Mathematical modeling of the apo and holo transcriptional regulation in Escherichia coli

Abstract

Transcription factors (TFs) modulate gene expression as a consequence of internal or exogenous changes in cell signaling. TFs can bind to DNA either with their effector bound (holo conformation), or as free proteins (apo conformation). With the aim of contributing to the understanding of the evolutionary fitness and organizational principles behind the different TF conformations, we inquire into the origins of these conformational differences by analyzing these two TF conformations from the perspective of Savageau's demand theory. For the control of a gene whose function is in high demand, we found that evolutionary constraints are responsible for activator TFs binding to DNA mainly in holo conformation whereas apo activation is under-represented. The mathematically controlled comparison of the apo and holo conformations reveals formal and evolutionary arguments in favor of this TF control asymmetry, which suggests that evolution favors holo activation under environmental conditions commonly found by E. coli in the human digestive tract. Specifically, the sensibility analysis performed for the holo conformation, in the positive mode of regulation, shows that the wild-type is more robust for situations where realizable changes in the model's parameters favored a better performance under non-stressful environmental conditions commonly found by E. coli in the human digestive tract. By contrast, the positive apo conformation is better adapted to adverse situations. On the other hand, the sensibility analysis performed for the negative mode of regulation showing none of the TF active conformations presents an advantage.