Biology Reference
In-Depth Information
Fig. 2. Generic GMA system and its HFPN representation. Each continuous variable
X
i
is represented by a double-lined circle,
while the continuous transitions are given as open rectangles.
associated with variable
X
i
is regarded as the
speed
of an
input transition
for
X
i
and every degradation
term
n
X
g
ijq
b
iq
j
j
=1
is regarded as the
speed
of an
output transition
. According to Petri Net philosophy, direct connectivity
exclusively reflects mass flow between places. A continuous place is graphically represented by a
double-lined circle, and a continuous transition by an open rectangle. By contrast, a discrete place is
depicted by a single-lined circle and a discrete transition by a solid rectangle.
Representation of delays and noise in the model of dopamine dynamics
In previous work [15,16] we developed a hybrid approach combining BST and HFPN that facilitates
simulations of biological systems containing different effects, including feedback regulations, switches,
randomness, and various delays. This modeling strategy can be applied directly to the dopamine signaling
system of interest here.
The main delay in the dopamine system is due to the fact that the transport of vesicular dopamine to
the synaptic cleft is slower than the biochemical reactions that are governing dopamine biosynthesis and
degradation [17]. Specifically, an appropriate signal received by the presynapse causes vesicle movement
and an upsurge in dopamine release from the vesicle (modeled as the DA-v pool) into the extracellular,
synaptic pool (modeled as DA-e), where it serves as a signaling molecule that binds to specific receptors
on the postsynaptic membrane (see Fig. 1). Figure 3 shows the HFPN implementation of the delay due
to dopamine translocation, as well as the representation of stochastic variations in the dopamine flux.
Because the exact extent of the delay and the magnitude of stochastic noise are not known, we will
explore several scenarios that appear to be most relevant. The HFPN implementation of the dopamine
signaling model with noise and delays has been submitted to a publically accessible database of models
(see [11]).
