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Yoshidome T. Four-dimensional imaging for cryo-electron microscopy experiments using molecular simulations and manifold learning. J Comput Chem 2024; 45:738-751. [PMID: 38112413 DOI: 10.1002/jcc.27290] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2023] [Revised: 11/20/2023] [Accepted: 12/01/2023] [Indexed: 12/21/2023]
Abstract
Elucidating protein conformational changes is essential because conformational changes are closely related to the functions of proteins. Cryo-electron microscopy (cryo-EM) experiment can be used to reconstruct protein conformational changes via a method that involves using the experimental data (two-dimensional protein images). In this study, a reconstruction method, referred to as the "four-dimensional imaging," was proposed. In our four-dimensional imaging technique, the protein conformational change was obtained using the two-dimensional protein images (the three-dimensional electron density maps used in previously proposed techniques were not used). The protein conformation for each two-dimensional protein image was obtained using our original protocol with molecular dynamics simulations. Using a manifold-learning technique and two-dimensional protein images, the protein conformations were arranged according to the conformational change of the protein. By arranging the protein conformations according to the arrangement of the protein images, four-dimensional imaging is constructed. A simulation for a cryo-EM experiment demonstrated the validity of our four-dimensional imaging technique.
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Affiliation(s)
- Takashi Yoshidome
- Department of Applied Physics, Graduate School of Engineering, Tohoku University, Sendai, Japan
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Hishikawa Y, Noya H, Nagatoishi S, Yoshidome T, Maity B, Tsumoto K, Abe S, Ueno T. Elucidating Conformational Dynamics and Thermostability of Designed Aromatic Clusters Using Protein Cages. Chemistry 2023:e202300488. [PMID: 37070368 DOI: 10.1002/chem.202300488] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2023] [Revised: 04/09/2023] [Accepted: 04/11/2023] [Indexed: 04/19/2023]
Abstract
Aromatic residues form clusters in proteins and play essential roles in biological systems. However, the stabilization mechanism and dynamic behavior of aromatic clusters remain unclear. Here, we describe designed aromatic interactions confined within a protein cage to reveal how aromatic clusters affect protein stability. The crystal structures and calorimetric measurements indicate that the formation of inter-subunit phenylalanine clusters enhance the interactions of inter-helices and increase the melting temperature. Theoretical calculations suggest that this is caused by the transformation of the T-shaped geometry into π-π stacking at high temperatures, and the hydration entropic gain. Thus, the isolated nano-environment in a protein cage allows reconstruction and detailed analysis of multiple clustering residues for elucidating the mechanisms of various biomolecular interactions in nature which can be applied to design of bionanomaterials.
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Affiliation(s)
- Yuki Hishikawa
- Tokyo Institute of Technology: Tokyo Kogyo Daigaku, Life Science and technology, JAPAN
| | - Hiroki Noya
- Tokyo Institute of Technology: Tokyo Kogyo Daigaku, School of life Science and technology, JAPAN
| | - Satoru Nagatoishi
- The University of Tokyo: Tokyo Daigaku, The Institute of Medical Science,, JAPAN
| | | | - Basudev Maity
- Tokyo Institute of Technology: Tokyo Kogyo Daigaku, Life science and technology, JAPAN
| | - Kouhei Tsumoto
- The University of Tokyo: Tokyo Daigaku, The Institute of Medical Science,, JAPAN
| | - Satoshi Abe
- Tokyo Institute of Technology: Tokyo Kogyo Daigaku, Life Science and Technology, JAPAN
| | - Takafumi Ueno
- Tokyo Institute of Technology, Graduate School of Bioscience and Biotechnology, Nagatsuta-cho 4259-B-55, Midori-ku, 226-8501, Yokohama, JAPAN
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3
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Fukushima Y, Yoshidome T. A deep-learning model for grid-based solvation free energy. Biophys J 2023; 122:141a-142a. [PMID: 36782645 DOI: 10.1016/j.bpj.2022.11.926] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/12/2023] Open
Affiliation(s)
- Yusaku Fukushima
- Department of Applied Physics, School of Engineering, Tohoku University, Sendai, Japan
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Kawama K, Fukushima Y, Ikeguchi M, Ohta M, Yoshidome T. gr Predictor: A Deep Learning Model for Predicting the Hydration Structures around Proteins. J Chem Inf Model 2022; 62:4460-4473. [PMID: 36068974 DOI: 10.1021/acs.jcim.2c00987] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Among the factors affecting biological processes such as protein folding and ligand binding, hydration, which is represented by a three-dimensional water site distribution function around the protein, is crucial. The typical methods for computing the distribution functions, including molecular dynamics simulations and the three-dimensional reference interaction site model (3D-RISM) theory, require a long computation time ranging from hours to tens of hours. Here, we propose a deep learning (DL) model that rapidly estimates the distribution functions around proteins obtained using the 3D-RISM theory from the protein 3D structure. The distribution functions predicted using our DL model are in good agreement with those obtained using the 3D-RISM theory. Particularly, the coefficient of determination between the distribution function obtained by the DL model and that obtained using the 3D-RISM theory is approximately 0.98. Furthermore, using a graphics processing unit, the prediction by the DL model is completed in less than 1 min, more than 2 orders of magnitude faster than the calculation time of the 3D-RISM theory. The position of water molecules around the protein was estimated based on the distribution function obtained by our DL model, and the position of waters estimated by our DL model was in good agreement with that of water molecules estimated using the 3D-RISM theory and of crystallographic waters. Therefore, our DL model provides a practical and efficient way to calculate the three-dimensional water site distribution functions and to estimate the position of water molecules around the protein. The program called "gr Predictor" is available under the GNU General Public License from https://github.com/YoshidomeGroup-Hydration/gr-predictor.
