1
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Koga N, Tatsumi-Koga R. Inventing Novel Protein Folds. J Mol Biol 2024; 436:168791. [PMID: 39260686 DOI: 10.1016/j.jmb.2024.168791] [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: 04/02/2024] [Revised: 09/04/2024] [Accepted: 09/05/2024] [Indexed: 09/13/2024]
Abstract
The vastness of unexplored protein fold universe remains a significant question. Through systematic de novo design of proteins with novel αβ-folds, we demonstrated that nature has only explored a tiny portion of the possible folds. Numerous possible protein folds are still untouched by nature. This review outlines this study and discusses the prospects for design of functional proteins with novel folds.
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Affiliation(s)
- Nobuyasu Koga
- Laboratory for Protein Design, Institute for Protein Research (IPR), Osaka University, Suita, Osaka 565-0871, Japan; Protein Design Group, Exploratory Research Center on Life and Living Systems (ExCELLS), National Institutes of Natural Sciences, Okazaki, Aichi 444-8585, Japan.
| | - Rie Tatsumi-Koga
- Laboratory for Protein Design, Institute for Protein Research (IPR), Osaka University, Suita, Osaka 565-0871, Japan
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2
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Qu Z, Xu L, Jiang F, Liu Y, Zhang WB. Folds from fold: Exploring topological isoforms of a single-domain protein. Proc Natl Acad Sci U S A 2024; 121:e2407355121. [PMID: 39405345 PMCID: PMC11513978 DOI: 10.1073/pnas.2407355121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2024] [Accepted: 09/06/2024] [Indexed: 10/30/2024] Open
Abstract
Expanding the protein fold space beyond linear chains is of fundamental significance, yet remains largely unexplored. Herein, we report the creation of seven topological isoforms (i.e., linear, cyclic, knot, lasso, pseudorotaxane, and catenane) from a single protein fold precursor by rewiring the connectivity of secondary structure elements of the SpyTag-SpyCatcher complex and mutating the reactive residue on SpyTag to abolish the isopeptide bonding. These topological isoforms can be directly expressed in cells. Their topologies were confirmed by combined techniques of proteolytic digestion, fluorescence correlation spectroscopy (FCS), size-exclusion chromatography (SEC), and topological transformation. To study the effects of topology on their structures and properties, their biophysical properties were characterized by differential scanning calorimetry (DSC), heteronuclear single quantum coherence nuclear magnetic resonance spectroscopy (HSQC-NMR), and circular dichroism (CD) spectroscopy. Molecular dynamics (MD) simulations were further performed to reveal the atomic details of structural changes upon unfolding. Both experimental and simulation results suggest that they share a similar, well-folded hydrophobic core but exhibit distinct folding/unfolding dynamic behaviors. These results shed light onto the folding landscape of topological isoforms derived from the same protein fold. As a model system, this work improves our understanding of protein structure and dynamics beyond linear chains and suggests that protein folds are highly amenable to topological variation.
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Affiliation(s)
- Zhiyu Qu
- Beijing National Laboratory for Molecular Sciences, Department of Polymer Science and Engineering, College of Chemistry and Molecular Engineering, Peking University, Beijing100871, People’s Republic of China
- Key Laboratory of Polymer Chemistry & Physics of Ministry of Education, Center for Soft Matter Science and Engineering, Peking University, Beijing100871, People’s Republic of China
| | - Lianjie Xu
- Beijing National Laboratory for Molecular Sciences, Department of Polymer Science and Engineering, College of Chemistry and Molecular Engineering, Peking University, Beijing100871, People’s Republic of China
- Key Laboratory of Polymer Chemistry & Physics of Ministry of Education, Center for Soft Matter Science and Engineering, Peking University, Beijing100871, People’s Republic of China
| | - Fengyi Jiang
- Beijing National Laboratory for Molecular Sciences, Department of Polymer Science and Engineering, College of Chemistry and Molecular Engineering, Peking University, Beijing100871, People’s Republic of China
- Key Laboratory of Polymer Chemistry & Physics of Ministry of Education, Center for Soft Matter Science and Engineering, Peking University, Beijing100871, People’s Republic of China
| | - Yuan Liu
- Beijing National Laboratory for Molecular Sciences, Department of Polymer Science and Engineering, College of Chemistry and Molecular Engineering, Peking University, Beijing100871, People’s Republic of China
| | - Wen-Bin Zhang
- Beijing National Laboratory for Molecular Sciences, Department of Polymer Science and Engineering, College of Chemistry and Molecular Engineering, Peking University, Beijing100871, People’s Republic of China
