Full-day CDC 2009 Pre-conference Workshop on Biomolecular Circuit Analysis and Design

Introduction

Systems and Synthetic Biology are two new interdisciplinary research areas that have received a lot of interest in the past years: the first one aims to understand how biological systems function, while the latter considers how such systems can be designed or redesigned for improved or new functionality. To that end, both areas use mathematical modelling and inevitably, tools from control engineering and dynamical systems have found direct and extensive application. At the same time, Systems and Synthetic Biology have driven the development of new control theoretical methods and tools for addressing the complexity and nonlinearity of the models that these disciplines employ. This workshop has three main aims:

to present the modelling tools that can be used to describe how biological systems behave at different organizational scales;
to review how traditional and new tools which are rooted in systems theory can be used for the analysis of these system descriptions; and
to show how such biological networks can be designed and/or redesigned for improved or new functionality both from a theoretical viewpoint and also from a practical one, putting emphasis on the technologies that facilitate this.

Workshop Goal/Central Theme

The goal of the workshop is provide the participants with a comprehensive review of the various modelling frameworks used in Systems and Synthetic Biology and then present various approaches, rooted in dynamical systems and control theory, for understanding how these systems operate and how they can be designed/redesigned for improved functionality, which is now enabled by technological advances.

The emphasis will be on how tools from dynamical systems and control theory can help answer questions posed by Systems and Synthetic Biology research, but also, how Systems and Synthetic Biology research has driven the development of new theoretical frameworks and tools in dynamical systems and control.

Workshop Content

The following topics will be covered in the workshop:

Modeling Tools at different organizational scales:
- Stochastic models: Chemical Master Equation, Chemical Langevin Equation.
- Deterministic models: Reaction Rate Equations, Michealis-Menten/Hill function dynamics, Chemical Reaction Networks.
Analysis Tools (Systems Biology):
- Analysis of stochastic differential equation models.
- Robust stability of Biological Networks – traditional and new tools. Limit cycles and singular perturbations.
- Bifurcation Analysis of Biological networks.
- Passivity methods for biochemical network analysis.
Design Tools (Synthetic Biology):
- Enabling technologies, design/fabrication examples.
- Design problems, design and redesign tools/approaches.

Potential Audience

Researchers at different levels interested to engage in systems and synthetic biology research, but also industrial participants who are interested in the potential benefits of systems and synthetic biology research in their field.

Prerequisite

Basic Dynamical Systems and Control Theory – the biological modelling tools will be presented in detail and no background knowledge is required.

Organizers and Speakers

Dr Antonis Papachristodoulou, Department of Engineering Science, University of Oxford.
Professor Domitilla Del Vecchio, Department of Electrical Engineering and Computer Science, University of Michigan at Ann Arbor.
Professor Mustafa Khammash, Department of Mechanical Engineering, University of California at Santa Barbara.
Professor Richard Murray, Control and Dynamical Systems, California Institute of Technology.
Professor Frank Allgöwer, Institute for Systems Theory and Automatic Control, University of Stuttgart.
Professor Murat Arcak, Electrical Engineering and Computer Science, University of California at Berkeley.

Workshop Schedule

Time	Presenter	Topic
8:30-8:45	Professor Domitilla Del Vecchio	Overview of workshop aims and objectives
8:45-9:45	Professor Mustafa Khammash	Stochastic Modelling and Analysis of Biochemical Networks
9:45-10:45	Dr Antonis Papachristodoulou	ODE Modelling and Analysis of Biochemical Networks
10:45-11:15	Coffee Break
11:15-12:15	Professor Frank Allgöwer	Robustness and Bifurcation Analysis of biochemical reaction networks
12:15-13:45	Lunch Break
13:45-14:45	Professor Murat Arcak	Passivity-based analysis of reaction networks
14:45-15:45	Professor Richard Murray	Feedback and Control in Biological Circuit Design
15:45-16:15	Coffee Break
16:15-17:15	Professor Domitilla Del Vecchio	From Retroactivity to Modularity in Bio-molecular Circuit Designs
17:15-17:30	Dr Antonis Papachristodoulou	Wrap-up

Abstracts

Professor Mustafa Khammash, "Stochastic Modelling and Analysis of Biochemical Networks"

