| Intracellular signaling molecules form pathways inside the cell. These pathways carry a signal to target proteins which results in cellular responses. We consider a spherical cell with two compartments containing localized activating enzymes. Two diffusible signaling molecules are activated at the compartments and later deactivated in the cytosol due to deactivating enzymes. The two signaling molecules act as molecular switches to form a self regulated system involving positive and negative feedback. Using a method known as matched asymptotic expansions we obtain approximate solutions of the steady state diffusion equation with a linear decay rate. Hence we obtain three dimensional concentration profiles for the signaling molecules. The profiles either decay exponentially or algebraically depending on the diffusion length of the molecule. We also investigate an extension of the above system with multiple compartments. Numerically, we show the speed of the signal is an increasing function of the number of compartments. |
