1
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Kleeorin Y, Russ WP, Rivoire O, Ranganathan R. Undersampling and the inference of coevolution in proteins. Cell Syst 2023; 14:210-219.e7. [PMID: 36693377 PMCID: PMC10911952 DOI: 10.1016/j.cels.2022.12.013] [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: 03/30/2021] [Revised: 01/02/2022] [Accepted: 12/23/2022] [Indexed: 01/24/2023]
Abstract
Protein structure, function, and evolution depend on local and collective epistatic interactions between amino acids. A powerful approach to defining these interactions is to construct models of couplings between amino acids that reproduce the empirical statistics (frequencies and correlations) observed in sequences comprising a protein family. The top couplings are then interpreted. Here, we show that as currently implemented, this inference unequally represents epistatic interactions, a problem that fundamentally arises from limited sampling of sequences in the context of distinct scales at which epistasis occurs in proteins. We show that these issues explain the ability of current approaches to predict tertiary contacts between amino acids and the inability to obviously expose larger networks of functionally relevant, collectively evolving residues called sectors. This work provides a necessary foundation for more deeply understanding and improving evolution-based models of proteins.
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Affiliation(s)
- Yaakov Kleeorin
- Center for Physics of Evolving Systems, Department of Biochemistry & Molecular Biology, University of Chicago, Chicago, IL 60637, USA
| | - William P Russ
- Green Center for Systems Biology, University of Texas Southwestern Medical Center, Dallas, TX 75390, USA
| | - Olivier Rivoire
- Center for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS, INSERM, PSL Research University, 75005 Paris, France.
| | - Rama Ranganathan
- Center for Physics of Evolving Systems, Department of Biochemistry & Molecular Biology, University of Chicago, Chicago, IL 60637, USA; The Pritzker School for Molecular Engineering, University of Chicago, Chicago, IL 60637, USA.
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2
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Ó'Fágáin C. Protein Stability: Enhancement and Measurement. Methods Mol Biol 2023; 2699:369-419. [PMID: 37647007 DOI: 10.1007/978-1-0716-3362-5_18] [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] [Indexed: 09/01/2023]
Abstract
This chapter defines protein stability, emphasizes its importance, and surveys the field of protein stabilization, with summary reference to a selection of 2014-2021 publications. One can enhance stability, particularly by protein engineering strategies but also by chemical modification and by other means. General protocols are set out on how to measure a given protein's (i) kinetic thermal stability and (ii) oxidative stability and (iii) how to undertake chemical modification of a protein in solution.
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Affiliation(s)
- Ciarán Ó'Fágáin
- School of Biotechnology, Dublin City University, Dublin, Ireland.
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3
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A linear reciprocal relationship between robustness and plasticity in homeostatic biological networks. PLoS One 2023; 18:e0277181. [PMID: 36701362 PMCID: PMC9879506 DOI: 10.1371/journal.pone.0277181] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2022] [Accepted: 10/21/2022] [Indexed: 01/27/2023] Open
Abstract
In physics of living systems, a search for relationships of a few macroscopic variables that emerge from many microscopic elements is a central issue. We evolved gene regulatory networks so that the expression of core genes (partial system) is insensitive to environmental changes. Then, we found the expression levels of the remaining genes autonomously increase to provide a plastic (sensitive) response. A feedforward structure from the non-core to core genes evolved autonomously. Negative proportionality was observed between the average changes in core and non-core genes, reflecting reciprocity between the macroscopic robustness of homeostatic genes and plasticity of regulator genes. The proportion coefficient between those genes is represented by their number ratio, as in the "lever principle", whereas the decrease in the ratio results in a transition from perfect to partial adaptation, in which only a portion of the core genes exhibits robustness against environmental changes. This reciprocity between robustness and plasticity was satisfied throughout the evolutionary course, imposing an evolutionary constraint. This result suggests a simple macroscopic law for the adaptation characteristic in evolved complex biological networks.
