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SPECIAL ISSUE ON SYSTEMS BIOLOGY, JANUARY 2008
Guest Editorial Special Issue on Systems Biology INTRODUCTION E, THE Guest Editors, take pleasure and pride in bringing to you this Special Issue on Systems Biology, published jointly by two widely respected IEEE Transactions—the IEEE TRANSACTIONS ON AUTOMATIC CONTROL, and the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS. The publication of a Joint Special Issue is in itself a “special” occurrence! On this occasion it is pertinent to address a few issues.
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Why is a special issue on systems biology needed now? What recent developments justify such an issue? While we engineers are justifiably proud of our contributions to computation, both in terms of hardware and software (including applications), our advances pale besides those currently happening in the world of biology. Starting in the late 1990’s, advances in experimentation have made it possible to generate “raw” biological data at an unprecedented pace, and at an affordable cost. The Genbank of DNA sequence information, and the Protein Database of protein sequence information, have both been doubling roughly every six to nine months. Compare this with the much-vaunted doubling of computer speed every eighteen months as per Moore’s law. Thus, there is a need for methods to cope with this flood of raw data into useful information which can be used to achieve a deeper understanding of the biology. It is often said that data is not information, information is not knowledge and knowledge is not wisdom. The availability of new genomic, transcriptomic, and proteomic data coupled with advances in the tools and techniques for manipulating and measuring biological variables make it possible to take a holistic approach to the understanding of biological complexity. Rather than studying parts in isolation, it is now possible to ask questions about how the interconnected parts result in the observed function and properties of the whole. This is the one of the goals of the emerging field of “systems biology.” While there are many definitions of systems biology, perhaps the one that most closely captures the nature of the contributions presented in this issue is this one: “Systems biology is the quantitative analysis of networks of dynamically interacting biological components, with the goal of reverse engineering these networks to understand how they robustly achieve biological function.” Underlying much of the complexity that characterizes biological networks is regulation. A central recurring theme in biological regulation is the notion of feedback. In fact feedback is so prevalent in biological systems that it can be found at all levels of organization, from the molecular and cellular levels,
Digital Object Identifier 10.1109/TAC.2007.913343
to the organism and ecological levels. It is impossible to overstate the importance of feedback as a strategy for the maintenance and evolution of life. Animals, for example, must strive to maintain their body fluids in a constant state (or within tight tolerances) in terms of pH levels, dissolved gas concentrations, nutrient concentrations, etc. despite being in an external environment that is very different from the desirable internal state. This feedback-mediated fundamental ability of animals to maintain a constant stable internal environment, or “homeostasis”, has made it possible for them to sustain life and to colonize new environments during their evolution. The idea of using differential equations to model biological systems is also many decades old. Indeed, one of the most widely cited models in developmental biology is the reaction-diffusion model proposed by Alan Turing in 1952. Turing developed these equations as a model for morphogenesis, and applied the model to simple one, two and three-dimensional cell networks. Other models developed over the years specify how concentrations of biochemical substances change in time, in and around cells, when influenced by the presence or absence of other molecules. Designing such models requires experimental data, and usually an initial hypothesis about how the components of the system are connected. The usefulness of the early models was restricted by the limited amount of experimental data: while these models could be used to validate the plausibility of hypotheses, they generally could not provide any information about the system’s function beyond that which the experimenters had already proposed to be true. Currently, with advances in molecular biology, genetic manipulation and the availability of complete genome sequences, new models are being developed that incorporate detailed dynamics of sets of biochemical interactions and have been successful in “bridging” the intuitive gap between a molecular level hypothesis or understanding, and its tissue level effects. Assuming that systems biology is relevant now, why are control/system theorists well-suited to studying the topic? Regulation is prevalent throughout biology, and it is through the understanding of the dynamics of the many underlying regulation mechanisms, as captured by mathematical models, that one can give complete explanations and make predictions. This is where mathematical feedback control methods can play a key role. Despite the success of these methods in engineering systems, they have seen relatively little utilization in the biological sciences. This is perhaps due to the large differences in culture, approach, and the tools used in the two fields. But as new discoveries emerge at the cellular level, and with the availability of new methods for collecting data and fast computers for the simulation and validation of models based on this data, it is reasonable to expect that ideas from control theory will lead to new understanding of the underlying biological processes.
