Assigning probes into a small number of pools separable by electrophoresis

Motivation: Measuring transcriptional expression levels (transcriptional profiling) has become one of the most important methods in functional genomics. Still, new measuring methods are needed to obtain more reliable, quantitative data about transcription on a genomic scale. In this paper we concentrate on certain computational optimization problems arising in the design of one such novel method. From a computational point of view the key feature of the new method is that the hybridized probes are distinguished from each other based on their different size. Therefore the probes have to be assigned into pools such that the probes in the same pool have unique sizes different enough from each other. Identification of expressed RNA is given by probe pool and probe size while quantification is given by the label of the probe, e.g. fluorescence intensity. Results: We show how to computationally find the probes and assign them into pools for a whole genome such that (i) each gene has a specific probe suitable for amplification and hybridization, and (ii) the expression level measurement can be done in a minimal number of pools separable by electrophoresis in order to minimize the total experiment cost of the measurement. Our main result is a polynomial-time approximation algorithm for assigning the probes into pools. We demonstrate the feasibility of the procedure by selecting probes for the yeast genome and assigning them into less than 100 pools. The probe sequences and their assignment into pools are available for academic research on request from the authors.