1
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McBride JM, Tlusty T. AI-Predicted Protein Deformation Encodes Energy Landscape Perturbation. PHYSICAL REVIEW LETTERS 2024; 133:098401. [PMID: 39270162 DOI: 10.1103/physrevlett.133.098401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2023] [Revised: 02/27/2024] [Accepted: 07/24/2024] [Indexed: 09/15/2024]
Abstract
AI algorithms have proven to be excellent predictors of protein structure, but whether and how much these algorithms can capture the underlying physics remains an open question. Here, we aim to test this question using the Alphafold2 (AF) algorithm: We use AF to predict the subtle structural deformation induced by single mutations, quantified by strain, and compare with experimental datasets of corresponding perturbations in folding free energy ΔΔG. Unexpectedly, we find that physical strain alone-without any additional data or computation-correlates almost as well with ΔΔG as state-of-the-art energy-based and machine-learning predictors. This indicates that the AF-predicted structures alone encode fine details about the energy landscape. In particular, the structures encode significant information on stability, enough to estimate (de-)stabilizing effects of mutations, thus paving the way for the development of novel, structure-based stability predictors for protein design and evolution.
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Affiliation(s)
- John M McBride
- Center for Algorithmic and Robotized Synthesis, Institute for Basic Science, Ulsan 44919, South Korea
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2
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Chalopin Y. GPCR Signaling: A Study of the Interplay Between Structure, Energy, and Function. Proteins 2024. [PMID: 39095933 DOI: 10.1002/prot.26724] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2024] [Revised: 04/26/2024] [Accepted: 06/12/2024] [Indexed: 08/04/2024]
Abstract
G protein-coupled receptors (GPCRs) exemplify sophisticated allosteric communication, transducing extracellular signals through ligand-induced structural rearrangements that resonate through the molecular scaffold. Despite extensive study, the biophysical underpinnings of how conformational changes spread remain unclear. This work employs a novel physics-based framework to characterize the role of energy dissipation in directing intramolecular signaling pathways. By modeling each residue as a network of coupled oscillators, we generate a localization landscape depicting the vibrational energy distribution throughout the protein scaffold. Quantifying directional energy flux between residues reveals distinct pathways for energy and information transfer, illuminating sequences of allosteric communication. Our analysis of CB1 and CCR5 crystal structures unveils an anisotropic pattern of energy dissipation aligning with key functional dynamics, such as activation-related conformational changes. These anisotropic patterns of vibrational energy flow constitute pre-configured channels for allosteric signaling. Elucidating the relationship between structural topology and energy dissipation patterns provides key insights into the thermodynamic drivers of conformational signaling. This methodology significantly advances our mechanistic understanding of allostery in GPCRs and presents a broadly applicable approach for rationally dissecting allosteric communication pathways, with potential implications for structure-based drug design targeting these critical receptors.
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Affiliation(s)
- Yann Chalopin
- Structures, Properties and Modeling of Solids Laboratory Physics Department, CentraleSupélec/National Center for the Scientific Research, University of Paris-Saclay, Gif-sur-Yvette, France
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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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Tripathy M, Srivastava A, Sastry S, Rao M. Protein as evolvable functionally constrained amorphous matter. J Biosci 2022. [DOI: 10.1007/s12038-022-00313-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
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5
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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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6
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Tang QY, Ren W, Wang J, Kaneko K. The Statistical Trends of Protein Evolution: A Lesson from AlphaFold Database. Mol Biol Evol 2022; 39:msac197. [PMID: 36108094 PMCID: PMC9550990 DOI: 10.1093/molbev/msac197] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
The recent development of artificial intelligence provides us with new and powerful tools for studying the mysterious relationship between organism evolution and protein evolution. In this work, based on the AlphaFold Protein Structure Database (AlphaFold DB), we perform comparative analyses of the proteins of different organisms. The statistics of AlphaFold-predicted structures show that, for organisms with higher complexity, their constituent proteins will have larger radii of gyration, higher coil fractions, and slower vibrations, statistically. By conducting normal mode analysis and scaling analyses, we demonstrate that higher organismal complexity correlates with lower fractal dimensions in both the structure and dynamics of the constituent proteins, suggesting that higher functional specialization is associated with higher organismal complexity. We also uncover the topology and sequence bases of these correlations. As the organismal complexity increases, the residue contact networks of the constituent proteins will be more assortative, and these proteins will have a higher degree of hydrophilic-hydrophobic segregation in the sequences. Furthermore, by comparing the statistical structural proximity across the proteomes with the phylogenetic tree of homologous proteins, we show that, statistical structural proximity across the proteomes may indirectly reflect the phylogenetic proximity, indicating a statistical trend of protein evolution in parallel with organism evolution. This study provides new insights into how the diversity in the functionality of proteins increases and how the dimensionality of the manifold of protein dynamics reduces during evolution, contributing to the understanding of the origin and evolution of lives.
