The multi-step phosphorelay mechanism of unorthodox two-component systems in E. coli realizes ultrasensitivity to stimuli while maintaining robustness to noises

Engineering two-component systems for advanced biosensing: From architecture to applications in biotechnology

Two-component systems (TCSs) are prevalent signaling pathways in bacteria. These systems mediate phosphotransfer between histidine kinase and a response regulator, facilitating responses to diverse physical, chemical, and biological stimuli. Advancements in synthetic and structural biology have repurposed TCSs for applications in monitoring heavy metals, disease-associated biomarkers, and the production of bioproducts. However, the utility of many TCS biosensors is hindered by undesired performance due to the lack of effective engineering methods. Here, we briefly discuss the architectures and regulatory mechanisms of TCSs. We also summarize the recent advancements in TCS engineering by experimental or computational-based methods to fine-tune the biosensor functional parameters, such as response curve and specificity. Engineered TCSs have great potential in the medical, environmental, and biorefinery fields, demonstrating a crucial role in a wide area of biotechnology.

Structural and functional insights underlying recognition of histidine phosphotransfer protein in fungal phosphorelay systems

In human pathogenic fungi, receiver domains from hybrid histidine kinases (hHK) have to recognize one HPt. To understand the recognition mechanism, we have assessed phosphorelay from receiver domains of five hHKs of group III, IV, V, VI, and XI to HPt from Chaetomium thermophilum and obtained the structures of Ct_HPt alone and in complex with the receiver domain of hHK group VI. Our data indicate that receiver domains phosphotransfer to Ct_HPt, show a low affinity for complex formation, and prevent a Leu-Thr switch to stabilize phosphoryl groups, also derived from the structures of the receiver domains of hHK group III and Candida albicans Sln1. Moreover, we have elucidated the envelope structure of C. albicans Ypd1 using small-angle X-ray scattering which reveals an extended flexible conformation of the long loop αD-αE which is not involved in phosphotransfer. Finally, we have analyzed the role of salt bridges in the structure of Ct_HPt alone.

EvgS/EvgA, the unorthodox two-component system regulating bacterial multiple resistance

IMPORTANCE

EvgS/EvgA, one of the five unorthodox two-component systems in Escherichia coli, plays an essential role in adjusting bacterial behaviors to adapt to the changing environment. Multiple resistance regulated by EvgS/EvgA endows bacteria to survive in adverse conditions such as acidic pH, multidrug, and heat. In this minireview, we summarize the specific structures and regulation mechanisms of EvgS/EvgA and its multiple resistance. By discussing several unresolved issues and proposing our speculations, this review will be helpful and enlightening for future directions about EvgS/EvgA.

Real-time detection of response regulator phosphorylation dynamics in live bacteria

Bacteria utilize two-component system (TCS) signal transduction pathways to sense and adapt to changing environments. In a typical TCS, a stimulus induces a sensor histidine kinase (SHK) to phosphorylate a response regulator (RR), which then dimerizes and activates a transcriptional response. Here, we demonstrate that oligomerization-dependent depolarization of excitation light by fused mNeonGreen fluorescent protein probes enables real-time monitoring of RR dimerization dynamics in live bacteria. Using inducible promoters to independently express SHKs and RRs, we detect RR dimerization within seconds of stimulus addition in several model pathways. We go on to combine experiments with mathematical modeling to reveal that TCS phosphosignaling accelerates with SHK expression but decelerates with RR expression and SHK phosphatase activity. We further observe pulsatile activation of the SHK NarX in response to addition and depletion of the extracellular electron acceptor nitrate when the corresponding TCS is expressed from both inducible systems and the native chromosomal operon. Finally, we combine our method with polarized light microscopy to enable single-cell measurements of RR dimerization under changing stimulus conditions. Direct in vivo characterization of RR oligomerization dynamics should enable insights into the regulation of bacterial physiology.

Promoting enrichment of sulfur-oxidizing autotrophic denitrifiers via static magnetic fields: Performance and mechanism of magnetic biological effects

Sulfur-driven autotrophic denitrification (SADN) is a promising technology for nitrogen removal from wastewater. In this study, different-strength SMFs (0, 5, 20, 50, 70 mT) were evaluated to investigate the potential of external static magnetic field (SMF) for enriching sulfur-oxidizing autotrophic denitrifiers (SOAD). 50-mT and 70-mT SMFs were most suitable to accelerate the growth of SOAD and the elimination of non-SOAD. The relative abundance of Thiobacillus significantly increased (p < 0.01) from 6.26% in control reactor to 36.15% under 50 mT and 52.51% under 70 mT. Under 50 mT, Thiobacillus denitrificans accumulated most rapidly, with the largest population. Furthermore, functional gene forecast by high-throughput and metagenomic sequencing indicated that SMF changed the two-component system, the adenosine 5'-monophosphate-activated protein kinase (AMPK) signaling system, the phosphotransferase system (PTS), as well as N/S-related enzymes to regulate stress-response and promote the growth of SOAD. The findings indicated that SMF accelerated the start-up of SADN.

