Abstract
A future quantitative genetics theory should link genetic variation to phenotypic variation in a causally cohesive way based on how genes actually work and interact. We provide a theoretical framework for predicting and understanding the manifestation of genetic variation in haploid and diploid regulatory networks with arbitrary feedback structures and intra-locus and inter-locus functional dependencies. Using results from network and graph theory, we define propagation functions describing how genetic variation in a locus is propagated through the network, and show how their derivatives are related to the network’s feedback structure. Similarly, feedback functions describe the effect of genotypic variation of a locus on itself, either directly or mediated by the network. A simple sign rule relates the sign of the derivative of the feedback function of any locus to the feedback loops involving that particular locus. We show that the sign of the phenotypically manifested interaction between alleles at a diploid locus is equal to the sign of the dominant feedback loop involving that particular locus, in accordance with recent results for a single locus system. Our results provide tools by which one can use observable equilibrium concentrations of gene products to disclose structural properties of the network architecture. Our work is a step towards a theory capable of explaining the pleiotropy and epistasis features of genetic variation in complex regulatory networks as functions of regulatory anatomy and functional location of the genetic variation.
Highlights
Understanding the genotype to phenotype map is essential for a whole range of problems in evolutionary biology, production biology and biomedicine
Based on these premises we provide a new vocabulary for analysing how genetic variation is manifested in a wide class of haploid and diploid gene regulatory networks possessing negative and positive feedback loops
Combining network theory and linear algebra results with mathematical models of gene regulatory networks, we have introduced relevant concepts and provided analytical insights on how genetic variation is propagated in gene networks
Summary
Understanding the genotype to phenotype map is essential for a whole range of problems in evolutionary biology, production biology and biomedicine. To fully understand the functional properties of a diploid gene it is desirable to model its two alleles as separate quantities This was first done by Omholt et al [13] to show how the phenomena of genetic dominance, overdominance, additivity, and epistasis could be seen as generic features of simple diploid gene regulatory networks. In the present paper we develop these ideas further by proposing a way by which a diploid gene modelled in this fashion can be represented as a single entity and described by a single ODE for its gene product Based on these premises we provide a new vocabulary for analysing how genetic variation is manifested in a wide class of haploid and diploid gene regulatory networks possessing negative and positive feedback loops. A brief explanation of our notation is found in Appendix A
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
