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ABSTRACT In starvingBacillus subtilisbacteria,the initiation of two survival programs—biofilm formation and sporulation—is controlled by the same phosphorylated master regulator, Spo0A~P. Its gene,spo0A,is transcribed from two promoters, Pvand Ps,that are, respectively, regulated by RNA polymerase (RNAP) holoenzymes bearing σ^Aand σ^H. Notably, transcription is directly autoregulated by Spo0A~P binding sites known as 0A1, 0A2, and 0A3 box, located in between the two promoters. It remains unclear whether, at the onset of starvation, these boxes activate or repressspo0Aexpression, and whether the Spo0A~P transcriptional feedback plays a role in the increase inspo0Aexpression. Based on the experimental data of the promoter activities under systematic perturbation of the promoter architecture, we developed a biophysical model of transcriptional regulation ofspo0Aby Spo0A~P binding to each of the 0A boxes. The model predicts that Spo0A~P binding to its boxes does not affect the RNAP recruitment to the promoters but instead affects the transcriptional initiation rate. Moreover, the effects of Spo0A~P binding to 0A boxes are mainly repressive and saturated early at the onset of starvation. Therefore, the increase inspo0Aexpression is mainly driven by the increase in RNAP holoenzyme levels. Additionally, we reveal that Spo0A~P affinity to 0A boxes is strongest at 0A3 and weakest at 0A2 and that there are attractive forces between the occupied 0A boxes. Our findings, in addition to clarifying how the sporulation master regulator is controlled, offer a framework to predict regulatory outcomes of complex gene-regulatory mechanisms. IMPORTANCECell differentiation is often critical for survival. In bacteria, differentiation decisions are controlled by transcriptional master regulators under transcriptional feedback control. Therefore, understanding how master regulators are transcriptionally regulated is required to understand differentiation. However, in many cases, the underlying regulation is complex, with multiple transcription factor binding sites and multiple promoters, making it challenging to dissect the exact mechanisms. Here, we address this problem for theBacillus subtilismaster regulator Spo0A. Using a biophysical model, we quantitatively characterize the effect of individual transcription factor binding sites on eachspo0Apromoter. Furthermore, the model allows us to identify the specific transcription step that is affected by transcription factor binding. Such a model is promising for the quantitative study of a wide range of master regulators involved in transcriptional feedback. 

Inferring underlying microscopic dynamics from low-dimensional experimental signals is a central problem in physics, chemistry, and biology. As a trade-off between molecular complexity and the low-dimensional nature of experimental data, mesoscopic descriptions such as the Markovian master equation are commonly used. The states in such descriptions usually include multiple microscopic states, and the ensuing coarse-grained dynamics are generally non-Markovian. It is frequently assumed that such dynamics can nevertheless be described as a Markov process because of the timescale separation between slow transitions from one observed coarse state to another and the fast interconversion within such states. Here, we use a simple model of a molecular motor with unobserved internal states to highlight that (1) dissipation estimated from the observed coarse dynamics may significantly underestimate microscopic dissipation even in the presence of timescale separation and even when mesoscopic states do not contain dissipative cycles and (2) timescale separation is not necessarily required for the Markov approximation to give the exact entropy production, provided that certain constraints on the microscopic rates are satisfied. When the Markov approximation is inadequate, we discuss whether including memory effects can improve the estimate. Surprisingly, when we do so in a “model-free” way by computing the Kullback–Leibler divergence between the observed probability distributions of forward trajectories and their time reverses, this leads to poorer estimates of entropy production. Finally, we argue that alternative approaches, such as hidden Markov models, may uncover the dissipative nature of the microscopic dynamics even when the observed coarse trajectories are completely time-reversible.