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

Sequestration of histidine kinases by non-cognate response regulators establishes a threshold level of stimulation for bacterial two-component signaling

Bacterial two-component systems (TCSs) consist of a sensor histidine kinase (HK) that perceives a specific signal, and a cognate response regulator (RR) that modulates the expression of target genes. Positive autoregulation improves TCS sensitivity to stimuli, but may trigger disproportionately large responses to weak signals, compromising bacterial fitness. Here, we combine experiments and mathematical modelling to reveal a general design that prevents such disproportionate responses: phosphorylated HKs (HK~Ps) can be sequestered by non-cognate RRs. We study five TCSs of Mycobacterium tuberculosis and find, for all of them, non-cognate RRs that show higher affinity than cognate RRs for HK~Ps. Indeed, in vitro assays show that HK~Ps preferentially bind higher affinity non-cognate RRs and get sequestered. Mathematical modelling indicates that this sequestration would introduce a 'threshold' stimulus strength for eliciting responses, thereby preventing responses to weak signals. Finally, we construct tunable expression systems in Mycobacterium bovis BCG to show that higher affinity non-cognate RRs suppress responses in vivo.

The inverse correlation between robustness and sensitivity to autoregulation in two-component systems

Two-component systems (TCS) are signal transduction systems in bacteria and many other organisms that relay the sensory signal to genetic components. TCS consist of two proteins: a histidine kinase and a response regulator that the histidine kinase activates. This seemingly simple machinery can generate complex regulatory dynamics that enables the level of gene expression that matches the input signal: many TCS response regulators act on their own genes as transcription factors, resulting in a positive autoregulation mechanism. This regulation, in return, modulates the transcription factor activity as a function of the input signal. Positive autoregulation does not necessarily result in positive feedback. Sensitivity to autoregulation is quantified as the output level amplification resulting from the positive autoregulation mechanism. Another structural property of these systems is formally characterized as "robustness": in a robust TCS, the output of the system is solely a function of the input signal. Thus, a robust TCS remains insensitive to fluctuations in the concentrations of its protein components and, this way, maintains the precision in the output transcription factor activity in response to input stimulus. In this paper, we show with a formal model that TCS operate on a spectrum of inverse correlation between robustness and sensitivity to autoregulation. Our model predicts that the modulation by positive autoregulation is a function of loss in TCS robustness, for example, by spontaneous dephosphorylation of the histidine kinase. Consequently, the loss in robustness provides a proportional modulation by positive autoregulation to widen the response range with a scaled amplification of the output. At the other end of the spectrum, in the presence of a strictly robust TCS machinery, amplification of the transcription factor activity by autoregulation is diminished. We show that our results are in agreement with published experimental results. Our results suggest that these TCS evolve to converge at a trade-off between robustness and positive autoregulation.

Biphasic regulation of transcriptional surge generated by the gene feedback loop in a two-component system

MOTIVATION

Transcriptional surges generated by two-component systems (TCSs) have been observed experimentally in various bacteria. Suppression of the transcriptional surge may reduce the activity, virulence, and drug resistance of bacteria. In order to investigate the general mechanisms, we use a PhoP/PhoQ TCS as a model system to derive a comprehensive mathematical modeling that governs the surge. PhoP is a response regulator, which serves as a transcription factor under a phosphorylation-dependent modulation by PhoQ, a histidine kinase.

RESULTS

Our model reveals two major signaling pathways to modulate the phosphorylated PhoP (P-PhoP) level, one of which promotes the generation of P-PhoP, while the other depresses the level of P-PhoP. The competition between the P-PhoP-promoting and the P-PhoP-depressing pathways determines the generation of the P-PhoP surge. Furthermore, besides PhoQ, PhoP is also a bifunctional modulator that contributes to the dynamic control of P-PhoP state, leading to a biphasic regulation of the surge by the gene feedback loop. In summary, the mechanisms derived from the PhoP/PhoQ system for the transcriptional surges provide a better understanding on such a sophisticated signal transduction system and aid to develop new antimicrobial strategies targeting TCSs.

AVAILABILITY

https://github.com/jianweishuai/TCS.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

The interplay of spatial organization and biochemistry in building blocks of cellular signalling pathways

