TI - NCA identifies transcription factors perturbed by isobutanol . AB - NCA uses transcription network connectivity to deduce transcription factor activities ( TFAs ) and control strengths ( CSs , quantified TF-gene interaction ) from gene -expression data . The following transcription regulation model is used : where mRNAi is the mRNA transcript level of genei , TFAj is the activity level of TFj , CSij is the control strength of TFj on the expression of genei , and ( t ) and (0) designate condition t and reference condition 0 . Equation (1) can be linearized by taking the log , and multiple experiments can be represented in matrix form using the equation where E is an ( N x M ) matrix of expression ratios , A is an ( N x L ) matrix of CSs , P is an ( L x M ) matrix of TFAs , N is the number of genes , L is the numbers of TFs , M is the number of experiments and Gamma is the residual of the model . As the decomposition of E into component matrices is inherently non-unique , NCA uses topological constraints from the transcription network connectivity to guarantee a unique solution up to a scaling factor ( Liao et al , 2003 ) . The element aij in matrix A is set to 0 if there is no evidence to suggest regulation of genei by TFj . Others are estimated together with P using the expression data , E . If the 0s in A satisfy the NCA uniqueness criteria ( Liao et al , 2003 ; Galbraith et al , 2006 ) , the decomposition shown in equation (2) is unique up to a scaling factor for any given residual Gamma . This criterion clearly links NCA results to the biological system and makes interpretation straightforward . A detailed derivation of NCA can be found in Liao et al . In this study , NCA was used to deduce TFA perturbations resulting from isobutanol stress . Gene -expression data were analyzed by NCA using transcription network connectivity obtained from Regulon DB ( Gama-Castro et al , 2008 ) to quantify TFAs and CSs . For NCA , training data are not required and were not used in this study ( Liao et al , 2003 ) . The transcription network is presented in Supplementary Table III . As the number of experiments ( M ) was less than the number of TFs ( L ) , a modified NCA criterion for use with limited microarray data was used ( Galbraith et al , 2006 ) . This criterion allows for the identification of a unique solution up to a scaling factor when M lt L , by requiring each gene to be regulated by not more than M TFs . The statistical significance of TFA perturbations was evaluated by comparing each TFA with a null distribution generated from randomization of the data using a z-test ( Materials and methods ) . Owing to the imposition of NCA uniqueness criteria on the transcription network connectivity , we were able to quantify TFAs and CSs for 67 TFs from E.coli . Among the 67 TFs analyzed , 16 TFs had significantly perturbed activities in response to isobutanol ( P-value [?] 0.01 ) . These TFs are listed along with their significance level ( low P-value = high likelihood TFA perturbed by isobutanol ) , biological function and regulon members that were significantly perturbed in Table I . A complete list of TFs analyzed along with their significance level can be found in Supplementary Table IV . It is evident from the three most significantly perturbed TFs ( ArcA , PdhR and FNR ) that isobutanol affects respiration . Under the assumption that isobutanol toxicity is mediated through membrane disruption , it is not surprising that respiration is affected . The purpose of respiration is to generate a PMF across the membrane , many critical respiratory processes occur at the membrane , and many respiratory components are membrane constituents . To explore this result , we looked at the known activation mechanisms for ArcA , PdhR and FNR , and the identities of their regulon members that were perturbed by isobutanol . The activities of AcrA , PdhR and FNR are mediated by PHOSphorylation , pyruvate and oxygen , respectively . All three are cytoplasmic proteins . However , ArcA forms a two-component system with ArcB , a membrane protein . PHOSphorylation of ArcA occurs when quinone inhibition of ArcB is released . Quinones are metabolites embedded in the membrane that function as electron carriers for respiratory processes . PdhR shares 10 of its 12 perturbed regulon members with ArcA , whereas FNR shares 50 of its 96 perturbed regulon members with ArcA . It should be noted here that NCA might have difficulty in separating TFAs for TFs with highly overlapping regulons . Considering this information , it is likely that the ArcA-ArcB system is the major regulator of respiratory genes in response to isobutanol . PdhR is a minor transcriptional regulator not known to associate with the membrane , the majority of whose perturbed regulon members are also regulated by ArcA . FNR , which is inactive under aerobic growth due to Fe-S oxygen binding , is unlikely to be active under the growth conditions used for transcriptome measurements in this work ( mid-log aerobic ) . In addition , more than half of the perturbed FNR regulon members are also regulated by ArcA , and 74 of its 96 perturbed regulon members are controlled by one or more of the other 14 TFs identified as significantly perturbed . Therefore , it is more likely that these genes were perturbed through the action of other regulators rather than by FNR . To verify that ArcA modulates gene expression in response to isobutanol , transcriptome measurements were obtained from a DeltaarcA strain treated with and without 1% isobutanol ( Materials and methods ) . We reasoned that if ArcA regulates geneX in response to isobutanol , then the response of geneX to isobutanol in DeltaarcA would be different from the response of geneX to isobutanol in wild type . Figure 2 shows the log10 expression ratios of ArcA-regulon members from wild-type and DeltaarcA experiments , along with an indication of whether the difference was significant at a P-value [?] 0.05 ( for exact P-values , see Supplementary Table V ) . The majority of ArcA-regulon members perturbed by isobutanol in wild type ( 47 out of 86 ) had significantly different expression ratios in DeltaarcA ( P-value [?] 0.05 ) . This provided additional evidence that ArcA participates in the E.coli response to isobutanol . The remaining 39 regulon members showed indistinguishable activation/repression ( P-value >005 ) in response to isobutanol in DeltaarcA compared with wild type . This could have resulted from the inherent noise of DNA microarrays , compensatory action by other regulators or expression of that gene being under the control of a different TF under isobutanol stress .