Exponential Signaling Gain at the Receptor Level Enhances Signal-to-Noise Ratio in Bacterial Chemotaxis

et al. (2014) Exponential Signaling Gain at the Receptor Level Enhances Signal-to-Noise Ratio in Bacterial Chemotaxis. PLoS ONE 9(4): e87815. doi:10.1371/journal.pone.0087815 Exponential Signaling Gain at the Receptor Level Enhances Signal-to-Noise Ratio in Bacterial Chemotaxis Silke Neumann 0 Linda Lvdok 0 Kajetan Bentele 0 Johannes Meisig 0 Ekkehard Ullner 0 Ferencz S. Paldy 0 Victor Sourjik 0 Markus Kollmann 0 Xiaofeng Ren, Northeast Agricultural University, China 0 1 Zentrum fu r Molekulare Biologie der Universita t Heidelberg, DKFZ-ZMBH Alliance , Heidelberg, Germany , 2 Institute for Theoretical Biology, Humboldt Universita t zu Berlin , Berlin, Germany , 3 Department of Physics and Institute for Complex Systems and Mathematical Biology (ICSMB) , Aberdeen , United Kingdom, 4 Department Biologie, Heinrich-Heine-Universita t Du sseldorf , Du sseldorf , Germany Cellular signaling systems show astonishing precision in their response to external stimuli despite strong fluctuations in the molecular components that determine pathway activity. To control the effects of noise on signaling most efficiently, living cells employ compensatory mechanisms that reach from simple negative feedback loops to robustly designed signaling architectures. Here, we report on a novel control mechanism that allows living cells to keep precision in their signaling characteristics - stationary pathway output, response amplitude, and relaxation time - in the presence of strong intracellular perturbations. The concept relies on the surprising fact that for systems showing perfect adaptation an exponential signal amplification at the receptor level suffices to eliminate slowly varying multiplicative noise. To show this mechanism at work in living systems, we quantified the response dynamics of the E. coli chemotaxis network after genetically perturbing the information flux between upstream and downstream signaling components. We give strong evidence that this signaling system results in dynamic invariance of the activated response regulator against multiplicative intracellular noise. We further demonstrate that for environmental conditions, for which precision in chemosensing is crucial, the invariant response behavior results in highest chemotactic efficiency. Our results resolve several puzzling features of the chemotaxis pathway that are widely conserved across prokaryotes but so far could not be attributed any functional role. - Funding: This work was supported by the DFG grants KO 3442/3-1 and KO 3442/1-1 (to MK) and SO 421/9-1 and SO 421/3-3 (to VS). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. Information processing in living cells is limited by a complex balance between randomizing and correcting intracellular forces [1]. In particular, the stochasticity of biochemical reactions leads to fluctuations in the abundance and activity of cellular components, including those involved in cellular signaling. Although rapid fluctuations within a signaling cascade arising from conformational changes, phosphorylation and binding events are in most cases filtered by the comparatively slow phenotypic response of the cell, fluctuations on slower time scale can strongly affect cells precision to adapt to changing environmental conditions. Consequently, stochastic bursts in protein synthesis can interfere with the response to extracellular stimuli, making noise in gene expression one of the dominant noise sources that produce significant cell-to-cell variation in the response behavior of clonal cells [2]. The canonical way to reduce molecular noise is to increase copy numbers of genes, mRNA, and protein and to optimize their associated turnover rates [3]. The obvious disadvantage is that these solutions are of high cost to the cell and it is therefore not surprising that unicellular organisms employ more resource efficient strategies to control intracellular noise. Significant research efforts have been devoted in the last years to understand noise compensatory strategies of cellular circuits and to identify the underlying mathematical principles [1, 48]. However, most of the previous work focused on the consequences of cellular noise on the stationary pathway output [9]. To what extent cellular systems manage to eliminate effects of noise on response amplitude and relaxation dynamics is yet unclear. In the following we investigate signaling pathways that show precise adaptation that is the relaxation of the output signal to its prestimulated level, even when the changed input persists. Adaptation can be realized by integral feedback or feedforward control [10] and allows living cells to ensure homeostasis of reaction fluxes and component concentrations, to expand the input range of molecular sensing devices, and to adjust the pre-stimulus activities of signaling cascades to the level of highest pathway sensitivity [11]. Well studied molecular circuits, where the existence of integral feedback loops have been experimentally confirmed, are the chemotaxis pathway in E. coli [12] and the hyperosmotic shock-response system [13] in S. cerevisiae. For these and most other cellular signaling systems there exists a strict time scale separation between rapid signal transduction from sensory molecules to the pathway output and comparatively slow changes of the dominant noise sources. Examples of the latter are stochasticity in synthesis and degradation of pathway components, assembly of large protein complexes, and changes in availability of cellular resources, such as ribosomes and RNA polymerases. These noise sources are in general multiplicative, show large standard deviations, and therefore do not allow description by linear noise approximation [3]. In this work we introduce a novel noise compensatory mechanism that allows to eliminate effects of multiplicative noise on signaling amplitude and response time for systems that show precise adaptation. The flow chart of Fig. 1 shows a simple example of adaptive signaling systems subject to slowly varying multiplicative noise z(t). Exact adaptation can be achieved by an integral feedback, mediated by an intermediate variable m(t). The dynamical system shown in Fig. 1 can be described by the equations where m_ denotes the time derivative. The monotone functions H and J determine signaling gain and adaptation kinetics, respectively, with H(w)0 for all real values w and J(w)~0 for w~0. These functional constraints on H and J ensure that the pathway output, y(t)0, always relaxes to the adapted state, y0, for u_(t)~0. The equations above can be written as a single equation y_~z Hw f (u) u_{Jy{y0 zOz_ , using the definition w : ~f (u)zm. Here, H and f denote the derivatives of H and f , respectively. If the characteristic time scales of changes in z are significantly longer than the adapt (...truncated)