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Affiliation(s)
- Kosuke Kawama
- Department of Applied Physics, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
| | - Yusaku Fukushima
- Department of Applied Physics, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
| | - Mitsunori Ikeguchi
- AI-Driven Drug Discovery Collaborative Unit, HPC- and AI-Driven Drug Development Platform Division, Center for Computational Science, RIKEN, 1-7-29, Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan.,Graduate School of Medical Life Science, Yokohama City University, 1-7-29, Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
| | - Masateru Ohta
- AI-Driven Drug Discovery Collaborative Unit, HPC- and AI-Driven Drug Development Platform Division, Center for Computational Science, RIKEN, 1-7-29, Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
| | - Takashi Yoshidome
- Department of Applied Physics, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
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Kawama K, Fukushima Y, Yoshidome T, Ikeguchi M, Ohta M. Development of a deep-learning model for predicting the hydration structures around proteins. Biophys J 2022. [DOI: 10.1016/j.bpj.2021.11.2047] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022] Open
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Kojima R, Yoshidome T. A measure for the identification of preferred particle orientations in cryo-electron microscopy data: A simulation study. Biophys Physicobiol 2021; 18:96-107. [PMID: 34026399 PMCID: PMC8116199 DOI: 10.2142/biophysico.bppb-v18.011] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2020] [Accepted: 03/12/2021] [Indexed: 12/01/2022] Open
Abstract
Cryo-electron microscopy (cryo-EM) is an important experimental technique for the structural analysis of biomolecules that are difficult or impossible to crystallize. The three-dimensional structure of a biomolecule can be reconstructed using two-dimensional electron-density maps, which are experimentally sampled via the electron beam irradiation of vitreous ice in which the target biomolecules are embedded. One assumption required for this reconstruction is that the orientation of the biomolecules in the vitreous ice is isotropic. However, this is not always the case and two-dimensional electron-density maps are often sampled using preferred biomolecular orientations, which can make reconstruction difficult or impossible. Compensation for under-represented views is computationally feasible for the reconstruction of three-dimensional electron density maps, but one must know whether or not there is any missing information in the sampled two-dimensional electron density maps. Thus, a measure to identify whether a cryo-EM data is obtained from the biomolecules adopting preferred orientations is required. In the present study, we propose a measure for which the geometry of manifold projected onto a low-dimensional space is used. To show the usefulness of the measure, we perform simulations for cryo-EM experiment of a protein. It is found that the geometry of manifold projected onto a two-dimensional space for a protein adopting a preferred biomolecular orientation is significantly different from that for a protein adopting a uniform orientation. This result suggests that the geometry of manifold projected onto a low-dimensional space can be used for the measure for the identification that the biomolecules adopt preferred orientations.
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Affiliation(s)
- Ryota Kojima
- Department of Applied Physics, Graduate School of Engineering, Tohoku University, Sendai, Miyagi 980-8579, Japan
| | - Takashi Yoshidome
- Department of Applied Physics, Graduate School of Engineering, Tohoku University, Sendai, Miyagi 980-8579, Japan
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Yoshidome T, Ikeguchi M, Ohta M. Comprehensive 3D-RISM Analysis of the Hydration of Small Molecule Binding Sites in Ligand-Free Protein Structures. Biophys J 2021. [DOI: 10.1016/j.bpj.2020.11.716] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022] Open
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Yoshidome T, Ikeguchi M, Ohta M. Comprehensive 3D-RISM analysis of the hydration of small molecule binding sites in ligand-free protein structures. J Comput Chem 2020; 41:2406-2419. [PMID: 32815201 PMCID: PMC7540010 DOI: 10.1002/jcc.26406] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2020] [Revised: 07/28/2020] [Accepted: 08/05/2020] [Indexed: 12/25/2022]
Abstract
Hydration is a critical factor in the ligand binding process. Herein, to examine the hydration states of ligand binding sites, the three‐dimensional distribution function for the water oxygen site, gO(r), is computed for 3,706 ligand‐free protein structures based on the corresponding small molecule–protein complexes using the 3D‐RISM theory. For crystallographic waters (CWs) close to the ligand, gO(r) reveals that several CWs are stabilized by interaction networks formed between the ligand, CW, and protein. Based on the gO(r) for the crystallographic binding pose of the ligand, hydrogen bond interactions are dominant in the highly hydrated regions while weak interactions such as CH‐O are dominant in the moderately hydrated regions. The polar heteroatoms of the ligand occupy the highly hydrated and moderately hydrated regions in the crystallographic (correct) and wrongly docked (incorrect) poses, respectively. Thus, the gO(r) of polar heteroatoms may be used to distinguish the correct binding poses.