Biochemical pathways and networks are central to cellular information processing. While a broad range of studies have dissected multiple aspects of information processing in biochemical pathways, the effect of spatial organization remains much less understood. It is clear that space is central to intracellular organization, plays important roles in cellular information processing and has been exploited in evolution; additionally, it is being increasingly exploited in synthetic biology through the development of artificial compartments, in a variety of ways. In this paper, we dissect different aspects of the interplay between spatial organization and biochemical pathways, by focusing on basic building blocks of these pathways: covalent modification cycles and two-component systems, with enzymes which may be monofunctional or bifunctional. Our analysis of spatial organization is performed by examining a range of 'spatial designs': patterns of localization or non-localization of enzymes/substrates, theoretically and computationally. Using these well-characterized in silico systems, we analyse the following. (i) The effect of different types of spatial organization on the overall kinetics of modification, and the role of distinct modification mechanisms therein. (ii) How different information processing characteristics seen experimentally and studied from the viewpoint of kinetics are perturbed, or generated. (iii) How the activity of enzymes (bifunctional enzymes in particular) may be spatially manipulated, and the relationship between localization and activity. (iv) How transitions in spatial organization (encountered either through evolution or through the lifetime of cells, as seen in multiple model organisms) impacts the kinetic module (and pathway) behaviour, and how transitions in chemistry may be impacted by prior spatial organization. The basic insights which emerge are central to understanding the role of spatial organization in biochemical pathways in both bacteria and eukaryotes, and are of direct relevance to engineering spatial organization of pathways in bottom-up synthetic biology in cellular and cell-free systems.

Trade-offs between effectiveness and cost in bifunctional enzyme circuit with concentration robustness

A fundamental trade-off in biological systems is whether they consume resources to perform biological functions or save resources. Bacteria need to reliably and rapidly respond to input signals by using limited cellular resources. However, excessive resource consumption will become a burden for bacteria growth. To investigate the relationship between functional effectiveness and resource cost, we study the ubiquitous bifunctional enzyme circuit, which is robust to fluctuations in protein concentration and responds quickly to signal changes. We show that trade-off relationships exist between functional effectiveness and protein cost. Expressing more proteins of the circuit increases concentration robustness and response speed but affects bacterial growth. In particular, our study reveals a general relationship between free-energy dissipation rate, response speed, and concentration robustness. The dissipation of free energy plays an important role in the concentration robustness and response speed. High robustness can only be achieved with a large amount of free-energy consumption and protein cost. In addition, the noise of the output increases with increasing protein cost, while the noise of the response time decreases with increasing protein cost. We also calculate the trade-off relationships in the EnvZ-OmpR system and the nitrogen assimilation system, which both have the bifunctional enzyme. Similar results indicate that these relationships are mainly derived from the specific feature of the bifunctional enzyme circuits and are not relevant to the details of the models. According to the trade-off relationships, bacteria take a compromise solution that reliably performs biological functions at a reasonable cost.

Two-Component Sensing and Regulation: How Do Histidine Kinases Talk with Response Regulators at the Molecular Level?

Perceiving environmental and internal information and reacting in adaptive ways are essential attributes of living organisms. Two-component systems are relevant protein machineries from prokaryotes and lower eukaryotes that enable cells to sense and process signals. Implicating sensory histidine kinases and response regulator proteins, both components take advantage of protein phosphorylation and flexibility to switch conformations in a signal-dependent way. Dozens of two-component systems act simultaneously in any given cell, challenging our understanding about the means that ensure proper connectivity. This review dives into the molecular level, attempting to summarize an emerging picture of how histidine kinases and cognate response regulators achieve required efficiency, specificity, and directionality of signaling pathways, properties that rely on protein:protein interactions. α helices that carry information through long distances, the fine combination of loose and specific kinase/regulator interactions, and malleable reaction centers built when the two components meet emerge as relevant universal principles.

Analysis of network motifs in cellular regulation: Structural similarities, input-output relations and signal integration

Much of the complexity of regulatory networks derives from the necessity to integrate multiple signals and to avoid malfunction due to cross-talk or harmful perturbations. Hence, one may expect that the input-output behavior of larger networks is not necessarily more complex than that of smaller network motifs which suggests that both can, under certain conditions, be described by similar equations. In this review, we illustrate this approach by discussing the similarities that exist in the steady state descriptions of a simple bimolecular reaction, covalent modification cycles and bacterial two-component systems. Interestingly, in all three systems fundamental input-output characteristics such as thresholds, ultrasensitivity or concentration robustness are described by structurally similar equations. Depending on the system the meaning of the parameters can differ ranging from protein concentrations and affinity constants to complex parameter combinations which allows for a quantitative understanding of signal integration in these systems. We argue that this approach may also be extended to larger regulatory networks.

Transient absolute robustness in stochastic biochemical networks

Absolute robustness allows biochemical networks to sustain a consistent steady-state output in the face of protein concentration variability from cell to cell. This property is structural and can be determined from the topology of the network alone regardless of rate parameters. An important question regarding these systems is the effect of discrete biochemical noise in the dynamical behaviour. In this paper, a variable freezing technique is developed to show that under mild hypotheses the corresponding stochastic system has a transiently robust behaviour. Specifically, after finite time the distribution of the output approximates a Poisson distribution, centred around the deterministic mean. The approximation becomes increasingly accurate, and it holds for increasingly long finite times, as the total protein concentrations grow to infinity. In particular, the stochastic system retains a transient, absolutely robust behaviour corresponding to the deterministic case. This result contrasts with the long-term dynamics of the stochastic system, which eventually must undergo an extinction event that eliminates robustness and is completely different from the deterministic dynamics. The transiently robust behaviour may be sufficient to carry out many forms of robust signal transduction and cellular decision-making in cellular organisms.

