RNA Transcript Assembly Using Inexact Flows

RNA-Seq technology allows for high-throughput, low cost measurement of gene expression. An important step in this process is the assembly of mRNA transcript short reads into full transcripts. The problem can be viewed as a flow decomposition problem in which the objective is to minimize the number of path flows needed to represent a given flow. In this work we relax the edge flow constraints to allow for some uncertainty in their measurement. We formulate this as the Inexact Flow Decomposition problem and propose an algorithmic strategy to solve it. In practice, real biological data has measurement errors and so experimentally-derived edge-weighted splice graphs are often not flows. The proposed method is the first approach to this problem that explicitly controls the error allowed on each edge in these graphs in order to achieve a flow. In an intermediate step, the method solves an exact flow decomposition instance; if a greedy method is used for this step, the overall running time is $O(\vert E\vert^{2}\vert V\vert^{2}+\vert P\vert^{3})$, where $P$ is the solution found to the flow decomposition instance. Preliminary results on simulated biological data sets show that in many cases the ground truth paths can be recovered at approximately correct abundances, even with noisy input data.