Alpha helices are more evolutionarily robust to environmental perturbations than beta sheets: Bayesian theory for evolution

Tomoei Takahashi; George Chikenji; Kei Tokita; Yoshiyuki Kabashima

Alpha helices are more evolutionarily robust to environmental perturbations than beta sheets: Bayesian theory for evolution

ORAL

Abstract

How typical elements that shape organisms, such as protein secondary structures, have evolved, or how evolutionarily susceptible/resistant they are to environmental changes, are significant issues in evolutionary biology, structural biology, and biophysics. According to Darwinian evolution, natural selection and genetic mutations are the primary drivers of biological evolution. However, the concept of "robustness of the phenotype to environmental perturbations across successive generations," which seems crucial from the perspective of natural selection, has not been formalized or analyzed. In this study, through Bayesian learning and statistical mechanics we formalize the stability of the free energy in the space of amino acid sequences that can design particular protein structure against perturbations of the chemical potential of water surrounding a protein as such robustness. This evolutionary stability is defined as a decreasing function of a quantity analogous to the susceptibility in the statistical mechanics of magnetic bodies specific to the amino acid sequence of a protein. Consequently, in a two-dimensional square lattice protein model composed of 36 residues, we found that as we increase the stability of the free energy against perturbations in environmental conditions, the structural space shows a steep step-like reduction. Furthermore, lattice protein structures with higher stability against perturbations in environmental conditions tend to have a higher proportion of alpha-helices and a lower proportion of beta-sheets. The latter result shows that protein structures rich in alpha-helices are more robust to environmental perturbations through successive generations than those rich in beta-sheets.

