Symbolic rewriting systems are gaining interest as tools for simulating biochemical dynamics. Compared to traditional methods based on differential equations, the symbolic approach allows a straightforward translation of a signal transduction network into a system of rewriting rules capable of describing the network dynamics by means of a proper application of these rules. Coherently with this design approach, our algorithm applies rewriting rules proportionally to the values assumed by specific reaction maps. Such maps are nonlinear functions of the state of the system. Preliminary results obtained using this algorithm in the simulation of a known model of circadian rhythms in Drosophila envision its potential applicability in reproducing complex biochemical networks, such as that presented here.