SUMMARY In cells, specific regulators often compete for limited amounts of a core enzymatic resource. It is typically assumed that competition leads to partitioning of core enzyme molecules among regulators at constant levels. Alternatively, however, different regulatory species could time share, or take turns utilizing, the core resource. Using quantitative time-lapse microscopy, we analyzed sigma factor activity dynamics, and their competition for RNA polymerase, in individual Bacillus subtilis cells under energy stress. Multiple alternative sigma factors were activated in ~1-hr pulses in stochastic and repetitive fashion. Pairwise analysis revealed that two sigma factors rarely pulse simultaneously and that some pairs are anti-correlated, indicating that RNAP utilization alternates among different sigma factors. Mathematical modeling revealed how stochastic time-sharing dynamics can emerge from pulse-generating sigma factor regulatory circuits actively competing for RNAP. Time sharing provides a mechanism for cells to dynamically control the distribution of cell states within a population. Since core molecular components are limiting in many other systems, time sharing may represent a general mode of regulation.

Gene regulatory circuits can receive multiple simultaneous inputs, which can enter the system through different locations. It is thus necessary to establish how these genetic circuits integrate multiple inputs as a function of their relative entry points. Here, we use the dynamic circuit regulating competence for DNA uptake in Bacillus subtilis as a model system to investigate this issue. Specifically, we map the response of single cells in vivo to a combination of (i) a chemical signal controlling the constitutive expression of key competence genes, and (ii) a genetic perturbation in the form of copy number variation of one of these genes, which mimics the level of stress signals sensed by the bacteria. Quantitative timelapse fluorescence microscopy shows that a variety of dynamical behaviors can be reached by the combination of the two inputs. Additionally, the integration depends strongly on the relative locations where the two perturbations enter the circuit. Specifically, when the two inputs act upon different circuit elements, their integration generates novel dynamical behavior, whereas inputs affecting the same element do not. An in silico bidimensional bifurcation analysis of a mathematical model of the circuit offers good quantitative agreement with the experimental observations, and sheds light on the dynamical mechanisms leading to the different integrated responses exhibited by the gene regulatory circuit.signal integration | genetic competence | excitability | bistability | genetic oscillations C ells are usually subject to multiple simultaneous sources of biochemical and physical signals, which they must integrate to respond adequately to their external environment and internal conditions. Previous efforts addressed at understanding signal integration in gene regulation have mainly concentrated on mapping the combinatorial response of single bacterial promoters to multiple transcription factors (1-5), and on quantifying the combined effect of bacterial cell-cell signaling molecules acting upon a shared phosphorelay pathway (6-8). However, in many instances different inputs operate in a distributed manner, acting upon distinct nodes (genes or proteins) of the gene regulation network. In those cases, it is the network itself, and not a particular promoter or phosphorylation reaction, that has to integrate the information at the system's level. It thus becomes necessary to understand how the integrated response of gene regulatory networks depends on the specific entry points of the inputs.Some studies have recently examined the population-level response of complex signaling pathways to ligand combinations (9-12). However, a systematic in vivo study at the single-cell level of the integration of distributed inputs by gene circuits is still lacking. It also remains unclear how these integration maps are related to the underlying regulatory circuitry. Here, we address these issues by means of a combination of time-lapse fluorescence microscopy and mathematical modeling of multiple simultaneous perturbat...