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4
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McBride JM, Eckmann JP, Tlusty T. General Theory of Specific Binding: Insights from a Genetic-Mechano-Chemical Protein Model. Mol Biol Evol 2022; 39:msac217. [PMID: 36208205 PMCID: PMC9641994 DOI: 10.1093/molbev/msac217] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
Proteins need to selectively interact with specific targets among a multitude of similar molecules in the cell. However, despite a firm physical understanding of binding interactions, we lack a general theory of how proteins evolve high specificity. Here, we present such a model that combines chemistry, mechanics, and genetics and explains how their interplay governs the evolution of specific protein-ligand interactions. The model shows that there are many routes to achieving molecular discrimination-by varying degrees of flexibility and shape/chemistry complementarity-but the key ingredient is precision. Harder discrimination tasks require more collective and precise coaction of structure, forces, and movements. Proteins can achieve this through correlated mutations extending far from a binding site, which fine-tune the localized interaction with the ligand. Thus, the solution of more complicated tasks is enabled by increasing the protein size, and proteins become more evolvable and robust when they are larger than the bare minimum required for discrimination. The model makes testable, specific predictions about the role of flexibility and shape mismatch in discrimination, and how evolution can independently tune affinity and specificity. Thus, the proposed theory of specific binding addresses the natural question of "why are proteins so big?". A possible answer is that molecular discrimination is often a hard task best performed by adding more layers to the protein.
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Affiliation(s)
- John M McBride
- Center for Soft and Living Matter, Institute for Basic Science, Ulsan 44919, South Korea
| | - Jean-Pierre Eckmann
- Département de Physique Théorique and Section de Mathématiques, University of Geneva, Geneva, Switzerland
| | - Tsvi Tlusty
- Center for Soft and Living Matter, Institute for Basic Science, Ulsan 44919, South Korea
- Departments of Physics and Chemistry, Ulsan National Institute of Science and Technology, Ulsan 44919, South Korea
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5
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Extracting phylogenetic dimensions of coevolution reveals hidden functional signals. Sci Rep 2022; 12:820. [PMID: 35039514 PMCID: PMC8764114 DOI: 10.1038/s41598-021-04260-1] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2021] [Accepted: 12/17/2021] [Indexed: 11/08/2022] Open
Abstract
Despite the structural and functional information contained in the statistical coupling between pairs of residues in a protein, coevolution associated with function is often obscured by artifactual signals such as genetic drift, which shapes a protein's phylogenetic history and gives rise to concurrent variation between protein sequences that is not driven by selection for function. Here, we introduce a background model for phylogenetic contributions of statistical coupling that separates the coevolution signal due to inter-clade and intra-clade sequence comparisons and demonstrate that coevolution can be measured on multiple phylogenetic timescales within a single protein. Our method, nested coevolution (NC), can be applied as an extension to any coevolution metric. We use NC to demonstrate that poorly conserved residues can nonetheless have important roles in protein function. Moreover, NC improved the structural-contact predictions of several coevolution-based methods, particularly in subsampled alignments with fewer sequences. NC also lowered the noise in detecting functional sectors of collectively coevolving residues. Sectors of coevolving residues identified after application of NC were more spatially compact and phylogenetically distinct from the rest of the protein, and strongly enriched for mutations that disrupt protein activity. Thus, our conceptualization of the phylogenetic separation of coevolution provides the potential to further elucidate relationships among protein evolution, function, and genetic diseases.
