Split histidine kinases enable ultrasensitivity and bistability in two-component signaling networks

A General Approach for the Modelling of Negative Feedback Physiological Control Systems

Mathematical models can improve the understanding of physiological systems behaviour, which is a fundamental topic in the bioengineering field. Having a reliable model enables researchers to carry out in silico experiments, which require less time and resources compared to their in vivo and in vitro counterparts. This work's objective is to capture the characteristics that a nonlinear dynamical mathematical model should exhibit, in order to describe physiological control systems at different scales. The similarities among various negative feedback physiological systems have been investigated and a unique general framework to describe them has been proposed. Within such a framework, both the existence and stability of equilibrium points are investigated. The model here introduced is based on a closed-loop topology, on which the homeostatic process is based. Finally, to validate the model, three paradigmatic examples of physiological control systems are illustrated and discussed: the ultrasensitivity mechanism for achieving homeostasis in biomolecular circuits, the blood glucose regulation, and the neuromuscular reflex arc (also referred to as muscle stretch reflex). The results show that, by a suitable choice of the modelling functions, the dynamic evolution of the systems under study can be described through the proposed general nonlinear model. Furthermore, the analysis of the equilibrium points and dynamics of the above-mentioned systems are consistent with the literature.

Exploring the mono-/bistability range of positively autoregulated signaling systems in the presence of competing transcription factor binding sites

Binding of transcription factor (TF) proteins to regulatory DNA sites is key to accurate control of gene expression in response to environmental stimuli. Theoretical modeling of transcription regulation is often focused on a limited set of genes of interest, while binding of the TF to other genomic sites is seldom considered. The total number of TF binding sites (TFBSs) affects the availability of TF protein molecules and sequestration of a TF by TFBSs can promote bistability. For many signaling systems where a graded response is desirable for continuous control over the input range, biochemical parameters of the regulatory proteins need be tuned to avoid bistability. Here we analyze the mono-/bistable parameter range for positively autoregulated two-component systems (TCSs) in the presence of different numbers of competing TFBSs. TCS signaling, one of the major bacterial signaling strategies, couples signal perception with output responses via protein phosphorylation. For bistability, competition for TF proteins by TFBSs lowers the requirement for high fold change of the autoregulated transcription but demands high phosphorylation activities of TCS proteins. We show that bistability can be avoided with a low phosphorylation capacity of TCSs, a high TF affinity for the autoregulated promoter or a low fold change in signaling protein levels upon induction. These may represent general design rules for TCSs to ensure uniform graded responses. Examining the mono-/bistability parameter range allows qualitative prediction of steady-state responses, which are experimentally validated in the E. coli CusRS system.

Multiple communication mechanisms between sensor kinases are crucial for virulence in Pseudomonas aeruginosa

Bacteria and many non-metazoan Eukaryotes respond to stresses and threats using two-component systems (TCSs) comprising sensor kinases (SKs) and response regulators (RRs). Multikinase networks, where multiple SKs work together, detect and integrate different signals to control important lifestyle decisions such as sporulation and virulence. Here, we study interactions between two SKs from Pseudomonas aeruginosa, GacS and RetS, which control the switch between acute and chronic virulence. We demonstrate three mechanisms by which RetS attenuates GacS signalling: RetS takes phosphoryl groups from GacS-P; RetS has transmitter phosphatase activity against the receiver domain of GacS-P; and RetS inhibits GacS autophosphorylation. These mechanisms play important roles in vivo and during infection, and exemplify an unprecedented degree of signal processing by SKs that may be exploited in other multikinase networks.

