Affiliations: School of Mathematics, Georgia Institute of
Technology, Atlanta, Georgia, USA | Department of Biomedical Engineering, Georgia
Institute of Technology and Emory University Medical School, Atlanta, Georgia,
USA
Abstract: Dopamine is a critical neurotransmitter for the normal functioning
of the central nervous system. Abnormal dopamine signal transmission in the
brain has been implicated in diseases such as Parkinson's disease (PD) and
schizophrenia, as well as in various types of drug addition. It is therefore
important to understand the dopamine signaling dynamics in the presynaptic
neuron of the striatum and the synaptic cleft, where dopamine synthesis,
degradation, compartmentalization, release, reuptake, and numerous regulatory
processes occur. The biochemical and biological processes governing this
dynamics consist of interacting discrete and continuous components, operate at
different time scales, and must function effectively in spite of intrinsic
stochasticity and external perturbations. Not fitting into the realm of purely
deterministic phenomena, the hybrid nature of the system requires special means
of mathematical modeling, simulation and analysis. We show here how hybrid
functional Petri-nets (HFPNs) and the software Cell
Illustrator® facilitate computational
analyses of systems that simultaneously contain deterministic, stochastic, and
delay components. We evaluate the robustness of dopamine signaling in the
presence of delays and noise and discuss implications for normal and abnormal
states of the system.
Keywords: Amphetamine, Biochemical System Theory (BST), delay, dopamine signaling, HFPN, hybrid modeling, Parkinson's disease, Petri nets, schizophrenia, stochasticity