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Affiliation(s)
- Takashi Yoshidome
- Department of Applied Physics, Graduate School of Engineering, Tohoku University, Sendai, Japan
| | - Mitsunori Ikeguchi
- Drug Development Data Intelligence Platform Group, Medical Science Innovation Hub Program, Cluster of Science, Technology and Innovation Hub, RIKEN, Yokohama, Japan.,Graduate School of Medical Life Science, Yokohama City University, Yokohama, Japan
| | - Masateru Ohta
- Drug Development Data Intelligence Platform Group, Medical Science Innovation Hub Program, Cluster of Science, Technology and Innovation Hub, RIKEN, Yokohama, Japan
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10
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Oroguchi T, Yoshidome T, Yamamoto T, Nakasako M. Growth of Cuprous Oxide Particles in Liquid-Phase Synthesis Investigated by X-ray Laser Diffraction. Nano Lett 2018; 18:5192-5197. [PMID: 29990436 DOI: 10.1021/acs.nanolett.8b02153] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Cuprous oxide (Cu2O) particles obtained by surfactant-assisted liquid-phase synthesis have cuboid shapes but the internal structures are difficult to be visualized by electron microscopy. Herein, we investigated the internal structures of numerous individual Cu2O particles with submicrometer dimensions by X-ray diffraction imaging (XDI) using X-ray free-electron laser (XFEL) pulses. The reconstructed two-dimensional electron density maps, which displayed inhomogeneous internal structures, were divided into five classes characterized by the positions and shapes of high and low electron density areas. Further analysis of the maps in each class by a manifold learning algorithm revealed that the internal structures of Cu2O particles varied in correlation with total electron density while retaining the characteristics within each class. On the basis of the analyses, we proposed a growth mechanism to yield the inhomogeneity in the internal structures of Cu2O particles in surfactant-mediated liquid-phase synthesis.
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Affiliation(s)
- Tomotaka Oroguchi
- Department of Physics, Faculty of Science and Technology , Keio University , 3-14-1 Hiyoshi , Kohoku-ku, Yokohama , 223-8522 Japan
- RIKEN SPring-8 Center , 1-1-1 Kohto, Sayo , Sayo-gun, Hyogo 679-5148 Japan
| | - Takashi Yoshidome
- Department of Applied Physics, Graduate School of Engineering , Tohoku University , 6-6-05, Aoba, Aramaki , Aoba-ku, Sendai 980-8579 , Japan
| | - Takahiro Yamamoto
- Department of Physics, Faculty of Science and Technology , Keio University , 3-14-1 Hiyoshi , Kohoku-ku, Yokohama , 223-8522 Japan
- RIKEN SPring-8 Center , 1-1-1 Kohto, Sayo , Sayo-gun, Hyogo 679-5148 Japan
| | - Masayoshi Nakasako
- Department of Physics, Faculty of Science and Technology , Keio University , 3-14-1 Hiyoshi , Kohoku-ku, Yokohama , 223-8522 Japan
- RIKEN SPring-8 Center , 1-1-1 Kohto, Sayo , Sayo-gun, Hyogo 679-5148 Japan
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11
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Ito R, Yoshidome T. An Accurate Computation of a Physical Quantity of a Protein with a Markov State Model Constructed using a Manifold-Learning Technique. Biophys J 2018. [DOI: 10.1016/j.bpj.2017.11.3649] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022] Open
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12
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Ito R, Yoshidome T. An accurate computational method for an order parameter with a Markov state model constructed using a manifold-learning technique. Chem Phys Lett 2018. [DOI: 10.1016/j.cplett.2017.10.057] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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Yoshidome T, Sekiguchi Y, Oroguchi T, Nakasako M, Ikeguchi M. Reconstruction of Three-Dimensional Structures of a Protein with Software ENMA and EMC Algorithm: A Simulation for XFEL-CXDI Experiment. Biophys J 2017. [DOI: 10.1016/j.bpj.2016.11.1561] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
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Hikiri S, Yoshidome T, Ikeguchi M. Computational Methods for Configurational Entropy Using Internal and Cartesian Coordinates. J Chem Theory Comput 2016; 12:5990-6000. [DOI: 10.1021/acs.jctc.6b00563] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Simon Hikiri
- Graduate School of Medical
Life Science, Yokohama City University, 1-7-29, Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
| | - Takashi Yoshidome
- Graduate School of Medical
Life Science, Yokohama City University, 1-7-29, Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
| | - Mitsunori Ikeguchi
- Graduate School of Medical
Life Science, Yokohama City University, 1-7-29, Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
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15
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Yoshidome T, Ekimoto T, Matubayasi N, Harano Y, Kinoshita M, Ikeguchi M. An Accurate and Efficient, Computational Method for the Hydration Free Energy of Large and Complex Molecules. Biophys J 2016. [DOI: 10.1016/j.bpj.2015.11.1767] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
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Yoshidome T, Oroguchi T, Nakasako M, Ikeguchi M. Classification of projection images of proteins with structural polymorphism by manifold: a simulation study for x-ray free-electron laser diffraction imaging. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 92:032710. [PMID: 26465501 DOI: 10.1103/physreve.92.032710] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2015] [Indexed: 06/05/2023]
Abstract
Coherent x-ray diffraction imaging (CXDI) enables us to visualize noncrystalline sample particles with micrometer to submicrometer dimensions. Using x-ray free-electron laser (XFEL) sources, two-dimensional diffraction patterns are collected from fresh samples supplied to the irradiation area in the "diffraction-before-destruction" scheme. A recent significant increase in the intensity of the XFEL pulse is promising and will allow us to visualize the three-dimensional structures of proteins using XFEL-CXDI in the future. For the protocol proposed for molecular structure determination using future XFEL-CXDI [T. Oroguchi and M. Nakasako, Phys. Rev. E 87, 022712 (2013)10.1103/PhysRevE.87.022712], we require an algorithm that can classify the data in accordance with the structural polymorphism of proteins arising from their conformational dynamics. However, most of the algorithms proposed primarily require the numbers of conformational classes, and then the results are biased by the numbers. To improve this point, here we examine whether a method based on the manifold concept can classify simulated XFEL-CXDI data with respect to the structural polymorphism of a protein that predominantly adopts two states. After random sampling of the conformations of the two states and in-between states from the trajectories of molecular dynamics simulations, a diffraction pattern is calculated from each conformation. Classification was performed by using our custom-made program suite named enma, in which the diffusion map (DM) method developed based on the manifold concept was implemented. We successfully classify most of the projection electron density maps phase retrieved from diffraction patterns into each of the two states and in-between conformations without the knowledge of the number of conformational classes. We also examined the classification of the projection electron density maps of each of the three states with respect to the Euler angle. The present results suggest that the DM method is imperative for future applications of XFEL-CXDI experiments for proteins, and clarify issues to be taken care of in the future application.