- Key Laboratory of Polymer Chemistry & Physics of Ministry of Education, Center for Soft Matter Science and Engineering, Peking University, Beijing100871, People’s Republic of China
- Artificial Intelligence for Science-Preferred Program, Shenzhen Graduate School, Peking University, Shenzhen518055, People’s Republic of China
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3
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Murata H, Toko K, Chikenji G. Protein superfolds are characterised as frustration-free topologies: A case study of pure parallel β-sheet topologies. PLoS Comput Biol 2024; 20:e1012282. [PMID: 39110764 PMCID: PMC11333010 DOI: 10.1371/journal.pcbi.1012282] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2023] [Revised: 08/19/2024] [Accepted: 06/26/2024] [Indexed: 08/21/2024] Open
Abstract
A protein superfold is a type of protein fold that is observed in at least three distinct, non-homologous protein families. Structural classification studies have revealed a limited number of prevalent superfolds alongside several infrequent occurring folds, and in α/β type superfolds, the C-terminal β-strand tends to favor the edge of the β-sheet, while the N-terminal β-strand is often found in the middle. The reasons behind these observations, whether they are due to evolutionary sampling bias or physical interactions, remain unclear. This article offers a physics-based explanation for these observations, specifically for pure parallel β-sheet topologies. Our investigation is grounded in several established structural rules that are based on physical interactions. We have identified "frustration-free topologies" which are topologies that can satisfy all the rules simultaneously. In contrast, topologies that cannot are termed "frustrated topologies." Our findings reveal that frustration-free topologies represent only a fraction of all theoretically possible patterns, these topologies strongly favor positioning the C-terminal β-strand at the edge of the β-sheet and the N-terminal β-strand in the middle, and there is significant overlap between frustration-free topologies and superfolds. We also used a lattice protein model to thoroughly investigate sequence-structure relationships. Our results show that frustration-free structures are highly designable, while frustrated structures are poorly designable. These findings suggest that superfolds are highly designable due to their lack of frustration, and the preference for positioning C-terminal β-strands at the edge of the β-sheet is a direct result of frustration-free topologies. These insights not only enhance our understanding of sequence-structure relationships but also have significant implications for de novo protein design.
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Affiliation(s)
- Hiroto Murata
- Department of Applied Physics, Nagoya University, Nagoya, Aichi, Japan
| | - Kazuma Toko
- Department of Applied Physics, Nagoya University, Nagoya, Aichi, Japan
| | - George Chikenji
- Department of Applied Physics, Nagoya University, Nagoya, Aichi, Japan
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4
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Gaschignard G, Millet M, Bruley A, Benzerara K, Dezi M, Skouri-Panet F, Duprat E, Callebaut I. AlphaFold2-guided description of CoBaHMA, a novel family of bacterial domains within the heavy-metal-associated superfamily. Proteins 2024; 92:776-794. [PMID: 38258321 DOI: 10.1002/prot.26668] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2023] [Revised: 12/22/2023] [Accepted: 01/01/2024] [Indexed: 01/24/2024]
Abstract
Three-dimensional (3D) structure information, now available at the proteome scale, may facilitate the detection of remote evolutionary relationships in protein superfamilies. Here, we illustrate this with the identification of a novel family of protein domains related to the ferredoxin-like superfold, by combining (i) transitive sequence similarity searches, (ii) clustering approaches, and (iii) the use of AlphaFold2 3D structure models. Domains of this family were initially identified in relation with the intracellular biomineralization of calcium carbonates by Cyanobacteria. They are part of the large heavy-metal-associated (HMA) superfamily, departing from the latter by specific sequence and structural features. In particular, most of them share conserved basic amino acids (hence their name CoBaHMA for Conserved Basic residues HMA), forming a positively charged surface, which is likely to interact with anionic partners. CoBaHMA domains are found in diverse modular organizations in bacteria, existing in the form of monodomain proteins or as part of larger proteins, some of which are membrane proteins involved in transport or lipid metabolism. This suggests that the CoBaHMA domains may exert a regulatory function, involving interactions with anionic lipids. This hypothesis might have a particular resonance in the context of the compartmentalization observed for cyanobacterial intracellular calcium carbonates.