Maximization of information transmission influences selection of native phosphorelay architectures

Phosphorelays are signal transduction circuits that sense environmental changes and adjust cellular metabolism. Five different circuit architectures account for 99% of all phosphorelay operons annotated in over 9,000 fully sequenced genomes. Here we asked what biological design principles, if any, could explain selection among those architectures in nature. We began by studying kinetically well characterized phosphorelays (Spo0 of Bacillus subtilis and Sln1 of Saccharomyces cerevisiae). We find that natural circuit architecture maximizes information transmission in both cases. We use mathematical models to compare information transmission among the architectures for a realistic range of concentration and parameter values. Mapping experimentally determined phosphorelay protein concentrations onto that range reveals that the native architecture maximizes information transmission in sixteen out of seventeen analyzed phosphorelays. These results suggest that maximization of information transmission is important in the selection of native phosphorelay architectures, parameter values and protein concentrations.

A Radical Reimagining of Fungal Two-Component Regulatory Systems

Bacterial two-component regulatory systems (TCSs) mediate signal transduction by transferring phosphoryl groups between sensor kinase and response regulator proteins, sometimes using intermediary histidine-phosphotransferase (Hpt) domains to form multistep phosphorelays. Because (i) almost all known fungal sensor kinases exhibit a domain architecture characteristic of bacterial TCS phosphorelays, (ii) all known fungal Hpts are stand-alone proteins suited to shuttle between cytoplasm and nucleus, and (iii) the best-characterized fungal TCS is a canonical phosphorelay, it is widely assumed that most or all fungal TCSs function via phosphorelays. However, fungi generally encode more sensor kinases than Hpts or response regulators, leading to a disparity between putative phosphorelay inputs and outputs. The simplest resolution of this paradox is to hypothesize that most fungal sensor kinases do not participate in phosphorelays. Reimagining how fungal TCSs might function leads to multiple testable predictions.

A logical network-based drug-screening platform for Alzheimer's disease representing pathological features of human brain organoids

Developing effective drugs for Alzheimer's disease (AD), the most common cause of dementia, has been difficult because of complicated pathogenesis. Here, we report an efficient, network-based drug-screening platform developed by integrating mathematical modeling and the pathological features of AD with human iPSC-derived cerebral organoids (iCOs), including CRISPR-Cas9-edited isogenic lines. We use 1300 organoids from 11 participants to build a high-content screening (HCS) system and test blood-brain barrier-permeable FDA-approved drugs. Our study provides a strategy for precision medicine through the convergence of mathematical modeling and a miniature pathological brain model using iCOs.

Boolean Feedforward Neural Network Modeling of Molecular Regulatory Networks for Cellular State Conversion

The molecular regulatory network (MRN) within a cell determines cellular states and transitions between them. Thus, modeling of MRNs is crucial, but this usually requires extensive analysis of time-series measurements, which is extremely difficult to obtain from biological experiments. However, single-cell measurement data such as single-cell RNA-sequencing databases have recently provided a new insight into resolving this problem by ordering thousands of cells in pseudo-time according to their differential gene expressions. Neural network modeling can be employed by using temporal data as learning data. In contrast, Boolean network modeling of MRNs has a growing interest, as it is a parameter-free logical modeling and thereby robust to noisy data while still capturing essential dynamics of biological networks. In this study, we propose a Boolean feedforward neural network (FFN) modeling by combining neural network and Boolean network modeling approach to reconstruct a practical and useful MRN model from large temporal data. Furthermore, analyzing the reconstructed MRN model can enable us to identify control targets for potential cellular state conversion. Here, we show the usefulness of Boolean FFN modeling by demonstrating its applicability through a toy model and biological networks.

Cotargeting BET proteins overcomes resistance arising from PI3K/mTOR blockade-induced protumorigenic senescence in colorectal cancer

Therapeutics targeting the phosphatidylinositol 3-kinase/mammalian target of rapamycin (PI3K/mTOR) pathway initially produce potent antitumor effects, but resistance frequently occurs. Using a phosphoproteome analysis, we found that colorectal cancer (CRC) cells exhibit resistance against PI3K/mTOR inhibition through feedback activation of multiple receptor tyrosine kinases, and their downstream focal adhesion kinase, Src and extracellular signal-regulated kinases signaling. Unexpectedly, PI3K/mTOR blockade causes senescence, mediated by the activation of the stress kinase p38. The senescent cancer cells induce the secretion of various cytokines and this senescence-associated secretome increases migration and invasion capabilities of CRC cells. We found that cotargeting PI3K/mTOR and bromodomain and extra-terminal domain can suppress activation of many oncogenic kinases involved in resistance to the PI3K/mTOR inhibition, induce cell death in vitro and tumor regression in vivo, and further prolong the survival of xenograft models. Our findings provide a rationale for a novel therapeutic strategy to overcome resistance to the PI3K/mTOR inhibitors in CRC.

