Chemistry Reference
In-Depth Information
the cells. However, assuming that ligand binding follows a Poisson distribution,
receptor occupancy on the whole surface of the cells can be calculated by numerical
simulations based onparameter values obtained experimentally forDictyosteliumcells.
Such simulations con
rm that input signals for chemotaxis are noisy.
Single-molecule imaging analysis has also revealed stochastic behaviors for other
signaling molecules responsible for chemotactic response [23, 24]. Crac, which is one
of the PH-domain-containing proteins, is stably localized at the pseudopod of che-
motaxing cells. We observed GFP-tagged Crac (Crac-GFP) and examined the mem-
brane-binding properties of Crac-GFP in cells undergoing chemotaxis. At the leading
edge of the pseudopod of chemotaxing cells, individual molecules of Crac-GFP bind
to the membrane in the order of
100ms, while populations of Crac-GFP molecules
appear to be localized in a stable manner on the membrane. Thus, Crac localization at
the pseudopod is maintained dynamically by rapid exchanges of the individual Crac-
GFP molecules. Such rapid exchanges of individual Crac molecules cause inevitable
fluctuations in the ensemble concentrations of Crac molecules at the pseudopod,
which is the molecular basis of signal noise. However, at the same time, the rapid
exchange ofmolecules provides amolecular basis for rapid reorientation in response to
directional changes in the chemical gradients, which can contribute to an accurate and
sensitive chemotactic response. These dynamic properties have also been found in
PTEN molecules [24]. Overall, this may be a general process for signaling molecules
involved in chemotaxis.
5.9
Stochastic Model of Transmembrane Signaling by Chemoattractant Receptors
How can signal and noise propagation during transmembrane signaling by the
receptors be characterized? What properties of the receptors are important for signal
and noise propagation? We consider a simple but general scheme for transmem-
brane signaling in which receptors receive ligands stochastically as signal inputs.
These activated receptors generate second messengers stochastically as outputs
(Scheme 1; Figure 5.7A) [25].
k
p
k
d
k
on
k
of f
R
;
R
þ
R
þ
X
;
X
!
R
þ
L
!
X
!
X
ð
5
:
1
Þ
where R, R
and L represent inactive receptors, active receptors and the ligand,
respectively. X and X
are inactive and active second messengers. X can be regarded
as the G protein for chemotactic signaling in Di
cty
ostelium cells. According
to
this
scheme, the average number of active receptors R
and second messengers X
per
cell can be calculated using Michaelis
-
Menten kinetics,
Þ
1
R
Þ
1
R
¼
X
¼
R
ð
R
total
L
ð
K
R
þ
L
;
X
total
K
X
þ
ð
5
:
2
Þ
where R
total
is the total molecular number of receptors per single cell, K
R
k
off
/k
on
is
the af
nity for the ligand with association and dissociation rate constants k
on
and k
off
,
¼