/ © 2008 IEEE
SPECIAL ISSUE ON SYSTEMS BIOLOGY, JANUARY 2008
Research on E. coli chemotactic signal transduction, on calcium homeostasis, and on the heat shock response in E. coli, presents three recent examples of how control theory can be used as a tool for creating new insights in biological systems. Though the three applications are quite different, in each case the key to success lays in bringing to bear the simple but powerful concepts based on integral control, the Internal Model Principle, and the nature of feedback and feedforward control. By showing that integral action must be present in the regulation mechanism and setting out to explain the mechanics of its implementation, new and important understanding is gained. For instance, in the case of plasma calcium regulation the “necessity” of the internal model has led in a natural way to postulate the existence of a certain hormone endowed with certain properties. Although such a hormone has been previously discovered and its mode of action on specific organs has been known, its exact role in the context of other regulating hormones was not clearly understood. This was because its role is fundamentally tied to the dynamical behavior of the regulated system, and studies based on steady-state analysis alone cannot reveal this role. In a similar way, integral feedback control has been shown to play a fundamental role in robust perfect adaptation in E. coli chemotaxis. In the example of the heat shock response, a controls perspective was essential for elucidating the complexity of the network architecture. Analysis of the heat shock system is important not only because it captures the behavior of the system, but because it decomposes the mechanism into intuitively comprehensible parts. And if the heat shock mechanism can be described and understood in terms of engineering control principles, it will surely be informative to apply these principles to a broad array of cellular regulatory mechanisms and thereby reveal the control architecture under which they operate. What are obstacles to scientific progress in this area? Are brand new theories needed? There is one extremely important aspect of biological control systems that sets them apart from man-made engineering systems, namely: extreme variability in the parameter values of the underlying models, but very little variation in the qualitative behavior of the overall system. The internal processes that underlie biological systems display the same relative invariance to parameter variations. When we engineers design and optimize a man-made system (such as the wing shape of an airplane or the mechanism of a distillation column), we strive to replicate the optimized model as close as possible in future copies of the system. In contrast, nature appears to have evolved a methodology based on multiple feedback and regulatory loops, many of which are time-varying and adaptive in nature, to cope with the inexactitude of the replication process. Entirely new modeling methodologies are need to model and to analyze such behavior. There are of course other obstacles, but for want of space they are not mentioned. Is systems biology by nature interdisciplinary “big science” (like particle physics), or is there still room for the individual researcher plugging away on his/her own? The contrast between “big science” and “good science” is beginning to be recognized as a major issue. Particle physics
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is perhaps the ultimate example of “big science,” where it is quite common to witness papers with a hundred or more authors. While theorists in particle physics can still hope to write singly authored papers, there is no going back from the reality of “big science” for experimental particle physics. Until now, systems biology does not appear to be going the same way. The interdisciplinary nature of systems biology is a given. It is simply not possible for a team of biologists to work in isolation from another team of control theorists, with each group “throwing over the wall” its share of the work, and yet achieve something worthwhile. Close, almost daily, interactions between interdisciplinary teams are a must. Having said that, we believe there is still room for individual researchers to make meaningful contributions to the subject. THE ISSUE AT A GLANCE The special issue consists of nineteen papers in nine areas. For the convenience of the reader, the papers within each area appear together. A. Stochastic Modeling Given that many biological systems display some form of randomness, the first set of papers addresses the issue of modeling. The first two papers, by Yoon and Vaidyanathan and by Vidyasagar et al., are focused on finding hidden Markov models (HMMs) for strings over the DNA or RNA alphabet. It is important here to distinguish between models and a causative explanation. Both papers advance the hypothesis that if two strings have similar statistical properties, then they are also biologically similar. This is a