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6
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Sesta L, Uguzzoni G, Fernandez-de-Cossio-Diaz J, Pagnani A. AMaLa: Analysis of Directed Evolution Experiments via Annealed Mutational Approximated Landscape. Int J Mol Sci 2021; 22:10908. [PMID: 34681569 PMCID: PMC8535593 DOI: 10.3390/ijms222010908] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2021] [Revised: 09/24/2021] [Accepted: 09/27/2021] [Indexed: 01/12/2023] Open
Abstract
We present Annealed Mutational approximated Landscape (AMaLa), a new method to infer fitness landscapes from Directed Evolution experiments sequencing data. Such experiments typically start from a single wild-type sequence, which undergoes Darwinian in vitro evolution via multiple rounds of mutation and selection for a target phenotype. In the last years, Directed Evolution is emerging as a powerful instrument to probe fitness landscapes under controlled experimental conditions and as a relevant testing ground to develop accurate statistical models and inference algorithms (thanks to high-throughput screening and sequencing). Fitness landscape modeling either uses the enrichment of variants abundances as input, thus requiring the observation of the same variants at different rounds or assuming the last sequenced round as being sampled from an equilibrium distribution. AMaLa aims at effectively leveraging the information encoded in the whole time evolution. To do so, while assuming statistical sampling independence between sequenced rounds, the possible trajectories in sequence space are gauged with a time-dependent statistical weight consisting of two contributions: (i) an energy term accounting for the selection process and (ii) a generalized Jukes-Cantor model for the purely mutational step. This simple scheme enables accurately describing the Directed Evolution dynamics and inferring a fitness landscape that correctly reproduces the measures of the phenotype under selection (e.g., antibiotic drug resistance), notably outperforming widely used inference strategies. In addition, we assess the reliability of AMaLa by showing how the inferred statistical model could be used to predict relevant structural properties of the wild-type sequence.
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Affiliation(s)
- Luca Sesta
- Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy; (L.S.); (G.U.); (A.P.)
| | - Guido Uguzzoni
- Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy; (L.S.); (G.U.); (A.P.)
| | - Jorge Fernandez-de-Cossio-Diaz
- Laboratory of Physics of the Ecole Normale Supérieure, CNRS UMR 8023 & PSL Research, Sorbonne Université, 24 rue Lhomond, 75005 Paris, France
- Center of Molecular Immunology, Systems Biology Department, Playa, Havana CP 11600, Cuba
| | - Andrea Pagnani
- Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy; (L.S.); (G.U.); (A.P.)
- Italian Institute for Genomic Medicine, IRCCS Candiolo, SP-142, I-10060 Candiolo, Italy
- INFN, Sezione di Torino, I-10125 Torino, Italy
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7
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Tang QY, Kaneko K. Dynamics-Evolution Correspondence in Protein Structures. PHYSICAL REVIEW LETTERS 2021; 127:098103. [PMID: 34506164 DOI: 10.1103/physrevlett.127.098103] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2021] [Accepted: 07/28/2021] [Indexed: 06/13/2023]
Abstract
The genotype-phenotype mapping of proteins is a fundamental question in structural biology. In this Letter, with the analysis of a large dataset of proteins from hundreds of protein families, we quantitatively demonstrate the correlations between the noise-induced protein dynamics and mutation-induced variations of native structures, indicating the dynamics-evolution correspondence of proteins. Based on the investigations of the linear responses of native proteins, the origin of such a correspondence is elucidated. It is essential that the noise- and mutation-induced deformations of the proteins are restricted on a common low-dimensional subspace, as confirmed from the data. These results suggest an evolutionary mechanism of the proteins gaining both dynamical flexibility and evolutionary structural variability.
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Affiliation(s)
- Qian-Yuan Tang
- Center for Complex Systems Biology, Universal Biology Institute, University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153-8902, Japan
- Lab for Neural Computation and Adaptation, RIKEN Center for Brain Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Kunihiko Kaneko
- Center for Complex Systems Biology, Universal Biology Institute, University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153-8902, Japan
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8
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Murugan A, Husain K, Rust MJ, Hepler C, Bass J, Pietsch JMJ, Swain PS, Jena SG, Toettcher JE, Chakraborty AK, Sprenger KG, Mora T, Walczak AM, Rivoire O, Wang S, Wood KB, Skanata A, Kussell E, Ranganathan R, Shih HY, Goldenfeld N. Roadmap on biology in time varying environments. Phys Biol 2021; 18:10.1088/1478-3975/abde8d. [PMID: 33477124 PMCID: PMC8652373 DOI: 10.1088/1478-3975/abde8d] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2020] [Accepted: 01/21/2021] [Indexed: 02/02/2023]
Abstract
Biological organisms experience constantly changing environments, from sudden changes in physiology brought about by feeding, to the regular rising and setting of the Sun, to ecological changes over evolutionary timescales. Living organisms have evolved to thrive in this changing world but the general principles by which organisms shape and are shaped by time varying environments remain elusive. Our understanding is particularly poor in the intermediate regime with no separation of timescales, where the environment changes on the same timescale as the physiological or evolutionary response. Experiments to systematically characterize the response to dynamic environments are challenging since such environments are inherently high dimensional. This roadmap deals with the unique role played by time varying environments in biological phenomena across scales, from physiology to evolution, seeking to emphasize the commonalities and the challenges faced in this emerging area of research.