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Affiliation(s)
- Takashi Yoshidome
- Graduate School of Medical Life Science, Yokohama City University, 1-7-29, Suehiro-cho, Tsurumi-ku, Yokohama, Kanagawa 230-0045, Japan
| | - Tomotaka Oroguchi
- Department of Physics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa 223-8522, Japan
- Research Infrastructure Group, Advanced Photon Technology Division, RIKEN Harima Institute, 1-1-1 Kouto, Mikaduki, Sayo, Hyogo, Japan
| | - Masayoshi Nakasako
- Department of Physics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa 223-8522, Japan
- Research Infrastructure Group, Advanced Photon Technology Division, RIKEN Harima Institute, 1-1-1 Kouto, Mikaduki, Sayo, Hyogo, Japan
| | - Mitsunori Ikeguchi
- Graduate School of Medical Life Science, Yokohama City University, 1-7-29, Suehiro-cho, Tsurumi-ku, Yokohama, Kanagawa 230-0045, Japan
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Yoshidome T, Ekimoto T, Matubayasi N, Harano Y, Kinoshita M, Ikeguchi M. An accurate and efficient computation method of the hydration free energy of a large, complex molecule. J Chem Phys 2015; 142:175101. [DOI: 10.1063/1.4919636] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Takashi Yoshidome
- Graduate School of Medical Life Science, Yokohama City University, 1-7-29, Suehiro-cho, Tsurumi-ku, Yokohama, Kanagawa 230-0045, Japan
| | - Toru Ekimoto
- Graduate School of Medical Life Science, Yokohama City University, 1-7-29, Suehiro-cho, Tsurumi-ku, Yokohama, Kanagawa 230-0045, Japan
| | - Nobuyuki Matubayasi
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
- Elements Strategy Initiative for Catalysts and Batteries, Kyoto University, Katsura, Kyoto 615-8520, Japan
| | - Yuichi Harano
- Faculty of Pharmaceutical Sciences, Himeji Dokkyo University, 7-2-1 Kamino, Himeji-shi, Hyogo 670-8524, Japan
| | - Masahiro Kinoshita
- Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan
| | - Mitsunori Ikeguchi
- Graduate School of Medical Life Science, Yokohama City University, 1-7-29, Suehiro-cho, Tsurumi-ku, Yokohama, Kanagawa 230-0045, Japan
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Yoshidome T, Oroguchi T, Nakasako M, Ikeguchi M. Classification Protocol of Projection Images by Manifold: Toward Analysis of Dynamics of Particles with Coherent X-Ray Diffraction Imaging. Biophys J 2014. [DOI: 10.1016/j.bpj.2013.11.2172] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022] Open
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Ito Y, Yoshidome T, Matubayasi N, Kinoshita M, Ikeguchi M. Molecular dynamics simulations of yeast F1-ATPase before and after 16° rotation of the γ subunit. J Phys Chem B 2013; 117:3298-307. [PMID: 23452086 DOI: 10.1021/jp312499u] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We have recently proposed the "packing exchange mechanism" for F1-ATPase, wherein the perturbation by a substrate binding/release or an ATP hydrolysis is followed by the reorganization of the asymmetric packing structure of the α3β3 complex, accompanying the γ subunit rotation. As part of a further investigation of this rotational mechanism, we performed all-atom molecular dynamics simulations for yeast F1-ATPase both before and after a 16° rotation of the γ subunit triggered by a Pi release. We analyzed the structural fluctuations, the subunit interface interactions, and the dynamics of the relative subunit arrangements before and after the rotation. We found that with the Pi release the αEβE subunit interface becomes looser, which also allosterically makes the αDPβDP subunit interface looser. This structural communication between these interfaces takes place through a tightening of the αTPβTP subunit interface. The γ subunit interacts less strongly with αDP and βDP and more strongly with αTP and βTP. After the Pi release, the tightly packed interfaces are reorganized from the interfaces around βDP to those around βTP, inducing the 16° rotation. These results, which are consistent with the packing exchange mechanism, allow us to deduce a view of the structural change during the 40° rotation.