A Systems Biology Approach to Identifying a Master Regulator That Can Transform the Fast Growing Cellular State to a Slowly Growing One in Early Colorectal Cancer Development Model

Colorectal cancer (CRC) has been most extensively studied for characterizing genetic mutations along its development. However, we still have a poor understanding of CRC initiation due to limited measures of its observation and analysis. If we can unveil CRC initiation events, we might identify novel prognostic markers and therapeutic targets for early cancer detection and prevention. To tackle this problem, we establish the early CRC development model and perform transcriptome analysis of its single cell RNA-sequencing data. Interestingly, we find two subtypes, fast growing vs. slowly growing populations of distinct growth rate and gene signatures, and identify CCDC85B as a master regulator that can transform the cellular state of fast growing subtype cells into that of slowly growing subtype cells. We further validate this by in vitro experiments and suggest CCDC85B as a novel potential therapeutic target that may prevent malignant CRC development by suppressing stemness and uncontrolled cell proliferation.

Realizing Cancer Precision Medicine by Integrating Systems Biology and Nanomaterial Engineering

Many clinical trials for cancer precision medicine have yielded unsatisfactory results due to challenges such as drug resistance and low efficacy. Drug resistance is often caused by the complex compensatory regulation within the biomolecular network in a cancer cell. Recently, systems biological studies have modeled and simulated such complex networks to unravel the hidden mechanisms of drug resistance and identify promising new drug targets or combinatorial or sequential treatments for overcoming resistance to anticancer drugs. However, many of the identified targets or treatments present major difficulties for drug development and clinical application. Nanocarriers represent a path forward for developing therapies with these "undruggable" targets or those that require precise combinatorial or sequential application, for which conventional drug delivery mechanisms are unsuitable. Conversely, a challenge in nanomedicine has been low efficacy due to heterogeneity of cancers in patients. This problem can also be resolved through systems biological approaches by identifying personalized targets for individual patients or promoting the drug responses. Therefore, integration of systems biology and nanomaterial engineering will enable the clinical application of cancer precision medicine to overcome both drug resistance of conventional treatments and low efficacy of nanomedicine due to patient heterogeneity.

Phosphoregulated orthogonal signal transduction in mammalian cells

Orthogonal tools for controlling protein function by post-translational modifications open up new possibilities for protein circuit engineering in synthetic biology. Phosphoregulation is a key mechanism of signal processing in all kingdoms of life, but tools to control the involved processes are very limited. Here, we repurpose components of bacterial two-component systems (TCSs) for chemically induced phosphotransfer in mammalian cells. TCSs are the most abundant multi-component signal-processing units in bacteria, but are not found in the animal kingdom. The presented phosphoregulated orthogonal signal transduction (POST) system uses induced nanobody dimerization to regulate the trans-autophosphorylation activity of engineered histidine kinases. Engineered response regulators use the phosphohistidine residue as a substrate to autophosphorylate an aspartate residue, inducing their own homodimerization. We verify this approach by demonstrating control of gene expression with engineered, dimerization-dependent transcription factors and propose a phosphoregulated relay system of protein dimerization as a basic building block for next-generation protein circuits.

Phosphoregulation is a key mechanism of signal processing. Here the authors build a phosphoregulated relay system in mammalian cells for orthogonal signal transduction.

The Signaling Molecule Indole Inhibits Induction of the AR2 Acid Resistance System in Escherichia coli

Induction of the AR2 acid response system of Escherichia coli occurs at a moderately low pH (pH 5.5) and leads to high levels of resistance to pH levels below 2.5 in the presence of glutamate. Induction is mediated in part by the EvgAS two component system. Here, we show that the bacterial signaling molecule indole inhibits the induction of key promoters in the AR2 system and blocks the development of glutamate-dependent acid resistance. The addition of tryptophan, the precursor for indole biosynthesis, had the same effects, and this block was relieved in a tnaA mutant, which is unable to synthesize indole. Expression of a constitutively active EvgS protein was able to relieve the inhibition caused by indole, consistent with EvgS being inhibited directly or indirectly by indole. Indole had no effect on autophosphorylation of the isolated cytoplasmic domain of EvgS. This is consistent with a model where indole directly or indirectly affects the ability of EvgS to detect its inducing signal or to transduce this information across the cytoplasmic membrane. The inhibitory activity of indole on the AR2 system is not related to its ability to act as an ionophore, and, conversely, the ionophore CCCP had no effect on acid-induced AR2 promoter activity, showing that the proton motive force is unlikely to be a signal for induction of the AR2 system.

Feedback analysis identifies a combination target for overcoming adaptive resistance to targeted cancer therapy

Targeted drugs aim to treat cancer by directly inhibiting oncogene activity or oncogenic pathways, but drug resistance frequently emerges. Due to the intricate dynamics of cancer signaling networks, which contain complex feedback regulations, cancer cells can rewire these networks to adapt to and counter the cytotoxic effects of a drug, thereby limiting the efficacy of targeted therapies. To identify a combinatorial drug target that can overcome such a limitation, we developed a Boolean network simulation and analysis framework and applied this approach to a large-scale signaling network of colorectal cancer with integrated genomic information. We discovered Src as a critical combination drug target that can overcome the adaptive resistance to the targeted inhibition of mitogen-activated protein kinase pathway by blocking the essential feedback regulation responsible for resistance. The proposed framework is generic and can be widely used to identify drug targets that can overcome adaptive resistance to targeted therapies.

