Enhancement of U4/U6 small nuclear ribonucleoprotein particle association in Cajal bodies predicted by mathematical modeling

Spliceosomal small nuclear ribonucleoprotein particles (snRNPs) undergo specific assembly steps in Cajal bodies (CBs), nonmembrane-bound compartments within cell nuclei. An example is the U4/U6 di-snRNP, assembled from U4 and U6 monomers. These snRNPs can also assemble in the nucleoplasm when cells lack CBs. Here, we address the hypothesis that snRNP concentration in CBs facilitates assembly, by comparing the predicted rates of U4 and U6 snRNP association in nuclei with and without CBs. This was accomplished by a random walk-and-capture simulation applied to a three-dimensional model of the HeLa cell nucleus, derived from measurements of living cells. Results of the simulations indicated that snRNP capture is optimal when nuclei contain three to four CBs. Interestingly, this is the observed number of CBs in most cells. Microinjection experiments showed that U4 snRNA targeting to CBs was U6 snRNP independent and that snRNA concentration in CBs is similar to 20-fold higher than in nucleoplasm. Finally, combination of the simulation with calculated association rates predicted that the presence of CBs enhances U4 and U6 snRNP association by up to 11-fold, largely owing to this concentration difference. This provides a chemical foundation for the proposal that these and other cellular compartments promote molecular interactions, by increasing the local concentration of individual components.