Mathematical modeling of transcription-independent splicing events in human gene expression

ElizabethTrofimenkoff

University of Lethbridge

"Mathematical modeling of transcription-independent splicing events in human gene expression"

Pre-mRNA often contains introns, which are non-coding sequences that need to be cut out or spliced before translation occurs. The spliceosome, an essential catalyst composed of several proteins with specific sequence affinities, is required for this process. Very long introns must be removed in pieces, a process known as recursive splicing. The experimental literature on the time it takes for the splicing process to occur is inconsistent. Splicing was traditionally believed to be a slow process that could take anywhere from one to tens of minutes per splicing event. However, recent reports suggest that some splicing events occur within a few tens of seconds. We developed the chemical master equation corresponding to the biochemical mechanism of splicing, allowing us to derive the system’s probability distribution, and perform a stability analysis on two conditions based on an unknown association constant parameter associated with the binding step of the scaffolding complex. We also concluded that the distribution of splice times for a single event ranges from a few tens of seconds to a few tens of minutes. Through sensitivity analyses, we have found that the mean splicing time and distribution are almost entirely dependent on the rate at which the spliceosome is activated in the assembly process—i.e. when the U1 and U4 splicing factors dissociate—which confirms that this is the rate limiting step in the catalytic process. Finally, we have examined the distributions of recursive splicing up to six events, and derived analytic solutions for these recursive splicing events in the case where the scaffolding complex strongly binds to the pre-mRNA complex (the condition thought to favor recursive binding), thus providing a model that can be fit to experimental data to in order to evaluate the number of recursive splicing events occurring.
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