Child pages
  • 5.1 - Linear Program
Skip to end of metadata
Go to start of metadata

We interpret G with each edge $e \in E$ 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 $e=(tail,head,exonic,T)$ the contribution of the supporting transcripts $\{t_1,\ldots,t_n\}\in T$ to the flux $X_e$ observed along e can be described by a linear equation

$\sum_{t_i\in T_e}(f_i t_i) \pm \Delta_e = X_e$

(Equation 1)

where fi represents a factor that expresses the fraction of the respective transcript expression ti observed between taile and heade. In the trivial case, fi corresponds to the proportion of the interval [taile; heade] in comparison to the entire length of the processed transcript. The correction factor $\Delta_e$ 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 ti 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 $e\in E$. Subsequently, the linear equations spanned by a locus are resolved by the objective function

$min(\sum_e \Delta_e)$

(Equation 2)

Solving the linear program (Eq.2) imposed by a locus intrinsically provides an estimate for the expression level ti of all alternative transcripts that are annotated.




  • No labels