The binary response of the GAL/MEL genetic switch of Saccharomyces cerevisiae is critically dependent on Gal80p-Gal4p interaction

Studies on the Saccharomyces cerevisiae GAL/MEL genetic switch have revealed that its bistability is dependent on ultrasensitivity that can be altered or abolished by disabling different combinations of nested feedback loops. In contrast, we have previously demonstrated that weakening of the interaction between Gal80p and Gal4p alone is sufficient to abolish the ultrasensitivity (Das Adhikari et al. 2014). Here, we demonstrate that altering the epistatic interaction between Gal80p and Gal4p also abolishes the bistability, and the switch response to galactose becomes graded instead of binary. However, the GAL/MEL switch of wild-type and epistatically altered strains responded in a graded fashion to melibiose. The properties of the epistatically altered strain resemble Kluyveromyces lactis, which separated from the Saccharomyces lineage 100 mya before whole-genome duplication (WGD). Based on the results reported here, we propose that epistatic interactions played a crucial role in the evolution of the fine regulation of S. cerevisiae GAL/MEL switch following WGD.

Ultrasensitive Negative Feedback Control: A Natural Approach for the Design of Synthetic Controllers

Many of the most important potential applications of Synthetic Biology will require the ability to design and implement high performance feedback control systems that can accurately regulate the dynamics of multiple molecular species within the cell. Here, we argue that the use of design strategies based on combining ultrasensitive response dynamics with negative feedback represents a natural approach to this problem that fully exploits the strongly nonlinear nature of cellular information processing. We propose that such feedback mechanisms can explain the adaptive responses observed in one of the most widely studied biomolecular feedback systems—the yeast osmoregulatory response network. Based on our analysis of such system, we identify strong links with a well-known branch of mathematical systems theory from the field of Control Engineering, known as Sliding Mode Control. These insights allow us to develop design guidelines that can inform the construction of feedback controllers for synthetic biological systems.

Molecular and cellular factors control signal transduction via switchable allosteric modulator proteins (SAMPs)

Background

Rap proteins from Bacilli directly target response regulators of bacterial two-component systems and modulate their activity. Their effects are controlled by binding of signaling peptides to an allosteric site. Hence Raps exemplify a class of monomeric signaling receptors, which we call switchable allosteric modulator proteins (SAMPs). These proteins have potential applications in diverse biomedical and biotechnical settings, but a quantitative understanding of the impact of molecular and cellular factors on signal transduction is lacking. Here we introduce mathematical models that elucidate how signals are propagated though the network upon receptor stimulation and control the level of active response regulator.

Results

Based on a systematic parameter analysis of the models, we show that key features of the dose-response behavior at steady state are controlled either by the molecular properties of the modulator or the signaling context. In particular, we find that the biochemical activity (i.e. non-enzymatic vs. enzymatic) and allosteric properties of the modulator control the response amplitude. The Hill coefficient and the EC₅₀ are controlled in addition by the relative ligand affinities. By tuning receptor properties, either graded or more switch-like (memory-less) response functions can be fashioned. Furthermore, we show that other contextual factors (e.g. relative concentrations of network components and kinase activity) have a substantial impact on the response, and we predict that there exists a modulator concentration which is optimal for response amplitude.

Conclusion

We discuss data on Rap-Phr systems in B. subtilis to show how our models can contribute to an integrated view of SAMP signaling by combining biochemical, structural and physiological insights. Our results also suggest that SAMPs could be evolved or engineered to implement diverse response behaviors. However—without additional regulatory controls—they can generate rather variable cellular outputs.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0274-3) contains supplementary material, which is available to authorized users.

