  In this paper we consider deterministic limits of molecular stochastic
systems with finite and infinite degrees of freedom. The method to obtain the
deterministic vector field is based on the continuum limit of such microscopic
systems which has been derived in [11]. With the aid of the theory we finally
develop a new approach for molecular systems that describe typical enzyme
kinetics or other interactions between molecular machines like genetic elements
and smaller communicating molecules. In contrast to the literature on enzyme
kinetics the resulting deterministic functional responses are not derived by
time-scale arguments on the macroscopic level, but are a result of time scaling
transition rates on the discrete microscopic level. We present several examples
of common functional responses found in the literature, like Michaelis-Menten
and Hill equation. We finally give examples of more complex but typical
macro-molecular machinery.