Combined Positive and Negative Feedback Allows Modulation of Neuronal Oscillation Frequency during Sensory Processing

A key step in sensory information processing involves modulation and integration of neuronal oscillations in disparate frequency bands, a poorly understood process. Here, we investigate how top-down input causes frequency changes in slow oscillations during sensory processing and, in turn, how the slow oscillations are combined with fast oscillations (which encode sensory input). Using experimental connectivity patterns and strengths of interneurons, we develop a system-level model of a neuronal circuit controlling these oscillatory behaviors, allowing us to understand the mechanisms responsible for the observed oscillatory behaviors. Our analysis discovers a circuit capable of producing the observed oscillatory behaviors and finds that a detailed balance in the strength of synaptic connections is the critical determinant to produce such oscillatory behaviors. We not only uncover how disparate frequency bands are modulated and combined but also give insights into the causes of abnormal neuronal activities present in brain disorders.

Signal flow control of complex signaling networks

Complex disease such as cancer is often caused by genetic mutations that eventually alter the signal flow in the intra-cellular signaling network and result in different cell fate. Therefore, it is crucial to identify control targets that can most effectively block such unwanted signal flow. For this purpose, systems biological analysis provides a useful framework, but mathematical modeling of complicated signaling networks requires massive time-series measurements of signaling protein activity levels for accurate estimation of kinetic parameter values or regulatory logics. Here, we present a novel method, called SFC (Signal Flow Control), for identifying control targets without the information of kinetic parameter values or regulatory logics. Our method requires only the structural information of a signaling network and is based on the topological estimation of signal flow through the network. SFC will be particularly useful for a large-scale signaling network to which parameter estimation or inference of regulatory logics is no longer applicable in practice. The identified control targets have significant implication in drug development as they can be putative drug targets.

Minimal intervening control of biomolecular networks leading to a desired cellular state

A cell phenotype can be represented by an attractor state of the underlying molecular regulatory network, to which other network states eventually converge. Here, the set of states converging to each attractor is called its basin of attraction. A central question is how to drive a particular cell state toward a desired attractor with minimal interventions on the network system. We develop a general control framework of complex Boolean networks to provide an answer to this question by identifying control targets on which one-time temporary perturbation can induce a state transition to the boundary of a desired attractor basin. Examples are shown to illustrate the proposed control framework which is also applicable to other types of complex Boolean networks.

Systems analysis identifies potential target genes to overcome cetuximab resistance in colorectal cancer cells

Cetuximab (CTX), a monoclonal antibody against epidermal growth factor receptor, is being widely used for colorectal cancer (CRC) with wild-type (WT) KRAS. However, its responsiveness is still very limited and WT KRAS is not enough to indicate such responsiveness. Here, by analyzing the gene expression data of CRC patients treated with CTX monotherapy, we have identified DUSP4, ETV5, GNB5, NT5E, and PHLDA1 as potential targets to overcome CTX resistance. We found that knockdown of any of these five genes can increase CTX sensitivity in KRAS WT cells. Interestingly, we further found that GNB5 knockdown can increase CTX sensitivity even for KRAS mutant cells. We unraveled that GNB5 overexpression contributes to CTX resistance by modulating the Akt signaling pathway from experiments and mathematical simulation. Overall, these results indicate that GNB5 might be a promising target for combination therapy with CTX irrespective of KRAS mutation.

The Hidden Control Architecture of Complex Brain Networks

The brain controls various cognitive functions in a robust and efficient way. What is the control architecture of brain networks that enables such robust and optimal control? Is this brain control architecture distinct from that of other complex networks? Here, we developed a framework to delineate a control architecture of a complex network that is compatible with the behavior of the network and applied the framework to structural brain networks and other complex networks. As a result, we revealed that the brain networks have a distributed and overlapping control architecture governed by a small number of control nodes, which may be responsible for the robust and efficient brain functions. Moreover, our artificial network evolution analysis showed that the distributed and overlapping control architecture of the brain network emerges when it evolves toward increasing both robustness and efficiency.

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We develop a framework to delineate the control architecture of brain networks

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The control architecture of brain networks is compared with other complex networks

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Brain networks have a distributed and overlapping control architecture

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Robust and efficient brain functions might be rooted in its control architecture

Structural and Functional Analysis of the Escherichia coli Acid-Sensing Histidine Kinase EvgS

The EvgS/EvgA two-component system of Escherichia coli is activated in response to low pH and alkali metals and regulates many genes, including those for the glutamate-dependent acid resistance system and a number of efflux pumps. EvgS, the sensor kinase, is one of five unconventional histidine kinases (HKs) in E. coli and has a large periplasmic domain and a cytoplasmic PAS domain in addition to phospho-acceptor, HK and dimerization, internal receiver, and phosphotransfer domains. Mutations that constitutively activate the protein at pH 7 map to the PAS domain. Here, we built a homology model of the periplasmic region of EvgS, based on the structure of the equivalent region of the BvgS homologue, to guide mutagenesis of potential key residues in this region. We show that histidine 226 is required for induction and that it is structurally colocated with a proline residue (P522) at the top of the predicted transmembrane helix that is expected to play a key role in passing information to the cytoplasmic domains. We also show that the constitutive mutations in the PAS domain can be further activated by low external pH. Expression of the cytoplasmic part of the protein alone also gives constitutive activation, which is lost if the constitutive PAS mutations are present. These findings are consistent with a model in which EvgS senses both external and internal pH and is activated by a shift from a tight inactive to a weak active dimer, and we present an analysis of the purified cytoplasmic portion of EvgS that supports this.