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Affiliation(s)
- Arvind Murugan
- James Franck Institute, Department of Physics, University of Chicago, Chicago, IL 60637, United States of America
| | - Kabir Husain
- James Franck Institute, Department of Physics, University of Chicago, Chicago, IL 60637, United States of America
| | - Michael J Rust
- Department of Molecular Genetics and Cell Biology, University of Chicago, Chicago, IL 60637, United States of America
- Department of Physics, University of Chicago, Chicago, IL 60637, United States of America
| | - Chelsea Hepler
- Department of Medicine, Feinberg School of Medicine, Division of Endocrinology, Metabolism and Molecular Medicine, Northwestern University, Chicago, IL 60611, United States of America
| | - Joseph Bass
- Department of Medicine, Feinberg School of Medicine, Division of Endocrinology, Metabolism and Molecular Medicine, Northwestern University, Chicago, IL 60611, United States of America
| | - Julian M J Pietsch
- SynthSys: Centre for Synthetic and Systems Biology, School of Biological Sciences, University of Edinburgh, Edinburgh EH9 3BF, United Kingdom
| | - Peter S Swain
- SynthSys: Centre for Synthetic and Systems Biology, School of Biological Sciences, University of Edinburgh, Edinburgh EH9 3BF, United Kingdom
| | - Siddhartha G Jena
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544, United States of America
| | - Jared E Toettcher
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544, United States of America
| | - Arup K Chakraborty
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, United States of America
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States of America
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, United States of America
- Institute for Medical Engineering & Science, Massachusetts Institute of Technology, Cambridge, MA 02139, United States of America
- Ragon Institute of the Massachusetts General Hospital, Massachusetts Institute of Technology, and Harvard, Cambridge, MA 02139, United States of America
| | - Kayla G Sprenger
- Institute for Medical Engineering & Science, Massachusetts Institute of Technology, Cambridge, MA 02139, United States of America
- Ragon Institute of the Massachusetts General Hospital, Massachusetts Institute of Technology, and Harvard, Cambridge, MA 02139, United States of America
| | - T Mora
- Laboratoire de physique, Ecole normale supérieure, CNRS, PSL Research University, Paris, France
| | - A M Walczak
- Laboratoire de physique, Ecole normale supérieure, CNRS, PSL Research University, Paris, France
| | - O Rivoire
- Center for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS, INSERM, PSL Research University, Paris, France
| | - Shenshen Wang
- Department of Physics and Astronomy, University of California, Los Angeles, Los Angeles, CA 90095, United States of America
| | - Kevin B Wood
- Departments of Biophysics and Physics, University of Michigan, Ann Arbor, MI 48109-1055, United States of America
| | - Antun Skanata
- Center for Genomics and Systems Biology, New York University, 12 Waverly Place, Rm. 206, New York, NY 10003, United States of America
| | - Edo Kussell
- Center for Genomics and Systems Biology, New York University, 12 Waverly Place, Rm. 206, New York, NY 10003, United States of America
| | - Rama Ranganathan
- Center for Physics of Evolving Systems, Biochemistry & Molecular Biology, and the Pritzker School for Molecular Engineering, University of Chicago, Chicago IL 60637, United States of America
| | - Hong-Yan Shih
- Department of Physics, University of Illinois at Urbana-Champaign, Champaign, Illinois 61801, United States of America
- Institute of Physics, Academia Sinica, Taipei 11529, Taiwan
| | - Nigel Goldenfeld
- Department of Physics, University of Illinois at Urbana-Champaign, Champaign, Illinois 61801, United States of America
- Carl R Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Champaign, Illinois 61801, United States of America
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9
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Antelo GT, Vila AJ, Giedroc DP, Capdevila DA. Molecular Evolution of Transition Metal Bioavailability at the Host-Pathogen Interface. Trends Microbiol 2021; 29:441-457. [PMID: 32951986 PMCID: PMC7969482 DOI: 10.1016/j.tim.2020.08.001] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Revised: 08/01/2020] [Accepted: 08/19/2020] [Indexed: 12/21/2022]
Abstract
