Implementation and System Identification of a Phosphorylation-Based Insulator in a Cell-Free Transcription-Translation System

An outstanding challenge in the design of synthetic biocircuits is the development of a robust and efficient strategy for interconnecting functional modules. Recent work demonstrated that a phosphorylation-based insulator (PBI) implementing a dual strategy of high gain and strong negative feedback can be used as a device to attenuate retroactivity. This paper describes the implementation of such a biological circuit in a cell-free transcription-translation system and the structural identifiability of the PBI in the system. We first show that the retroactivity also exists in the cell-free system by testing a simple negative regulation circuit. Then we demonstrate that the PBI circuit helps attenuate the retroactivity significantly compared to the control. We consider a complex model that provides an intricate description of all chemical reactions and leveraging specific physiologically plausible assumptions. We derive a rigorous simplified model that captures the output dynamics of the PBI. We performed standard system identification analysis and determined that the model is globally identifiable with respect to three critical parameters. These three parameters are identifiable under specific experimental conditions and we performed these experiments to estimate the parameters. Our experimental results suggest that the functional form of our simplified model is sufficient to describe the reporter dynamics and enable parameter estimation. In general, this research illustrates the utility of the cell-free expression system as an alternate platform for biocircuit implementation and system identification and it can provide interesting insights into future biological circuit designs

Investigating modularity in the analysis of process algebra models of biochemical systems

Compositionality is a key feature of process algebras which is often cited as one of their advantages as a modelling technique. It is certainly true that in biochemical systems, as in many other systems, model construction is made easier in a formalism which allows the problem to be tackled compositionally. In this paper we consider the extent to which the compositional structure which is inherent in process algebra models of biochemical systems can be exploited during model solution. In essence this means using the compositional structure to guide decomposed solution and analysis. Unfortunately the dynamic behaviour of biochemical systems exhibits strong interdependencies between the components of the model making decomposed solution a difficult task. Nevertheless we believe that if such decomposition based on process algebras could be established it would demonstrate substantial benefits for systems biology modelling. In this paper we present our preliminary investigations based on a case study of the pheromone pathway in yeast, modelling in the stochastic process algebra Bio-PEPA

Optimal design of phosphorylation-based insulation devices

We seek to minimize both the retroactivity to the output and the retroactivity to the input of a phosphorylation-based insulation device by finding an optimal substrate concentration. Characterizing and improving the performance of insulation devices brings us a step closer to their successful implementation in biological circuits, and thus to modularity. Previous works have mainly focused on attenuating retroactivity effects to the output using high substrate concentrations. This, however, worsens the retroactivity to the input, creating an error that propagates back to the output. Employing singular perturbation and contraction theory tools, this work provides a framework to determine an optimal substrate concentration to reach a tradeoff between the retroactivity to the input and the retroactivity to the output.Grant FA9550-12-1-021

Signaling architectures that transmit unidirectional information

Submitted for review.A signaling pathway transmits information from an upstream system to downstream systems, ideally unidirectionally. A key bottleneck to unidirectional transmission is retroactivity, which is the additional reaction flux that affects a system once its species interact with those of downstream systems. This raises the question of whether signaling pathways have developed specialized architectures that overcome retroactivity and transmit unidirectional signals. Here, we propose a general mathematical framework that provides an answer to this question. Using this framework, we analyze the ability of a variety of signaling architectures to transmit signals unidirectionally as key biological parameters are tuned. In particular, we find that single stage phosphorylation and phosphotransfer systems that transmit signals from a kinase show the following trade-off: either they impart a large retroactivity to their upstream system or they are significantly impacted by the retroactivity due to their downstream system. However, cascades of these architectures, which are highly represented in nature, can overcome this trade-off and thus enable unidirectional information transmission. By contrast, single and double phosphorylation cycles that transmit signals from a substrate impart a large retroactivity to their upstream system and are also unable to attenuate retroactivity due to their downstream system. Our findings identify signaling architectures that ensure unidirectional signal transmission and minimize crosstalk among multiple targets. Our results thus establish a way to decompose a signal transduction network into architectures that transmit information unidirectionally, while also providing a library of devices that can be used in synthetic biology to facilitate modular circuit design.NSF Expedition award number 1521925, NIGMS grant P50 GMO9879