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Affiliation(s)
- Qian-Yuan Tang
- Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, 2-1 Hirosawa, Wako, Saitama 351-0106, Japan
| | - Weitong Ren
- Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Jun Wang
- School of Physics, National Laboratory of Solid State Microstructure, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People’s Republic of China
| | - Kunihiko Kaneko
- Center for Complex Systems Biology, Universal Biology Institute, University of Tokyo, Komaba, Meguro, Tokyo 153-8902, Japan
- The Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen 2100-DK, Denmark
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7
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Eckmann JP, Tlusty T. Dimensional reduction in complex living systems: Where, why, and how. Bioessays 2021; 43:e2100062. [PMID: 34245050 DOI: 10.1002/bies.202100062] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2021] [Revised: 06/18/2021] [Accepted: 06/22/2021] [Indexed: 12/20/2022]
Abstract
The unprecedented prowess of measurement techniques provides a detailed, multi-scale look into the depths of living systems. Understanding these avalanches of high-dimensional data-by distilling underlying principles and mechanisms-necessitates dimensional reduction. We propose that living systems achieve exquisite dimensional reduction, originating from their capacity to learn, through evolution and phenotypic plasticity, the relevant aspects of a non-random, smooth physical reality. We explain how geometric insights by mathematicians allow one to identify these genuine hallmarks of life and distinguish them from universal properties of generic data sets. We illustrate these principles in a concrete example of protein evolution, suggesting a simple general recipe that can be applied to understand other biological systems.
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Affiliation(s)
- Jean-Pierre Eckmann
- Département de Physique Théorique and Section de Mathématiques, Université de Genève, Geneva 4, Switzerland
| | - Tsvi Tlusty
- Center for Soft and Living Matter, Institute for Basic Science, Ulsan, Republic of Korea.,Departments of Physics and Chemistry, UNIST, Ulsan, Republic of Korea
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8
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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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9
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Allostery and Epistasis: Emergent Properties of Anisotropic Networks. ENTROPY 2020; 22:e22060667. [PMID: 33286439 PMCID: PMC7517209 DOI: 10.3390/e22060667] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/24/2020] [Revised: 06/02/2020] [Accepted: 06/08/2020] [Indexed: 11/17/2022]
Abstract
Understanding the underlying mechanisms behind protein allostery and non-additivity of substitution outcomes (i.e., epistasis) is critical when attempting to predict the functional impact of mutations, particularly at non-conserved sites. In an effort to model these two biological properties, we extend the framework of our metric to calculate dynamic coupling between residues, the Dynamic Coupling Index (DCI) to two new metrics: (i) EpiScore, which quantifies the difference between the residue fluctuation response of a functional site when two other positions are perturbed with random Brownian kicks simultaneously versus individually to capture the degree of cooperativity of these two other positions in modulating the dynamics of the functional site and (ii) DCIasym, which measures the degree of asymmetry between the residue fluctuation response of two sites when one or the other is perturbed with a random force. Applied to four independent systems, we successfully show that EpiScore and DCIasym can capture important biophysical properties in dual mutant substitution outcomes. We propose that allosteric regulation and the mechanisms underlying non-additive amino acid substitution outcomes (i.e., epistasis) can be understood as emergent properties of an anisotropic network of interactions where the inclusion of the full network of interactions is critical for accurate modeling. Consequently, mutations which drive towards a new function may require a fine balance between functional site asymmetry and strength of dynamic coupling with the functional sites. These two tools will provide mechanistic insight into both understanding and predicting the outcome of dual mutations.