Operating regimes of covalent modification cycles at high enzyme concentrations

The Goldbeter-Koshland model has been a paradigm for ultrasensitivity in biological networks for more than 30 years. Despite its simplicity the validity of this model is restricted to conditions when the substrate is in excess over the converter enzymes - a condition that is easy to satisfy in vitro, but which is rarely satisfied in vivo. Here, we analyze the Goldbeter-Koshland model by means of the total quasi-steady state approximation which yields a comprehensive classification of the steady state operating regimes under conditions when the enzyme concentrations are comparable to or larger than that of the substrate. Where possible we derive simple expressions characterizing the input-output behavior of the system. Our analysis suggests that enhanced sensitivity occurs if the concentration of at least one of the converter enzymes is smaller (but not necessarily much smaller) than that of the substrate and if that enzyme is saturated. Conversely, if both enzymes are saturated and at least one of the enzyme concentrations exceeds that of the substrate the system exhibits concentration robustness with respect to changes in that enzyme concentration. Also, depending on the enzyme's saturation degrees and the ratio between their maximal reaction rates the total fraction of phosphorylated substrate may increase, decrease or change nonmonotonically as a function of the total substrate concentration. The latter finding may aid the interpretation of experiments involving genetic perturbations of enzyme and substrate abundances.

Identification and Functional Validation of Autolysis-Associated Genes in Lactobacillus bulgaricus ATCC BAA-365

Lactic acid bacteria (LAB) are important organisms in food production. Indeed, LAB autolysis is very critical in dairy processing. For example, it influences the development of cheese flavor by releasing intracellular enzymes, and controls cell growth in yogurts and probiotic products. Two component systems (TCS) constitute essential environmental sensors and effectors of signal transduction in most bacteria. In the present work, mutants of one TCS (LBUL_RS00115/LBUL_RS00110) were generated to assess the relationship between TCS and cell autolysis. The mutants displayed decreased autolysis in comparison with wild type; meanwhile, complementation reversed this effect. The interaction between LBUL_RS00115 and LBUL_RS00110 was confirmed by yeast two-hybrid analysis. These observations suggested that the TCS (LBUL_RS00115/LBUL_RS00110) was involved in autolysis in Lactobacillus delbrueckii subsp. bulgaricus.

Cyclic di-GMP mediates a histidine kinase/phosphatase switch by noncovalent domain cross-linking

Histidine kinases are key components of regulatory networks in bacteria. Although many of these enzymes are bifunctional, mediating both phosphorylation and dephosphorylation of downstream targets, the molecular details of this central regulatory switch are unclear. We showed recently that the universal second messenger cyclic di-guanosine monophosphate (c-di-GMP) drives Caulobacter crescentus cell cycle progression by forcing the cell cycle kinase CckA from its default kinase into phosphatase mode. We use a combination of structure determination, modeling, and functional analysis to demonstrate that c-di-GMP reciprocally regulates the two antagonistic CckA activities through noncovalent cross-linking of the catalytic domain with the dimerization histidine phosphotransfer (DHp) domain. We demonstrate that both c-di-GMP and ADP (adenosine diphosphate) promote phosphatase activity and propose that c-di-GMP stabilizes the ADP-bound quaternary structure, which allows the receiver domain to access the dimeric DHp stem for dephosphorylation. In silico analyses predict that c-di-GMP control is widespread among bacterial histidine kinases, arguing that it can replace or modulate canonical transmembrane signaling.

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.

Invariants reveal multiple forms of robustness in bifunctional enzyme systems

Experimental and theoretical studies have suggested that bifunctional enzymes catalyzing opposing modification and demodification reactions can confer steady-state concentration robustness to their substrates. However, the types of robustness and the biochemical basis for them have remained elusive. Here we report a systematic study of the most general biochemical reaction network for a bifunctional enzyme acting on a substrate with one modification site, along with eleven sub-networks with more specialized biochemical assumptions. We exploit ideas from computational algebraic geometry, introduced in previous work, to find a polynomial expression (an invariant) between the steady state concentrations of the modified and unmodified substrate for each network. We use these invariants to identify five classes of robust behavior: robust upper bounds on concentration, robust two-sided bounds on concentration ratio, hybrid robustness, absolute concentration robustness (ACR), and robust concentration ratio. This analysis demonstrates that robustness can take a variety of forms and that the type of robustness is sensitive to many biochemical details, with small changes in biochemistry leading to very different steady-state behaviors. In particular, we find that the widely-studied ACR requires highly specialized assumptions in addition to bifunctionality. An unexpected result is that the robust bounds derived from invariants are strictly tighter than those derived by ad hoc manipulation of the underlying differential equations, confirming the value of invariants as a tool to gain insight into biochemical reaction networks. Furthermore, invariants yield multiple experimentally testable predictions and illuminate new strategies for inferring enzymatic mechanisms from steady-state measurements.