Next we show that positional clustering improves robustness to the addition of DSs (Figures 2 and 3) . Such sequences arise from inclusion of promoter regions in input sets without direct binding to the TF either due to experimental error or computational mis-annotation (17, 22) . In the STE12 example studied, linear regression models indicate our approach will maintain an advantage over traditional Gibbs sampling through addition of up to 150% noise to the original signal (Supplementary Figure S4) . Empirical data, however, show a sharp decrease in improvement close to the addition of 45 DSs, or roughly double the input set ( Figure 2 ). Moreover, evaluations using promoters co-regulated by other TFs Figure 6 . Double-stranded oligonucleotide functional assay for GABRA4 regulation. Primary cultures of rat neocortical neurons were treated with DOTAP (N-[1-(2,3-dioleoyloxy)propyl]-N,N,N-trimethylammonium methylsulfate) alone (Mock) or with DOTAP and phosphothioate oligonucleotides from either a cAMP response element (CRE Decoy) or a sequence from the GABA-A4 promoter predicted using positional clustering (GABA-A4 Decoy) (GTGCACACACACGCCCACCGCGGCTCGGG). mRNA was harvested after 24 h, and real-time RT-PCR was performed with GABA-A4 specific primers. Error bars refer to individual experiments; i.e. different platings of cells from different animals. Data was normalized to rRNA levels, and expressed as relative mRNA levels (GABA-A4/rRNA). Results are shown as mean ± SEM, N ¼ 3, asterisk indicates significantly different from control at the 95% confidence interval. Figure 5 . EMSA of three putative TF binding sites form DNA-protein complexes in neocortical and fibroblast nuclear extracts. Neocortical (NEO) and fibroblast (FIB) nuclear extracts from E18 rat embryos were incubated with three 32 P-radiolabeled probes from human A4 and D receptor subunits. Cold wild-type oligonucleotides were used to define specificity through competition. Cold oligonucleotides were added at 100-fold excess over probe. indicate positional clustering is less likely to improve predictions when Gibbs sampling identifies a correct site in <20% of repetitions ( Figure 3 ). Thus, it is possible the rather simplistic linear model overestimates improvement in robustness beyond what is practically achievable. Moreover, when multiple motifs exist in the input promoters, preliminary evidence suggests positional clustering will uniquely identify a single dominant motif (Supplementary Figure S5) . With further refinement, however, it may be possible to recover subordinate motifs, enabling identification of cis-regulatory modules. In spite of these limitations, using positional clustering of repeated runs, researchers can successfully apply sampling algorithms in identification of functional binding sites in datasets with a significant proportion of noise.