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Affiliation(s)
- Geoffroy Gaschignard
- Sorbonne Université, Muséum National d'Histoire Naturelle, UMR CNRS 7590, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, IMPMC, Paris, France
| | - Maxime Millet
- Sorbonne Université, Muséum National d'Histoire Naturelle, UMR CNRS 7590, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, IMPMC, Paris, France
| | - Apolline Bruley
- Sorbonne Université, Muséum National d'Histoire Naturelle, UMR CNRS 7590, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, IMPMC, Paris, France
| | - Karim Benzerara
- Sorbonne Université, Muséum National d'Histoire Naturelle, UMR CNRS 7590, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, IMPMC, Paris, France
| | - Manuela Dezi
- Sorbonne Université, Muséum National d'Histoire Naturelle, UMR CNRS 7590, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, IMPMC, Paris, France
| | - Feriel Skouri-Panet
- Sorbonne Université, Muséum National d'Histoire Naturelle, UMR CNRS 7590, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, IMPMC, Paris, France
| | - Elodie Duprat
- Sorbonne Université, Muséum National d'Histoire Naturelle, UMR CNRS 7590, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, IMPMC, Paris, France
| | - Isabelle Callebaut
- Sorbonne Université, Muséum National d'Histoire Naturelle, UMR CNRS 7590, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, IMPMC, Paris, France
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5
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Minami S, Kobayashi N, Sugiki T, Nagashima T, Fujiwara T, Tatsumi-Koga R, Chikenji G, Koga N. Exploration of novel αβ-protein folds through de novo design. Nat Struct Mol Biol 2023; 30:1132-1140. [PMID: 37400653 PMCID: PMC10442233 DOI: 10.1038/s41594-023-01029-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2021] [Accepted: 05/30/2023] [Indexed: 07/05/2023]
Abstract
A fundamental question in protein evolution is whether nature has exhaustively sampled nearly all possible protein folds throughout evolution, or whether a large fraction of the possible folds remains unexplored. To address this question, we defined a set of rules for β-sheet topology to predict novel αβ-folds and carried out a systematic de novo protein design exploration of the novel αβ-folds predicted by the rules. The designs for all eight of the predicted novel αβ-folds with a four-stranded β-sheet, including a knot-forming one, folded into structures close to the design models. Further, the rules predicted more than 10,000 novel αβ-folds with five- to eight-stranded β-sheets; this number far exceeds the number of αβ-folds observed in nature so far. This result suggests that a vast number of αβ-folds are possible, but have not emerged or have become extinct due to evolutionary bias.
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Affiliation(s)
- Shintaro Minami
- Protein Design Group, Exploratory Research Center on Life and Living Systems (ExCELLS), National Institutes of Natural Sciences (NINS), Okazaki, Japan
| | - Naohiro Kobayashi
- Institute for Protein Research (IPR), Osaka University, Osaka, Japan
- RIKEN Center for Biosystems Dynamics Research, RIKEN, Yokohama, Japan
| | - Toshihiko Sugiki
- Institute for Protein Research (IPR), Osaka University, Osaka, Japan
| | - Toshio Nagashima
- RIKEN Center for Biosystems Dynamics Research, RIKEN, Yokohama, Japan
| | | | - Rie Tatsumi-Koga
- Protein Design Group, Exploratory Research Center on Life and Living Systems (ExCELLS), National Institutes of Natural Sciences (NINS), Okazaki, Japan
| | - George Chikenji
- Department of Applied Physics, Graduate School of Engineering, Nagoya University, Nagoya, Japan
| | - Nobuyasu Koga
- Protein Design Group, Exploratory Research Center on Life and Living Systems (ExCELLS), National Institutes of Natural Sciences (NINS), Okazaki, Japan.
- SOKENDAI, The Graduate University for Advanced Studies, Hayama, Japan.
- Research Center of Integrative Molecular Systems, Institute for Molecular Science (IMS), National Institutes of Natural Sciences (NINS), Okazaki, Japan.
- Laboratory for Protein Design, Institute for Protein Research (IPR), Osaka University, Osaka, Japan.
