Murugan R

Eukaryotic genes are typically split into exons that need to be spliced together to form the mature mRNA. The splicing process depends on the dynamics and interactions among transcription by the RNA polymerase II complex (RNAPII) and the spliceosomal complex consisting of multiple small nuclear ribonucleo proteins (snRNPs). Here we propose a biophysically plausible initial theory of splicing that aims to explain the effects of the stochastic dynamics of snRNPs on the splicing patterns of eukaryotic genes. We consider two different ways to model the dynamics of snRNPs: pure three-dimensional diffusion and a combination of three- and one-dimensional diffusion along the emerging pre-mRNA. Our theoretical analysis shows that there exists an optimum position of the splice sites on the growing pre-mRNA at which the time required for snRNPs to find the 5′ donor site is minimized. The minimization of the overall search time is achieved mainly via the increase in non-specific interactions between the snRNPs and the growing pre-mRNA. The theory further predicts that there exists an optimum transcript length that maximizes the probabilities for exons to interact with the snRNPs. We evaluate these theoretical predictions by considering human and mouse exon microarray data as well as RNAseq data from multiple different tissues. We observe that there is a broad optimum position of splice sites on the growing pre-mRNA and an optimum transcript length, which are roughly consistent with the theoretical predictions. The theoretical and experimental analyses suggest that there is a strong interaction between the dynamics of RNAPII and the stochastic nature of snRNP search for 5′ donor splicing sites. © 2012 Murugan, Kreiman.

The temporal dynamics of the concentrations of several proteins are tightly regulated, particularly for critical nodes in biological networks such as transcription factors. An important mechanism to control transcription factor levels is through autoregulatory feedback loops where the protein can bind its own promoter. Here we use theoretical tools and computational simulations to further our understanding of transcription-factor autoregulatory loops. We show that the stochastic dynamics of feedback and mRNA synthesis can significantly influence the speed of response of autoregulatory genetic networks toward external stimuli. The fluctuations in the response-times associated with the accumulation of the transcription factor in the presence of negative or positive autoregulation can be minimized by confining the ratio of mRNA/protein lifetimes within 1:10. This predicted range of mRNA/protein lifetime agrees with ranges observed empirically in prokaryotes and eukaryotes. The theory can quantitatively and systematically account for the influence of regulatory element binding and unbinding dynamics on the transcription-factor concentration rise-times. The simulation results are robust against changes in several system parameters of the gene expression machinery. © 2011 Biophysical Society.