Trp-Cage. J Phys Chem Lett 2015; 6:521-6. [PMID: 26120378 PMCID: PMC4479204 DOI: 10.1021/jz502654q] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2014] [Accepted: 01/22/2015] [Indexed: 05/23/2023]
Abstract
The attempt frequency or prefactor (k0) of the transition-state rate equation of protein folding kinetics has been estimated to be on the order of 10(6) s(-1), which is many orders of magnitude smaller than that of chemical reactions. Herein we use the mini-protein Trp-cage to show that it is possible to significantly increase the value of k0 for a protein folding reaction by rigidifying the transition state. This is achieved by reducing the conformational flexibility of a key structural element (i.e., an α-helix) formed in the transition state via photoisomerization of an azobenzene cross-linker. We find that this strategy not only decreases the folding time of the Trp-cage peptide by more than an order of magnitude (to ∼100 ns at 25°C) but also exposes parallel folding pathways, allowing us to provide, to the best of our knowledge, the first quantitative assessment of the curvature of the transition-state free-energy surface of a protein.
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Affiliation(s)
- Rachel M. Abaskharon
- Department of Chemistry and Department
of Biochemistry & Biophysics, University of Pennsylvania,
231 South 34th Street, Philadelphia, Pennsylvania 19104, United
States
| | - Robert M. Culik
- Department of Chemistry and Department
of Biochemistry & Biophysics, University of Pennsylvania,
231 South 34th Street, Philadelphia, Pennsylvania 19104, United
States
| | - G. Andrew Woolley
- Department of Chemistry, University of
Toronto, 80 Saint George Street, Toronto, Ontario M5S 3H6,
Canada
| | - Feng Gai
- Department of Chemistry and Department
of Biochemistry & Biophysics, University of Pennsylvania,
231 South 34th Street, Philadelphia, Pennsylvania 19104, United
States
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19
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Du W, Bolhuis PG. Equilibrium kinetic network of the villin headpiece in implicit solvent. Biophys J 2015; 108:368-78. [PMID: 25606685 PMCID: PMC4302211 DOI: 10.1016/j.bpj.2014.11.3476] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2014] [Revised: 11/06/2014] [Accepted: 11/14/2014] [Indexed: 11/18/2022] Open
Abstract
We applied the single-replica multiple-state transition-interface sampling method to elucidate the equilibrium kinetic network of the 35-residue-fragment (HP-35) villin headpiece in implicit water at room temperature. Starting from the native Protein Data Bank structure, nine (meta)stable states of the system were identified, from which the kinetic network was built by sampling pathways between these states. Application of transition path theory allowed analysis of the (un)folding mechanism. The resulting (un)folding rates agree well with experiments. This work demonstrates that high (un)folding barriers can now be studied.
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Affiliation(s)
- Weina Du
- van 't Hoff Institute for Molecular Sciences, University of Amsterdam, Amsterdam, The Netherlands
| | - Peter G Bolhuis
- van 't Hoff Institute for Molecular Sciences, University of Amsterdam, Amsterdam, The Netherlands.
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20
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Byrne A, Williams DV, Barua B, Hagen SJ, Kier BL, Andersen NH. Folding dynamics and pathways of the trp-cage miniproteins. Biochemistry 2014; 53:6011-21. [PMID: 25184759 PMCID: PMC4179588 DOI: 10.1021/bi501021r] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
Using alternate measures of fold stability for a wide variety of Trp-cage mutants has raised the possibility that prior dynamics T-jump measures may not be reporting on complete cage formation for some species. NMR relaxation studies using probes that only achieve large chemical shift difference from unfolded values on complete cage formation indicate slower folding in some but not all cases. Fourteen species have been examined, with cage formation time constants (1/kF) ranging from 0.9-7.5 μs at 300 K. The present study does not change the status of the Trp-cage as a fast folding, essentially two-state system, although it does alter the stage at which this description applies. A diversity of prestructuring events, depending on the specific analogue examined, may appear in the folding scenario, but in all cases, formation of the N-terminal helix is complete either at or before the cage-formation transition state. In contrast, the fold-stabilizing H-bonding interactions of the buried Ser14 side chain and the Arg/Asp salt bridge are post-transition state features on the folding pathway. The study has also found instances in which a [P12W] mutation is fold destabilizing but still serves to accelerate the folding process.
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Affiliation(s)
- Aimee Byrne
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
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