A mathematical analysis of second messenger compartmentalization

Intracellular compartmentalization of second messengers can lead to microdomains of elevated concentration that are thought to be involved in ensuring signaling specificity. Most experimental evidence for this compartmentalization involves the second messenger adenosine monophosphate (cAMP), which is degraded by phosphodiesterases (PDEs). One possible way of creating these compartments, supported by recent experiments, is to spatially separate the source of cAMP from regions of elevated PDE concentration. To quantify this possibility, we study here a simplified geometry in two dimensions (2D) and in three dimensions (3D), containing a cAMP point source and regions with different degradation constants. Using the symmetry of our geometry, we are able to derive steady state solutions for the cAMP concentration as a function of the system parameters. Furthermore, we show, using analytics as well as direct numerical simulations, that for physiologically relevant time scales the steady state solution has been reached. Our results indicate that elevating the degradation constant throughout the cell, except for a small microdomain surrounding the source, requires an unphysiologically high cellular PDE concentration. On the other hand, a tight spatial relationship of localized PDEs with the cAMP source can result in functional microdomains while maintaining a physiologically plausible cellular PDE concentration.

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