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

Computing global shape measures

Global shape measures are a convenient way to describe regions. They are generally simple and efficient to extract, and provide an easy means for high level tasks such as classification as well as helping direct low-level computer vision processes such as segmentation. In this chapter a large selection of global shape measures (some from the standard literature as well as other newer methods) are described and demonstrated

An investigation into dynamic and functional properties of prokaryotic signalling networks

In this thesis, I investigate dynamic and computational properties of prokaryotic signalling architectures commonly known as the Two Component Signalling networks and phosphorelays. The aim of this study is to understand the information processing capabilities of different prokaryotic signalling architectures by examining the dynamics they exhibit. I present original investigations into the dynamics of different phosphorelay architectures and identify network architectures that include a commonly found four step phosphorelay architecture with a capacity for tuning its steady state output to implement different signal-response behaviours viz. sigmoidal and hyperbolic response. Biologically, this tuning can be implemented through physiological processes like regulating total protein concentrations (e.g. via transcriptional regulation or feedback), altering reaction rate constants through binding of auxiliary proteins on relay components, or by regulating bi-functional activity in relays which are mediated by bifunctional histidine kinases. This study explores the importance of different biochemical arrangements of signalling networks and their corresponding response dynamics. Following investigations into the significance of various biochemical reactions and topological variants of a four step relay architecture, I explore the effects of having different types of proteins in signalling networks. I show how multi-domain proteins in a phosphorelay architecture with multiple phosphotransfer steps occurring on the same protein can exhibit multistability through a combination of double negative and positive feedback loops. I derive a minimal multistable (core) architecture and show how component sharing amongst networks containing this multistable core can implement computational logic (like AND, OR and ADDER functions) that allows cells to integrate multiple inputs and compute an appropriate response. I examine the genomic distribution of single and multi domain kinases and annotate their partner response regulator proteins across prokaryotic genomes to find the biological significance of dynamics that these networks embed and the processes they regulate in a cell. I extract data from a prokaryotic two component protein database and take a sequence based functional annotation approach to identify the process, function and localisation of different response regulators as signalling partners in these networks. In summary, work presented in this thesis explores the dynamic and computational properties of different prokaryotic signalling networks and uses them to draw an insight into the biological significance of multidomain sensor kinases in living cells. The thesis concludes with a discussion on how this understanding of the dynamic and computational properties of prokaryotic signalling networks can be used to design synthetic circuits involving different proteins comprising two component and phosphorelay architectures.Dorothy Hodgkin Studentship funded by EPSRC and Microsoft Research

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

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

Fundamental investigations into the factors affecting the response of laccase-based electrochemical biosensors

Given their widespread effects and distribution in both natural and industrial environments, the monitoring of phenolic compounds is of considerable analytical interest. Electrochemical biosensor technologies, in particular those comprising laccase enzymes, afford many potential benefits to address this analytical need. However, several key factors affecting sensor response currently limit their applicability. This Thesis reports on the fabrication and optimisation of an electrochemical laccase-based biosensor towards the application of the monitoring of phenolic compounds. Selected factors considered to affect sensor response were investigated using the optimised biosensor. These included: electrochemical, biochemical and substrate-dependent factors, which were found to intersect in modulating biosensor response signals. Through the application of transducer-dependent and substrate-dependent parameters, the selective and simultaneous detection of a mixture of different phenolic analytes is successfully demonstrated. This Thesis also investigates the use of Quartz-Crystal Microbalance with Dissipation (QCM-D) technology, an analytical technique that measures physical parameters of thin-film structures, towards the successful monitoring of enzyme immobilisation strategies. These strategies are fundamental to the successful fabrication of biosensors, and the real-time monitoring of immobilised film formations is of considerable research interest. In the studies reported on in this Thesis, QCM-D technology was demonstrated to be an effective complementary technology in the prediction of film immobilisation techniques on the resultant biochemical kinetics of immobilised enzymes

Fundamental investigations into the factors affecting the response of laccase-based electrochemical biosensors

