Structural Controllability of Boolean Control Networks under Partial Information

It is worth noting that both nodes’ coupling connections and logical updating functions play a vital role in state evolutions of Boolean networks (BNs). In this paper, a new concept named structural controllability (SC) about Boolean control networks (BCNs) with known partial information on nodes’ connections is studied. Then, by referring to semi-tensor product (STP) techniques, several types of SC are presented according to different issues of Boolean functions. Thereafter, several necessary and sufficient conditions are derived for SC of BCNs. Finally, a biological model of the lactose operon in Escherichia coli is simulated to show the effectiveness of the main theoretical results.

Effector Overlap between the lac and mel Operons of Escherichia coli: Induction of the mel Operon with β-Galactosides

ABSTRACT The lac (lactose) operon (which processes β-galactosides) and the mel (melibiose) operon (which processes α-galactosides) of Escherichia coli have a close historical connection. A number of shared substrates and effectors of the permeases and regulatory proteins have been reported over the years. Until now, β-thiogalactosides like TMG (methyl-β-d-thiogalactopyranoside) and IPTG (isopropyl-β-d-thiogalactopyranoside) have not generally been considered to be inducers of the mel operon. The same is true for β-galactosides such as lactose [β-d-galactopyranosyl-(1→4)-d-glucose], which is a substrate but is not itself an inducer of the lac operon. This report shows that all three sugars can induce the mel operon significantly when they are accumulated in the cell by Lac permease. Strong induction by β-thiogalactosides is observed in the presence of Lac permease, and strong induction by lactose (more than 200-fold) is observed in the absence of β-galactosidase. This finding calls for reevaluation of TMG uptake experiments as assays for Lac permease that were performed with mel + strains. IMPORTANCE The typical textbook picture of bacterial operons is that of stand-alone units of genetic information that perform, in a regulated manner, well-defined cellular functions. Less attention is given to the extensive interactions that can be found between operons. Well-described examples of such interactions are the effector molecules shared by the lac and mel operons. Here, we show that this set has to be extended to include β-galactosides, which have been, until now, considered not to effect the expression of the mel operon. That they can be inducers of the mel operon as well as the lac operon has not been noted in decades of research because of the Escherichia coli genetic background used in previous studies.

RNA polymerase supply and flux through the lac operon in Escherichia coli

Chromatin immunoprecipitation, followed by quantification of immunoprecipitated DNA, can be used to measure RNA polymerase binding to any DNA segment in Escherichia coli . By calibrating measurements against the signal from a single RNA polymerase bound at a single promoter, we can calculate both promoter occupancy levels and the flux of transcribing RNA polymerase through transcription units. Here, we have applied the methodology to the E. coli lactose operon promoter. We confirm that promoter occupancy is limited by recruitment and that the supply of RNA polymerase to the lactose operon promoter depends on its location in the E. coli chromosome. Measurements of RNA polymerase binding to DNA segments within the lactose operon show that flux of RNA polymerase through the operon is low, with, on average, over 18 s elapsing between the passage of transcribing polymerases. Similar low levels of flux were found when semi-synthetic promoters were used to drive transcript initiation, even when the promoter elements were changed to ensure full occupancy of the promoter by RNA polymerase. This article is part of the themed issue ‘The new bacteriology’.