We interpret *G* with each edge colored by read mappings as a flow network, considering the read volume assigned to every (super-) edge as a flux created by the expression of the underlying supporting transcripts *T*.Consequently, given an edge the contribution of the supporting transcripts to the flux observed along e can be described by a linear equation

(**Equation 1**)

where *f*_{i} represents a factor that expresses the fraction of the respective transcript expression *t*_{i} observed between *tail*_{e} and *head*_{e}. In the trivial case, *f*_{i} corresponds to the proportion of the interval [*tail*_{e};* head*_{e}] in comparison to the entire length of the processed transcript. The correction factor in Eq.1 is to compensate for divergence from the expectation created by stochastical sampling intrinsic to RNA-Seq experiments.

The crux of the flux is that an RNA-Seq experiment provides a series of observations on the underlying expression level *t*_{i} along the transcript body. Following tradition in transportation problems, we model all of these observations as a system of linear equations by inferring Equation 1 on all . Subsequently, the linear equations spanned by a locus are resolved by the objective function

(**Equation 2**)

Solving the linear program (Eq.2) imposed by a locus intrinsically provides an estimate for the expression level *t*_{i} of all alternative transcripts that are annotated.

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