Modularity in signaling systems

Modularity is a property by which the behavior of a system does not change upon interconnection. It is crucial for understanding the behavior of a complex system from the behavior of the composing subsystems. Whether modularity holds in biology is an intriguing and largely debated question. In this paper, we discuss this question taking a control system theory view and focusing on signaling systems. In particular, we argue that, despite signaling systems being constituted of structural modules, such as covalent modification cycles, modularity does not hold in general. As in any engineering system, impedance-like effects, called retroactivity, appear at interconnections and alter the behavior of connected modules. We further argue that while signaling systems have evolved sophisticated ways to counter-act retroactivity and enforce modularity, retroactivity may also be exploited to finely control the information processing of signaling pathways. Testable predictions and experimental evidence are discussed with their implications

Retroactivity attenuation in signaling cascades

It has been shown in an earlier work that impedance-like effects, called retroactivity, are found at the interconnection of biomolecular systems just as they occur in several engineering systems. These effects are particularly relevant in signaling cascades that have several downstream targets. These cascades have been extensively studied to determine how a stimulus at the top of the cascade is transmitted and amplified as it propagates toward the bottom of the cascade. In principle, because of retroactivity, a perturbation at the bottom of the cascade can propagate upstream. In this paper, we study the extent to which this propagation occurs by analytically finding retroactivity gains at each stage of the cascade. These gains determine whether a perturbation at the bottom of the cascade is amplified or attenuated as it propagates upstream.United States. Air Force Office of Scientific Research (Grant FA9550-09-1-0211

Modular Composition of Gene Transcription Networks

Predicting the dynamic behavior of a large network from that of the composing modules is a central problem in systems and synthetic biology. Yet, this predictive ability is still largely missing because modules display context-dependent behavior. One cause of context-dependence is retroactivity, a phenomenon similar to loading that influences in non-trivial ways the dynamic performance of a module upon connection to other modules. Here, we establish an analysis framework for gene transcription networks that explicitly accounts for retroactivity. Specifically, a module's key properties are encoded by three retroactivity matrices: internal, scaling, and mixing retroactivity. All of them have a physical interpretation and can be computed from macroscopic parameters (dissociation constants and promoter concentrations) and from the modules' topology. The internal retroactivity quantifies the effect of intramodular connections on an isolated module's dynamics. The scaling and mixing retroactivity establish how intermodular connections change the dynamics of connected modules. Based on these matrices and on the dynamics of modules in isolation, we can accurately predict how loading will affect the behavior of an arbitrary interconnection of modules. We illustrate implications of internal, scaling, and mixing retroactivity on the performance of recurrent network motifs, including negative autoregulation, combinatorial regulation, two-gene clocks, the toggle switch, and the single-input motif. We further provide a quantitative metric that determines how robust the dynamic behavior of a module is to interconnection with other modules. This metric can be employed both to evaluate the extent of modularity of natural networks and to establish concrete design guidelines to minimize retroactivity between modules in synthetic systems.United States. Air Force Office of Scientific Research (FA9550-12-1-0129

Understanding the mechanisms of robustness in intracellular protein signalling cascades and gene expression