far cry from stating that nature actually uses statistical models to generate DNA or RNA strings. The first paper by Yoon and Vaidyanathan introduces a new class of context-sensitive HMMs, called profile cs-HMMs, that can be used to detect similarity between strings over the RNA alphabet. As in all HMM-type of problems, the challenge is maximum likelihood decoding, that is, finding the most likely sequence of states corresponding to an observed output sequence. The major challenge here is that the well-known Viterbi algorithm cannot be directly used to find the optimal state sequence corresponding to an observed output sequence. The authors advance a variety of ways to solve this problem for profile cs-HMMs. The second paper by Vidyasagar et al. proposes a method for identifying genes in prokaryotic (lower) organisms, by modeling the coding and non-coding regions of a genome as sample paths of two multi-step Markov chains. Then an order reduction method is introduced and its impact is quantified. The next two papers in this section analyze two very specific problems in the regulation of biological systems. The first paper by Cinquemani et al. analyzes the production of subtilin, an antibiotic naturally produced by the organism Bacillus subtilis. The authors argue that the process of subtilin production is naturally modeled using a stochastic hybrid system, that is, a combination of two sets of differential equations where the switching from one model to another takes place as a result of a fictitious stochastic input. The emphasis of the paper is on identifying the parameters of the overall hybrid system on the basis of observations. The last paper in this section addresses a very well-studied problem, namely: the lactose regulation system of Escherichia
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coli. The authors develop a stochastic hybrid model that is structurally correct, based on the known biochemical processes, and then proceed to derive a controller design strategy that can be used to manipulate the large scale behavior of the system. B. Stability and Stabilization The next three papers address the issues of stability and stabilization of biological systems. As has been observed above, biological systems exhibit rather amazing stability properties in the face of extremely large parameter variations. The first paper by Mazenc et al. studies a chemostat with two species, and shows that it is possible to stabilize the periodic trajectories of the chemostat by applying linear feedback control. By using nonlinear feedback, global attractiveness to the desired trajectory is obtained. In the second paper by Jovanovic et al., a class of spatial–temporal systems exhibiting a cyclical interconnection pattern is studied, and it is shown that stability is guaranteed if a so-called “secant criterion” is satisfied. In earlier work on such systems, there was no spatial component, and the scope of study was limited to sets of ordinary differential equations. In the present paper, this approach is extended to systems described by partial differential equations. In the final paper by Chaves et al., a general formulation is proposed that permits the system under study to exhibit two or more “stable” regimes. The extra feature here is that “stability” does not necessarily to a fixed point, but rather to the forward invariance of a set under the dynamics of the system. C. Identification The next two papers study the problem of parameter identification in the context of biological systems. The first paper by Rehak et al. studies the identification problem for a model of the growth of algae under photosynthesis. It is assumed that the “forcing function” arises from a harmonic oscillator, and since the unforced system is exponentially stable, it follows that the steady state trajectory of the forced system is also periodic. This periodic steady state trajectory can be computed by determining the center manifold graph of the system, which in turn can be found by solving a first order partial differential equation. In the paper by Raffard et al., the problem of parameter identification for biological systems is approached via an adjoint formulation. This approach is numerically superior to parameter search algorithms that do not make use of the adjoint formulation. D. Modeling and Control The next two papers address issues of modeling and control in biological systems. The paper by Liu et al. studies so-called “descriptor biological complexity systems,” and establishes their passivity and optimality under suitable conditions. In spite of the adjective “descriptor” the systems are not descriptor systems, but are conventional differential equations. The paper by Krishnan and Iglesias analyzes the regulatory processes involved in the biological process of directed cell locomotion, known as chemotaxis. Attention is focused on a subprocess of chemotaxis called gradient perception. But the insights developed have broader applicability than the specific problem studied here.
