Phosphorelays provide tunable signal processing capabilities for the cell

Achieving a complete understanding of cellular signal transduction requires deciphering the relation between structural and biochemical features of a signaling system and the shape of the signal-response relationship it embeds. Using explicit analytical expressions and numerical simulations, we present here this relation for four-layered phosphorelays, which are signaling systems that are ubiquitous in prokaryotes and also found in lower eukaryotes and plants. We derive an analytical expression that relates the shape of the signal-response relationship in a relay to the kinetic rates of forward, reverse phosphorylation and hydrolysis reactions. This reveals a set of mathematical conditions which, when satisfied, dictate the shape of the signal-response relationship. We find that a specific topology also observed in nature can satisfy these conditions in such a way to allow plasticity among hyperbolic and sigmoidal signal-response relationships. Particularly, the shape of the signal-response relationship of this relay topology can be tuned by altering kinetic rates and total protein levels at different parts of the relay. These findings provide an important step towards predicting response dynamics of phosphorelays, and the nature of subsequent physiological responses that they mediate, solely from topological features and few composite measurements; measuring the ratio of reverse and forward phosphorylation rate constants could be sufficient to determine the shape of the signal-response relationship the relay exhibits. Furthermore, they highlight the potential ways in which selective pressures on signal processing could have played a role in the evolution of the observed structural and biochemical characteristic in phosphorelays

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

Published onlineJournal ArticleResearch Support, Non-U.S. Gov'tSynthetic 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.Exeter University Science Strateg

Computational modelling and analysis of the molecular network regulating sporulation initiation in Bacillus subtilis

BACKGROUND: Bacterial spores are important contaminants in food, and the spore forming bacteria are often implicated in food safety and food quality considerations. Spore formation is a complex developmental process involving the expression of more than 500 genes over the course of 6 to 8 hrs. The process culminates in the formation of resting cells capable of resisting environmental extremes and remaining dormant for long periods of time, germinating when conditions promote further vegetative growth. Experimental observations of sporulation and germination are problematic and time consuming so that reliable models are an invaluable asset in terms of prediction and risk assessment. In this report we develop a model which assists in the interpretation of sporulation dynamics. RESULTS: This paper defines and analyses a mathematical model for the network regulating Bacillus subtilis sporulation initiation, from sensing of sporulation signals down to the activation of the early genes under control of the master regulator Spo0A. Our model summarises and extends other published modelling studies, by allowing the user to execute sporulation initiation in a scenario where Isopropyl β-D-1-thiogalactopyranoside (IPTG) is used as an artificial sporulation initiator as well as in modelling the induction of sporulation in wild-type cells. The analysis of the model results and the comparison with experimental data indicate that the model is good at predicting inducible responses to sporulation signals. However, the model is unable to reproduce experimentally observed accumulation of phosphorelay sporulation proteins in wild type B. subtilis. This model also highlights that the phosphorelay sub-component, which relays the signals detected by the sensor kinases to the master regulator Spo0A, is crucial in determining the response dynamics of the system. CONCLUSION: We show that there is a complex connectivity between the phosphorelay features and the master regulatory Spo0A. Additional we discovered that the experimentally observed regulation of the phosphotransferase Spo0B for wild-type B. subtilis may be playing an important role in the network which suggests that modelling of sporulation initiation may require additional experimental support. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12918-014-0119-x) contains supplementary material, which is available to authorized users

Time series analysis of the Bacillus subtilis sporulation network reveals low dimensional chaotic dynamics

Chaotic behavior refers to a behavior which, albeit irregular, is generated by an underlying deterministic process. Therefore, a chaotic behavior is potentially controllable. This possibility becomes practically amenable especially when chaos is shown to be low-dimensional, i.e., to be attributable to a small fraction of the total systems components. In this case, indeed, including the major drivers of chaos in a system into the modeling approach allows us to improve predictability of the systems dynamics. Here, we analyzed the numerical simulations of an accurate ordinary differential equation model of the gene network regulating sporulation initiation in Bacillus subtilis to explore whether the non-linearity underlying time series data is due to low-dimensional chaos. Low-dimensional chaos is expectedly common in systems with few degrees of freedom, but rare in systems with many degrees of freedom such as the B. subtilis sporulation network. The estimation of a number of indices, which reflect the chaotic nature of a system, indicates that the dynamics of this network is affected by deterministic chaos. The neat separation between the indices obtained from the time series simulated from the model and those obtained from time series generated by Gaussian white and colored noise confirmed that the B. subtilis sporulation network dynamics is affected by low dimensional chaos rather than by noise. Furthermore, our analysis identifies the principal driver of the networks chaotic dynamics to be sporulation initiation phosphotransferase B (Spo0B). We then analyzed the parameters and the phase space of the system to characterize the instability points of the network dynamics, and, in turn, to identify the ranges of values of Spo0B and of the other drivers of the chaotic dynamics, for which the whole system is highly sensitive to minimal perturbation. In summary, we described an unappreciated source of complexity in the B. subtilis sporulation network by gathering evidence for the chaotic behavior of the system, and by suggesting candidate molecules driving chaos in the system. The results of our chaos analysis can increase our understanding of the intricacies of the regulatory network under analysis, and suggest experimental work to refine our behavior of the mechanisms underlying B. subtilis sporulation initiation control