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10
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Loutchko D, Flechsig H. Allosteric communication in molecular machines via information exchange: what can be learned from dynamical modeling. Biophys Rev 2020; 12:443-452. [PMID: 32198636 DOI: 10.1007/s12551-020-00667-8] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2020] [Accepted: 02/25/2020] [Indexed: 02/07/2023] Open
Abstract
Allosteric regulation is crucial for the operation of protein machines and molecular motors. A major challenge is to characterize and quantify the information exchange underlying allosteric communication between remote functional sites in a protein, and to identify the involved relevant pathways. We review applications of two topical approaches of dynamical protein modeling, a kinetic-based single-molecule stochastic model, which employs information thermodynamics to quantify allosteric interactions, and structure-based coarse-grained modeling to characterize intra-molecular couplings in terms of conformational motions and propagating mechanical strain. Both descriptions resolve the directionality of allosteric responses within a protein, emphasizing the concept of causality as the principal hallmark of protein allostery. We discuss the application of techniques from information thermodynamics to dynamic protein elastic networks and evolutionary designed model structures, and the ramifications for protein allostery.
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Affiliation(s)
- Dimitri Loutchko
- Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba, 277-8561, Japan
| | - Holger Flechsig
- Nano Life Science Institute (WPI-NanoLSI), Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa, 920-1192, Japan.
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11
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Bravi B, Ravasio R, Brito C, Wyart M. Direct coupling analysis of epistasis in allosteric materials. PLoS Comput Biol 2020; 16:e1007630. [PMID: 32119660 PMCID: PMC7067494 DOI: 10.1371/journal.pcbi.1007630] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2019] [Revised: 03/12/2020] [Accepted: 01/03/2020] [Indexed: 11/22/2022] Open
Abstract
In allosteric proteins, the binding of a ligand modifies function at a distant active site. Such allosteric pathways can be used as target for drug design, generating considerable interest in inferring them from sequence alignment data. Currently, different methods lead to conflicting results, in particular on the existence of long-range evolutionary couplings between distant amino-acids mediating allostery. Here we propose a resolution of this conundrum, by studying epistasis and its inference in models where an allosteric material is evolved in silico to perform a mechanical task. We find in our model the four types of epistasis (Synergistic, Sign, Antagonistic, Saturation), which can be both short or long-range and have a simple mechanical interpretation. We perform a Direct Coupling Analysis (DCA) and find that DCA predicts well the cost of point mutations but is a rather poor generative model. Strikingly, it can predict short-range epistasis but fails to capture long-range epistasis, in consistence with empirical findings. We propose that such failure is generic when function requires subparts to work in concert. We illustrate this idea with a simple model, which suggests that other methods may be better suited to capture long-range effects. Allostery in proteins is the property of highly specific responses to ligand binding at a distant site. To inform protocols of de novo drug design, it is fundamental to understand the impact of mutations on allosteric regulation and whether it can be predicted from evolutionary correlations. In this work we consider allosteric architectures artificially evolved to optimize the cooperativity of binding at allosteric and active site. We first characterize the emergent pattern of epistasis as well as the underlying mechanical phenomena, finding the four types of epistasis (Synergistic, Sign, Antagonistic, Saturation), which can be both short or long-range. The numerical evolution of these allosteric architectures allows us to benchmark Direct Coupling Analysis, a method which relies on co-evolution in sequence data to infer direct evolutionary couplings, in connection to allostery. We show that Direct Coupling Analysis predicts quantitatively point mutation costs but underestimates strong long-range epistasis. We provide an argument, based on a simplified model, illustrating the reasons for this discrepancy. Our analysis suggests neural networks as more promising tool to measure epistasis.