Unlimited multistability and Boolean logic in microbial signalling

The ability to map environmental signals onto distinct internal physiological states or programmes is critical for single-celled microbes. A crucial systems dynamics feature underpinning such ability is multistability. While unlimited multistability is known to arise from multi-site phosphorylation seen in the signalling networks of eukaryotic cells, a similarly universal mechanism has not been identified in microbial signalling systems. These systems are generally known as two-component systems comprising histidine kinase (HK) receptors and response regulator proteins engaging in phosphotransfer reactions. We develop a mathematical framework for analysing microbial systems with multi-domain HK receptors known as hybrid and unorthodox HKs. We show that these systems embed a simple core network that exhibits multistability, thereby unveiling a novel biochemical mechanism for multistability. We further prove that sharing of downstream components allows a system with n multi-domain hybrid HKs to attain 3n steady states. We find that such systems, when sensing distinct signals, can readily implement Boolean logic functions on these signals. Using two experimentally studied examples of two-component systems implementing hybrid HKs, we show that bistability and implementation of logic functions are possible under biologically feasible reaction rates. Furthermore, we show that all sequenced microbial genomes contain significant numbers of hybrid and unorthodox HKs, and some genomes have a larger fraction of these proteins compared with regular HKs. Microbial cells are thus theoretically unbounded in mapping distinct environmental signals onto distinct physiological states and perform complex computations on them. These findings facilitate the understanding of natural two-component systems and allow their engineering through synthetic biology.

Logical-continuous modelling of post-translationally regulated bistability of curli fiber expression in Escherichia coli

BACKGROUND

Bacteria have developed a repertoire of signalling mechanisms that enable adaptive responses to fluctuating environmental conditions. The formation of biofilm, for example, allows persisting in times of external stresses, e.g. induced by antibiotics or a lack of nutrients. Adhesive curli fibers, the major extracellular matrix components in Escherichia coli biofilms, exhibit heterogeneous expression in isogenic cells exposed to identical external conditions. The dynamical mechanisms underlying this heterogeneity remain poorly understood. In this work, we elucidate the potential role of post-translational bistability as a source for this heterogeneity.

RESULTS

We introduce a structured modelling workflow combining logical network topology analysis with time-continuous deterministic and stochastic modelling. The aim is to evaluate the topological structure of the underlying signalling network and to identify and analyse model parameterisations that satisfy observations from a set of genetic knockout experiments. Our work supports the hypothesis that the phenotypic heterogeneity of curli expression in biofilm cells is induced by bistable regulation at the post-translational level. Stochastic modelling suggests diverse noise-induced switching behaviours between the stable states, depending on the expression levels of the c-di-GMP-producing (diguanylate cyclases, DGCs) and -degrading (phosphodiesterases, PDEs) enzymes and reveals the quantitative difference in stable c-di-GMP levels between distinct phenotypes. The most dominant type of behaviour is characterised by a fast switching from curli-off to curli-on with a slow switching in the reverse direction and the second most dominant type is a long-term differentiation into curli-on or curli-off cells. This behaviour may implicate an intrinsic feature of the system allowing for a fast adaptive response (curli-on) versus a slow transition to the curli-off state, in line with experimental observations.

CONCLUSION

The combination of logical and continuous modelling enables a thorough analysis of different determinants of bistable regulation, i.e. network topology and biochemical kinetics, and allows for an incorporation of experimental data from heterogeneous sources. Our approach yields a mechanistic explanation for the phenotypic heterogeneity of curli fiber expression. Furthermore, the presented work provides a detailed insight into the interactions between the multiple DGC- and PDE-type enzymes and the role of c-di-GMP in dynamical regulation of cellular decisions.

A minimal model for metabolism-dependent chemotaxis in Rhodobacter sphaeroides (†)

Chemotaxis is vital cellular movement in response to environmental chemicals. Unlike the canonical chemotactic pathway in Escherichia coli, Rhodobacter sphaeroides has both transmembrane and cytoplasmic sensory clusters, with the latter possibly interacting with essential components in the electron transport system. However, the effect of the cytoplasmic sensor and the mechanism of signal integration from both sensory clusters remain unclear. Based on a minimal model of the chemotaxis pathway in this species, we show that signal integration at the motor level produces realistic chemotactic behaviour in line with experimental observations. Our model also suggests that the core pathway of R. sphaeroides, at least its ancestor, may represent a metabolism-dependent selective stopping strategy, which alone can steer cells to favourable environments. Our results not only clarify the potential roles of the two sensory clusters but also put in question the current definitions of attractants and repellents.

