  The paper analyses stochastic systems describing reacting molecular systems
with a combination of two types of state spaces, a finite-dimensional, and an
infinite dimenional part. As a typical situation consider the interaction of
larger macro-molecules, finite and small in numbers per cell (like protein
complexes), with smaller, very abundant molecules, for example metabolites. We
study the construction of the continuum approximation of the associated Master
Equation (ME) by using the Trotter approximation [27]. The continuum limit
shows regimes where the finite degrees of freedom evolve faster than the
infinite ones. Then we develop a rigourous asymptotic adiabatic theory upon the
condition that the jump process arising from the finite degrees of freedom of
the Markov Chain (MC, typically describing conformational changes of the
macro-molecules) occurs with large frequency. In a second part of this work,
the theory is applied to derive typical enzyme kinetics in an alternative way
and interpretation within this framework.
