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experimentally for Dictyostelium cells. Figure 5.7C shows the dependence of the SNR
on the average ligand concentration with a 2% gradient. The SNR dependence
resembles the dependence of chemotactic accuracy on ligand concentration mea-
sured experimentally for Dictyostelium cells [16]. This agreement between the SNR
and the accuracy of chemotaxis indicates that the ability of directional sensing is
limited by the stochastic noise generated inherently during the transmembrane
signaling of receptors. Furthermore, it suggests that chemotactic accuracy is deter-
mined primarily at themost upstream reactions of the chemotactic signaling system.
Our stochastic model can be further applied to other chemotactic cells. Similar
dependence of chemotactic accuracy has been also observed in mammalian leuko-
cytes and neurons [15, 29].
Equation 5.5 suggests how the SNR of chemotactic signals is enhanced or
diminished by the properties of the receptors and the downstream second messen-
ger. The time constants and the gains of the signaling reactions determine the signal
and noise propagation and hence the SNR of chemotactic signals. For example, a
longer lifetime of the second messenger leads to more effective noise reduction by
time-averaging the extrinsic noise because the time constant,
t
X
, becomes larger,
suggesting that the regulatory mechanism for second messenger inactivation may
play a pivotal role in signal enhancement during chemotaxis. The GTPase-activating
proteins such as regulators of G protein signaling (RGS) can regulate the quality of
the signal by modulating the inactivation rates of the G protein. Modulation of the
time constant,
R
, also has an effect on the SNR of chemotactic signals. Acceleration
of the on-rate (k
on
) and the off-rate (k
off
) in the ligand-binding reaction would cause a
decrease in
t
R
leading to an enhancement in the SNR. Polarity in receptor kinetic
states along the length of chemotactic cells has been observed by single-molecule
measurements [22], suggesting a polarity in the SNR of chemotactic signals. This
may provide a molecular basis for the polarity observed in the chemotactic response
of Dictyostelium cells [30]. When the secondmessenger is produced by a reaction with
cooperativity, the gain, g
X
, may become larger, causing noise reduction by decreasing
the intrinsic noise [28].
It is important to emphasize that signal transduction systems can carry out signal
processing under the strong in
t
ll their
functions, cells must have some mechanism which makes them resistant to such
strong noise. In particular, chemotactic cellsmust overcome the noise in order to gain
high sensitivity for shallow gradients within a wide dynamic range. In addition, cells
could also be taking advantage of the molecular noise to undertake their functions,
which could not be achieved without noise. We show here that the gain-
uctuation
relationship can be applied successfully to a stochastic signaling system. The signaling
processes such as association/dissociation, enzymatic catalysis and chemical modi-
fication of signaling molecules have been described by Michaelis
-
Menten method-
ology and its extended equations. However these only explain the relationship
between signal inputs and outputs on average. The gain-
uctuation relationship can
be used to describe not only the signal but also the noise propagation along signaling
cascades. According to the relationship, it is important to determine the time
uence of molecular noise. In order to ful