The molecular evolution of the adaptive response at the host-pathogen interface has been frequently referred to as an 'arms race' between the host and bacterial pathogens. The innate immune system employs multiple strategies to starve microbes of metals. Pathogens, in turn, develop successful strategies to maintain access to bioavailable metal ions under conditions of extreme restriction of transition metals, or nutritional immunity. However, the processes by which evolution repurposes or re-engineers host and pathogen proteins to perform or refine new functions have been explored only recently. Here we review the molecular evolution of several human metalloproteins charged with restricting bacterial access to transition metals. These include the transition metal-chelating S100 proteins, natural resistance-associated macrophage protein-1 (NRAMP-1), transferrin, lactoferrin, and heme-binding proteins. We examine their coevolution with bacterial transition metal acquisition systems, involving siderophores and membrane-spanning metal importers, and the biological specificity of allosteric transcriptional regulatory proteins tasked with maintaining bacterial metallostasis. We also discuss the evolution of metallo-β-lactamases; this illustrates how rapid antibiotic-mediated evolution of a zinc metalloenzyme obligatorily occurs in the context of host-imposed nutritional immunity.
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Affiliation(s)
- Giuliano T Antelo
- Fundación Instituto Leloir, Instituto de Investigaciones Bioquímicas de Buenos Aires (IIBBA-CONICET), C1405BWE Ciudad Autónoma de Buenos Aires, Buenos Aires, Argentina
| | - Alejandro J Vila
- Instituto de Biología Molecular y Celular de Rosario (IBR, CONICET-UNR), Ocampo and Esmeralda, S2002LRK Rosario, Argentina; Área Biofísica, Facultad de Ciencias Bioquímicas y Farmacéuticas, Universidad Nacional de Rosario, S2002LRK Rosario, Argentina
| | - David P Giedroc
- Department of Chemistry, Indiana University, Bloomington, IN 47405, USA; Department of Molecular and Cellular Biochemistry, Indiana University, Bloomington, IN 47405, USA.
| | - Daiana A Capdevila
- Fundación Instituto Leloir, Instituto de Investigaciones Bioquímicas de Buenos Aires (IIBBA-CONICET), C1405BWE Ciudad Autónoma de Buenos Aires, Buenos Aires, Argentina.
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10
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Abstract
Living systems evolve one mutation at a time, but a single mutation can alter the effect of subsequent mutations. The underlying mechanistic determinants of such epistasis are unclear. Here, we demonstrate that the physical dynamics of a biological system can generically constrain epistasis. We analyze models and experimental data on proteins and regulatory networks. In each, we find that if the long-time physical dynamics is dominated by a slow, collective mode, then the dimensionality of mutational effects is reduced. Consequently, epistatic coefficients for different combinations of mutations are no longer independent, even if individually strong. Such epistasis can be summarized as resulting from a global nonlinearity applied to an underlying linear trait, that is, as global epistasis. This constraint, in turn, reduces the ruggedness of the sequence-to-function map. By providing a generic mechanistic origin for experimentally observed global epistasis, our work suggests that slow collective physical modes can make biological systems evolvable.
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Affiliation(s)
- Kabir Husain
- Department of Physics, University of Chicago, Chicago, IL
| | - Arvind Murugan
- Department of Physics, University of Chicago, Chicago, IL
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11
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Sakata A, Kaneko K. Dimensional Reduction in Evolving Spin-Glass Model: Correlation of Phenotypic Responses to Environmental and Mutational Changes. PHYSICAL REVIEW LETTERS 2020; 124:218101. [PMID: 32530655 DOI: 10.1103/physrevlett.124.218101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2020] [Accepted: 05/05/2020] [Indexed: 06/11/2023]
Abstract
The evolution of high-dimensional phenotypes is investigated using a statistical physics model consisting of interacting spins, in which phenotypes, genotypes, and environments are represented by spin configurations, interaction matrices, and external fields, respectively. We found that phenotypic changes upon diverse environmental change and genetic variation are highly correlated across all spins, consistent with recent experimental observations of biological systems. The dimension reduction in phenotypic changes is shown to be a result of the evolution of the robustness to thermal noise, achieved at the replica symmetric phase.