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6
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Nishina T, Nakajima M, Sasai M, Chikenji G. The Structural Rule Distinguishing a Superfold: A Case Study of Ferredoxin Fold and the Reverse Ferredoxin Fold. Molecules 2022; 27:3547. [PMID: 35684484 PMCID: PMC9181952 DOI: 10.3390/molecules27113547] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Revised: 05/24/2022] [Accepted: 05/28/2022] [Indexed: 01/27/2023] Open
Abstract
Superfolds are folds commonly observed among evolutionarily unrelated multiple superfamilies of proteins. Since discovering superfolds almost two decades ago, structural rules distinguishing superfolds from the other ordinary folds have been explored but remained elusive. Here, we analyzed a typical superfold, the ferredoxin fold, and the fold which reverses the N to C terminus direction from the ferredoxin fold as a case study to find the rule to distinguish superfolds from the other folds. Though all the known structural characteristics for superfolds apply to both the ferredoxin fold and the reverse ferredoxin fold, the reverse fold has been found only in a single superfamily. The database analyses in the present study revealed the structural preferences of αβ- and βα-units; the preferences separate two α-helices in the ferredoxin fold, preventing their collision and stabilizing the fold. In contrast, in the reverse ferredoxin fold, the preferences bring two helices near each other, inducing structural conflict. The Rosetta folding simulations suggested that the ferredoxin fold is physically much more realizable than the reverse ferredoxin fold. Therefore, we propose that minimal structural conflict or minimal frustration among secondary structures is the rule to distinguish a superfold from ordinary folds. Intriguingly, the database analyses revealed that a most stringent structural rule in proteins, the right-handedness of the βαβ-unit, is broken in a set of structures to prevent the frustration, suggesting the proposed rule of minimum frustration among secondary structural units is comparably strong as the right-handedness rule of the βαβ-unit.
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Affiliation(s)
- Takumi Nishina
- Department of Applied Physics, Nagoya University, Nagoya 464-8601, Japan; (T.N.); (M.N.)
| | - Megumi Nakajima
- Department of Applied Physics, Nagoya University, Nagoya 464-8601, Japan; (T.N.); (M.N.)
| | - Masaki Sasai
- Department of Applied Physics, Nagoya University, Nagoya 464-8601, Japan; (T.N.); (M.N.)
- Department of Complex Systems Science, Nagoya University, Nagoya 464-8601, Japan
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8501, Japan
| | - George Chikenji
- Department of Applied Physics, Nagoya University, Nagoya 464-8601, Japan; (T.N.); (M.N.)
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7
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Liang S, Li Z, Zhan J, Zhou Y. De novo protein design by an energy function based on series expansion in distance and orientation dependence. Bioinformatics 2021; 38:86-93. [PMID: 34406339 DOI: 10.1093/bioinformatics/btab598] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2021] [Revised: 08/11/2021] [Accepted: 08/16/2021] [Indexed: 02/03/2023] Open
Abstract
MOTIVATION Despite many successes, de novo protein design is not yet a solved problem as its success rate remains low. The low success rate is largely because we do not yet have an accurate energy function for describing the solvent-mediated interaction between amino acid residues in a protein chain. Previous studies showed that an energy function based on series expansions with its parameters optimized for side-chain and loop conformations can lead to one of the most accurate methods for side chain (OSCAR) and loop prediction (LEAP). Following the same strategy, we developed an energy function based on series expansions with the parameters optimized in four separate stages (recovering single-residue types without and with orientation dependence, selecting loop decoys and maintaining the composition of amino acids). We tested the energy function for de novo design by using Monte Carlo simulated annealing. RESULTS The method for protein design (OSCAR-Design) is found to be as accurate as OSCAR and LEAP for side-chain and loop prediction, respectively. In de novo design, it can recover native residue types ranging from 38% to 43% depending on test sets, conserve hydrophobic/hydrophilic residues at ∼75%, and yield the overall similarity in amino acid compositions at more than 90%. These performance measures are all statistically significantly better than several protein design programs compared. Moreover, the largest hydrophobic patch areas in designed proteins are near or smaller than those in native proteins. Thus, an energy function based on series expansion can be made useful for protein design. AVAILABILITY AND IMPLEMENTATION The Linux executable version is freely available for academic users at http://zhouyq-lab.szbl.ac.cn/resources/.
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Affiliation(s)
- Shide Liang
- Department of R & D, Bio-Thera Solutions, Guangzhou 510530, China
| | - Zhixiu Li
- Institute of Health and Biomedical Innovation, Queensland University of Technology at Translational Research Institute, Woolloongabba, QLD 3001, Australia
| | - Jian Zhan
- Institute for Glycomics and School of Information and Communication Technology, Griffith University, Gold Coast Campus, Southport, QLD 4222, Australia.,Institute for Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, China
| | - Yaoqi Zhou
- Institute for Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, China.,Peking University Shenzhen Graduate School, Shenzhen 518055, China
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8
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Konagurthu AS, Subramanian R, Allison L, Abramson D, Stuckey PJ, Garcia de la Banda M, Lesk AM. Universal Architectural Concepts Underlying Protein Folding Patterns. Front Mol Biosci 2021; 7:612920. [PMID: 33996891 PMCID: PMC8120156 DOI: 10.3389/fmolb.2020.612920] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2020] [Accepted: 12/16/2020] [Indexed: 11/17/2022] Open
Abstract
What is the architectural “basis set” of the observed universe of protein structures? Using information-theoretic inference, we answer this question with a dictionary of 1,493 substructures—called concepts—typically at a subdomain level, based on an unbiased subset of known protein structures. Each concept represents a topologically conserved assembly of helices and strands that make contact. Any protein structure can be dissected into instances of concepts from this dictionary. We dissected the Protein Data Bank and completely inventoried all the concept instances. This yields many insights, including correlations between concepts and catalytic activities or binding sites, useful for rational drug design; local amino-acid sequence–structure correlations, useful for ab initio structure prediction methods; and information supporting the recognition and exploration of evolutionary relationships, useful for structural studies. An interactive site, Proçodic, at http://lcb.infotech.monash.edu.au/prosodic (click), provides access to and navigation of the entire dictionary of concepts and their usages, and all associated information. This report is part of a continuing programme with the goal of elucidating fundamental principles of protein architecture, in the spirit of the work of Cyrus Chothia.