Phosphate sink containing two-component signaling systems as tunable threshold devices

Synthetic biology aims to design de novo biological systems and reengineer existing ones. These efforts have mostly focused on transcriptional circuits, with reengineering of signaling circuits hampered by limited understanding of their systems dynamics and experimental challenges. Bacterial two-component signaling systems offer a rich diversity of sensory systems that are built around a core phosphotransfer reaction between histidine kinases and their output response regulator proteins, and thus are a good target for reengineering through synthetic biology. Here, we explore the signal-response relationship arising from a specific motif found in two-component signaling. In this motif, a single histidine kinase (HK) phosphotransfers reversibly to two separate output response regulator (RR) proteins. We show that, under the experimentally observed parameters from bacteria and yeast, this motif not only allows rapid signal termination, whereby one of the RRs acts as a phosphate sink towards the other RR (i.e. the output RR), but also implements a sigmoidal signal-response relationship. We identify two mathematical conditions on system parameters that are necessary for sigmoidal signal-response relationships and define key parameters that control threshold levels and sensitivity of the signal-response curve. We confirm these findings experimentally, by in vitro reconstitution of the one HK-two RR motif found in the Sinorhizobium meliloti chemotaxis pathway and measuring the resulting signal-response curve. We find that the level of sigmoidality in this system can be experimentally controlled by the presence of the sink RR, and also through an auxiliary protein that is shown to bind to the HK (yielding Hill coefficients of above 7). These findings show that the one HK-two RR motif allows bacteria and yeast to implement tunable switch-like signal processing and provides an ideal basis for developing threshold devices for synthetic biology applications.

Two-component signaling systems are found in bacteria, fungi and plants. Their modular structures make them ideal targets for de novo engineering through synthetic biology. Here, we explore the signal-response relationship arising from a common two-component system, where a single HK phosphotransfers reversibly to two separate output RRs. We show that under the experimentally observed parameters, this motif implements a sigmoidal signal-response relationship, whereby one of the RRs acts as a phosphate sink towards the other. We identify two mathematical conditions on the system parameters that are necessary for sigmoidality and define key parameters that control threshold levels and sensitivity. We confirm these findings experimentally by in vitro reconstitution of the “one HK-two RR” motif found in S. meliloti. Particularly, we show that the level of sigmoidality in this system can be experimentally controlled by the amount of sink RR and also through an auxiliary protein, CheS. These findings show that the one HK-two RR motif can open the way to the design of novel threshold systems in synthetic biology.

A novel signal transduction pathway that modulates rhl quorum sensing and bacterial virulence in Pseudomonas aeruginosa

The rhl quorum-sensing (QS) system plays critical roles in the pathogenesis of P. aeruginosa. However, the regulatory effects that occur directly upstream of the rhl QS system are poorly understood. Here, we show that deletion of gene encoding for the two-component sensor BfmS leads to the activation of its cognate response regulator BfmR, which in turn directly binds to the promoter and decreases the expression of the rhlR gene that encodes the QS regulator RhlR, causing the inhibition of the rhl QS system. In the absence of bfmS, the Acka-Pta pathway can modulate the regulatory activity of BfmR. In addition, BfmS tunes the expression of 202 genes that comprise 3.6% of the P. aeruginosa genome. We further demonstrate that deletion of bfmS causes substantially reduced virulence in lettuce leaf, reduced cytotoxicity, enhanced invasion, and reduced bacterial survival during acute mouse lung infection. Intriguingly, specific missense mutations, which occur naturally in the bfmS gene in P. aeruginosa cystic fibrosis (CF) isolates such as DK2 strains and RP73 strain, can produce BfmS variants (BfmS_L181P, BfmS_L181P/E376Q, and BfmS_R393H) that no longer repress, but instead activate BfmR. As a result, BfmS variants, but not the wild-type BfmS, inhibit the rhl QS system. This study thus uncovers a previously unexplored signal transduction pathway, BfmS/BfmR/RhlR, for the regulation of rhl QS in P. aeruginosa. We propose that BfmRS TCS may have an important role in the regulation and evolution of P. aeruginosa virulence during chronic infection in CF lungs.

