MIG Seminar – Barbara Holland – 2nd August, 2019

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Andrew Siebel


T: +61 3 8344 0707

Barbara Holland

Associate Professor of Mathematics, School of Natural Sciences
University of Tasmania

Friday 2nd August
Agar Theatre, BioSciences 4 Building, The University of Melbourne

Models for the evolution of gene-duplicates

Joint work with: Tristan Stark, Malgorzata O’Reilly, David Liberles, Jiahao Diao

Genomes typically contain thousands of genes that perform different functions. Rather than all arising independently, these genes group into families that share a common evolutionary origin. Gene families arise because of gene duplication, however, genes are only preserved in genomes if they have a function that is maintained by selection, and at the time of origin a duplicated gene is identical to another gene with the same functions. A duplicate gene can suffer one of several fates: it may be lost (nonfunctionalisation) leaving its partner to carry out all the gene's functions; both copies may be retained but with complementary and reduced functionality (subfunctionalisation); or it may acquire a new function (neofunctionalisation) that comes to be protected by selection.

In 2017 Stark et. al developed and analyzed a mathematical model for the fate of a pair of duplicated genes. In this model it is assumed that each gene can carry out a number of functions that are controlled by different regulatory regions (e.g. different transcription factor binding sites might activate the gene in different pathways). All the functions are assumed to be protected by selection. Immediately following duplication the genes are both able to perform all of the functions. Over time mutations (modelled as a Poisson process) are able to knock-out regulatory regions or the coding region of different genes. A mutation to the coding region of a gene will inactivate all of its functions. Eventually the genes will meet one of two fates: either one gene will be lost (nonfunctionalisation) or both genes will be retained but with complementary functions (subfunctionalisation). The innovation in Stark et. al (2017) was to express this stochastic process as an absorbing state Markov chain and to recognize that the results from the rich literature of Phase-Type distributions could be applied to give analytic solutions for the time to absorption into different states.

In this talk I will introduce the model above and also discuss some initial results that extend the framework to cases where:

  • There are more than two genes.
  • New functions can arise due to de novo creation of a regulatory region.

Enquiries: Andrew Siebel (asiebel@unimelb.edu.au)