March 17, 2025, 3:30 PM – March 17, 2025, 3:42 PM

Publication: [1] Tobias Sikosek and Hue Sun Chan. Biophysics of protein evolution and evolutionary protein biophysics. Journal of The Royal Society Interface, 11(100):20140419, 2014. [2] Yu Xia and Michael Levitt. Roles of mutation and re- combination in the evolution of protein thermodynam- ics. Proceedings of the National Academy of Sciences, 99(16):10382–10387, 2002. [3] Jesse D Bloom, Zhongyi Lu, David Chen, Alpan Raval, Ophelia S Venturelli, and Frances H Arnold. Evolution favors protein mutational robustness in sufficiently large populations. BMC biology, 5:1–21, 2007. [4] Vijay Jayaraman, Saacnicteh Toledo-Pati˜no, Lianet Noda-Garc´ıa, and Paola Laurino. Mechanisms of protein evolution. Protein Science, 31:e4362, 2022. [5] Jorge A Vila. Analysis of proteins in the light of muta- tions. European Biophysics Journal, pages 1–11, 2024. [6] Julia Hartling and Junhyong Kim. Mutational robust- ness and geometrical form in protein structures. Journal of Experimental Zoology Part B: Molecular and Develop- mental Evolution, 310(3):216–226, 2008. [7] Christian Schaefer, Avner Schlessinger, and Burkhard Rost. Protein secondary structure appears to be robust under in silico evolution while protein disorder appears not to be. Bioinformatics, 26(5):625–631, 2010. [8] Mary McLeod Rorick and Gunter P Wagner. Structural robustness confers evolvability in proteins. In 2010 AAAI Fall Symposium Series, 2010. [9] Mary M Rorick and G¨unter P Wagner. Protein structural modularity and robustness are associated with evolvabil- ity. Genome biology and evolution, 3:456–475, 2011. [10] Iain G Johnston, Kamaludin Dingle, Sam F Greenbury, Chico Q Camargo, Jonathan PK Doye, Sebastian E Ah- nert, and Ard A Louis. Symmetry and simplicity spon- taneously emerge from the algorithmic nature of evolu- tion. Proceedings of the National Academy of Sciences, 119(11):e2113883119, 2022. [11] Qian-Yuan Tang, Tetsuhiro S Hatakeyama, and Kunihiko Kaneko. Functional sensitivity and mutational robust- ness of proteins. Physical Review Research, 2(3):033452, 2020. [12] Qian-Yuan Tang and Kunihiko Kaneko. Dynamics- evolution correspondence in protein structures. Physical review letters, 127(9):098103, 2021. [13] Ayaka Sakata and Kunihiko Kaneko. Dimensional re- duction in evolving spin-glass model: correlation of phenotypic responses to environmental and mutational changes. Physical Review Letters, 124(21):218101, 2020. [14] Shintaro Nagata and Macoto Kikuchi. Emergence of co- operative bistability and robustness of gene regulatory networks. PLoS computational biology, 16(6):e1007969, 2020. [15] Tadamune Kaneko and Macoto Kikuchi. Evolution en- hances mutational robustness and suppresses the emer- gence of a new phenotype: A new computational ap- proach for studying evolution. PLOS Computational Bi- ology, 18(1):e1009796, 2022. [16] Kunihiko Kaneko. Evolution of robustness to noise and mutation in gene expression dynamics. PLoS one, 2(5):e434, 2007. [17] Stefano Ciliberti, Olivier C Martin, and Andreas Wag- ner. Robustness can evolve gradually in complex regula- tory gene networks with varying topology. PLoS compu- tational biology, 3(2):e15, 2007. [18] Kit Fun Lau and Ken A Dill. A lattice statistical mechan- ics model of the conformational and sequence spaces of proteins. Macromolecules, 22(10):3986–3997, 1989. [19] Helen M Berman, John Westbrook, Zukang Feng, Gary Gilliland, Talapady N Bhat, Helge Weissig, Ilya N Shindyalov, and Philip E Bourne. The protein data bank. Nucleic acids research, 28(1):235–242, 2000. [20] Hu Chen, Xin Zhou, and Zhong-Can Ou-Yang. Secondary-structure-favored hydrophobic-polar lattice model of protein folding. Physical Review E, 64(4):041905, 2001. [21] Marek Cieplak and Jayanth R Banavar. Energy land- scape and dynamics of proteins: an exact analysis of a simplified lattice model. Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 88(4):040702, 2013. [22] Guangjie Shi, Thomas W¨ust, and David P Landau. Char- acterizing folding funnels with replica exchange wang- landau simulation of lattice proteins. Physical Review E, 94(5):050402, 2016. [23] Erik Van Dijk, Patrick Varilly, Tuomas PJ Knowles, Daan Frenkel, and Sanne Abeln. Consistent treatment of hydrophobicity in protein lattice models accounts for cold denaturation. Physical review letters, 116(7):078101, 2016. [24] Christian Holzgr¨afe, Anders Irb¨ack, and Carl Troein. Mutation-induced fold switching among lattice proteins. The Journal of chemical physics, 135(19), 2011. [25] Guangjie Shi, Thomas Vogel, Thomas W¨ust, Ying Wai Li, and David P Landau. Effect of single-site mutations on hydrophobic-polar lattice proteins. Physical Review E, 90(3):033307, 2014. [26] Shi-Jie Chen and Ken A Dill. Rna folding energy land- scapes. Proceedings of the National Academy of Sciences, 97(2):646–651, 2000. [27] Tomoei Takahashi, George Chikenji, and Kei Tokita. Lat- tice protein design using bayesian learning. Physical Re- view E, 104:014404, 2021. [28] Valentino Bianco, Giancarlo Franzese, Christoph Del- lago, and Ivan Coluzza. Role of water in the selection of stable proteins at ambient and extreme thermodynamic conditions. Physical Review X, 7(2):021047, 2017. [29] Themis Lazaridis and Martin Karplus. Effective energy function for proteins in solution. Proteins: Structure, Function, and Bioinformatics, 35(2):133–152, 1999. [30] Tomoei Takahashi, George Chikenji, and Kei Tokita. The cavity method to protein design problem. Jour- nal of Statistical Mechanics: Theory and Experiment, 2022(10):103403, 2022. [31] Ivan Coluzza. Computational protein design: a review. Journal of Physics: Condensed Matter, 29(14):143001, 2017. [32] Simona Cocco, Christoph Feinauer, Matteo Figliuzzi, R´emi Monasson, and Martin Weigt. Inverse statistical physics of protein sequences: a key issues review. Re- ports on Progress in Physics, 81(3):032601, 2018. [33] Christian B Anfinsen. Principles that govern the folding of protein chains. Science, 181(4096):223–230, 1973. [34] Charles C Bigelow. On the average hydrophobicity of proteins and the relation between it and protein struc- 12 ture. Journal of Theoretical Biology, 16(2):187–211, 1967. [35] Yoshiyuki Kabashima and David Saad. Belief propa- gation vs. tap for decoding corrupted messages. Euro- physics Letters, 44(5):668, 1998. [36] Hue Sun Chan and Ken A Dill. Compact polymers. Macromolecules, 22(12):4559–4573, 1989. [37] Khoi Tan Nguyen, St´ephanie V Le Clair, Shuji Ye, and Zhan Chen. Orientation determination of protein helical secondary structures using linear and nonlinear vibra- tional spectroscopy. The journal of physical chemistry B, 113(36):12169–12180, 2009. [38] Motoo Kimura et al. Evolutionary rate at the molecular level. Nature, 217(5129):624–626, 1968. [39] Gy¨orgy Abrus´an and Joseph A Marsh. Alpha helices are more robust to mutations than beta strands. PLoS computational biology, 12(12):e1005242, 2016. [40] George Chikenji, Macoto Kikuchi, and Yukito Iba. Multi- self-overlap ensemble for protein folding: ground state search and thermodynamics. Physical Review Letters, 83(9):1886, 1999. [41] Nobu C Shirai and Macoto Kikuchi. Multicanonical sim- ulation of the domb-joyce model and the g¯o model: new enumeration methods for self-avoiding walks. In Journal of Physics: Conference Series, volume 454, page 012039. IOP Publishing, 2013. [42] Marc M´ezard and Giorgio Parisi. The bethe lattice spin glass revisited. The European Physical Journal B- Condensed Matter and Complex Systems, 20:217–233, 2001. [43] Marc Mezard and Andrea Montanari. Information, physics, and computation. Oxford University Press, 2009.

Presenters

Tomoei Takahashi

The University of Tokyo

Authors

Tomoei Takahashi

The University of Tokyo
George Chikenji

Nagoya University
Kei Tokita

Nagoya University
Yoshiyuki Kabashima

The University of Tokyo