  A macroscopic theory for describing cellular states during steady-growth is
presented, which is based on the consistency between cellular growth and
molecular replication, as well as the robustness of phenotypes against
perturbations. Adaptive changes in high-dimensional phenotypes were shown to be
restricted within a low-dimensional slow manifold, from which a macroscopic law
for cellular states was derived, which was confirmed by adaptation experiments
on bacteria under stress. Next, the theory was extended to phenotypic
evolution, leading to proportionality between phenotypic responses against
genetic evolution and environmental adaptation. The link between robustness to
noise and mutation, as a result of robustness in developmental dynamics to
perturbations, showed proportionality between phenotypic plasticity by genetic
changes and by environmental noise. Accordingly, directionality and constraint
in phenotypic evolution was quantitatively formulated in terms of phenotypic
fluctuation and the response against environmental change. The evolutionary
relevance of slow modes in controlling high-dimensional phenotypes is
discussed.