STRUCTURAL AND MUTAGENESIS STUDIES OF THE YEAST PHOSPHORELAY SIGNALING PROTEINS YPD1 AND SSK1

His-Asp signaling systems are ubiquitous in bacteria, archaea, and certain plants and fungi. Little structural information is known about the protein-protein interactions within these signaling pathways, leaving an incomplete picture of how these essential systems operate. In this dissertation, the focus of my work in the West laboratory was the receiver domain of the fungal response regulator protein Ssk1, and its interaction with the histidine phosphotransfer protein Ypd1. In Saccharomyces cerevisiae (Sc), Ypd1 interacts with receiver domains from upstream Sln1 and downstream Ssk1 on a common hydrophobic docking site. The main portion of this thesis presents the co-crystal complex of Ypd1 and Ssk1-R2W638A and the accompanying analysis to explain key differences in the physiological functions of Ssk1-R2 and Sln1-R1. Protein-protein interactions were characterized using a newly developed fluorescence binding assay and in vitro 32P-phosphotransfer experiments. In addition, the co-crystallization of Ssk1-R2W638A and a point mutant of Ypd1 (Ypd1-G68Q) is described. Ssk1 protein constructs from the human pathogen Cryptococcus neoformans (Cn) were designed in order to biochemically characterize interactions with C. neoformans Ypd1, but these proteins were either insoluble or inactive. Lastly, my work in the Cichewicz laboratory describes the discovery of three new secondary metabolites from a previously uncharacterized microbial mat fungus (clearanols C, D and E)

Exploring and Understanding Signal-response Relationships and Response Dynamics of Microbial Two-Component Signaling Systems

Two-component signaling systems are found in bacteria, fungi and plants. They mediate many of the physiological responses of these organisms to their environment and display several conserved biochemical and structural features. This thesis identifies a potential functional role for two commonly found architectures in two-component signaling system, the split kinases and phosphate sink, which suggests that by enabling switch-like behaviors they could underlie physiological decision making. I report that split histidine kinases, where autophosphorylation and phosphotransfer activities are segregated onto distinct proteins capable of complex formation, enable ultrasensitivity and bistability. By employing computer simulations and analytical approaches, I show that the specific biochemical features of split kinases “by design” enable higher nonlinearity in the system response compared to conventional two-component systems and those using bifunctional (but not split) kinases. I experimentally show that one of these requirements, namely segregation of the phosphatase activity only to the free form of one of the proteins making up the split kinase, is met in proteins isolated from Rhodobacter sphaeroides. While the split kinase I study from R. sphaeroides is specifically involved in chemotaxis, other split kinases are involved in diverse responses. Genomics studies suggest 2.3% of all chemotaxis kinases, and 2.8% of all kinases could be functioning as split kinases. Combining theoretical and experimental approaches, I show that the phosphate sink motif found in microbial and plant TCSs allows threshold behaviors. This motif involves a single histidine kinase that can phosphotransfer reversibly to two separate response regulators and examples are found in bacteria, yeast and plants. My results show that one of the response regulators can act as a “sink” or “buffer” that needs to be saturated before the system can generate significant responses. This sink, thereby allows the generation of a signal threshold that needs to be exceeded for there to be significant phosphoryl group flow to the other response regulator. Thus, this system can enable cells to display switch-like behavior to external signals. Using an analytical approach, I identify mathematical conditions on the system parameters that are necessary for threshold dynamics. I find these conditions to be satisfied in both of the natural systems where the system parameters have been measured. Further, by in vitro reconstitution of a sample system, I experimentally demonstrate threshold dynamics for a phosphate-sink containing two-component system. This study provides a link between these architectures of TCSs and signal-response relationship, thereby enabling experimentally testable hypotheses in these diverse two-component systems. These findings indicate split kinases and phosphate as a microbial alternative for enabling ultrasensitivity and bistability - known to be crucial for cellular decision making. By demonstrating ultrasensitivity, threshold dynamics and their mechanistic basis in a common class of two-component system, this study allows a better understanding of cellular signaling in a diverse range of organisms and will open the way to the design of novel threshold systems in synthetic biology. Thus, I believe that this study will have broad implications not only for microbiologists but also systems biologists who aim to decipher conserved dynamical features of cellular networks.University of Exete

A COMPUTATIONAL APPROACH FOR ACCESSING PHOSPHORYLATED RESPONSE REGULATOR CONFORMATIONS AND SIGNALING COMPLEXES INVOLVING THE FUNGAL PHOSPHORELAY PROTEIN YPD1

