Circuit architecture explains functional similarity of bacterial heat shock responses

Heat shock response is a stress response to temperature changes and a consecutive increase in amounts of unfolded proteins. To restore homeostasis, cells upregulate chaperones facilitating protein folding by means of transcription factors (TFs). We here investigate two heat shock systems: one characteristic to gram negative bacteria, mediated by transcriptional activator σ(32) in E. coli, and another characteristic to gram positive bacteria, mediated by transcriptional repressor HrcA in L. lactis. We construct simple mathematical models of the two systems focusing on the negative feedbacks, where free chaperones suppress σ(32) activation in the former, while they activate HrcA repression in the latter. We demonstrate that both systems, in spite of the difference at the TF regulation level, are capable of showing very similar heat shock dynamics. We find that differences in regulation impose distinct constraints on chaperone-TF binding affinities: the binding constant of free σ(32) to chaperone DnaK, known to be in 100 nM range, set the lower limit of amount of free chaperone that the system can sense the change at the heat shock, while the binding affinity of HrcA to chaperone GroE set the upper limit and have to be rather large extending into the micromolar range.