Temporal fluctuation of nuclear pore complex localization by single diffusing mRNP complexes

There is now compelling evidence that messenger ribonucleoprotein (mRNP) complexes after the release from the transcription/processing sites execute essentially unhindered Brownian movements in the nucleoplasm and target nuclear pore complexes (NPCs) by chance encounter. For the majority of genes expressed in eukaryotic cells, only single/few transcript copies are generated, which reinforces the stochastic nature of NPC localization. In this paper, I analyse the NPC localization by freely diffusing single mRNPs and discuss the implications for the temporal progression of gene expression and consecutive processes associated with the gene products. To this end, a walk-and-capture model is considered, assuming a spherical nuclear compartment with a partially absorbing boundary. Perfect absorption and perfect reflection mark the extreme outcomes. For this model, the closed-form analytic solution of the first-passage time probability density function (FPT p.d.f.), the mean passage time and variance have been obtained. The FPT p.d.f. enables to calculate the probability that single mRNPs localize the nuclear boundary and dock to NPCs within certain time windows. For freely moving mRNP complexes in osteosarcoma cell nuclei, a mean apparent diffusion coefficient (D) of 0.04 μm2 s−1 (range 0.01–0.09 μm2 s−1) has been reported. Assuming a nuclear radius of 8 μm and D=0.04 μm2 s−1, the position-averaged minimum mean passage time 〈 τ ( r 0 ) 〉 min for the considered model is 1.8 min, which presupposes perfect absorption of the mRNP complex at the first encounter with the nuclear boundary. In this case, the probability of capture in the time interval ( 0 , 〈 τ ( r 0 ) 〉 min ) is 0.67. In smaller sized yeast cell nuclei with a radius of 0.8 μm and D=0.04 μm2 s−1, single diffusing mRNPs would localize an NPC within tens of seconds, rather than minutes.