  Biological organisms are open, adaptve systems that can respond to changes in
environment in specific ways. Adaptation and response can be posed as an
optimization problem, with a tradeoff between the benefit obtained from a
response and the cost of producing environment-specific responses. Using recent
results in stochastic thermodynamics, we formulate the cost as the mutual
information between the environment and the stochastic response. The problem of
designing an optimally performing network now reduces to a problem in rate
distortion theory -- a branch of information theory that deals with lossy data
compression. We find that as the cost of unit information goes down, the system
undergoes a sequence of transitions, corresponding to the recruitment of an
increasing number of responses, thus improving response specificity as well as
the net payoff. We derive formal equations for the transition points and
exactly solve them for special cases. The first transition point, also called
the {\it coding transition}, demarcates the boundary between a passive response
and an active decision-making by the system. We study this transition point in
detail, and derive three classes of asymptotic behavior, corresponding to the
three limiting distributions of the statistics of extreme values. Our work
points to the necessity of a union between information theory and the theory of
adaptive biomolecular networks, in particular metabolic networks.