IMPORTANCE One of the ways bacteria sense their environment is through two-component systems, which have one membrane-bound protein to do the sensing and another inside the cell to turn genes on or off in response to what the membrane-bound protein has detected. The membrane-bound protein must thus be able to detect the stress and signal this detection event to the protein inside the cell. To understand this process, we studied a protein that helps E. coli to survive exposure to low pH, which it must do before taking up residence in the gastrointestinal tract. We describe a predicted structure for the main sensing part of the protein and identify some key residues within it that are involved in the sensing and signaling processes. We propose a mechanism for how the protein may become activated and present some evidence to support our proposal.

L p -Adaptation: Simultaneous Design Centering and Robustness Estimation of Electronic and Biological Systems

The design of systems or models that work robustly under uncertainty and environmental fluctuations is a key challenge in both engineering and science. This is formalized in the design-centering problem, which is defined as finding a design that fulfills given specifications and has a high probability of still doing so if the system parameters or the specifications fluctuate randomly. Design centering is often accompanied by the problem of quantifying the robustness of a system. Here we present a novel adaptive statistical method to simultaneously address both problems. Our method, L_p-Adaptation, is inspired by the evolution of robustness in biological systems and by randomized schemes for convex volume computation. It is able to address both problems in the general, non-convex case and at low computational cost. We describe the concept and the algorithm, test it on known benchmarks, and demonstrate its real-world applicability in electronic and biological systems. In all cases, the present method outperforms the previous state of the art. This enables re-formulating optimization problems in engineering and biology as design centering problems, taking global system robustness into account.

Phosphoryl Group Flow within the Pseudomonas aeruginosa Pil-Chp Chemosensory System: DIFFERENTIAL FUNCTION OF THE EIGHT PHOSPHOTRANSFERASE AND THREE RECEIVER DOMAINS

Bacterial chemosensory signal transduction systems that regulate motility by type IV pili (T4P) can be markedly more complex than related flagellum-based chemotaxis systems. In T4P-based systems, the CheA kinase often contains numerous potential sites of phosphorylation, but the signaling mechanisms of these systems are unknown. In Pseudomonas aeruginosa, the Pil-Chp system regulates T4P-mediated twitching motility and cAMP levels, both of which play roles in pathogenesis. The Pil-Chp histidine kinase (ChpA) has eight "Xpt" domains; six are canonical histidine-containing phosphotransfer (Hpt) domains and two have a threonine (Tpt) or serine (Spt) in place of the histidine. Additionally, there are two stand-alone receiver domains (PilG and PilH) and a ChpA C-terminal receiver domain (ChpArec). Here, we demonstrate that the ChpA Xpts are functionally divided into three categories as follows: (i) those phosphorylated with ATP (Hpt4-6); (ii) those reversibly phosphorylated by ChpArec (Hpt2-6), and (iii) those with no detectable phosphorylation (Hpt1, Spt, and Tpt). There was rapid phosphotransfer from Hpt2-6 to ChpArec and from Hpt3 to PilH, whereas transfer to PilG was slower. ChpArec also had a rapid rate of autodephosphorylation. The biochemical results together with in vivo cAMP and twitching phenotypes of key ChpA phosphorylation site point mutants supported a scheme whereby ChpArec functions both as a phosphate sink and a phosphotransfer element linking Hpt4-6 to Hpt2-3. Hpt2 and Hpt3 are likely the dominant sources of phosphoryl groups for PilG and PilH, respectively. The data are synthesized in a signaling circuit that contains fundamental features of two-component phosphorelays.

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.

Balance between Coiled-Coil Stability and Dynamics Regulates Activity of BvgS Sensor Kinase in Bordetella

The two-component system BvgAS controls the expression of the virulence regulon of Bordetella pertussis. BvgS is a prototype of bacterial sensor kinases with extracytoplasmic Venus flytrap perception domains. Following its transmembrane segment, BvgS harbors a cytoplasmic Per-Arnt-Sim (PAS) domain and then a predicted 2-helix coiled coil that precede the dimerization-histidine-phosphotransfer domain of the kinase. BvgS homologs have a similar domain organization, or they harbor only a predicted coiled coil between the transmembrane and the dimerization-histidine-phosphotransfer domains. Here, we show that the 2-helix coiled coil of BvgS regulates the enzymatic activity in a mechanical manner. Its marginally stable hydrophobic interface enables a switch between a state of great rotational dynamics in the kinase mode and a more rigid conformation in the phosphatase mode in response to signal perception by the periplasmic domains. We further show that the activity of BvgS is controlled in the same manner if its PAS domain is replaced with the natural α-helical sequences of PAS-less homologs. Clamshell motions of the Venus flytrap domains trigger the shift of the coiled coil's dynamics. Thus, we have uncovered a general mechanism of regulation for the BvgS family of Venus flytrap-containing two-component sensor kinases.