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Affiliation(s)
- Arun S Konagurthu
- Department of Data Science and Artificial Intelligence, Faculty of Information Technology, Monash University, Clayton, VIC, Australia
| | - Ramanan Subramanian
- Department of Data Science and Artificial Intelligence, Faculty of Information Technology, Monash University, Clayton, VIC, Australia
| | - Lloyd Allison
- Department of Data Science and Artificial Intelligence, Faculty of Information Technology, Monash University, Clayton, VIC, Australia
| | - David Abramson
- Research Computing Center, University of Queensland, Brisbane, QLD, Australia
| | - Peter J Stuckey
- Department of Data Science and Artificial Intelligence, Faculty of Information Technology, Monash University, Clayton, VIC, Australia.,School of Computing and Information Systems, University of Melbourne, Melbourne, VIC, Australia
| | - Maria Garcia de la Banda
- Department of Data Science and Artificial Intelligence, Faculty of Information Technology, Monash University, Clayton, VIC, Australia
| | - Arthur M Lesk
- Department of Biochemistry and Molecular Biology, Pennsylvania State University, University Park, PA, United States.,MRC Laboratory of Molecular Biology, Cambridge, United Kingdom
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9
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Yang N, Fan X, Yu W, Huang Y, Yu C, Konno K, Dong X. Effects of microbial transglutaminase on gel formation of frozen-stored longtail southern cod (Patagonotothen ramsayi) mince. Lebensm Wiss Technol 2020. [DOI: 10.1016/j.lwt.2020.109444] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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10
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11
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Minami S, Chikenji G, Ota M. Rules for connectivity of secondary structure elements in protein: Two-layer αβ sandwiches. Protein Sci 2017; 26:2257-2267. [PMID: 28856751 DOI: 10.1002/pro.3285] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2017] [Revised: 08/21/2017] [Accepted: 08/26/2017] [Indexed: 11/09/2022]
Abstract
In protein structures, the fold is described according to the spatial arrangement of secondary structure elements (SSEs: α-helices and β-strands) and their connectivity. The connectivity or the pattern of links among SSEs is one of the most important factors for understanding the variety of protein folds. In this study, we introduced the connectivity strings that encode the connectivities by using the types, positions, and connections of SSEs, and computationally enumerated all the connectivities of two-layer αβ sandwiches. The calculated connectivities were compared with those in natural proteins determined using MICAN, a nonsequential structure comparison method. For 2α-4β, among 23,000 of all connectivities, only 48 were free from irregular connectivities such as loop crossing. Of these, only 20 were found in natural proteins and the superfamilies were biased toward certain types of connectivities. A similar disproportional distribution was confirmed for most of other spatial arrangements of SSEs in the two-layer αβ sandwiches. We found two connectivity rules that explain the bias well: the abundances of interlayer connecting loops that bridge SSEs in the distinct layers; and nonlocal β-strand pairs, two spatially adjacent β-strands located at discontinuous positions in the amino acid sequence. A two-dimensional plot of these two properties indicated that the two connectivity rules are not independent, which may be interpreted as a rule for the cooperativity of proteins.
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Affiliation(s)
- Shintaro Minami
- Department of Complex Systems Science, Graduate School of Informatics, Nagoya University, Nagoya, 464-8601, Japan
| | - George Chikenji
- Department of Computational Science and Engineering, Graduate School of Engineering, Nagoya University, Nagoya, 464-8601, Japan
| | - Motonori Ota
- Department of Complex Systems Science, Graduate School of Informatics, Nagoya University, Nagoya, 464-8601, Japan
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