Given their widespread effects and distribution in both natural and industrial environments, the monitoring of phenolic compounds is of considerable analytical interest. Electrochemical biosensor technologies, in particular those comprising laccase enzymes, afford many potential benefits to address this analytical need. However, several key factors affecting sensor response currently limit their applicability. This Thesis reports on the fabrication and optimisation of an electrochemical laccase-based biosensor towards the application of the monitoring of phenolic compounds. Selected factors considered to affect sensor response were investigated using the optimised biosensor. These included: electrochemical, biochemical and substrate-dependent factors, which were found to intersect in modulating biosensor response signals. Through the application of transducer-dependent and substrate-dependent parameters, the selective and simultaneous detection of a mixture of different phenolic analytes is successfully demonstrated. This Thesis also investigates the use of Quartz-Crystal Microbalance with Dissipation (QCM-D) technology, an analytical technique that measures physical parameters of thin-film structures, towards the successful monitoring of enzyme immobilisation strategies. These strategies are fundamental to the successful fabrication of biosensors, and the real-time monitoring of immobilised film formations is of considerable research interest. In the studies reported on in this Thesis, QCM-D technology was demonstrated to be an effective complementary technology in the prediction of film immobilisation techniques on the resultant biochemical kinetics of immobilised enzymes

The Structural Basis for Kinetic and Allosteric Differences between Two Bacterial Phosphofructokinases

The fructose 6-phosphate (Fru-6P) saturation curve for phosphofructokinase (PFK) from E. coli is sigmoidal in the presence of saturating MgATP levels, while the corresponding curve for B. stearothermophilus PFK is essentially hyperbolic. Sigmoidality can be due to apparent cooperativity arising from the kinetic mechanism of an enzyme. We have determined the kinetic mechanism of B. stearothermophilus PFK (BsPFK). BsPFK was found to obey a non rapid-equilibrium random mechanism similar to the one E. coli PFK (EcPFK) follows. Substrate inhibition by MgATP was observed. We propose that substrates bind to BsPFK through two alternative pathways, one of which is slower. The substrate inhibition arises in part from reaction flux through the slower pathway. Although EcPFK and BsPFK obey similar kinetic mechanisms, they are inhibited differently by MgATP: EcPFK is profoundly inhibited, BsPFK only weakly. The structural basis for this difference could be closure of the active site via a conformational transition that occurs in EcPFK, but not BsPFK. To investigate the importance of this transition for MgATP inhibition of EcPFK, we have constructed a chimeric enzyme (ChiPFK) that contains the "rigid" ATP-binding domain of BsPFK grafted onto the remainder of the EcPFK subunit. Our results indicate that ChiPFK is locked in an "open" structure resembling the activated form of EcPFK. It is insensitive to heterotropic regulation. Nevertheless, ChiPFK exhibits residual cooperativity. Possible explanations for the cooperativity are discussed. The 6F loop is proposed to be important in PFK allosteric behavior. Residues along the loop are largely conserved between BsPFK and EcPFK, except for 161, which is a glutamate in BsPFK, and a glutamine in EcPFK. Using site-directed mutagenesis, Glu 161 of BsPFK has been changed to glutamine and alanine. Similarly, Gin 161 of EcPFK has been changed to glutamate, arginine and alanine. Of the five mutants, one, QA161, was particularly interesting. Though activated normally by GDP, it was completely insensitive to PEP inhibition. This indicates that the hydrogen-bonding ability of residue 161 is critical for PEP inhibition of EcPFK, and that GDP activation and PEP inhibition follow different structural pathways

On the Hausdorff distance between the shifted Heaviside step function and the transmuted Stannard growth function

In this paper we study the one-sided Hausdorff distance between the shifted Heaviside step--function and the transmuted Stannard growth function. Precise upper and lower bounds for the Hausdorff distance have been obtained. We present a software module (intellectual property) within the programming environment CAS Mathematica for the analysis of the growth curves. Numerical examples, illustrating our results are given, too