Retroactivity attenuation through signal transduction cascades

This paper considers the problem of attenuating retroactivity, that is, the effect of loads in biological networks and demonstrates that signal transduction cascades incorporating phosphotransfer modules have remarkable retroactivity attenuation ability. Uncovering the biological mechanisms for retroactivity attenuation is relevant in synthetic biology to enable bottom-up modular composition of complex circuits. It is also important in systems biology for deepening our current understanding of natural principles of modular organization. In this paper, we perform a combined theoretical and computational study of a cascade system comprising two phosphotransfer modules, ubiquitous in eukaryotic signal transduction, when subject to load from downstream targets. Employing singular perturbation on the finite time interval, we demonstrate that this system implements retroactivity attenuation when the input signal is sufficiently slow. Employing trajectory sensitivity analysis about nominal parameters that we have identified from in vivo data, we further demonstrate that the key parameters for retroactivity attenuation are those controlling the timescale of the system.Grant FA9550-12-1-0219National Science Foundation (U.S.). Division of Computing and Communication Foundations (1058127

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

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

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

Modular cell biology: retroactivity and insulation

Modularity plays a fundamental role in the prediction of the behavior of a system from the behavior of its components, guaranteeing that the properties of individual components do not change upon interconnection. Just as electrical, hydraulic, and other physical systems often do not display modularity, nor do many biochemical systems, and specifically, genetic networks. Here, we study the effect of interconnections on the input–output dynamic characteristics of transcriptional components, focusing on a property, which we call ‘retroactivity', that plays a role analogous to non-zero output impedance in electrical systems. In transcriptional networks, retroactivity is large when the amount of transcription factor is comparable to, or smaller than, the amount of promoter-binding sites, or when the affinity of such binding sites is high. To attenuate the effect of retroactivity, we propose a feedback mechanism inspired by the design of amplifiers in electronics. We introduce, in particular, a mechanism based on a phosphorylation–dephosphorylation cycle. This mechanism enjoys a remarkable insulation property, due to the fast timescales of the phosphorylation and dephosphorylation reactions

Fan-out in Gene Regulatory Networks

In synthetic biology, gene regulatory circuits are often constructed by combining smaller circuit components. Connections between components are achieved by transcription factors acting on promoters. If the individual components behave as true modules and certain module interface conditions are satisfied, the function of the composite circuits can in principle be predicted. In this paper, we investigate one of the interface conditions: fan-out. We quantify the fan-out, a concept widely used in electric engineering, to indicate the maximum number of the downstream inputs that an upstream output transcription factor can regulate. We show that the fan-out is closely related to retroactivity studied by Del Vecchio, et al. We propose an efficient operational method for measuring the fan-out that can be applied to various types of module interfaces. We also show that the fan-out can be enhanced by self-inhibitory regulation on the output. We discuss the potential role of the inhibitory regulations found in gene regulatory networks and protein signal pathways. The proposed estimation method for fanout not only provides an experimentally efficient way for quantifying the level of modularity in gene regulatory circuits but also helps characterize and design module interfaces, enabling the modular construction of gene circuits.Comment: 28 pages, 5 figure

A control theoretic framework for modular analysis and design of biomolecular networks

Control theory has been instrumental for the analysis and design of a number of engineering systems, including aerospace and transportation systems, robotics and intelligent machines, manufacturing chains, electrical, power, and information networks. In the past several years, the ability of de novo creating biomolecular networks and of measuring key physical quantities has come to a point in which quantitative analysis and design of biological systems is possible. While a modular approach to analyze and design complex systems has proven critical in most control theory applications, it is still subject of debate whether a modular approach is viable in biomolecular networks. In fact, biomolecular networks display context-dependent behavior, that is, the input/output dynamical properties of a module change once this is part of a network. One cause of context dependence, similar to what found in many engineering systems, is retroactivity, that is, the effect of loads applied on a module by downstream systems. In this paper, we focus on retroactivity and review techniques, based on nonlinear control and dynamical systems theory, that we have developed to quantify the extent of modularity of biomolecular systems and to establish modular analysis and design techniques

An N-stage Cascade of Phosphorylation Cycles as an Insulation Device for Synthetic Biological Circuits

Single phosphorylation cycles have been found to have insulation device abilities, that is, they attenuate the effect of retroactivity applied by downstream systems and hence facilitate modular design in synthetic biology. It was recently discovered that this retroactivity attenuation property comes at the expense of an increased retroactivity to the input of the insulation device, wherein the device slows down the signal it receives from its upstream system. In this paper, we demonstrate that insulation devices built of cascaded phosphorylation cycles can break this tradeoff allowing to attenuate the retroactivity applied by downstream systems while keeping a small retroactivity to the input. In particular, we show that there is an optimal number of cycles that maximally extends the linear operating region of the insulation device while keeping the desired retroactivity properties, when a common phosphatase is used. These findings provide optimal design strategies of insulation devices for synthetic biology applications.NIH P50 GMO98792 gran