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Thorvaldsen S, Hössjer O. Use of directed quasi-metric distances for quantifying the information of gene families. Biosystems 2024; 243:105256. [PMID: 38871243 DOI: 10.1016/j.biosystems.2024.105256] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2024] [Revised: 06/06/2024] [Accepted: 06/11/2024] [Indexed: 06/15/2024]
Abstract
A large hindrance to analyzing information in genetic or protein sequence data has been a lack of a mathematical framework for doing so. In this paper, we present a multinomial probability space X as a general foundation for multicategory discrete data, where categories refer to variants/alleles of biosequences. The external information that is infused in order to generate a sample of such data is quantified as a distance on X between the prior distribution of data and the empirical distribution of the sample. A number of distances on X are treated. All of them have an information theoretic interpretation, reflecting the information that the sampling mechanism provides about which variants that have a selective advantage and therefore appear more frequently compared to prior expectations. This includes distances on X based on mutual information, conditional mutual information, active information, and functional information. The functional information distance is singled out as particularly useful. It is simple and has intuitive interpretations in terms of 1) a rejection sampling mechanism, where functional entities are retained, whereas non-functional categories are censored, and 2) evolutionary waiting times. The functional information is also a quasi-metric on X, with information being measured in an asymmetric, mountainous landscape. This quasi-metric property is also retained for a robustified version of the functional information distance that allows for mutations in the sampling mechanism. The functional information quasi-metric has been applied with success on bioinformatics data sets, for proteins and sequence alignment of protein families.
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Affiliation(s)
- Steinar Thorvaldsen
- Dept. of Education, Division of Science, UiT the Arctic University of Norway, Norway.
| | - Ola Hössjer
- Dept. of Mathematics, Stockholm University, Sweden.
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Marchant A, Cisneros AF, Dubé AK, Gagnon-Arsenault I, Ascencio D, Jain H, Aubé S, Eberlein C, Evans-Yamamoto D, Yachie N, Landry CR. The role of structural pleiotropy and regulatory evolution in the retention of heteromers of paralogs. eLife 2019; 8:46754. [PMID: 31454312 PMCID: PMC6711710 DOI: 10.7554/elife.46754] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2019] [Accepted: 08/11/2019] [Indexed: 01/07/2023] Open
Abstract
Gene duplication is a driver of the evolution of new functions. The duplication of genes encoding homomeric proteins leads to the formation of homomers and heteromers of paralogs, creating new complexes after a single duplication event. The loss of these heteromers may be required for the two paralogs to evolve independent functions. Using yeast as a model, we find that heteromerization is frequent among duplicated homomers and correlates with functional similarity between paralogs. Using in silico evolution, we show that for homomers and heteromers sharing binding interfaces, mutations in one paralog can have structural pleiotropic effects on both interactions, resulting in highly correlated responses of the complexes to selection. Therefore, heteromerization could be preserved indirectly due to selection for the maintenance of homomers, thus slowing down functional divergence between paralogs. We suggest that paralogs can overcome the obstacle of structural pleiotropy by regulatory evolution at the transcriptional and post-translational levels.
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Affiliation(s)
- Axelle Marchant
- Département de biochimie, de microbiologie et de bio-informatique, Université Laval, Québec, Canada.,PROTEO, le réseau québécois de recherche sur la fonction, la structure et l'ingénierie des protéines, Université Laval, Québec, Canada.,Centre de Recherche en Données Massives (CRDM), Université Laval, Québec, Canada.,Département de biologie, Université Laval, Québec, Canada
| | - Angel F Cisneros
- Département de biochimie, de microbiologie et de bio-informatique, Université Laval, Québec, Canada.,PROTEO, le réseau québécois de recherche sur la fonction, la structure et l'ingénierie des protéines, Université Laval, Québec, Canada.,Centre de Recherche en Données Massives (CRDM), Université Laval, Québec, Canada
| | - Alexandre K Dubé
- Département de biochimie, de microbiologie et de bio-informatique, Université Laval, Québec, Canada.,PROTEO, le réseau québécois de recherche sur la fonction, la structure et l'ingénierie des protéines, Université Laval, Québec, Canada.,Centre de Recherche en Données Massives (CRDM), Université Laval, Québec, Canada.,Département de biologie, Université Laval, Québec, Canada
| | - Isabelle Gagnon-Arsenault
- Département de biochimie, de microbiologie et de bio-informatique, Université Laval, Québec, Canada.,PROTEO, le réseau québécois de recherche sur la fonction, la structure et l'ingénierie des protéines, Université Laval, Québec, Canada.,Centre de Recherche en Données Massives (CRDM), Université Laval, Québec, Canada.,Département de biologie, Université Laval, Québec, Canada
| | - Diana Ascencio
- Département de biochimie, de microbiologie et de bio-informatique, Université Laval, Québec, Canada.,PROTEO, le réseau québécois de recherche sur la fonction, la structure et l'ingénierie des protéines, Université Laval, Québec, Canada.,Centre de Recherche en Données Massives (CRDM), Université Laval, Québec, Canada.,Département de biologie, Université Laval, Québec, Canada
| | - Honey Jain
- Département de biochimie, de microbiologie et de bio-informatique, Université Laval, Québec, Canada.,PROTEO, le réseau québécois de recherche sur la fonction, la structure et l'ingénierie des protéines, Université Laval, Québec, Canada.,Centre de Recherche en Données Massives (CRDM), Université Laval, Québec, Canada.,Department of Biological Sciences, Birla Institute of Technology and Sciences, Pilani, India
| | - Simon Aubé
- Département de biochimie, de microbiologie et de bio-informatique, Université Laval, Québec, Canada.,PROTEO, le réseau québécois de recherche sur la fonction, la structure et l'ingénierie des protéines, Université Laval, Québec, Canada.,Centre de Recherche en Données Massives (CRDM), Université Laval, Québec, Canada
| | - Chris Eberlein
- PROTEO, le réseau québécois de recherche sur la fonction, la structure et l'ingénierie des protéines, Université Laval, Québec, Canada.,Centre de Recherche en Données Massives (CRDM), Université Laval, Québec, Canada.,Département de biologie, Université Laval, Québec, Canada
| | - Daniel Evans-Yamamoto
- Research Center for Advanced Science and Technology, University of Tokyo, Tokyo, Japan.,Institute for Advanced Biosciences, Keio University, Tsuruoka, Japan.,Graduate School of Media and Governance, Keio University, Fujisawa, Japan
| | - Nozomu Yachie
- Research Center for Advanced Science and Technology, University of Tokyo, Tokyo, Japan.,Institute for Advanced Biosciences, Keio University, Tsuruoka, Japan.,Graduate School of Media and Governance, Keio University, Fujisawa, Japan.,Department of Biological Sciences, Graduate School of Science, University of Tokyo, Tokyo, Japan
| | - Christian R Landry
- Département de biochimie, de microbiologie et de bio-informatique, Université Laval, Québec, Canada.,PROTEO, le réseau québécois de recherche sur la fonction, la structure et l'ingénierie des protéines, Université Laval, Québec, Canada.,Centre de Recherche en Données Massives (CRDM), Université Laval, Québec, Canada.,Département de biologie, Université Laval, Québec, Canada
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