Two-component signaling is the primary means by which bacteria, archaea and certain eukaryotes sense and respond to their environments. Signal transfer proceeds through sequential His-to-Asp phosphorylation of upstream histidine kinases and downstream response regulators. These systems share highly modular designs and have been incorporated into a myriad of cellular processes. The highly labile chemical natures of phosphoaspartate and phosphohistidine lead to relatively short experimental life-times, making study of the modified signaling proteins challenging. The focus of this research was to develop computational and experimental approaches for characterizing phosphorylated two-component signaling proteins. Following an introductory chapter, the first experimental section presents a computational technique for simulating the activation of individual response regulator proteins. This is accomplished using known experimental data on conserved active site chemistry to define a common set of restraints to drive each simulation. The protocol was verified on five genetically diverse response regulators with known experimental structures. The second section applies this principle to signaling complexes to study the effects of phosphorylation on protein- protein interactions within the Saccharomyces cerevisiae osmoregulatory signaling system. The third section describes the experimental characterization of a specific signaling complex from Saccharomyces cerevisiae between the response regulator Ssk1 and a point mutant (G68Q) of the histidine phosphotransfer protein Ypd1 using X-ray crystallography. This mutation occurs near the active site of both proteins and appears to interfere with phosphotransfer. Further in silico studies were performed to observe the role of G68 in catalysis of phosphotransfer

Exploring design principles of cellular information processing

As a summary, this work attempts to explore and uncovered design principles of certain dynamics of cellular networks by combining evolution in silico with rule-based modelling approach. Biological systems exhibit complex dynamics, due to the complex interactions in the intra- and inter- cellular biochemical reaction networks. For instance, signalling networks are composed of many enzymes and scaffolding proteins which have combinatorial interactions. These complex systems often generate response dynamics that are essential for correct decision-makings in cells. Especially, these complex interactions are results of long term of evolutionary process. With such evolutionary complexity, systems biologists aim to decipher the structure and dynamics of signalling and regulatory networks underpinning cellular responses; synthetic biologists can use this insight to alter existing networks or engineer de novo ones. Both tasks will benefit from an understanding of which structural and dynamic features of networks can emerge from evolutionary processes, through which intermediary steps these arise, and whether they embody general design principles. As natural evolution at the level of network dynamics is difficult to study, in silico evolution of network models can provide important insights. However, current tools used for in silico evolution of network dynamics are limited to ad hoc computer simulations and models. In my PhD study, with collaborators I construct the BioJazz, an extendable, user-friendly tool for simulating the evolution of dynamic biochemical networks. Unlike previous tools for in silico evolution, BioJazz allows for evolution of cellular networks with theoretically unbounded complexity by combining rule-based modelling with an encoding of networks that is akin to a genome. BioJazz can be used to implement biologically realistic selective pressures, and allows exploration of the space of network architectures and dynamics that implement prescribed physiological functions. It is provided as an open-source tool to facilitate its further development and use. I use this tool to explore the possible biochemical designs for signalling networks displaying ultrasensitive and adaptive response dynamics. By running evolutionary simulations mimicking different biochemical scenarios, we find that enzyme sequestration emerges as a key biochemical mechanism for both dynamics. Detailed analysis of these evolved networks revealed that enzyme sequestration enables both ultrasensitive and adaptive response dynamics. I verified this proposition by designing a generic model of a signalling cycle, featuring two enzymes and a sequestering (scaffold) protein. This simple system is capable of displaying both ultrasensitive and adaptive response dynamics, even more interestingly modulating the system switching between two response dynamics through perturbing the scaffold protein. These results show that enzyme sequestration can be exploited by evolution so to generate diverse response dynamics in signalling networks. From evolutionary simulations towards ultrasensitivity, bistable dynamics emerged as an alternative solution. On one hand, inspired by such results I used the fitness function as an objective function combined with different constraints to design and optimise bistable signalling networks with completely new structure and mechanism. Studying designed bistable signalling network explicates how such bistable network can be experimentally implemented. On the other hand, from studying the evolved bistable networks allosteric enzymes catalysing futile cycles appear to be a new mechanism of bistability in signalling networks. Furthermore, one of the smallest bistable signalling motifs is derived. This motif is composed of one kinase protein with two distinct conformational states and one substrate subject to phosphorylation by the kinase and auto-dephosphorylation reactions. The sufficient and necessary condition on parameters, with which the signalling motif displays bistable response dynamics, is analytically defined. By expanding the systems with more kinases, unlimited multistability emerges with potentials of implementing complex logic gates and cell state transitions. Further exploring the discovered and natural signalling networks implies shared design patterns. Motivated by searching structural boundaries between monostationary and multistationary networks, I performed algorithmic searching of multistationary signalling networks intending to find the sufficient structural conditions for multistationarity in signalling networks