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Affiliation(s)
- Yuko Ito
- Graduate School of Nanobioscience, Yokohama City University, 1-7-29, Yokohama, 230-0045 Japan
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Ito Y, Yoshidome T, Matubayasi N, Kinoshita M, Ikeguchi M. Molecular Dynamics Simulations of Yeast F1-ATPase Before and after 16-Degree Rotation of the Gamma Subunit. Biophys J 2013. [DOI: 10.1016/j.bpj.2012.11.1846] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022] Open
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21
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Yoshidome T, Ito Y, Matubayasi N, Ikeguchi M, Kinoshita M. Structural characteristics of yeast F1-ATPase before and after 16-degree rotation of the γ subunit: theoretical analysis focused on the water-entropy effect. J Chem Phys 2012; 137:035102. [PMID: 22830731 DOI: 10.1063/1.4734298] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We have recently proposed a novel picture of the rotation mechanism for F(1)-ATPase [T. Yoshidome, Y. Ito, M. Ikeguchi, and M. Kinoshita, J. Am. Chem. Soc. 133, 4030 (2011)]. In the picture, the asymmetric packing in F(1)-ATPase, originating from the water-entropy effect, plays the key role in the rotation. Here, we analyze the differences between the experimentally determined structures of yeast F(1)-ATPase before and after 16° rotation of the γ subunit with the emphasis on the water-entropy effect. For each of these structures, we calculate the hydration entropies of three sub-complexes comprising the γ subunit, one of the β subunits, and two α subunits adjacent to them. The β(E), β(TP), and β(DP) subunits are involved in sub-complexes I, II, and III, respectively. The calculation is performed using a hybrid of the angle-dependent integral equation theory combined with the molecular model for water and the morphometric approach. The absolute value of the hydration entropy is in the following order: sub-complex I > sub-complex II > sub-complex III. The packing efficiency of the sub-complex follows the opposite order. The rotation gives rise to less efficient packing in sub-complex III and a corresponding water-entropy loss. However, the other two sub-complexes, accompanying water-entropy gains, become more efficiently packed. These results are consistent with our picture of the rotation mechanism, supporting its validity. The water-entropy analysis shows that the interfaces of α(DP)-β(DP) and α(E)-β(E) become more open after the rotation, which is in accord with the experimental observation.
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Affiliation(s)
- Takashi Yoshidome
- Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan
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Yoshidome T, Kinoshita M. Physical origin of hydrophobicity studied in terms of cold denaturation of proteins: comparison between water and simple fluids. Phys Chem Chem Phys 2012; 14:14554-66. [PMID: 23014986 DOI: 10.1039/c2cp41738c] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A clue to the physical origin of the hydrophobicity is in the experimental observations, which show that it is weakened at low temperatures. By considering a solvophobic model protein immersed in water and three species of simple solvents, we analyze the temperature dependence of the changes in free energy, energy, and entropy of the solvent upon protein unfolding. The angle-dependent and radial-symmetric integral equation theories and the morphometric approach are employed in the analysis. Each of the changes is decomposed into two terms, which depend on the excluded volume and on the area and curvature of the solvent-accessible surface, respectively. The excluded-volume term of the entropy change is further decomposed into two components representing the protein-solvent pair correlation and the protein-solvent-solvent triplet and higher-order correlation, respectively. We show that water crowding in the system becomes more serious upon protein unfolding but this effect becomes weaker as the temperature is lowered. If the hydrophobicity originated from the water structuring near a nonpolar solute, it would be strengthened upon lowering of the temperature. Among the three species of simple solvents, considerable weakening of the solvophobicity at low temperatures is observed only for the solvent where the particles interact through a strong attractive potential and the particle size is as small as that of water. Even in the case of this solvent, however, cold denaturation of a protein cannot be reproduced. It would be reproducible if the attractive potential was substantially enhanced, but such enhancement causes the appearance of the metastability limit for a single liquid phase.
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Affiliation(s)
- Takashi Yoshidome
- Institute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto, Japan
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Mishima H, Yasuda S, Yoshidome T, Oshima H, Harano Y, Ikeguchi M, Kinoshita M. Characterization of experimentally determined native-structure models of a protein using energetic and entropic components of free-energy function. J Phys Chem B 2012; 116:7776-86. [PMID: 22697465 DOI: 10.1021/jp301541z] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
We show how to characterize the native-structure models of a protein using our free-energy function F which is based on hydration thermodynamics. Ubiquitin is adopted as an example protein. We consider models determined by the X-ray crystallography and two types of NMR model sets. A model set of type 1 comprises candidate models for a fixed native structure, and that of type 2 forms an ensemble of structures representing the structural variability of the native state. In general, the X-ray models give lower F than the NMR models. There is a trend that, as a model deviates more from the model with the lowest F among the X-ray models, its F becomes higher. Model sets of type 1 and those of type 2, respectively, exhibit two different characteristics with respect to the correlation between the deviation and F. It is argued that the total amount of constraints such as NOEs effectively taken into account in constructing the NMR models can be examined by analyzing the behavior of F. We investigate structural characteristics of the models in terms of the energetic and entropic components of F which are relevant to intramolecular hydrogen bonding and to backbone and side-chain packing, respectively.
