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that dopamine imbalance is the underlying mechanism for symptoms of the disease. Accordingly, the
main medication has been the administration of antipsychotics that reduce dopaminergic activity through
blockade of the dopamine D2 receptor. Finally, the dopamine signaling system is compromised in many
types of drug addiction, for instance to cocaine or methamphetamine, either through competition between
the drug and dopamine in the presynaptic neuron or by competition for receptors exposed to the synaptic
cleft.
The abnormal activity of dopamine signaling in PD, schizophrenia, and drug addiction demonstrates
the important role of dopamine dynamics in the presynaptic neuron of the striatum and the synaptic
cleft, where dopamine synthesis, degradation, compartmentalization, release, reuptake, and numerous
regulatory processes occur (Fig. 1). On the presynaptic side, the biosynthetic dopamine pathway
begins with the precursor tyrosine, which is converted into L-DOPA and subsequently into the key
neurotransmitter dopamine. Dopamine is packed into intracellular vesicles by the vesicular monoamine
transporter. The packed dopamine is released into the synaptic cleft, where it can bind to dopamine
receptors on the postsynaptic membrane. Some of the dopamine in the cleft also diffuses out of the cleft,
or is transported back into the cytosol of the presynaptic neuron by the dopamine transporter. In addition
to this cycle, dopamine can be degraded by the enzymes catechol O-methyltransferase and monoamine
oxidase.
Under normal, unstimulated conditions, relatively small amounts of dopamine cycle between the
presynaptic cytosol, vesicle, and synaptic cleft. However, if there is a stimulus, an action potential is
produced 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 specific receptors on the
postsynaptic membrane. Inside the postsynapse, various downstream signaling cascades are triggered,
and the signal is successfully transduced.
The functionality of dopaminergic neurons is altered when these are exposed to certain drugs like
amphetamine and methamphetamine. According to current observations, amphetamine and metham-
phetamine cause dopamine to leak from the vesicles into the cytosol, resulting in significant increases in
the cytosolic dopamine level. This excess consequently produces an efflux of dopamine into the synaptic
cleft through dopamine transporters instead of the reverse flux that is typical for intact neurons [4-
7]. At the same time, amphetamine and methamphetamine regulate the generation and degradation
of dopamine [8,9]. Through these mechanisms, the drugs substantially alter the neurotransmission
characteristics of the dopaminergic synapse.
The dopamine recycling process involves neurotransmitter packaging, release, binding, disassociation,
and reuptake. Some of the biological steps associated with these processes take an appreciable amount
of time to perform, thereby in effect causing delays. Since these delays must be expected to affect the
dynamics of dopamine transmission, and since such effects might be different between intact and diseased
systems, it is important to study the consequences of delays on dopamine transmission systematically.
Moreover, like most every biological process, dopamine signaling is subject to germane stochasticity
and external perturbations. For example, the rate of an enzymatic or transport process is typically
considered constant, leading to a deterministic kinetic description. However, in reality the dynamics of
the reaction is a random process, which is strongly exacerbated if only small numbers of reactants are
involved (e.g., [10]). Accounting for stochasticity in a dynamic system requires specialized software,
and if the system also contains delays, it is difficult to find a suitable modeling framework, along with
supporting software. We show here how Hybrid Functional Petri Nets (HFPNs) and the software Cell
Illustrator facilitate the computational analysis of systems that contain deterministic, stochastic, and
delay components and demonstrate their utility with an analysis of dopamine signaling. The model
describing these aspects has been submitted to a publically accessible model database (see [11]).
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