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Analysis of epistatic interactions and fitness landscapes using a new geometric approach

Beerenwinkel, Niko and Pachter, Lior and Sturmfels, Bernd and Elena, Santiago F. and Lenski, Richard E. (2007) Analysis of epistatic interactions and fitness landscapes using a new geometric approach. BMC Evolutionary Biology, 7 . Art. No. 60. ISSN 1471-2148. PMCID PMC1865543. doi:10.1186/1471-2148-7-60. https://resolver.caltech.edu/CaltechAUTHORS:20170307-131928305

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Abstract

Background: Understanding interactions between mutations and how they affect fitness is a central problem in evolutionary biology that bears on such fundamental issues as the structure of fitness landscapes and the evolution of sex. To date, analyses of fitness landscapes have focused either on the overall directional curvature of the fitness landscape or on the distribution of pairwise interactions. In this paper, we propose and employ a new mathematical approach that allows a more complete description of multi-way interactions and provides new insights into the structure of fitness landscapes. Results: We apply the mathematical theory of gene interactions developed by Beerenwinkel et al. to a fitness landscape for Escherichia coli obtained by Elena and Lenski. The genotypes were constructed by introducing nine mutations into a wild-type strain and constructing a restricted set of 27 double mutants. Despite the absence of mutants higher than second order, our analysis of this genotypic space points to previously unappreciated gene interactions, in addition to the standard pairwise epistasis. Our analysis confirms Elena and Lenski's inference that the fitness landscape is complex, so that an overall measure of curvature obscures a diversity of interaction types. We also demonstrate that some mutations contribute disproportionately to this complexity. In particular, some mutations are systematically better than others at mixing with other mutations. We also find a strong correlation between epistasis and the average fitness loss caused by deleterious mutations. In particular, the epistatic deviations from multiplicative expectations tend toward more positive values in the context of more deleterious mutations, emphasizing that pairwise epistasis is a local property of the fitness landscape. Finally, we determine the geometry of the fitness landscape, which reflects many of these biologically interesting features. Conclusion: A full description of complex fitness landscapes requires more information than the average curvature or the distribution of independent pairwise interactions. We have proposed a mathematical approach that, in principle, allows a complete description and, in practice, can suggest new insights into the structure of real fitness landscapes. Our analysis emphasizes the value of non-independent genotypes for these inferences.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://dx.doi.org/10.1186/1471-2148-7-60DOIArticle
http://bmcevolbiol.biomedcentral.com/articles/10.1186/1471-2148-7-60PublisherArticle
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1865543/PubMed CentralArticle
ORCID:
AuthorORCID
Pachter, Lior0000-0002-9164-6231
Elena, Santiago F.0000-0001-8249-5593
Lenski, Richard E.0000-0002-1064-8375
Additional Information:© Beerenwinkel et al; licensee BioMed Central Ltd. 2007. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Received: 17 October 2006. Accepted: 13 April 2007. Published: 13 April 2007. This work was supported by the "FunBio" grant from DARPA to Simon Levin (Princeton University). We thank Simon Levin and Ben Mann (DARPA) for facilitating this math-bio collaboration, Peter Bates and Charles Ofria for helpful discussions, Peter Malkin for an improved program for computing circuits, Mike Stillman for writing and improving the Macaulay 2 code, and three anonymous reviewers for suggestions. Collection of the dataset used in this study was funded by a fellowship from the Spanish MEC to S.F.E. and a grant from the NSF to R.E.L. N.B. was funded by a grant from the Bill & Melinda Gates foundation through the Grand Challenges in Global Health Initiative.
Funders:
Funding AgencyGrant Number
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Ministerio de Educación y Ciencia (MEC)UNSPECIFIED
NSFUNSPECIFIED
Bill and Melinda Gates FoundationUNSPECIFIED
PubMed Central ID:PMC1865543
DOI:10.1186/1471-2148-7-60
Record Number:CaltechAUTHORS:20170307-131928305
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170307-131928305
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74859
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:07 Mar 2017 21:58
Last Modified:15 Nov 2021 16:28

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