IMPORTANCE

The two-component system BvgAS of the whooping cough agent Bordetella pertussis regulates the virulence factors necessary for infection in a coordinated manner. BvgS is the prototype of a family of sensor kinase proteins found in major bacterial pathogens. When BvgS functions as a kinase, B. pertussis is virulent, and the bacterium shifts to an avirulent phase after BvgS senses chemicals that make it switch to phosphatase. Our goal is to decipher the signaling mechanisms of BvgS in order to understand virulence regulation in Bordetella, which may lead to new antimicrobial treatments targeting those two-component systems. We discovered that the activity of BvgS is regulated in a mechanical manner. A short region of the protein that precedes the enzymatic domain switches between two states in response to signal perception by other BvgS domains. This switch region is conserved among BvgS homologs, and thus, the regulation uncovered here will likely be relevant for the family.

Phosphorelay of non-orthodox two component systems functions through a bi-molecular mechanism in vivo: the case of ArcB

Two-component systems play a central part in bacterial signal transduction. Phosphorelay mechanisms have been linked to more robust and ultra-sensitive signalling dynamics. The molecular machinery that facilitates such a signalling is, however, only understood in outline. In particular the functional relevance of the dimerization of a non-orthodox or hybrid histidine kinase along which the phosphorelay takes place has been a subject of debate. We use a combination of molecular and genetic approaches, coupled to mathematical and statistical modelling, to demonstrate that the different possible intra- and inter-molecular mechanisms of phosphotransfer are formally non-identifiable in Escherichia coli expressing the ArcB non-orthodox histidine kinase used in anoxic redox control. In order to resolve this issue we further analyse the mathematical model in order to identify discriminatory experiments, which are then performed to address cis- and trans-phosphorelay mechanisms. The results suggest that exclusive cis- and trans-mechanisms will not be operating, instead the functional phosphorelay is likely to build around a sequence of allosteric interactions among the domain pairs in the histidine kinase. This is the first detailed mechanistic analysis of the molecular processes involved in non-orthodox two-component signalling and our results suggest strongly that dimerization facilitates more discriminatory proof-reading of external signals, via these allosteric reactions, prior to them being further processed.

The Escherichia coli Acid Stress Response and Its Significance for Pathogenesis

Escherichia coli has a remarkable ability to survive low pH and possesses a number of different genetic systems that enable it to do this. These may be expressed constitutively, typically in stationary phase, or induced by growth under a variety of conditions. The activities of these systems have been implicated in the ability of E. coli to pass the acidic barrier of the stomach and to become established in the gastrointestinal tract, something causing serious infections. However, much of the work characterizing these systems has been done on standard laboratory strains of E. coli and under conditions which do not closely resemble those found in the human gut. Here we review what is known about acid resistance in E. coli as a model laboratory organism and in the context of its lifestyle as an inhabitant-sometimes an unwelcome one-of the human gut.

Characterization of mutations in the PAS domain of the EvgS sensor kinase selected by laboratory evolution for acid resistance in Escherichia coli

Laboratory-based evolution and whole-genome sequencing can link genotype and phenotype. We used evolution of acid resistance in exponential phase Escherichia coli to study resistance to a lethal stress. Iterative selection at pH 2.5 generated five populations that were resistant to low pH in early exponential phase. Genome sequencing revealed multiple mutations, but the only gene mutated in all strains was evgS, part of a two-component system that has already been implicated in acid resistance. All these mutations were in the cytoplasmic PAS domain of EvgS, and were shown to be solely responsible for the resistant phenotype, causing strong upregulation at neutral pH of genes normally induced by low pH. Resistance to pH 2.5 in these strains did not require the transporter GadC, or the sigma factor RpoS. We found that EvgS-dependent constitutive acid resistance to pH 2.5 was retained in the absence of the regulators GadE or YdeO, but was lost if the oxidoreductase YdeP was also absent. A deletion in the periplasmic domain of EvgS abolished the response to low pH, but not the activity of the constitutive mutants. On the basis of these results we propose a model for how EvgS may become activated by low pH.

Coping with low pH: molecular strategies in neutralophilic bacteria

As part of their life cycle, neutralophilic bacteria are often exposed to varying environmental stresses, among which fluctuations in pH are the most frequent. In particular, acid environments can be encountered in many situations from fermented food to the gastric compartment of the animal host. Herein, we review the current knowledge of the molecular mechanisms adopted by a range of Gram-positive and Gram-negative bacteria, mostly those affecting human health, for coping with acid stress. Because organic and inorganic acids have deleterious effects on the activity of the biological macromolecules to the point of significantly reducing growth and even threatening their viability, it is not unexpected that neutralophilic bacteria have evolved a number of different protective mechanisms, which provide them with an advantage in otherwise life-threatening conditions. The overall logic of these is to protect the cell from the deleterious effects of a harmful level of protons. Among the most favoured mechanisms are the pumping out of protons, production of ammonia and proton-consuming decarboxylation reactions, as well as modifications of the lipid content in the membrane. Several examples are provided to describe mechanisms adopted to sense the external acidic pH. Particular attention is paid to Escherichia coli extreme acid resistance mechanisms, the activity of which ensure survival and may be directly linked to 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.

