Biology Reference
In-Depth Information
Fig. 1. The chemical synapse of a dopaminergic neuron and its role in signal transduction. The top part of the diagram
schematically shows key features of the dopamine pathway in the presynapse and, below, in the synaptic cleft of the dopaminergic
neuron. Triangles represent the neurotransmitter dopamine, while circles indicate calcium (Ca
2+
) ions. An external stimulus
triggers an action potential at the dopaminergic terminal and induces calcium influx into the cytosol. The calcium influx spikes
dopamine release into the cleft, where the neurotransmitter binds to its receptor on the postsynaptic membrane.
Inside the
postsynapse, various downstream signaling cascades are triggered, and the signal is successfully transduced.
METHODS
The dopamine signaling system as described above consists of interacting discrete and continuous
components and processes that operate at different time scales. The hybrid nature of this system requires
special means of analysis, because it does not fit neatly into the realm of deterministic models, where sets
of ordinary differential equations (ODEs) are used to represent the continuous changes of the participating
system components over time. Furthermore, the system is too complicated to permit comprehensive
stochastic models and simulations that are based on the Chemical Master Equation, even if these are
implemented as stochastic kinetic systems in advanced versions of the Gillespie algorithm [12]. Instead,
it is necessary to develop a hybrid modeling methodology that allows us to merge seamlessly the
deterministic and stochastic aspects of the system into a unifying framework for integrative systems
analyses. A good candidate for this task is a
Hybrid Functional Petri Net
(HFPN, [13]). In previous
work, we showed that HFPNs can be combined effectively with methods of
Biochemical Systems Theory
(BST, [14]) for the analysis of largely continuous systems, which however are affected significantly by
delays and stochastic noise [15,16]. We show here how this hybrid methodology can be used to explore the
performance of the dopamine signaling system under typical perturbations as well as under disturbances