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Affiliation(s)
- Hirokazu Mishima
- Graduate School of Energy Science, Kyoto University , Uji, Kyoto 611-0011, Japan
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Yoshidome T, Ito Y, Matubayasi N, Ikeguchi M, Kinoshita M. A Novel Rotation Mechanism of F1-ATPase Based on the Water-Entropy Effect. Biophys J 2012. [DOI: 10.1016/j.bpj.2011.11.1358] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
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Abstract
We briefly review our theoretical study on the rotation scheme of F1-ATPase. In the scheme, the key factor is the water entropy which has been shown to drive a variety of self-assembly processes in biological systems. We decompose the crystal structure of F1-ATPase into three sub-complexes each of which is composed of the γ subunit, one of the β subunits, and two α subunits adjacent to them. The βE, βTP, and βDP subunits are involved in the sub-complexes I, II, and III, respectively. We calculate the hydration entropy of each sub-complex using a hybrid of the integral equation theory for molecular liquids and the morphometric approach. It is found that the absolute value of the hydration entropy follows the order, sub-complex I > sub-complex II > sub-complex III. Moreover, the differences are quite large, which manifests highly asymmetrical packing of F1-ATPase. In our picture, this asymmetrical packing plays crucially important roles in the rotation of the γ subunit. We discuss how the rotation is induced by the water-entropy effect coupled with such chemical processes as ATP binding, ATP hydrolysis, and release of the products.
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Affiliation(s)
- Takashi Yoshidome
- Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan
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Yasuda S, Yoshidome T, Harano Y, Roth R, Oshima H, Oda K, Sugita Y, Ikeguchi M, Kinoshita M. Free-energy function for discriminating the native fold of a protein from misfolded decoys. Proteins 2011; 79:2161-71. [PMID: 21557318 DOI: 10.1002/prot.23036] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2010] [Revised: 02/24/2011] [Accepted: 03/13/2011] [Indexed: 11/08/2022]
Affiliation(s)
- Satoshi Yasuda
- Graduate School of Energy Science, Kyoto University, Uji, Kyoto 611-0011, Japan
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Oda K, Kodama R, Yoshidome T, Yamanaka M, Sambongi Y, Kinoshita M. Effects of heme on the thermal stability of mesophilic and thermophilic cytochromes c: comparison between experimental and theoretical results. J Chem Phys 2011; 134:025101. [PMID: 21241149 DOI: 10.1063/1.3519814] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We have recently proposed a measure of the thermal stability of a protein: the water-entropy gain at 25 °C upon folding normalized by the number of residues, which is calculated using a hybrid of the angle-dependent integral equation theory combined with the multipolar water model and the morphometric approach. A protein with a larger value of the measure is thermally more stable. Here we extend the study to analyses on the effects of heme on the thermal stability of four cytochromes c (PA c(551), PH c(552), HT c(552), and AA c(555)) whose denaturation temperatures are considerably different from one another despite that they share significantly high sequence homology and similar three-dimensional folds. The major conclusions are as follows. For all the four cytochromes c, the thermal stability is largely enhanced by the heme binding in terms of the water entropy. For the holo states, the measure is the largest for AA c(555). However, AA c(555) has the lowest packing efficiency of heme and the apo polypeptide with hololike structure, which is unfavorable for the water entropy. The highest stability of AA c(555) is ascribed primarily to the highest efficiency of side-chain packing of the apo polypeptide itself. We argue for all the four cytochromes c that due to covalent heme linkages, the number of accessible conformations of the denatured state is decreased by the steric hindrance of heme, and the conformational-entropy loss upon folding becomes smaller, leading to an enhancement of the thermal stability. As for the apo state modeled as the native structure whose heme is removed, AA c(555) has a much larger value of the measure than the other three. Overall, the theoretical results are quite consistent with the experimental observations (e.g., at 25 °C the α-helix content of the apo state of AA c(555) is almost equal to that of the holo state while almost all helices are collapsed in the apo states of PA c(551), PH c(552), and HT c(552)).
