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with one another, resulting in a suboptimal number of effective responses. As indicated by the results in
Figs 6 and 7, noise may have the following effects:
1. Not surprisingly, for a fixed noise frequency, noise with larger amplitude imposes more serious
distortions on signal transduction than small amplitude noise. Specifically, it results in a significantly
reduced number of effective responses.
2. For fixed amplitude, decreased noise frequency of the type tested here leads to reductions in effective
responses.
3. In the absence of a signal, noise alone does not significantly change the system dynamics for wide
ranges of frequencies and amplitudes (Fig. 7).
These results indicate that the signaling system is very robust to noise of high frequency, such as 100 Hz,
while it is much more vulnerable to perturbations with frequencies lower than 10 Hz.
Combined effects of delays and noise
The discussions in the previous sections have demonstrated that both noise and delay, when separately
in effect, have the tendency to distort signal transduction. These findings raise the question of whether
the combination of delay and noise would make the situation even worse. This answer is very difficult to
obtain with intuition and hard thinking alone. Thus, we systematically investigated combined effects of
various delays and noise using representative signals with w 1 = 0.01s, w 2 = 0.2s. As before, a response
was counted as effective when the DA-e level surpassed the threshold of 185% of the baseline.
Figure 8 shows that the two effects may counteract each other and that, surprisingly, the signaling
system is more effective in its responses when noise is accompanied by short delays. For instance, the
influence of 100 Hz noise is best reduced in a system with 0.05s delay, while 40 Hz and 20 Hz noise
is well counteracted by a 0.1s delay. However, if the delay is very long, such as 0.2s, noise and delay
exacerbate each other's effects and lead to misfiring that appears to be quite unreliable.
DISCUSSION
Every signal transduction process starts with an initial stimulus that triggers one or more signaling
cascades. The final component of the signaling cascade has a direct effect on gene expression or on the
activation of relevant metabolic pathways. In the case of dopamine signaling, the initial stimulus is an
action potential that is converted into a rapid influx of calcium into the presynaptic neuron. This influx
triggers the release of dopamine into the synaptic cleft, binding to receptors on the postsynaptic mem-
brane, and signal processing by the postsynaptic DARPP-32 protein, which ultimately leads to genomic,
metabolic or neurophysiological responses. Predicting the functioning of the dopamine signaling system
is difficult, because many molecular components are involved and because dopamine itself is subject
to biosynthesis, degradation, diffusion out of the synaptic cleft, and other processes that change over
time and are adaptive in nature. For instance, dopamine may affect the proper functioning of dopamine
receptors on the postsynaptic cell membrane. These receptors are normally stable, but exhibit greatly
diminished receptor activity in response to sharp or prolonged increases in dopamine concentration. In
cases of amphetamine and cocaine abuse, this type of down-regulation of dopamine receptors has been
associated with a shortened attention span, further drug craving, and loss of interest in social activities
even if they are otherwise considered pleasant.
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