We seek to understand the structural as well as the mechanistic basis of robustness in intracellular protein signalling cascades and in transcriptional regulation of gene expression. For protein signalling cascades, we employ a comparison based study involving a single, a double and a cascade of two double phosphorylation-dephosphorylation (PD) cycles. Using deterministic modelling approaches based on ordinary differential equations (ODE), we observe that the cascade of two double PD cycles exhibits robust output behaviour compared to that of a single and a double PD cycle upon constant as well as time- varying input perturbations. Furthermore, a system theoretic analysis reveals that the protein phosphorylation cascades act as an efficient low-pass filter that attenuates the noise mimicked as high-frequency input signals. Afterwards, we extend the study for a stochastic environment. Simulation results based on the stochastic simulation algorithm (SSA) reveal a novel phenomenon called dynamic sequestration that plays an ambivalent role as an intrinsic noise filter. Overall, the analysis indicates that complexity can be one of the basic principles of robust biological designs such as intracellular protein signalling cascades. A major function of intracellular signalling cascades is to transmit the extracellular signal to the nucleus to initiate the process of gene expression. Gene expression is an intrinsically stochastic process that results into cell-to-cell variability in protein and messenger RNA (mRNA) levels, often termed as the expression noise. In spite of such noise, how cells achieve robustness is therefore a fundamental biological problem. We conclude the thesis by introducing a rule-based modelling approach based on the Kappa (κ) platform with the goal to understand the underlying mechanisms that ensure robust cellular functioning during gene expression. In particular, we introduce a gene expression model that keeps the process of transcription and excludes the process of translation. Therefore, we quantify the expression noise using mRNA which is the end product of transcription. Besides, the motivation behind adopting a rule-based modelling approach is that unlike the ODE-based approach, the former subsumes the combinatorial complexity arises due to various binding configurations of transcription factors (TF) for regulation of gene expression and offers a compact graphical representation of the same. Afterwards, the representation is transformed into an equivalent set of executable κ rules that are simulated using the SSA to obtain distributions of mRNA copy numbers corresponding to different regulatory mechanisms.Wir wollen sowohl die strukturellen als auch die mechanistischen Grundlagen der Robustheit in intrazellulären Proteinsignalkaskaden und in der transkriptionellen Regulation der Genexpression verstehen. Für die Untersuchung von Proteinsignalkaskaden verwenden wir eine vergleichsbasierte Studie mit einer Einzelphosphorylierung, einer Doppelphosphorylierung und einer Kaskade von zwei Doppelphosphorylierungs-Dephosphorylierungs-(PD)-Zyklen. Zur Modellierung verwenden wir deterministische Ansätze, die auf gewöhnlichen Differentialgleichungen (ODE) basieren. Im Gegensatz zu einem einzelnen und einem doppelten PD-Zyklus weist die Kaskade von zwei doppelten PD-Zyklen ein robustes Ausgabeverhalten bei konstanten sowie zeitvariablen Eingangsstörungen auf. Darüber hinaus zeigt eine systemtheoretische Analyse, dass die Proteinphosphorylierungskaskaden als effizienter Tiefpassfilter wirken, der hochfrequente Eingangssignale dämpft. Anschließend erweitern wir die Studie mit einer stochastischen Umgebung. Simulationsergebnisse, die auf dem stochastischen Simulationsalgorithmus (SSA) basieren, zeigen ein neuartiges Phänomen namens "Dynamic Sequestration", das eine ambivalente Rolle als intrinsischer Rauschfilter spielt. Insgesamt zeigt die Analyse, dass Komplexität eines der Grundprinzipien robuster biologischer Systeme wie intrazellulärer Proteinsignalkaskaden sein kann. Eine der Hauptfunktionen intrazellulärer Signalkaskaden besteht darin das extrazelluläre Signal an den Kern zu übertragen, um den Prozess der Genexpression einzuleiten. Die Genexpression ist ein intrinsisch stochastischer Prozess, der zu einer Variabilität