Simplifying biochemical models with intermediate species

Mathematical models are increasingly being used to understand complex biochemical systems, to analyse experimental data and make predictions about unobserved quantities. However, we rarely know how robust our conclusions are with respect to the choice and uncertainties of the model. Using algebraic techniques, we study systematically the effects of intermediate, or transient, species in biochemical systems and provide a simple, yet rigorous mathematical classification of all models obtained from a core model by including intermediates. Main examples include enzymatic and post-translational modification systems, where intermediates often are considered insignificant and neglected in a model, or they are not included because we are unaware of their existence. All possible models obtained from the core model are classified into a finite number of classes. Each class is defined by a mathematically simple canonical model that characterizes crucial dynamical properties, such as mono- and multistationarity and stability of steady states, of all models in the class. We show that if the core model does not have conservation laws, then the introduction of intermediates does not change the steady-state concentrations of the species in the core model, after suitable matching of parameters. Importantly, our results provide guidelines to the modeller in choosing between models and in distinguishing their properties. Further, our work provides a formal way of comparing models that share a common skeleton.

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

Bacteria sense and respond to their environment through signaling cascades generally referred to as two-component signaling networks. These networks comprise histidine kinases and their cognate response regulators. Histidine kinases have a number of biochemical activities: ATP binding, autophosphorylation, the ability to act as a phosphodonor for their response regulators, and in many cases the ability to catalyze the hydrolytic dephosphorylation of their response regulator. Here, we explore the functional role of "split kinases" where the ATP binding and phosphotransfer activities of a conventional histidine kinase are split onto two distinct proteins that form a complex. We find that this unusual configuration can enable ultrasensitivity and bistability in the signal-response relationship of the resulting system. These dynamics are displayed under a wide parameter range but only when specific biochemical requirements are met. We experimentally show that one of these requirements, namely segregation of the phosphatase activity predominantly onto the free form of one of the proteins making up the split kinase, is met in Rhodobacter sphaeroides. These findings indicate split kinases as a bacterial alternative for enabling ultrasensitivity and bistability in signaling networks. Genomic analyses reveal that up 1.7% of all identified histidine kinases have the potential to be split and bifunctional.

Positive feedback and temperature mediated molecular switch controls differential gene regulation in Bordetella pertussis

Based on the phosphorelay kinetics operative within BvgAS two component system we propose a mathematical framework for signal transduction and gene regulation of phenotypic phases in Bordetella pertussis. The proposed model identifies a novel mechanism of transcriptional interference between two promoters present in the bvg locus. To understand the system behavior under elevated temperature, the developed model has been studied in two different ways. First, a quasi-steady state analysis has been carried out for the two component system, comprising of sensor BvgS and response regulator BvgA. The quasi-steady state analysis reveals temperature induced sharp molecular switch, leading to amplification in the output of BvgA. Accumulation of a large pool of BvgA thus results into differential regulation of the downstream genes, including the gene encoding toxin. Numerical integration of the full network kinetics is then carried out to explore time dependent behavior of different system components, that qualitatively capture the essential features of experimental results performed in vivo. Furthermore, the developed model has been utilized to study mutants that are impaired in their ability to phosphorylate the transcription factor, BvgA, of the signaling network.

Bayesian design of synthetic biological systems

Here we introduce a new design framework for synthetic biology that exploits the advantages of Bayesian model selection. We will argue that the difference between inference and design is that in the former we try to reconstruct the system that has given rise to the data that we observe, whereas in the latter, we seek to construct the system that produces the data that we would like to observe, i.e., the desired behavior. Our approach allows us to exploit methods from Bayesian statistics, including efficient exploration of models spaces and high-dimensional parameter spaces, and the ability to rank models with respect to their ability to generate certain types of data. Bayesian model selection furthermore automatically strikes a balance between complexity and (predictive or explanatory) performance of mathematical models. To deal with the complexities of molecular systems we employ an approximate Bayesian computation scheme which only requires us to simulate from different competing models to arrive at rational criteria for choosing between them. We illustrate the advantages resulting from combining the design and modeling (or in silico prototyping) stages currently seen as separate in synthetic biology by reference to deterministic and stochastic model systems exhibiting adaptive and switch-like behavior, as well as bacterial two-component signaling systems.

The evolution of the phage shock protein response system: interplay between protein function, genomic organization, and system function

Sensing the environment and responding appropriately to it are key capabilities for the survival of an organism. All extant organisms must have evolved suitable sensors, signaling systems, and response mechanisms allowing them to survive under the conditions they are likely to encounter. Here, we investigate in detail the evolutionary history of one such system: The phage shock protein (Psp) stress response system is an important part of the stress response machinery in many bacteria, including Escherichia coli K12.

Here, we use a systematic analysis of the genes that make up and regulate the Psp system in E. coli in order to elucidate the evolutionary history of the system. We compare gene sharing, sequence evolution, and conservation of protein-coding as well as noncoding DNA sequences and link these to comparative analyses of genome/operon organization across 698 bacterial genomes. Finally, we evaluate experimentally the biological advantage/disadvantage of a simplified version of the Psp system under different oxygen-related environments.

