An extension of the Walsh-Hadamard transform to calculate and model epistasis in genetic landscapes of arbitrary shape and complexity.

Publisher: Public Library of Science Country of Publication: United States NLM ID: 101238922 Publication Model: eCollection Cited Medium: Internet ISSN: 1553-7358 (Electronic) Linking ISSN: 1553734X NLM ISO Abbreviation: PLoS Comput Biol Subsets: MEDLINE

Original Publication: San Francisco, CA : Public Library of Science, [2005]-

Epistasis, Genetic*/genetics ; Models, Genetic*; Computational Biology/methods ; Algorithms ; Mutation/genetics ; Genotype

Accurate models describing the relationship between genotype and phenotype are necessary in order to understand and predict how mutations to biological sequences affect the fitness and evolution of living organisms. The apparent abundance of epistasis (genetic interactions), both between and within genes, complicates this task and how to build mechanistic models that incorporate epistatic coefficients (genetic interaction terms) is an open question. The Walsh-Hadamard transform represents a rigorous computational framework for calculating and modeling epistatic interactions at the level of individual genotypic values (known as genetical, biological or physiological epistasis), and can therefore be used to address fundamental questions related to sequence-to-function encodings. However, one of its main limitations is that it can only accommodate two alleles (amino acid or nucleotide states) per sequence position. In this paper we provide an extension of the Walsh-Hadamard transform that allows the calculation and modeling of background-averaged epistasis (also known as ensemble epistasis) in genetic landscapes with an arbitrary number of states per position (20 for amino acids, 4 for nucleotides, etc.). We also provide a recursive formula for the inverse matrix and then derive formulae to directly extract any element of either matrix without having to rely on the computationally intensive task of constructing or inverting large matrices. Finally, we demonstrate the utility of our theory by using it to model epistasis within both simulated and empirical multiallelic fitness landscapes, revealing that both pairwise and higher-order genetic interactions are enriched between physically interacting positions.
Competing Interests: I have read the journal’s policy and the authors of this manuscript have the following competing interests: A.J.F. and B.L. are founders, employees and shareholders of ALLOX.
(Copyright: © 2024 Faure et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Nat Commun. 2022 Aug 17;13(1):4847. (PMID: 35977956)
Evolution. 2022 Feb;76(S1):37-48. (PMID: 34989399)
PLoS Genet. 2021 Feb 1;17(2):e1009353. (PMID: 33524037)
Nat Commun. 2022 Nov 16;13(1):7011. (PMID: 36384919)
Cell. 2019 Jan 24;176(3):549-563.e23. (PMID: 30661752)
Annu Rev Genomics Hum Genet. 2019 Aug 31;20:433-460. (PMID: 31082279)
Elife. 2018 Dec 20;7:. (PMID: 30570483)
Nat Commun. 2020 Apr 14;11(1):1782. (PMID: 32286265)
PLoS Comput Biol. 2016 Jun 23;12(6):e1004771. (PMID: 27337695)
Genome Biol. 2022 Apr 15;23(1):98. (PMID: 35428271)
Nat Methods. 2014 Aug;11(8):801-7. (PMID: 25075907)
Proc Natl Acad Sci U S A. 2010 May 18;107(20):9158-63. (PMID: 20439748)
Proc Natl Acad Sci U S A. 2022 Sep 27;119(39):e2204233119. (PMID: 36129941)
PLoS Biol. 2019 May 28;17(5):e3000300. (PMID: 31136568)
Nature. 2022 Apr;604(7904):175-183. (PMID: 35388192)
Nat Rev Genet. 2014 Jul;15(7):480-90. (PMID: 24913663)
PLoS Genet. 2019 Apr 10;15(4):e1008079. (PMID: 30969963)
Curr Opin Genet Dev. 2013 Dec;23(6):700-7. (PMID: 24290990)
Proc Natl Acad Sci U S A. 2022 Jan 4;119(1):. (PMID: 34937698)
Nature. 2018 Jun;558(7708):117-121. (PMID: 29849145)
Proc Natl Acad Sci U S A. 2018 Aug 7;115(32):E7550-E7558. (PMID: 30037990)
Nat Commun. 2019 Sep 16;10(1):4213. (PMID: 31527666)
Genome Biol. 2020 Aug 17;21(1):207. (PMID: 32799905)
Nat Rev Genet. 2008 Nov;9(11):855-67. (PMID: 18852697)

Date Created: 20240528 Date Completed: 20240607 Latest Revision: 20240609

20240609

PMC11161127

10.1371/journal.pcbi.1012132

38805561