Functional sensitivity and mutational robustness of proteins

Tang, Qianying; Hatakeyama, Tetsuhiro; Kaneko, Kunihiko

doi:10.1103/physrevresearch.2.033452

Cited by 13 publications

(10 citation statements)

References 83 publications

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“…To quantify such a scale-free property, it is necessary to introduce the power laws to describe the vibrations of the proteins. Previous studies have shown that the vibrational spectrum of proteins obeys a power-law distribution (Reuveni et al 2008), and the rank-size distribution of the inverse of eigenvalues follows a Zipf-like distribution (Tang et al 2020; Tang and Kaneko 2021; Xie et al 2022). In SI Fig.…”

Section: Resultsmentioning

confidence: 99%

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The Statistical Trends of Protein Evolution: A Lesson from AlphaFold Database

Tang

Ren²,

Wang

et al. 2022

Preprint

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The relationship between species evolution and protein evolution has been remaining as a mystery. The recent development of artificial intelligence provides us with new and powerful tools for studying the evolution of proteins and species. In this work, based on the AlphaFold Protein Structure Database (AlphaFold DB), we perform comparative analyses of the protein structures of different species. The statistics of AlphaFold-predicted structures show that, as species evolve from prokaryotes to eukaryotes, from unicellular to multicellular organisms, from invertebrates to vertebrates, and so on, the proteins within them evolve towards larger radii of gyration, higher coil fractions, higher modularity, and slower relaxations, indicating that the average flexibility of proteins gradually increases in the species evolution. With the scaling analyses, the size dependence of proteins' shape, topology, and dynamics suggest a decreasing fractal dimension of the proteins in species evolution. This evolutionary trend is accompanied by the increasing eigengaps in the vibration spectra of proteins, implying that the proteins are statistically evolving towards higher functional specificity and lower dimensionality in the equilibrium dynamics. Furthermore, we also uncover the topology and sequence bases of this evolutionary trend. The residue contact networks of the proteins are evolving towards higher assortativity, and the hydrophobic and hydrophilic amino acid residues are evolving to have increasing segregations in the sequences. This study provides new insights into how the diversity in the functionality of the proteins increases and their plasticity grows in evolution. The evolutionary laws implied by these statistical results may also shed light on the study of protein design.

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Section: Resultsmentioning

confidence: 99%

“…S2). Moreover, our study focuses primarily on the global dynamics (e.g., slowest modes) that are robust to the local variations in native structures (Bahar et al 2010; Tang et al 2020). Such insensitivity to prediction confidence can further strengthen our conclusions.…”

Section: Discussionmentioning

confidence: 99%

The Statistical Trends of Protein Evolution: A Lesson from AlphaFold Database

Tang

Ren²,

Wang

et al. 2022

Preprint

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“…These remarkable population-spanning correlations were replicated for a network model of the brain with experimentally based interareal connectivity when the network dynamics was tuned to criticality (Haimovici et al, 2013). Since then, they have also been observed for bacterial colonies (Chen et al, 2012), insect swarms (Attanasi et al, 2014b), and globular proteins (Tang et al, 2017(Tang et al, , 2020. Here, we explore specifically the analogy in scale-free correlations between animal groups and brain dynamics at the scale of local population activity during motor outputs in nonhuman primates and down to the cellular scale of single neuron interactions during sensory processing in mice.…”

Section: Introductionmentioning

confidence: 70%

Scale-Free Dynamics in Animal Groups and Brain Networks

Ribeiro

Chialvo

Plenz

2021

Front. Syst. Neurosci.

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Collective phenomena fascinate by the emergence of order in systems composed of a myriad of small entities. They are ubiquitous in nature and can be found over a vast range of scales in physical and biological systems. Their key feature is the seemingly effortless emergence of adaptive collective behavior that cannot be trivially explained by the properties of the system's individual components. This perspective focuses on recent insights into the similarities of correlations for two apparently disparate phenomena: flocking in animal groups and neuronal ensemble activity in the brain. We first will summarize findings on the spontaneous organization in bird flocks and macro-scale human brain activity utilizing correlation functions and insights from critical dynamics. We then will discuss recent experimental findings that apply these approaches to the collective response of neurons to visual and motor processing, i.e., to local perturbations of neuronal networks at the meso- and microscale. We show how scale-free correlation functions capture the collective organization of neuronal avalanches in evoked neuronal populations in nonhuman primates and between neurons during visual processing in rodents. These experimental findings suggest that the coherent collective neural activity observed at scales much larger than the length of the direct neuronal interactions is demonstrative of a phase transition and we discuss the experimental support for either discontinuous or continuous phase transitions. We conclude that at or near a phase-transition neuronal information can propagate in the brain with similar efficiency as proposed to occur in the collective adaptive response observed in some animal groups.

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“…To quantify such a scale-free property, it is necessary to introduce the power laws to describe the vibrations of the proteins. Previous studies have shown that the vibrational spectrum of proteins obeys a power-law distribution ( Reuveni et al 2008 ), and the rank-size distribution of the inverse of eigenvalues follows a Zipf-like distribution ( Tang et al 2020 ; Tang and Kaneko 2021 ; Xie et al 2022 ). In supplementary figure S6, Supplementary Material online, several proteins are provided as examples.…”

Section: Resultsmentioning

confidence: 99%

The Statistical Trends of Protein Evolution: A Lesson from AlphaFold Database

Tang

Ren

Wang

et al. 2022

Molecular Biology and Evolution

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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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Functional sensitivity and mutational robustness of proteins

Cited by 13 publications

References 83 publications

The Statistical Trends of Protein Evolution: A Lesson from AlphaFold Database

The Statistical Trends of Protein Evolution: A Lesson from AlphaFold Database

Scale-Free Dynamics in Animal Groups and Brain Networks

The Statistical Trends of Protein Evolution: A Lesson from AlphaFold Database

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