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We present a novel formulation for biochemical reaction networks in thecontext of signal transduction. The model consists of input-output transferfunctions, which are derived from differential equations, using stableequilibria. We select a set of 'source' species, which receive input signals.Signals are transmitted to all other species in the system (the 'target'species) with a specific delay and transmission strength. The delay is computedas the maximal reaction time until a stable equilibrium for the target speciesis reached, in the context of all other reactions in the system. Thetransmission strength is the concentration change of the target species. Thecomputed input-output transfer functions can be stored in a matrix, fitted withparameters, and recalled to build discrete dynamical models. By separatingreaction time and concentration we can greatly simplify the model,circumventing typical problems of complex dynamical systems. The transferfunction transformation can be applied to mass-action kinetic models of signaltransduction. The paper shows that this approach yields significant insight,while remaining an executable dynamical model for signal transduction. Inparticular we can deconstruct the complex system into local transfer functionsbetween individual species. As an example, we examine modularity and signalintegration using a published model of striatal neural plasticity. The modulesthat emerge correspond to a known biological distinction betweencalcium-dependent and cAMP-dependent pathways. We also found that overallinterconnectedness depends on the magnitude of input, with high connectivity atlow input and less connectivity at moderate to high input. This general result,which directly follows from the properties of individual transfer functions,contradicts notions of ubiquitous complexity by showing input-dependent signaltransmission inactivation.

Transfer Functions for Protein Signal Transduction: Application to a Model of Striatal Neural Plasticity