Plahte Erik, Gjuvsland Arne B, Omholt Stig W
Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, P.O. Box 5003, N - 1432 Ås, Norway ; CIGENE (Centre for Integrative Genetics), Norwegian University of Life Sciences, N - 1432 Ås, Norway.
Physica D. 2013 Aug 1;256-257:7-20. doi: 10.1016/j.physd.2013.04.002.
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.
未来的数量遗传学理论应基于基因实际的工作方式和相互作用方式，以因果连贯的方式将遗传变异与表型变异联系起来。我们提供了一个理论框架，用于预测和理解具有任意反馈结构以及基因座内和基因座间功能依赖性的单倍体和二倍体调控网络中遗传变异的表现。利用网络和图论的结果，我们定义了传播函数，描述基因座中的遗传变异如何在网络中传播，并展示了它们的导数如何与网络的反馈结构相关。同样，反馈函数描述了一个基因座的基因型变异对其自身的影响，这种影响可以是直接的，也可以是由网络介导的。一个简单的符号规则将任何基因座的反馈函数的导数符号与涉及该特定基因座的反馈环联系起来。我们表明，根据单基因座系统的最新结果，二倍体基因座上等位基因之间表型表现的相互作用符号等于涉及该特定基因座的显性反馈环的符号。我们的结果提供了一些工具，通过这些工具可以利用可观察到的基因产物平衡浓度来揭示网络结构的特性。我们的工作朝着一种理论迈出了一步，该理论能够将复杂调控网络中遗传变异的多效性和上位性特征解释为遗传变异的调控结构和功能位置的函数。