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Affiliation(s)
- Koji Oda
- Taisho Pharmaceutical Co., Ltd., Yoshino-cho, Kita-ku, Saitama 331-9530, Japan
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Yoshidome T, Ito Y, Ikeguchi M, Kinoshita M. Rotation Mechanism of F1-ATPase: Crucial Importance of the Water Entropy Effect. J Am Chem Soc 2011; 133:4030-9. [PMID: 21348521 DOI: 10.1021/ja109594y] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Takashi Yoshidome
- Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan
| | - Yuko Ito
- Graduate School of Nanobioscience, Yokohama City University, 1-7-29, Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
| | - Mitsunori Ikeguchi
- Graduate School of Nanobioscience, Yokohama City University, 1-7-29, Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
| | - Masahiro Kinoshita
- Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan
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Oshima H, Yasuda S, Yoshidome T, Ikeguchi M, Kinoshita M. Crucial importance of the water-entropy effect in predicting hot spots in protein–protein complexes. Phys Chem Chem Phys 2011; 13:16236-46. [DOI: 10.1039/c1cp21597c] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
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Amano KI, Yoshidome T, Iwaki M, Suzuki M, Kinoshita M. Entropic potential field formed for a linear-motor protein near a filament: Statistical-mechanical analyses using simple models. J Chem Phys 2010; 133:045103. [PMID: 20687691 DOI: 10.1063/1.3462279] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We report a new progress in elucidating the mechanism of the unidirectional movement of a linear-motor protein (e.g., myosin) along a filament (e.g., F-actin). The basic concept emphasized here is that a potential field is entropically formed for the protein on the filament immersed in solvent due to the effect of the translational displacement of solvent molecules. The entropic potential field is strongly dependent on geometric features of the protein and the filament, their overall shapes as well as details of the polyatomic structures. The features and the corresponding field are judiciously adjusted by the binding of adenosine triphosphate (ATP) to the protein, hydrolysis of ATP into adenosine diphosphate (ADP)+Pi, and release of Pi and ADP. As the first step, we propose the following physical picture: The potential field formed along the filament for the protein without the binding of ATP or ADP+Pi to it is largely different from that for the protein with the binding, and the directed movement is realized by repeated switches from one of the fields to the other. To illustrate the picture, we analyze the spatial distribution of the entropic potential between a large solute and a large body using the three-dimensional integral equation theory. The solute is modeled as a large hard sphere. Two model filaments are considered as the body: model 1 is a set of one-dimensionally connected large hard spheres and model 2 is a double helical structure formed by two sets of connected large hard spheres. The solute and the filament are immersed in small hard spheres forming the solvent. The major findings are as follows. The solute is strongly confined within a narrow space in contact with the filament. Within the space there are locations with sharply deep local potential minima along the filament, and the distance between two adjacent locations is equal to the diameter of the large spheres constituting the filament. The potential minima form a ringlike domain in model 1 while they form a pointlike one in model 2. We then examine the effects of geometric features of the solute on the amplitudes and asymmetry of the entropic potential field acting on the solute along the filament. A large aspherical solute with a cleft near the solute-filament interface, which mimics the myosin motor domain, is considered in the examination. Thus, the two fields in our physical picture described above are qualitatively reproduced. The factors to be taken into account in further studies are also discussed.
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Affiliation(s)
- Ken-Ichi Amano
- Graduate School of Energy Science, Kyoto University, Uji, Kyoto 611-0011, Japan
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Oshima H, Yoshidome T, Amano KI, Kinoshita M. A theoretical analysis on characteristics of protein structures induced by cold denaturation. J Chem Phys 2010; 131:205102. [PMID: 19947708 DOI: 10.1063/1.3265985] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Yeast frataxin is a protein exhibiting cold denaturation at an exceptionally high temperature (280 K). We show that the microscopic mechanism of cold denaturation, which has recently been suggested by us [Yoshidome and Kinoshita, Phys. Rev. E 79, 030905(R) (2009)], is also applicable to yeast frataxin. The hybrid of the angle-dependent integral equation theory combined with the multipolar water model and the morphometric approach is employed for calculating hydration thermodynamic quantities of the protein with a prescribed structure. In order to investigate the characteristics of the cold-denatured structures of yeast frataxin, we consider the entropy change upon denaturation comprising the loss of the water entropy and the gain in the protein conformational entropy. The minimum and maximum values of the conformational-entropy gain (i.e., the range within which the exact value lies) are estimated via two routes. The range of the water-entropy loss is then determined from the entropy change experimentally obtained [Pastore et al., J. Am. Chem. Soc. 129, 5374 (2007)]. We calculate the water-entropy loss upon the transition from the native structure to a variety of unfolded structures. We then select the unfolded structures for which the water-entropy loss falls within the determined range. The selection is performed at cold and heat denaturation temperatures of yeast frataxin. The structures characterizing cold and heat denaturations are thus obtained. It is found that the average values of the radius of gyration, excluded volume, and water-accessible surface area for the cold-denatured structures are almost the same as those for the heat-denatured ones. We theoretically estimate the cold denaturation temperature of yeast frataxin from the experimental data for the enthalpy, entropy, and heat-capacity changes upon denaturation. The finding is that the temperature is considerably higher than 273 K. These results are in qualitatively good accord with the experimental observations.
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Affiliation(s)
- Hiraku Oshima
- Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan.
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Yasuda S, Yoshidome T, Oshima H, Kodama R, Harano Y, Kinoshita M. Effects of side-chain packing on the formation of secondary structures in protein folding. J Chem Phys 2010; 132:065105. [PMID: 20151761 DOI: 10.1063/1.3319509] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Satoshi Yasuda
- Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan
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Abstract
The hydrophobic and hydrophilic hydrations are analyzed with the emphasis on the sign of the heat capacity of hydration (HCH). The angle-dependent integral equation theory combined with a multipolar water model is employed in the analysis. The hydration entropy (HE) is decomposed into the translational and orientational parts. It is found that the orientational part governs the temperature dependence of the HE. The orientational part is further decomposed into the solute-water pair correlation component (component 1) and the water reorganization component (component 2). For hydrophilic solutes, components 1 and 2 are negative and positive, respectively. As the temperature becomes higher, component 1 increases while component 2 decreases: They make positive and negative contributions to the HCH, respectively. The strong solute-water electrostatic attractive interactions induce the distortion of water structure near the solute and the break of hydrogen bonds. As the temperature increases, the effect of the attractive interactions becomes smaller and the distortion of water structure is reduced (i.e., more hydrogen bonds are recovered with increasing temperature). The latter effect dominates, leading to negative HCH. During the heat addition the formation of hydrogen bonds, which accompanies heat generation, occurs near the solute. Consequently, the addition of the same amount of heat leads to a larger increase in the thermal energy (or equivalently, in the temperature) than in the case of pure water. The hydrophobic hydration, which is opposite to the hydrophilic hydration in many respects, is also discussed in detail.