SPECIAL ISSUE ON SYSTEMS BIOLOGY, JANUARY 2008
E. Piecewise-Affine Systems The next two papers study piecewise-affine (PWA) systems, which have become very popular in the modeling of biological systems. PWA systems have the very desirable property of being closed under various forms of interconnection. The paper by Azuma et al. studies PWA systems, and derives conditions under which such systems are controllable. The paper by Drulhe et al. studies the problem of identification for PWA systems, with particular emphasis on identifying the switching thresholds between various subsystems. F. Oscillations The next two papers study oscillations in biological systems. Oscillations are an essential feature of biological systems, either under external stimulus or with no input. The paper by Angeli and Sontag studies the presence of oscillations in monotone systems. The non-satisfaction of the small gain theorem is a necessary condition for the existence of oscillations. This paper provides an approach to the verification of the needed properties, and illustrates the approach via a study of circadian oscillations. Circadian clocks also make their appearance in the paper by Taylor et al., where the topic is the robustness of the circadian phase behavior. The robustness of the behavior is studied via sensitivity analysis. G. Noise Noise is an inherent part of biological systems, either as a means of exciting the system, or as an unavoidable external disturbance, or both. The two papers in this section both address the so-called chemical master equation. The paper by Lestas et al. shows how a noise filtering set up with an operator theoretic interpretation can be relevant for analyzing the intrinsic stochasticity in jump processes described by master equations. The paper by Munsky and Khammash explores the approximation of high order chemical master equations by much simpler models using finite state projection methods, and quantifies the resulting error (and ways to control this error). H. Networks The collective behavior of biological systems often manifests itself only when a system is viewed as a network consisting of an interconnection of simpler systems. The paper by Batt et al. studies gene networks when the underlying parameters are themselves uncertain, and are varying under prespecified temporal logic rules. The analysis is quite intricate and is applicable to a broad class of networks. I. HIV One of the most successful applications of a “systems” approach to disease diagnosis and treatment is in the area of HIV. The mathematical modeling of the HIV virus and its temporal evolution began in the 1990s and has advanced rapidly since. In the paper by Outtara et al., a clinical trial has been set up to show that a mathematical analysis is able to assist medical doctors to carry out an early clinical diagnosis of HIV infected patients. The identification of some of the parameters of the standard 4D model can be used to evaluate the efficacy of some standard treatment regimes.
SPECIAL ISSUE ON SYSTEMS BIOLOGY, JANUARY 2008
REVIEWERS FOR THE SPECIAL ISSUE The special issue received 55 submissions. Processing so many papers in a timely manner would have been impossible but for the timely and active cooperation of the reviewers, many of whom graciously reviewed more than one paper each. The Guest Editors take this opportunity to thank them all. Alessandro Abate Frank Allgower David Angeli Murat Arcak Shun-Ichi Azuma Gregory Batt Colin Belta Sergio Bittanti Mark Borodovsky Eric Bullinger Madalena Chaves
Jun-Ichi Imura Mahailo Jovanonic Kang Li Kenneth Loparo John Lygeros Michael Malisoff Frederic Mazenc Claude Moog Djomangan Adama Outtara Elvia Palacios George Pappas
Bo-Wei Chen Bor-Sen Chen Eugenio Cinquemani Gheorghe Craciun Bhaskar Dasgupta Francis Doyle Denis Efimov Gerardo Espinosa-Perez
Marco Punta Robin Raffard Branislav Rehak John Rice Hyungbo Shim Ambuj Singh Eduardo Sontag Rajgopal Srinivasan
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Laura Giarre Jorge Goncalves Jan Gorodkin Jean-Luc Gouze Adam Halacz Joao Hespanha Haiyan Huang Pablo Iglesias
Joerg Stelling Gianna Maria Toffolo Gonzolo Robledo Veloso Glenn Vinnicombe Eberhard Voit Liming Wang Xiaohua Xia Hao Ying
MUSTAFA KHAMMASH, Guest Editor Department of Mechanical Engineering University of California Santa Barbara, CA 93106-50 USA
[email protected] CLAIRE JENNIFER TOMLIN, Guest Editor Department of Aeronautics and Astronautics Stanford University Stanford, CA 94305-9035 USA
[email protected] M. VIDYASAGAR, Guest Editor Advanced Technology Center Tata Consultancy Services 500081 Hyderabad, India
[email protected] 
