Multi-method TRND integration
Each of the above individual methods provides a score for each gene/TF interaction. The statistical significance of the score is assessed by the ratio of the probability of that score in the training set to that in the random set. For a given method we determine a score R for each gene/TF interaction as above. An experimentally-verified TRN of E. coli [14] is used as the training set to determine ftrk MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGMbGzdaqhaaWcbaGaemiDaqNaemOCaihabaGaem4AaSgaaaaa@326B@(R), the fraction of the known interactions in the training set in each of a number of intervals of R for methodology k, similarly frandk MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGMbGzdaqhaaWcbaGaemOCaiNaemyyaeMaemOBa4MaemizaqgabaGaem4AaSgaaaaa@34FB@(R) is obtained for randomly chosen gene/TF interactions for methodology k. If ftrk MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGMbGzdaqhaaWcbaGaemiDaqNaemOCaihabaGaem4AaSgaaaaa@326B@(R)/frandk MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGMbGzdaqhaaWcbaGaemOCaiNaemyyaeMaemOBa4MaemizaqgabaGaem4AaSgaaaaa@34FB@(R) >> 1, an interaction with a score R for a given method is highly likely to be correct. These Bayesian ratios are computed for each method and gene/TF interaction. The sum of the log10 of these ratios is taken to be the multi-method confidence measure Kin:
K i n   = ∑ k = 1  N m e t h     w k  log ⁡  10   ( f t r  k  ( R i n  k  )  f r a n d  k  ( R i n  k  )    )          ( 4 )    MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@6960@
where wk is a weighting factor, Nmeth is the number of TRN construction methodologies, Rink MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGsbGudaqhaaWcbaGaemyAaKMaemOBa4gabaGaem4AaSgaaaaa@3225@ is the score for TF n and gene i using methodology k, ftrk MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGMbGzdaqhaaWcbaGaemiDaqNaemOCaihabaGaem4AaSgaaaaa@326B@ and frandk MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGMbGzdaqhaaWcbaGaemOCaiNaemyyaeMaemOBa4MaemizaqgabaGaem4AaSgaaaaa@34FB@ are the probability distributions for the training set and random set, respectively. If a methodology fails to have a prediction for a gene-TF pair, it is excluded in the above calculation. The weighting factors are taken to be unity in this study.