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Affiliation(s)
- Barbara Bravi
- Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
- * E-mail: (BB); (MW)
| | - Riccardo Ravasio
- Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | - Carolina Brito
- Instituto de Fìsica, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil
| | - Matthieu Wyart
- Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
- * E-mail: (BB); (MW)
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12
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Ravasio R, Flatt SM, Yan L, Zamuner S, Brito C, Wyart M. Mechanics of Allostery: Contrasting the Induced Fit and Population Shift Scenarios. Biophys J 2019; 117:1954-1962. [PMID: 31653447 PMCID: PMC7031744 DOI: 10.1016/j.bpj.2019.10.002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2019] [Revised: 09/27/2019] [Accepted: 10/03/2019] [Indexed: 12/11/2022] Open
Abstract
In allosteric proteins, binding a ligand can affect function at a distant location, for example, by changing the binding affinity of a substrate at the active site. The induced fit and population shift models, which differ by the assumed number of stable configurations, explain such cooperative binding from a thermodynamic viewpoint. Yet, understanding what mechanical principles constrain these models remains a challenge. Here, we provide an empirical study on 34 proteins supporting the idea that allosteric conformational change generally occurs along a soft elastic mode presenting extended regions of high shear. We argue, based on a detailed analysis of how the energy profile along such a mode depends on binding, that in the induced fit scenario, there is an optimal stiffness ka∗ ∼ 1/N for cooperative binding, where N is the number of residues. We find that the population shift scenario is more robust to mutations affecting stiffness because binding becomes more and more cooperative with stiffness up to the same characteristic value ka∗, beyond which cooperativity saturates instead of decaying. We numerically confirm these findings in a nonlinear mechanical model. Dynamical considerations suggest that a stiffness of order ka∗ is favorable in that scenario as well, supporting that for proper function, proteins must evolve a functional elastic mode that is softer as their size increases. In consistency with this view, we find a fair anticorrelation between the stiffness of the allosteric response and protein size in our data set.
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Affiliation(s)
- Riccardo Ravasio
- Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.
| | - Solange Marie Flatt
- Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | - Le Yan
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California
| | - Stefano Zamuner
- Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | - Carolina Brito
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, State of Rio Grande do Sul, Brazil
| | - Matthieu Wyart
- Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.
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13
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Abstract
While belonging to the nanoscale, protein machines are so complex that tracing even a small fraction of their cycle requires weeks of calculations on supercomputers. Surprisingly, many aspects of their operation can be however already reproduced by using very simple mechanical models of elastic networks. The analysis suggests that, similar to other self-organized complex systems, functional collective dynamics in such proteins is effectively reduced to a low-dimensional attractive manifold.
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Affiliation(s)
- Holger Flechsig
- 1 Nano Life Science Institute (WPI-NanoLSI), Kanazawa University , Kakuma-machi, 920-1192 Kanazawa , Japan
| | - Alexander S Mikhailov
- 1 Nano Life Science Institute (WPI-NanoLSI), Kanazawa University , Kakuma-machi, 920-1192 Kanazawa , Japan.,2 Department of Physical Chemistry, Fritz Haber Institute of the Max Planck Society , Faradayweg 4-6, 14195 Berlin , Germany
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14
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Thirumalai D, Hyeon C, Zhuravlev PI, Lorimer GH. Symmetry, Rigidity, and Allosteric Signaling: From Monomeric Proteins to Molecular Machines. Chem Rev 2019; 119:6788-6821. [DOI: 10.1021/acs.chemrev.8b00760] [Citation(s) in RCA: 51] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- D. Thirumalai
- Department of Chemistry, The University of Texas, Austin, Texas 78712, United States
| | - Changbong Hyeon
- Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
| | - Pavel I. Zhuravlev
- Biophysics Program, Institute for Physical Science and Technology and Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, United States
| | - George H. Lorimer
- Biophysics Program, Institute for Physical Science and Technology and Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, United States
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15
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Wang SW, Bitbol AF, Wingreen NS. Revealing evolutionary constraints on proteins through sequence analysis. PLoS Comput Biol 2019; 15:e1007010. [PMID: 31017888 PMCID: PMC6502352 DOI: 10.1371/journal.pcbi.1007010] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2019] [Revised: 05/06/2019] [Accepted: 04/06/2019] [Indexed: 02/03/2023] Open
Abstract
Statistical analysis of alignments of large numbers of protein sequences has revealed "sectors" of collectively coevolving amino acids in several protein families. Here, we show that selection acting on any functional property of a protein, represented by an additive trait, can give rise to such a sector. As an illustration of a selected trait, we consider the elastic energy of an important conformational change within an elastic network model, and we show that selection acting on this energy leads to correlations among residues. For this concrete example and more generally, we demonstrate that the main signature of functional sectors lies in the small-eigenvalue modes of the covariance matrix of the selected sequences. However, secondary signatures of these functional sectors also exist in the extensively-studied large-eigenvalue modes. Our simple, general model leads us to propose a principled method to identify functional sectors, along with the magnitudes of mutational effects, from sequence data. We further demonstrate the robustness of these functional sectors to various forms of selection, and the robustness of our approach to the identification of multiple selected traits.
