  We introduce a quantitative measure of the capacity of a small biological
network to evolve. We apply our measure to a stochastic description of the
experimental setup of Guet et al. (Science 296:1466, 2002), treating chemical
inducers as functional inputs to biochemical networks and the expression of a
reporter gene as the functional output. We take an information-theoretic
approach, allowing the system to set parameters that optimize signal processing
ability, thus enumerating each network's highest-fidelity functions. We find
that all networks studied are highly evolvable by our measure, meaning that
change in function has little dependence on change in parameters. Moreover, we
find that each network's functions are connected by paths in the parameter
space along which information is not significantly lowered, meaning a network
may continuously change its functionality without losing it along the way. This
property further underscores the evolvability of the networks.
