UCSF

The problem of understanding the connection between network topology and dynamical output represents a critical challenge for modern biology. We begin by reviewing recent progress in the evolution of Boolean models that seek to gain insight into this problem for specific biological systems. Like the sketchpad for an artist, the Boolean model enables one to capture the essential features of a cellular landscape. Often, the Boolean sketch is sufficient to generate insights yielding testable hypotheses in settings ranging from developmental networks to neural circuits. However, the Boolean approach has another, little explored advantage. Owing to its relative computational efficiency, a Boolean framework permits a comprehensive theoretical exploration of the relationship between network topology and dynamical output.

Pursuing this thought, we investigate the connection between network topology (genotype) and dynamical output (phenotype) for an ensemble of several million small networks, utilizing a Boolean model. We hypothesize that a global approach to understanding biological network design may reveal principles that are difficult to identify by examining specific systems. By exhaustive enumeration of three and four node networks, we demonstrate that certain dynamical phenotypes are highly designable, in that they can be generated by an atypically broad spectrum of topologies. The topologies that encode highly designable phenotypes possess two classes of connections: a fully conserved core that encodes the stable dynamical phenotype and a partially conserved set that controls the transient dynamics. By comparing the topologies and dynamics of the three and four node ensembles, we discover "mutational buffers", whereby a fourth node suppresses phenotypic variation amongst a set of three node networks.

We next consider the concept of designability more broadly and its possible role in the evolution of biological phenotypes. We test the notion of designability on a real biological system by analyzing the dynamics of the yeast cell cycle. A comparison of the designability of the cell cycle phenotype with the designabilities of a pool of perturbed phenotypes reveals that the designability of the cell cycle dynamics is near optimal. This finding provides some evidence for the hypothesis that designability may couple with the traditional fitness landscape to influence the evolution of biological phenotypes.