Linear control analysis of the autocatalytic glycolysis system

Autocatalysis is necessary and ubiquitous in both engineered and biological systems but can aggravate control performance and cause instability. We analyze the properties of autocatalysis in the universal and well studied glycolytic pathway. A simple two-state model incorporating ATP autocatalysis and inhibitory feedback control captures the essential dynamics, including limit cycle oscillations, observed experimentally. System performance is limited by the inherent autocatalytic stoichiometry and higher levels of autocatalysis exacerbate stability and performance. We show that glycolytic oscillations are not merely a "frozen accident" but a result of the intrinsic stability tradeoffs emerging from the autocatalytic mechanism. This model has pedagogical value as well as appearing to be the simplest and most complete illustration yet of Bode’s integral formula

A Symmetric Dual Feedback System Provides a Robust and Entrainable Oscillator

Many organisms have evolved molecular clocks to anticipate daily changes in their environment. The molecular mechanisms by which the circadian clock network produces sustained cycles have extensively been studied and transcriptional-translational feedback loops are common structures to many organisms. Although a simple or single feedback loop is sufficient for sustained oscillations, circadian clocks implement multiple, complicated feedback loops. In general, different types of feedback loops are suggested to affect the robustness and entrainment of circadian rhythms

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

CAM Models: Lessons and Implications for CAM Evolution

The evolution of Crassulacean acid metabolism (CAM) by plants has been one of the most successful strategies in response to aridity. On the onset of climate change, expanding the use of water efficient crops and engineering higher water use efficiency into C3 and C4 crops constitute a plausible solution for the problems of agriculture in hotter and drier environments. A firm understanding of CAM is thus crucial for the development of agricultural responses to climate change. Computational models on CAM can contribute significantly to this understanding. Two types of models have been used so far. Early CAM models based on ordinary differential equations (ODE) reproduced the typical diel CAM features with a minimal set of components and investigated endogenous day/night rhythmicity. This line of research brought to light the preponderant role of vacuolar malate accumulation in diel rhythms. A second wave of CAM models used flux balance analysis (FBA) to better understand the role of CO2 uptake in flux distribution. They showed that flux distributions resembling CAM metabolism emerge upon constraining CO2 uptake by the system. We discuss the evolutionary implications of this and also how CAM components from unrelated pathways could have integrated along evolution

Mathematical Identification of Critical Reactions in the Interlocked Feedback Model

Dynamic simulations are necessary for understanding the mechanism of how biochemical networks generate robust properties to environmental stresses or genetic changes. Sensitivity analysis allows the linking of robustness to network structure. However, it yields only local properties regarding a particular choice of plausible parameter values, because it is hard to know the exact parameter values in vivo. Global and firm results are needed that do not depend on particular parameter values. We propose mathematical analysis for robustness (MAR) that consists of the novel evolutionary search that explores all possible solution vectors of kinetic parameters satisfying the target dynamics and robustness analysis. New criteria, parameter spectrum width and the variability of solution vectors for parameters, are introduced to determine whether the search is exhaustive. In robustness analysis, in addition to single parameter sensitivity analysis, robustness to multiple parameter perturbation is defined. Combining the sensitivity analysis and the robustness analysis to multiple parameter perturbation enables identifying critical reactions. Use of MAR clearly identified the critical reactions responsible for determining the circadian cycle in the Drosophila interlocked circadian clock model. In highly robust models, while the parameter vectors are greatly varied, the critical reactions with a high sensitivity are uniquely determined. Interestingly, not only the per-tim loop but also the dclk-cyc loop strongly affect the period of PER, although the dclk-cyc loop hardly changes its amplitude and it is not potentially influential. In conclusion, MAR is a powerful method to explore wide parameter space without human-biases and to link a robust property to network architectures without knowing the exact parameter values. MAR identifies the reactions critically responsible for determining the period and amplitude in the interlocked feedback model and suggests that the circadian clock intensively evolves or designs the kinetic parameters so that it creates a highly robust cycle

Two Component Systems: Physiological Effect of a Third Component

Signal transduction systems mediate the response and adaptation of organisms to environmental changes. In prokaryotes, this signal transduction is often done through Two Component Systems (TCS). These TCS are phosphotransfer protein cascades, and in their prototypical form they are composed by a kinase that senses the environmental signals (SK) and by a response regulator (RR) that regulates the cellular response. This basic motif can be modified by the addition of a third protein that interacts either with the SK or the RR in a way that could change the dynamic response of the TCS module. In this work we aim at understanding the effect of such an additional protein (which we call “third component”) on the functional properties of a prototypical TCS. To do so we build mathematical models of TCS with alternative designs for their interaction with that third component. These mathematical models are analyzed in order to identify the differences in dynamic behavior inherent to each design, with respect to functionally relevant properties such as sensitivity to changes in either the parameter values or the molecular concentrations, temporal responsiveness, possibility of multiple steady states, or stochastic fluctuations in the system. The differences are then correlated to the physiological requirements that impinge on the functioning of the TCS. This analysis sheds light on both, the dynamic behavior of synthetically designed TCS, and the conditions under which natural selection might favor each of the designs. We find that a third component that modulates SK activity increases the parameter space where a bistable response of the TCS module to signals is possible, if SK is monofunctional, but decreases it when the SK is bifunctional. The presence of a third component that modulates RR activity decreases the parameter space where a bistable response of the TCS module to signals is possible

Comparative analysis of prototype two-component systems with either bifunctional or monofunctional sensors: differences in molecular structure and physiological function

