title: Potential unsatisfiability of cyclic constraints on stochastic biological networks biases selection towards hierarchical architectures.
abstract: Constraints placed upon the phenotypes of organisms result from their interactions with the environment. Over evolutionary time scales, these constraints feed back onto smaller molecular subnetworks comprising the organism. The evolution of biological networks is studied by considering a network of a few nodes embedded in a larger context. Taking into account this fact that any network under study is actually embedded in a larger context, we define network architecture, not on the basis of physical interactions alone, but rather as a specification of the manner in which constraints are placed upon the states of its nodes. We show that such network architectures possessing cycles in their topology, in contrast to those that do not, may be subjected to unsatisfiable constraints. This may be a significant factor leading to selection biased against those network architectures where such inconsistent constraints are more likely to arise. We proceed to quantify the likelihood of inconsistency arising as a function of network architecture finding that, in the absence of sampling bias over the space of possible constraints and for a given network size, networks with a larger number of cycles are more likely to have unsatisfiable constraints placed upon them. Our results identify a constraint that, at least in isolation, would contribute to a bias in the evolutionary process towards more hierarchical -modular versus completely connected network architectures. Together, these results highlight the context dependence of the functionality of biological networks.
authors.affiliation: Department of Systems and Computational Biology, Albert Einstein College of Medicine, 1301 Morris Park Avenue, Bronx, NY 10461, USA.
authors.forename: Cameron
authors.identifier: http://orcid.org/0000-0002-6347-7506
authors.initials: C
authors.lastname: Smith
authors.affiliation: Department of Systems and Computational Biology, Albert Einstein College of Medicine, 1301 Morris Park Avenue, Bronx, NY 10461, USA.
authors.forename: Ximo
authors.identifier: http://orcid.org/0000-0001-8938-7931
authors.initials: X
authors.lastname: Pechuan
authors.affiliation: Department of Systems and Computational Biology, Albert Einstein College of Medicine, 1301 Morris Park Avenue, Bronx, NY 10461, USA.
authors.forename: Raymond S
authors.identifier: http://orcid.org/0000-0001-8866-436X
authors.initials: RS
authors.lastname: Puzio
authors.affiliation: Department of Systems and Computational Biology, Albert Einstein College of Medicine, 1301 Morris Park Avenue, Bronx, NY 10461, USA.
authors.forename: Daniel
authors.identifier: http://orcid.org/0000-0002-2100-5527
authors.initials: D
authors.lastname: Biro
authors.affiliation: Department of Systems and Computational Biology, Albert Einstein College of Medicine, 1301 Morris Park Avenue, Bronx, NY 10461, USA Dominick P. Purpura Department of Neuroscience, Albert Einstein College of Medicine, 1301 Morris Park Avenue, Bronx, NY 10461, USA Department of Pathology, Albert Einstein College of Medicine, 1301 Morris Park Avenue, Bronx, NY 10461, USA Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA aviv@einstein.yu.edu.
authors.forename: Aviv
authors.identifier: http://orcid.org/0000-0002-6340-2125
authors.initials: A
authors.lastname: Bergman
mesh_terms: D005075:Biological Evolution; D008954:Models, Biological; D013269:Stochastic Processes
keywords: biological networks; evolution; genotype–phenotype map; systems biology