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Affiliation(s)
- Shou-Wen Wang
- Department of Engineering Physics, Tsinghua University, Beijing, China
- Beijing Computational Science Research Center, Beijing, China
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey, United States of America
| | - Anne-Florence Bitbol
- Sorbonne Université, CNRS, Laboratoire Jean Perrin (UMR 8237), F-75005 Paris, France
| | - Ned S. Wingreen
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey, United States of America
- Department of Molecular Biology, Princeton University, Princeton, New Jersey, United States of America
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16
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Abstract
Catalysis and mobility of reactants in fluid are normally thought to be decoupled. Violating this classical paradigm, this paper presents the catalyst laws of motion. Comparing experimental data to the theory presented here, we conclude that part of the free energy released by chemical reaction is channeled into driving catalysts to execute wormlike trajectories by piconewton forces performing work of a few kBT against fluid viscosity, where the rotational diffusion rate dictates the trajectory persistence length. This active motion agitates the fluid medium and produces antichemotaxis, the migration of catalyst down the gradient of the reactant concentration. Alternative explanations of enhanced catalyst mobility are examined critically. Using a microscopic theory to analyze experiments, we demonstrate that enzymes are active matter. Superresolution fluorescence measurements—performed across four orders of magnitude of substrate concentration, with emphasis on the biologically relevant regime around or below the Michaelis–Menten constant—show that catalysis boosts the motion of enzymes to be superdiffusive for a few microseconds, enhancing their effective diffusivity over longer timescales. Occurring at the catalytic turnover rate, these fast ballistic leaps maintain direction over a duration limited by rotational diffusion, driving enzymes to execute wormlike trajectories by piconewton forces performing work of a few kBT against viscosity. The boosts are more frequent at high substrate concentrations, biasing the trajectories toward substrate-poor regions, thus exhibiting antichemotaxis, demonstrated here experimentally over a wide range of aqueous concentrations. Alternative noncatalytic, passive mechanisms that predict chemotaxis, cross-diffusion, and phoresis, are critically analyzed. We examine the physical interpretation of our findings, speculate on the underlying mechanism, and discuss the avenues they open with biological and technological implications. These findings violate the classical paradigm that chemical reaction and motility are distinct processes, and suggest reaction–motion coupling as a general principle of catalysis.
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17
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Flechsig H, Togashi Y. Designed Elastic Networks: Models of Complex Protein Machinery. Int J Mol Sci 2018; 19:E3152. [PMID: 30322149 PMCID: PMC6214024 DOI: 10.3390/ijms19103152] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2018] [Revised: 10/04/2018] [Accepted: 10/11/2018] [Indexed: 12/14/2022] Open
Abstract
Recently, the design of mechanical networks with protein-inspired responses has become increasingly popular. Here, we review contributions which were motivated by studies of protein dynamics employing coarse-grained elastic network models. First, the concept of evolutionary optimization that we developed to design network structures which execute prescribed tasks is explained. We then review what presumably marks the origin of the idea to design complex functional networks which encode protein-inspired behavior, namely the design of an elastic network structure which emulates the cycles of ATP-powered conformational motion in protein machines. Two recent applications are reviewed. First, the construction of a model molecular motor, whose operation incorporates both the tight coupling power stroke as well as the loose coupling Brownian ratchet mechanism, is discussed. Second, the evolutionary design of network structures which encode optimal long-range communication between remote sites and represent mechanical models of allosteric proteins is presented. We discuss the prospects of designed protein-mimicking elastic networks as model systems to elucidate the design principles and functional signatures underlying the operation of complex protein machinery.
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Affiliation(s)
- Holger Flechsig
- Nano Life Science Institute (WPI-NanoLSI), Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa 920-1192, Japan.
| | - Yuichi Togashi
- Department of Mathematical and Life Sciences, Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan.
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