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Affiliation(s)
- Ayaka Sakata
- Department of Statistical Inference & Mathematics, Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan
| | - Kunihiko Kaneko
- Center for Complex Systems Biology, Universal Biology Institute, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
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12
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Tang QY, Kaneko K. Long-range correlation in protein dynamics: Confirmation by structural data and normal mode analysis. PLoS Comput Biol 2020; 16:e1007670. [PMID: 32053592 PMCID: PMC7043781 DOI: 10.1371/journal.pcbi.1007670] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2019] [Revised: 02/26/2020] [Accepted: 01/21/2020] [Indexed: 11/18/2022] Open
Abstract
Proteins in cellular environments are highly susceptible. Local perturbations to any residue can be sensed by other spatially distal residues in the protein molecule, showing long-range correlations in the native dynamics of proteins. The long-range correlations of proteins contribute to many biological processes such as allostery, catalysis, and transportation. Revealing the structural origin of such long-range correlations is of great significance in understanding the design principle of biologically functional proteins. In this work, based on a large set of globular proteins determined by X-ray crystallography, by conducting normal mode analysis with the elastic network models, we demonstrate that such long-range correlations are encoded in the native topology of the proteins. To understand how native topology defines the structure and the dynamics of the proteins, we conduct scaling analysis on the size dependence of the slowest vibration mode, average path length, and modularity. Our results quantitatively describe how native proteins balance between order and disorder, showing both dense packing and fractal topology. It is suggested that the balance between stability and flexibility acts as an evolutionary constraint for proteins at different sizes. Overall, our result not only gives a new perspective bridging the protein structure and its dynamics but also reveals a universal principle in the evolution of proteins at all different sizes. The long-range correlated fluctuations are closely related to many biological processes of the proteins, such as catalysis, ligand binding, biomolecular recognition, and transportation. In this paper, we elucidate the structural origin of the long-range correlation and describe how native contact topology defines the slow-mode dynamics of the native proteins. Our result suggests an evolutionary constraint for proteins at different sizes, which may shed light on solving many biophysical problems such as structure prediction, multi-scale molecular simulations, and the design of molecular machines. Moreover, in statistical physics, as the long-range correlations are notable signs of the critical point, unveiling the origin of such criticality can extend our understanding of the organizing principle of a large variety of complex systems.
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Affiliation(s)
- Qian-Yuan Tang
- Center for Complex Systems Biology, Universal Biology Institute, University of Tokyo, Tokyo, Japan
- * E-mail:
| | - Kunihiko Kaneko
- Center for Complex Systems Biology, Universal Biology Institute, University of Tokyo, Tokyo, Japan
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13
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Rivoire O. Geometry and Flexibility of Optimal Catalysts in a Minimal Elastic Model. J Phys Chem B 2020; 124:807-813. [PMID: 31990545 DOI: 10.1021/acs.jpcb.0c00244] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We have general knowledge of the principles by which catalysts accelerate the rate of chemical reactions but no precise understanding of the geometrical and physical constraints to which their design is subject. To analyze these constraints, we introduce a minimal model of catalysis based on elastic networks where the implications of the geometry and flexibility of a catalyst can be studied systematically. The model demonstrates the relevance and limitations of the principle of transition-state stabilization: optimal catalysts are found to have a geometry complementary to the transition state but a degree of flexibility that nontrivially depends on the parameters of the reaction as well as on external parameters such as the concentrations of reactants and products. The results illustrate how simple physical models can provide valuable insights into the design of catalysts.
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Affiliation(s)
- Olivier Rivoire
- Center for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS, INSERM , PSL Research University , 75005 Paris , France
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