The rhl quorum-sensing (QS) system allows P. aeruginosa to regulate diverse metabolic adaptations and virulence. However, how rhl QS system is regulated remains largely unknown. Here, we report that two-component sensor BfmS controls rhl QS system by repressing its cognate response regulator BfmR, which directly suppresses the expression of rhl QS regulator RhlR gene and reduces the production of QS signal molecule N-butanoyl-L-homoserine lactone (C4-HSL). We find that BfmS is critical to the ability of P. aeruginosa to modulate the expression of virulence-associated traits and adapt to the host. Intriguingly, although wild-type BfmS is a repressor of BfmR, naturally occurring missense mutation (L181P, L181P/E376Q, or R393H) can convert its function from a repressor to an activator of BfmR, leading to BfmR activation, which in turn reduces the level of rhl QS signal C4-HSL. These results, therefore, provide important and novel insight into the regulation and evolution of P. aeruginosa virulence.

Reciprocal regulation as a source of ultrasensitivity in two-component systems with a bifunctional sensor kinase

Two-component signal transduction systems, where the phosphorylation state of a regulator protein is modulated by a sensor kinase, are common in bacteria and other microbes. In many of these systems, the sensor kinase is bifunctional catalyzing both, the phosphorylation and the dephosphorylation of the regulator protein in response to input signals. Previous studies have shown that systems with a bifunctional enzyme can adjust the phosphorylation level of the regulator protein independently of the total protein concentrations – a property known as concentration robustness. Here, I argue that two-component systems with a bifunctional enzyme may also exhibit ultrasensitivity if the input signal reciprocally affects multiple activities of the sensor kinase. To this end, I consider the case where an allosteric effector inhibits autophosphorylation and, concomitantly, activates the enzyme's phosphatase activity, as observed experimentally in the PhoQ/PhoP and NRII/NRI systems. A theoretical analysis reveals two operating regimes under steady state conditions depending on the effector affinity: If the affinity is low the system produces a graded response with respect to input signals and exhibits stimulus-dependent concentration robustness – consistent with previous experiments. In contrast, a high-affinity effector may generate ultrasensitivity by a similar mechanism as phosphorylation-dephosphorylation cycles with distinct converter enzymes. The occurrence of ultrasensitivity requires saturation of the sensor kinase's phosphatase activity, but is restricted to low effector concentrations, which suggests that this mode of operation might be employed for the detection and amplification of low abundant input signals. Interestingly, the same mechanism also applies to covalent modification cycles with a bifunctional converter enzyme, which suggests that reciprocal regulation, as a mechanism to generate ultrasensitivity, is not restricted to two-component systems, but may apply more generally to bifunctional enzyme systems.

Bacteria often use two-component systems to sense and respond to environmental changes, which involves autophosphorylation of a sensor kinase and phosphotransfer to a cognate response regulator. However, despite conservation of this ‘classical’ scheme there exist substantial variations in the mechanism of phosphotransfer among systems. Also, many sensor kinases exhibit phosphatase activity raising the question whether such a bifunctional architecture enables special regulatory properties in the response behavior to input signals. According to previous studies, classical two-component systems are unlikely to produce sigmoidal response curves (ultrasensitivity) if the sensor protein is bifunctional. Here, I argue that this is not necessarily true if the input stimulus (allosteric effector) reciprocally affects multiple activities of the sensor kinase, as it seems to be common for bifunctional enzymes. To this end, I propose and analyze an extension of the experimentally well-supported Batchelor-Goulian model which shows that ultrasensitivity requires a high-affinity effector and saturation of the phosphatase activity. The underlying mechanism involves sequestration of the effector by the sensor kinase which restricts the occurrence of ultrasensitivity to sufficiently low effector concentrations. Hence, this operating regime might be useful to sense effector limitations or to amplify weak input signals.