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

Molecular Systems with Infinite and Finite Degrees of Freedom. Part II: Deterministic Dynamics and Examples