It has been shown in pancreatic acinar cells (Craske et al. 1999) that calmodulin (CaM) undergoes intracellular redistribution after application of the calcium-releasing agonists, acetylcholine (ACh) and cholecystokinin (CCK). A large cytosolic calcium transient generated by a super-maximal dose of ACh caused a rapid rise of [CaM] in apical region and a rapid drop in the basal region while the [CaM] in the nucleus rose more slowly, and lasted long after the termination of the calcium transient. Global cytosolic calcium spikes generated by 5 pM CCK caused [CaM] spikes in the apical region that resembled cytosolic calcium spikes, and [CaM] in the basal region showed the mirror image of the apical [CaM] spikes with smaller magnitude. On the other hand, [CaM] in the nucleus showed a delayed, slower and steadier increase that stabilized in about 100 s and its fluctuations were much smaller than those of [CaM] in apical or basal region.
In order to understand these behaviours of [CaM] during the agonist stimulations, we developed computational models using FEMLAB, an interactive environment for modelling mathematical problems based on a system of coupled partial differential equations. The model had one-dimensional geometry with three subdomains which represented the nucleus, apical and basal cytosolic regions. We assumed that calcium-free calmodulin (apoCaM) and calcium-bound calmodulin (CaCaM) could diffuse freely in the cytosol or in the nucleus, or bind to non-diffusible binding partners (apoCaM-binding proteins and CaCaM-binding proteins, respectively). It was also assumed that the diffusion between the cytosol and the nucleus was limited by nuclear pores whose permeability for CaM was dependent on cytosolic calcium concentration. Calcium concentration was set to be spatially uniform.
Our computational models showed (1) that a heterogeneous distribution of calmodulin binding proteins and the calcium dependence of the permeability of nuclear pores for CaM were the basis of the translocation of CaM induced by the change of cytosolic calcium, (2) a positive effect of calcium on the permeability for CaM explaining the delay in the accumulation of CaM in the nucleus which was observed experimentally, and (3) that binding proteins for apoCaM worked against the translocation by stabilizing free CaM concentration.
Our models can be used for the analysis of translocation of other calcium binding proteins with different properties (e.g. translocation from the cytosol to the plasma membrane or organellar membranes).