der Protein- und Messenger-RNA (mRNA)-Menge von Zelle zu Zelle führt, die oft als Expressionsrauschen bezeichnet wird. Trotz des Rauschens ist es daher ein grundlegendes biologisches Problem, wie Zellen ihre Robustheit erreichen. Um zugrunde liegende Mechanismen zu verstehen, die eine robuste zelluläre Funktion während der Genexpression gewährleisten, schließen wir die Arbeit mit der Einüfhrung eines regelbasierten Modellierungsansatzes auf Basis der Kappa (κ)-Plattform ab. Insbesondere stellen wir ein Genexpressionsmodell vor, das den Prozess der Transkription beibehält und den Prozess der Translation ausschließt. Daher quantifizieren wir das Expressionsrauschen mit Hilfe der mRNA, die das Endprodukt der Transkription ist. Darüber hinaus ist die Motivation für die Verwendung eines regelbasierten Modellierungsansatzes, dass im Gegensatz zum ODE-basierten Ansatz die kombinatorische Komplexität durch verschiedene Bindungskonfigurationen von Transkriptionsfaktoren (TF) zur Regulierung der Genexpression abgebildet wird und eine kompakte grafische Darstellung derselben geboten wird. Anschließend wird die Darstellung in einen äquivalenten Satz von ausführbaren κ-Regeln umgewandelt, die mit Hilfe der SSA simuliert werden, um Verteilungen von mRNA-Molekülen zu erhalten, die verschiedenen Regulationsmechanismen entsprechen. Wir wollen sowohl die strukturellen als auch die mechanistischen Grundlagen der Robustheit in intrazellulären Proteinsignalkaskaden und in der transkriptionellen Regulation der Genexpression verstehen. Für die Untersuchung von Proteinsignalkaskaden verwenden wir eine vergleichsbasierte Studie mit einer Einzelphosphorylierung, einer Doppelphosphorylierung und einer Kaskade von zwei Doppelphosphorylierungs-Dephosphorylierungs-(PD)-Zyklen. Zur Modellierung verwenden wir deterministische Ansätze, die auf gewöhnlichen Differentialgleichungen (ODE) basieren. Im Gegensatz zu einem einzelnen und einem doppelten PD-Zyklus weist die Kaskade von zwei doppelten PD-Zyklen ein robustes Ausgabeverhalten bei konstanten sowie zeitvariablen Eingangsstörungen auf. Darüber hinaus zeigt eine systemtheoretische Analyse, dass die Proteinphosphorylierungskaskaden als effizienter Tiefpassfilter wirken, der hochfrequente Eingangssignale dämpft. Anschließend erweitern wir die Studie mit einer stochastischen Umgebung. Simulationsergebnisse, die auf dem stochastischen Simulationsalgorithmus (SSA) basieren, zeigen ein neuartiges Phänomen namens "Dynamic Sequestration", das eine ambivalente Rolle als intrinsischer Rauschfilter spielt. Insgesamt zeigt die Analyse, dass Komplexität eines der Grundprinzipien robuster biologischer Systeme wie intrazellulärer Proteinsignalkaskaden sein kann. Eine der Hauptfunktionen intrazellulärer Signalkaskaden besteht darin das extrazelluläre Signal an den Kern zu übertragen, um den Prozess der Genexpression einzuleiten. Die Genexpression ist ein intrinsisch stochastischer Prozess, der zu einer Variabilität der Protein- und Messenger-RNA (mRNA)-Menge von Zelle zu Zelle führt, die oft als Expressionsrauschen bezeichnet wird. Trotz des Rauschens ist es daher ein grundlegendes biologisches Problem, wie Zellen ihre Robustheit erreichen. Um zugrunde liegende Mechanismen zu verstehen, die eine robuste zelluläre Funktion während der Genexpression gewährleisten, schließen wir die Arbeit mit der Einüfhrung eines regelbasierten Modellierungsansatzes auf Basis der Kappa (κ)-Plattform ab. Insbesondere stellen wir ein Genexpressionsmodell vor, das den Prozess der Transkription beibehält und den Prozess der Translation ausschließt. Daher quantifizieren wir das Expressionsrauschen mit Hilfe der mRNA, die das Endprodukt der Transkription ist. Darüber hinaus ist die Motivation für die Verwendung eines regelbasierten Modellierungsansatzes, dass im Gegensatz zum ODE-basierten Ansatz die kombinatorische Komplexität durch verschiedene Bindungskonfigurationen von Transkriptionsfaktoren (TF) zur Regulierung der Genexpression abgebildet wird und eine kompakte grafische Darstellung derselben geboten wird. Anschließend wird die Darstellung in einen äquivalenten Satz von ausführbaren κ-Regeln umgewandelt, die mit Hilfe der SSA simuliert werden, um Verteilungen von mRNA-Molekülen zu erhalten, die verschiedenen Regulationsmechanismen entsprechen