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Affiliation(s)
- Masahiro Kinoshita
- Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan.
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Affiliation(s)
- Takashi Yoshidome
- Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan
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Yoshidome T, Kinoshita M. Hydrophobicity at low temperatures and cold denaturation of a protein. Phys Rev E Stat Nonlin Soft Matter Phys 2009; 79:030905. [PMID: 19391894 DOI: 10.1103/physreve.79.030905] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2008] [Indexed: 05/27/2023]
Abstract
We elucidate the microscopic mechanism of the weakening of the hydrophobicity at low temperatures by investigating cold denaturation of a protein. We employ an elaborate statistical-mechanical theory combined with a realistic water model. At low temperatures, the ordered structure with enhanced hydrogen bonds of water molecules is formed near nonpolar groups, leading to entropic loss and energy gain which are both quite large. However, they are canceled out and make no contribution to the free-energy change. We argue that a different factor, which is responsible for the weakening of the hydrophobicity at low temperatures, induces cold denaturation.
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Affiliation(s)
- Takashi Yoshidome
- Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan
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Yoshidome T, Harano Y, Kinoshita M. Pressure effects on structures formed by entropically driven self-assembly: illustration for denaturation of proteins. Phys Rev E Stat Nonlin Soft Matter Phys 2009; 79:011912. [PMID: 19257074 DOI: 10.1103/physreve.79.011912] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2008] [Indexed: 05/27/2023]
Abstract
We propose a general framework of pressure effects on the structures formed by the self-assembly of solute molecules immersed in solvent. The integral equation theory combined with the morphometric approach is employed for a hard-body model system. Our picture is that protein folding and ordered association of proteins are driven by the solvent entropy: At low pressures, the structures almost minimizing the excluded volume (EV) generated for solvent particles are stabilized. Such structures appear to be even more stabilized at high pressures. However, it is experimentally known that the native structure of a protein is unfolded, and ordered aggregates such as amyloid fibrils and actin filaments are dissociated by applying high pressures. This initially puzzling result can also be elucidated in terms of the solvent entropy. A clue to the basic mechanism is in the phenomenon that, when a large hard-sphere solute is immersed in small hard spheres forming the solvent, the small hard spheres are enriched near the solute and this enrichment becomes greater as the pressure increases. We argue that "attraction" is entropically provided between the solute surface and solvent particles, and the attraction becomes higher with rising pressure. Due to this effect, at high pressures, the structures possessing the largest possible solvent-accessible surface area together with sufficiently small EV become more stable in terms of the solvent entropy. To illustrate this concept, we perform an analysis of pressure denaturation of three different proteins. It is shown that only the structures that have the characteristics described above exhibit interesting behavior. They first become more destabilized relative to the native structure as the pressure increases, but beyond a threshold pressure the relative instability begins to decrease and they eventually become more stable than the native structure.
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Affiliation(s)
- Takashi Yoshidome
- Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan
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Yoshidome T, Kinoshita M, Hirota S, Baden N, Terazima M. Thermodynamics of apoplastocyanin folding: Comparison between experimental and theoretical results. J Chem Phys 2008; 128:225104. [PMID: 18554061 DOI: 10.1063/1.2929836] [Citation(s) in RCA: 77] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Takashi Yoshidome
- Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan
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Yoshidome T, Odagaki T, Yoshimori A. Free-energy landscape for a tagged particle in a dense hard-sphere fluid. Phys Rev E Stat Nonlin Soft Matter Phys 2008; 77:061503. [PMID: 18643268 DOI: 10.1103/physreve.77.061503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2007] [Indexed: 05/26/2023]
Abstract
Exploiting the thermodynamic potential functional provided by density functional theory, we determine analytically the free-energy landscape (FEL) in a hard-sphere fluid. The FEL is represented in the three-dimensional coordinate space of the tagged particle. We also analyze the distribution of the free-energy barrier between adjacent basins and show that the most provable value and the average of the free-energy barrier are increasing functions of the density. Since the size of the cooperatively rearranging region (CRR) is also increased as the density is raised [Yoshidome, Phys. Rev. E 76, 021506 (2007)], the present result is consistent with the Adam-Gibbs theory in which the increase of the activation energy is due to the increase of the size of the CRR.
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Yoshidome T, Yoshimori A, Odagaki T. Free energy landscape and cooperatively rearranging region in a hard sphere glass. Phys Rev E Stat Nonlin Soft Matter Phys 2007; 76:021506. [PMID: 17930043 DOI: 10.1103/physreve.76.021506] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2007] [Indexed: 05/25/2023]
Abstract
Exploiting the density functional theory, we calculate the free energy landscape (FEL) of the hard sphere glass in three dimensions. From the FEL, we estimate the number of the particles in the cooperatively rearranging region (CRR). We find that the density dependence of the number of the particles in the CRR is expressed as a power law function of the density. Analyzing the relaxation process in the CRR, we also find that the string motion is the elementary process for the structural relaxation, which leads to the natural definition of the simultaneously rearranging region as the particles displaced in the string motion.
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