(a)
(b) Stimulus = 0.1 µM
Stimulus = 1 µM 70%
Active receptors
70% Uncoupled
Uncoupled
50%
50%
30%
30% Coupled
0%
-5
Coupled
0
5
10
0%
-5
0
5
10
Time (s)
Figure 10.3 The enhancement of response achieved by coupling interactions in the receptor cluster model. Changes in total receptor activity during a doubling of stimulus at two background concentrations, (a) 0.1 µM and (b) 1 µM are shown. The concentration of ligand was doubled at time 0 in both (a) and (b). Significant enhancement is observed at both concentrations; the coupled array shows clear amplification of the ligand signal in (a), and in (b) only the coupled array shows a significant response to the doubling of attractant, demonstrating that the coupling could also act to increase the range of concentrations to which the system can respond.
ters were first adapted to various background concentrations of attractant and tested for their response to a subsequent doubling in stimulus, significant amplification of the signal is observed (Figure 10.3). The level of amplification is not as high as that reported previously (Bray et al., 1998; Duke et al., 1999), but the performance of the receptor cluster is less dependent on the precise value of the coupling strength. These differences arise because the previous models did not consider the multiple methylation states of the receptors, which can be covalently modified with up to four methyl groups. We are now investigating the effect of spatial patterns of methylation, an example of which is shown in Figure 10.4. FUTURE DIRECTIONS
The obvious next steps for development of STOCHSIM are the implementation of other geometries (e.g. triangular and hexagonal) for the twodimensional arrays, further extending the spatial representation to a third dimension, and the development of a more generally accessible interface. Recent models of the neuromuscular junction include a realistic representation of the folds of the muscle membrane surface, the position and state of individual synaptic vesicles, and even the location of individual calcium ions (Stiles and Bartol, 2000). Three-dimensional representation of a cell may require some form of compartmentalization of its contents, whether into regularly spaced volume elements (voxels) or more biologically relevant compartments, such as nucleus, and membrane cortex. The interface development is now focused around a cross-platform
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Computational Cell Biology — The Stochastic Approach