A modular gradient‐sensing network for chemotaxis in Escherichia coli revealed by responses to time‐varying stimuli

Abstract

Combining in vivo FRET with time-varying stimuli, such as steps, ramps, and sinusoids allowed deduction of the molecular mechanisms underlying cellular signal processing.The bacterial chemotaxis pathway can be described as a two-module feedback circuit, the transfer functions of which we have characterized quantitatively by experiment. Model-driven experimental design allowed the use of a single FRET pair for measurements of both transfer functions of the pathway.The adaptation module's transfer function revealed that feedback near steady state is weak, consistent with high sensitivity to shallow gradients, but also strong steady-state fluctuations in pathway output.The measured response to oscillatory stimuli defines the frequency band over which the chemotaxis system can compute time derivatives.

Response rescaling in bacterial chemotaxis

“…A FRET pair, consisting of CheY and its phosphatase, CheZ, fused to yellow and cyan fluorescent proteins (YFP and CFP), respectively (17), provides a real-time readout proportional to a(t) for timescales greater than the relaxation time of the CheY phosphorylation cycle. In addition to enabling studies on receptor sensitivity (14,18,19), this FRET system has been combined with time-varying stimuli to measure the in vivo kinetics of the adaptation enzymes CheR and CheB (20), which provide negative feedback through covalent receptor modification (reversible methylation at multiple sites) and determine the slower timescale of the adaptation response, τ m .…”

“…One can use any function for λ(t) to test for FCD, which, by definition, holds for arbitrary input waveforms. We chose an oscillatory waveform with a frequency, ν = 0.01 Hz, close to the characteristic frequency of the system's adaptation kinetics, v m ∼ 0.006 Hz (at 22°C) (20), with a Gaussian amplitude modulation (see SI Text for the exact expression) to probe both the low-amplitude regime, where the stimulus-response relation is expected to be linear (i.e., ΔFRET ∝ Δ[L]), and the high-amplitude regime, where the stimulus-response relation saturates (i.e., ΔFRET → ΔFRET sat ). We hereafter refer to these regimes as FCD1 and FCD2, respectively, and to the low concentration regime, where the response amplitude depended on the background level ( Fig.…”

“…3A) signifies that the methylation effect on the total free energy, f t , is directly proportional to the current methylation level, m. Of these three conditions for FCD, conditions i and ii are sufficient for Weber's law for step stimuli (15). Thus, the only additional requirement for FCD is condition iii, that the slope of the methylation-dependent free energy must be a constant or, in other words, that f m (m) must be a linear function of m. Such a linear dependence was discovered in recent FRET experiments using step stimuli (20), where the function f m ðmÞ ¼ αðm * − mÞ yielded good fits to the data with α ∼ 2 and m* ∼ 0.5. The requirement for a constant α can be understood intuitively by examining the dynamics of this model, which predicts (15) that the characteristic timescale, τ m , of chemotactic adaptation [defined as the relaxation time for the decay of the response, Δa(t), after a small step change in input; SI Text] is inversely proportional to α: τ m ¼ ðNa 0 ð1 − a 0 ÞαF ′ ða 0 ÞÞ − 1 .…”

“…However, this observation does not rule out the possibility that τ m depends on the background concentration over a broader range than each FCD regime. We reasoned that appreciable changes in τ m would be observable as distortions in the output waveforms because this timescale directly determines the characteristic cutoff frequency, ν m ¼ ð2πτ m Þ − 1 , for the linear signal filtering performed by the chemotaxis pathway (15,20). Therefore, we compared the output waveforms between the two FCD regimes, as well as the no FCD regime, by superimposing the FRET response time series (Fig.…”

Long-term model predictive control of gene expression at the population and single-cell levels

“…The properties of a living system are often inferred from the observation of its response to static perturbations. Timevarying perturbations have the potential to be much more informative regarding the dynamics of cellular functions (7)(8)(9)(10)(11)(12). Currently, it is not possible to precisely perturb protein levels in an analogous manner, even though this perturbation would be instrumental in our understanding of gene regulatory networks.…”