The geometry of evolutionary constraints on dynamic structure-function relationships

Abstract

The genomic era has demonstrated that understanding the relationship between genotype and phenotype is crucial. In addition to its necessity for the basic understanding of biological systems, this is also necessary to be able to extract useful knowledge from -omic data. The major focus of this thesis is the investigation of dynamic structure-function relationships. Structure here is to be interpreted broadly as referring, for example, to the topology of a gene regulatory network. Function is also to be interpreted broadly, as the overall dynamics of metabolite, transcript, and protein copy numbers. From this perspective, the goal of this thesis is to contribute to an understanding of how these structure-function relationships evolve in the context of internal, logical, or environmentally imposed constraints.;Questions of this sort can be asked in two different directions. One is: Given a particular structure or collection of structures, which functions or dynamics are they capable of generating? The other is: Given a specification of dynamics deriving from some environmental constraints, which structures are capable of satisfying them? We ask and provide answers to two questions of the latter sort. The first is: Which network architectures are more or less likely to be robust to perturbations to their structure? Such perturbations may arise, for example, from fluctuations in the environmental conditions. We demonstrate, given suitable definitions of robustness and network hierarchy, that the most hierarchical network structures are the most robust. The second question we address is, for each manner in which a collection of constraints can be applied to a biological network, which are more or less likely to impose constraints that cannot be satisfied? Here we find that the probability of imposing unsatisfiable constraints upon a network generally increases with the number of cycles in the structure that specifies the manner in which constraints are imposed upon it. This leads to the conclusion that architectures possessing fewer cycles may be selected in preference to those containing a larger number. In the long-term, this intrinsic pressure suggests a bias toward networks that are globally hierarchical, but may locally possess small modules with a few cycles.