Signal transduction by a traditional two-component system involves a sensor protein that recognizes a physiological signal, autophosphorylates and transfers its phosphate, and a response regulator protein that receives the phosphate, alters its affinity toward specific target proteins or DNA sequences and causes change in metabolic activity or gene expression. In some cases the sensor protein, when unphosphorylated, has a positive effect upon the rate of dephosphorylation of the regulator protein (bifunctional sensor), whereas in other cases it has no such effect (monofunctional sensor). In this work we identify structural and functional differences between these two designs. In the first part of the paper we use sequence data for two-component systems from several organisms and homology modelling techniques to determine structural features for response regulators and for sensors. Our results indicate that each type of reference sensor (bifunctional and monofunctional) has a distinctive structural feature, which we use to make predictions regarding the functionality of other sensors. In the second part of the paper we use mathematical models to analyse and compare the physiological function of systems that differ in the type of sensor and are otherwise equivalent. Our results show that a bifunctional sensor is better than a monofunctional sensor both at amplifying changes in the phosphorylation level of the regulator caused by signals from the sensor and at attenuating changes caused by signals from small phosphodonors. Cross-talk to or from other two-component systems is better suppressed if the transmitting sensor is monofunctional, which is the more appropriate design when such cross-talk represents pathological noise. Cross-talk to or from other two-component systems is better amplified if the transmitting sensor is bifunctional, which is the more appropriate design when such cross-talk represents a physiological signal. These results provide a functional rationale for the selection of each design that is consistent with available experimental evidence for several two-component systems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74871/1/j.1365-2958.2003.03344.x.pd

概日時計におけるインターロック逆位相振動子の設計原理

In system biology, mathematical models have long tradition are used to understand complex biological control processes/ systems, for example, circadian clock oscillatory mechanism. Circadian rhythms (~24 hour) is ubiquitous in almost the living species ranging from mammals to cyanobacteria shows the robustness of key oscillatory features such as the phase, period and amplitude against external and internal variations. These autonomous oscillations are formed by the complex interactions of the interactive molecules. A transcriptional-translational feedback loop is typically characterized as a common principle for this sustained oscillations. Recently studies, it has broadly been established that the robustness of biochemical oscillators, like the Drosophila circadian clocks, can be generated by interlocked transcriptional-translational feedback loops, where two negative feedback loops are coupled through mutual activations. The mechanisms by which such coupling protocols have survived out of many possible protocols remain to be revealed. To address this question, we investigated two distinct coupling protocols: activator-coupled oscillators (ACO) and repressor-coupled oscillators (RCO). We focused on the two coupling parameters: coupling dissociation constant and coupling time delay. Interestingly, the ACO was able to produce anti-phase or morning-evening cycles, whereas the RCO produced in-phase ones. Deterministic and stochastic analyses demonstrated that the anti-phase ACO provided greater fluctuations in amplitude not only with respect to changes in coupling parameters but also to random parameter perturbations than the in-phase RCO. Moreover, the ACO deteriorated the entrainability to the day-night master clock, whereas the RCO produced high entrainability. Considering that the real, interlocked feedback loops have evolved as the ACO, instead of the RCO, we first proposed a hypothesis that the morning-evening or anti-phase cycle is more essential for Drosophila than achieving the robustness and entrainability.九州工業大学博士学位論文 学位記番号:情工博甲第352号 学位授与年月日:令和2年9月25日1 BACKGROUND|2 THE DYNAMICS MODELS OF CIRCADIAN RHYTHMS|3 MODELING THE INTERLOCKED NEGATIVE FEEDBACK LOOPS|4 ROBUSTNESS OF THE INTERLOCKED CIRCADIAN OSCILLATORS|5 ENTRAINABILITY OF THE COUPLED OSCILLATORS|6 CONCLUSIONS AND FUTURE WORK九州工業大学令和2年

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

Mathematical and Computational Analyses of Immunological Signaling Networks Affecting Mycobacterium tuberculosis Infection.

Immunological signaling pathways between and within cells are central determinants of the success of immune responses. One major characteristic of immune signaling is a balance that is struck between pro-inflammatory responses to pathogens and anti-inflammatory regulation that stabilizes and modulates immunity. Mycobacterium tuberculosis is a successful human pathogen that preferentially survives within host macrophages, the very immune cells that act to eliminate it. Exploitation of the balance between pro- and anti-inflammatory mechanisms may be a strategy for M. tuberculosis survival within macrophages. This work first explores the evolved design principles of intracellular macrophage activation pathways relevant to countering M. tuberculosis infection. I used a mathematical model of the macrophage intracellular signaling network to predict that multiple synergistic activation signals are balanced by negative (anti-inflammatory) feedback from a single output, the killing effector nitric oxide. Without the presence of two activation signals, the feedback is antagonistic toward high levels of activation. I next implemented a representation of a growing intracellular population of M. tuberculosis in the macrophage signaling model. This shows that negative feedback of nitric oxide to activation signaling may not optimally kill bacteria compared to a possible positive feedback design. However, the model predicts that negative feedback imparts a kinetic advantage to elevating nitric oxide levels. The kinetics of nitric oxide induction offset the disadvantage of negative feedback if the timing of activating cytokine delivery occurs near the time of macrophage infection. On a different biological scale, I explored the roles of activation signals in M. tuberculosis infection with a computational agent-based model of granuloma formation. Model results suggest that multiple effects of the pleiotropic cytokine tumor necrosis factor-a (TNF) are an essential feature of TNF function: loss of single TNF activities did not result in granuloma structures comparable to deletion of all TNF activity. Perturbation of multiple TNF activities simultaneously showed synergistic and competitive effects of individual TNF activities in granuloma formation. Finally, I explored possible ways to integrate a single-cell stochastic model of macrophage gene regulation into an agent-based model to simulate the roles of intracellular signaling in the context of the granuloma environment.Ph.D.Microbiology & ImmunologyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/58442/1/jjray_1.pd