Our results suggest that the Psp system evolved around a core response mechanism by gradually co-opting genes into the system to provide more nuanced sensory, signaling, and effector functionalities. We find that recruitment of new genes into the response machinery is closely linked to incorporation of these genes into a psp operon as is seen in E. coli, which contains the bulk of genes involved in the response. The organization of this operon allows for surprising levels of additional transcriptional control and flexibility. The results discussed here suggest that the components of such signaling systems will only be evolutionarily conserved if the overall functionality of the system can be maintained.

Managing membrane stress: the phage shock protein (Psp) response, from molecular mechanisms to physiology

The bacterial phage shock protein (Psp) response functions to help cells manage the impacts of agents impairing cell membrane function. The system has relevance to biotechnology and to medicine. Originally discovered in Escherichia coli, Psp proteins and homologues are found in Gram-positive and Gram-negative bacteria, in archaea and in plants. Study of the E. coli and Yersinia enterocolitica Psp systems provides insights into how membrane-associated sensory Psp proteins might perceive membrane stress, signal to the transcription apparatus and use an ATP-hydrolysing transcription activator to produce effector proteins to overcome the stress. Progress in understanding the mechanism of signal transduction by the membrane-bound Psp proteins, regulation of the psp gene-specific transcription activator and the cell biology of the system is presented and discussed. Many features of the action of the Psp system appear to be dominated by states of self-association of the master effector, PspA, and the transcription activator, PspF, alongside a signalling pathway that displays strong conditionality in its requirement.

Response dynamics of phosphorelays suggest their potential utility in cell signalling

Phosphorelays are extended two-component signalling systems found in diverse bacteria, lower eukaryotes and plants. Only few of these systems are characterized, and we still lack a full understanding of their signalling abilities. Here, we aim to achieve a global understanding of phosphorelay signalling and its dynamical properties. We develop a generic model, allowing us to systematically analyse response dynamics under different assumptions. Using this model, we find that the steady-state concentration of phosphorylated protein at the final layer of a phosphorelay is a linearly increasing, but eventually saturating function of the input. In contrast, the intermediate layers can display ultrasensitivity. We find that such ultrasensitivity is a direct result of the phosphorelay biochemistry; shuttling of a single phosphate group from the first to the last layer. The response dynamics of the phosphorelay results in tolerance of cross-talk, especially when it occurs as cross-deactivation. Further, it leads to a high signal-to-noise ratio for the final layer. We find that a relay length of four, which is most commonly observed, acts as a saturating point for these dynamic properties. These findings suggest that phosphorelays could act as a mechanism to reduce noise and effects of cross-talk on the final layer of the relay and enforce its input–response relation to be linear. In addition, our analysis suggests that middle layers of phosphorelays could embed thresholds. We discuss the consequence of these findings in relation to why cells might use phosphorelays along with enzymatic kinase cascades.

A mathematical model of the Gac/Rsm quorum sensing network in Pseudomonas fluorescens

I present a deterministic model of the dynamics of signal transduction and gene expression in the Gac/Rsm network of the soil-dwelling bacterium Pseudomonas fluorescens. The network is involved in quorum sensing and governs antifungal production in this important biocontrol agent. A central role is played by small untranslated RNAs, which sequester regulatory mRNA-binding proteins. The model provides a reasonable match to the available data, which consists primarily of time series from reporter gene fusions. I use the model to investigate the information-processing properties of the Gac/Rsm network, in part by comparing it to a simplified model capable of quorum sensing. The results suggest that the complexity and redundancy of the Gac/Rsm network have evolved to meet the conflicting requirements of high sensitivity to environmental conditions and a conservative, robust response to variability in parameter values. Similar systems exist in a wide variety of bacteria, where they control a diverse set of population-dependent behaviors. This makes them important subjects for mathematical models that can help link empirical understanding of network structure to theoretical insights into how these networks have evolved to function under natural conditions.

Two-component signaling circuit structure and properties

Various modeling and experimental studies have analyzed the reactions, interconnections, and motifs in two-component systems, with an eye toward understanding their physiological implications and the differences between alternative designs. Examples where recent progress has been made include aspects of autoregulation, signal integration in branched pathways, cross-talk suppression, and cross-regulation via connector proteins.

Physical, functional and conditional interactions between ArcAB and phage shock proteins upon secretin-induced stress in Escherichia coli

The phage shock protein (Psp) system found in enterobacteria is induced in response to impaired inner membrane integrity (where the Psp response is thought to help maintain the proton motive force of the cell) and is implicated in the virulence of pathogens such as Yersinia and Salmonella. We provided evidence that the two-component ArcAB system was involved in induction of the Psp response in Escherichia coli and now report that role of ArcAB is conditional. ArcAB, predominantly through the action of ArcA regulated genes, but also via a direct ArcB-Psp interaction, is required to propagate the protein IV (pIV)-dependent psp-inducing signal(s) during microaerobiosis, but not during aerobiosis or anaerobiosis. We show that ArcB directly interacts with the PspB, possibly by means of the PspB leucine zipper motif, thereby allowing cross-communication between the two systems. In addition we demonstrate that the pIV-dependent induction of psp expression in anaerobiosis is independent of PspBC, establishing that PspA and PspF can function as a minimal Psp system responsive to inner membrane stress.