Modeling biochemical reaction networks is key to understanding life at the most basic level. One of the challenges to the analysis and synthesis of genetic networks is that the cellular environment in which these circuits function is abuzz with noise. Cellular noise results in random fluctuations (over time) within individual cells and is a potential source of phenotypic variability among clonal cellular populations. The richness of stochastic phenomena in biology underscores the importance of proper modeling, and analysis of cellular noise. In this talk, we motivate the need for stochastic models and outline the key tools for the modeling and analysis of stochasticity inside living cells. We also show that noise induced ﬂuctuations carry within them valuable information about the underlying genetic network. Far from being a nuisance, the ever-present cellular noise acts as a rich source of excitation that, when processed through a biochemical network, carries its distinctive ﬁngerprint that encodes a wealth of information about that network. This establishes a potentially powerful approach for the identiﬁcation of genetic networks and offers a new window into their dynamic character.

Dr Antonis Papachristodoulou, "Modelling and Analysis of Biochemical Reaction Networks"

Mathematical modeling is a key tool in Systems Biology. Modeling and analyzing biological networks presents a number of mathematical and computational challenges, as the models that are considered are usually complicated nonlinear differential equations with several time-scales and unknown parameters. In this part of the workshop, we review various modeling techniques for biological systems at different time and space scales and then present mathematical and algorithmic tools to quantify their robustness - both the stability and performance in the presence of parametric uncertainties. These tools are rooted in robust control and dynamical systems theory, but use recent developments in the theory of positive polynomials. At the same time, they have great practical promise and relevance, which we explore through a series of biologically meaningful examples. We discuss how these models can be model-reduced or decomposed into meaningful modules ready for more detailed analysis and design.

Professor Frank Allgöwer, "Robustness and Bifurcation Analysis of biochemical reaction networks"

Unlike in the engineering disciplines or for example in physics, measured data in biology typically have rather large uncertainties associated with them. Many important quantities cannot be measured at all or can only be measured by destroying the biological entity to be investigated. Together with the fact that often the fundamental knowledge about the biological systems under investigation is also still in its early stages, this leads to significant uncertainties that have to be considered when investigating biological systems. In this part of the workshop we give an overview over some new methods to analyze both the steady state and the dynamical behavior of biochemical reaction networks under uncertainty. With a number of examples we will show that suitably developed systems theoretical methods are well suited to make an important contribution to biological research.

Professor Murat Arcak, "Passivity-based analysis of reaction networks"

This talk presents a simplifying approach to the analysis of reaction networks that breaks up the network into smaller, tractable, components that satisfy appropriate passivity properties. The main result determines stability of the network from conditions imposed on a network matrix which incorporates information about the passivity properties of the components, the interconnection structure of the network, and the signs of the feedback terms. This stability test encompasses the classical “secant criterion” for cyclic networks and extends it to general interconnection structures represented by graphs. This test also guarantees robustness of stability against diffusion in spatially distributed models, thus ruling out Turing-type diffusion-driven instabilities. The results will be illustrated on several examples from gene regulation and cell signaling.

Professor Richard Murray, "Feedback and Control in Biological Circuit Design"

Biological systems make use of feedback in an extraordinary number of ways, on scales ranging from molecules to cells to organisms to ecosystems. In this talk I will discuss the use of concepts from control and dynamical systems in the analysis and design of biological feedback circuits at the molecular level. After a brief survey of relevant concepts from synthetic biology, I will present some recent results that combine modeling, identification, design and experimental implementation of biological feedback circuits. These results include the use of intrinsic noise for system identification in transcriptional regulatory networks, development of an in vitro circuit for regulating the rates of transcription of two independent genetic sequences, and design of dynamics of for an in vivo oscillator using transcriptional delay. Using these results as examples, I will discuss some of the open problems and research challenges in the area feedback control using biological circuits.

Professor Domitilla Del Vecchio, "From Retroactivity to Modularity in Bio-molecular Circuit Designs"

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 bio-molecular systems, and specifically, genetic and signaling 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 similar to impedance in electrical circuits. In order to attenuate the effect of retroactivity, we propose to design insulation devices based on a feedback mechanism inspired by the design of amplifiers in electronics and provide a bio-molecular realization. We show that natural bio-molecular systems already employ recurrent motifs, that is, phosphorylation/dephosphorylation cycles, which can work as remarkable insulation devices.

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