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Constraints placed upon the phenotypes of organisms result from theirinteractions with the environment. Over evolutionary timescales, theseconstraints feed back onto smaller molecular subnetworks comprising theorganism. The evolution of biological networks is studied by considering anetwork of a few nodes embedded in a larger context. Taking into account thisfact that any network under study is actually embedded in a larger context, wedefine network architecture, not on the basis of physical interactions alone,but rather as a specification of the manner in which constraints are placedupon the states of its nodes. We show that such network architecturespossessing cycles in their topology, in contrast to those that do not, may besubjected to unsatisfiable constraints. This may be a significant factorleading to selection biased against those network architectures where suchinconsistent constraints are more likely to arise. We proceed to quantify thelikelihood of inconsistency arising as a function of network architecturefinding that, in the absence of sampling bias over the space of possibleconstraints and for a given network size, networks with a larger number ofcycles are more likely to have unsatisfiable constraints placed upon them. Ourresults identify a constraint that, at least in isolation, would contribute toa bias in the evolutionary process toward more hierarchical-modular versuscompletely connected network architectures. Together, these results highlightthe context-dependence of the functionality of biological networks.

Potential unsatisfiability of cyclic constraints on stochastic biological networks biases selection toward hierarchical architectures