Homepage of Agung Julius

My research interests lie on the intersection of systems and control theory, systems biology, and computer science. Engineers and natural scientists are facing the problem of dealing with ever more complex systems. The advance of technology has spurred the emergence of more complex engineering systems. It has also made available a large quantity of experimental data that requires systems understanding of natural systems. This is particularly true in the field of molecular biology, with the availability of genome scale genetic expression profiling technology. This development poses a research challenge. The design and synthesis of complex engineering and biological systems requires rigorous analysis to ensure that they will function as intended. Analyzing complex systems require extensive computational resources, if it is possible at all. The challenge thus lies in devising correct methodologies, with which the complexity can be reduced.

The approach to biology that highlights the use of quantitative models and reasoning based on systems and control theory leads to the field of systems biology. There are many problems in systems biology that are essentially engineering problems, and require engineering mindset to solve.

Several areas that I have been working on are listed below (click to go to the subject).

• Identification of genetic regulatory networks in molecular biology

• Modeling and control of the lactose regulation system of E. coli

• Utilization of flagellated bacteria as microactuators

• Abstraction of complex hybrid systems and its applications

• Theoretical research on the interface between systems theory, computer science and systems biology

Identification of genetic regulatory networks in molecular biology

Experimental data from cellular and molecular biology suggest that entities in cellular systems influence one another and can be thought of as forming a vast and complex network. With the advent of experimental and measurement technology, obtaining a large quantity of data, such as genome scale expression profiles of microorganisms is possible. The availability of these data gives rise to new challenges in identifying the vast, complex, yet structured network that generates the data. In systems biology, this is often called reverse engineering of the network. Network structures in systems biology appear in many levels, for example, genetic regulatory network, protein-protein interaction, and metabolic networks. My research interest in this topic is in utilization of optimization techniques in identification and analysis of such networks.

Gene regulatory networks capture interactions between genes and other cell substances, resulting in various models for the fundamental biological process of transcription and translation. We have developed a novel method for identification of genetic regulatory networks based on transcription perturbation data. Genetic regulatory network identification is a very important part of systems biology and plays a key role in new drugs discovery and design. In this work, I am collaborating with Prof. Stephen Boyd from Stanford University in devising a convex optimization based method that is able to handle combinatorially hard problem of finding the sparsest network that matches the experimental data. Numerical results show that our method performs better than the ones reported in the literature (see Gardner et. al. 2003, Bansal et. al. 2007). I participated in DREAM2 Challenge, a competition for reverse engineering of genetic networks, and was invited to present a poster as one of the best performers.

References:

1. M. Bansal, V. Belcastro, A. Ambesi-Impiombato, and D. di Bernardo, How to infer gene networks from expression profiles, Molecular Systems Biology, 3 (2007).

2. T.S. Gardner, D. di Bernardo, D. Lorenz, and J.J. Collins, Inferring genetic networks and identifying compound mode of action via expression profiling, Science, 301 (2003), pp. 102 - 105.

3. A.A. Julius, M. Zavlanos, S. Boyd, and G.J. Pappas, Genetic network identification using convex programming. poster and abstract at the 8th Int. Conf. Systems Biology, also submitted for publication, 2007.

Collaborators: George Pappas, Michael Zavlanos, Stephen Boyd, John Hogenesch

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Modeling and control of lactose regulation system in E. coli

In systems biology, there are a few organisms that have been designated as model systems. Similarity in the basic principles among many organisms leads biologists to concentrate on several model systems that facilitate easy comparison and sharing of research results. The bacteria Escherichia coli are one of the model systems.

An important feature of the lactose regulation system of E. coli is that it has two phenotypical steady states, the induced and uninduced states. Multistability in biochemical networks is an important phenomenon. It is, for example, the underlying mechanism behind the lysis-lysogeny cycle of bacteriophage, and the celebrated design of genetic toggle switch.

We developed a hybrid stochastic model of the system that is based on first principles. Existing models that are derived from first principle are deterministic. The introduction of a stochastic model is necessary as deterministic models are not able to explain spontaneous transitions between the stable states. The same idea is also used by my collaborators (Harvey Rubin and Adam Halasz) to explain the emergence of persistence behavior of E. coli bacteria, which is an important topic in medicine.

To reduce the complexity when analyzing the behavior of a large number of bacteria, we formulate an abstraction that reduces the complex model to a finite state Markov chain. We show that although this abstract model is simple, it is a good approximation for the average behavior of a colony of a large number of bacteria, while retaining the spontaneous transitions feature. We subsequently use the abstract model to design feedback control strategies to influence the bacteria colony.

References:

1. A.A. Julius, A. Halasz, M.S. Sakar, V. Kumar, H. Rubin, and G. J. Pappas, Stochastic modeling and control of biological systems: the lactose regulation system of Escherichia coli. to appear in the IEEE Trans. Automatic Control and IEEE Trans. Circuits and Systems joint special issue on Systems Biology, 2008.

2. A.A. Julius, A. Halasz, V. Kumar, and G. J. Pappas, A finite model for the random behavior in the lactose regulation system of Escherichia coli. poster and abstract at the 7th Int. Conf. Systems Biology, Yokohama, Japan, 2006.
3. A.A. Julius, A. Halasz, V. Kumar, and G. J. Pappas, Finite state abstraction of a stochastic model of the lactose regulation system of Escherichia coli, in Proc. 44th IEEE Conf. Decision and Control, San Diego, USA, 2006.
4. A.A. Julius, A. Halasz, V. Kumar, and G. J. Pappas, Controlling biological systems: the lactose regulation system of Escherichia coli, in Proc. American Control Conference, New York, USA, 2007, IEEE.

5. A.A. Julius, M.S. Sakar, A. Bemporad, and G.J. Pappas, Hybrid model predictive control of induction of Escherichia coli, in the Proc. 45th IEEE Conf. Decision and Control, New Orleans, USA, 2007.

Collaborators: George Pappas, Adam Halasz, Selman Sakar, Vijay Kumar, Harvey Rubin, Alberto Bemporad

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Utilization of flagellated bacteria as microactuators

The idea of using flagellated bacteria as actuators for microscale structures is very appealing and a recent breakthrough in engineering, particularly because they are very easy and cheap to produce (see Kim 2007). The challenge in this field is to understand the colony scale motile behavior of the bacteria and the hydrodynamic properties of the whole system. While the underlying
principle behind the locomotion of flagellated bacteria has been understood by microbiologists, a quantitative description of the chemotactic and phototactic behavior of flagellated bacteria, particularly at the colony-scale is still missing.

I am collaborating with Dr. MinJun Kim from Drexel University, who has an experimental setup, in which Serratia marcescens bacteria are used to provide propulsion to microfabricated structures. My research interest is in building a mathematical model of the random behavior of the bacteria under chemotactic environment and the microstructures in a low Reynold number environment that enables understanding and control of the colony-scale behavior. So far, our model has been able to reproduce and provide a clear explanation for the puzzling experimental results, where a colony-scale synchrony seems to arise from completely random individual behavior (see references).

Visit Kim's group website for video clips of the experiments.

References:

1. M.J. Kim and K.S. Breuer, Use of bacterial carpets to enhance mixing in microfluidic systems, Journal of Fluids Engineering, 129 (2007), pp. 319 - 324.

2. M.S. Sakar, E. Steager, A.A. Julius, V. Kumar, M.J. Kim, and G.J. Pappas, Microfabricated structures powered by flagellated bacteria. poster and abstract at the 8th Int. Conf. Systems Biology,
2007.

Collaborators: George Pappas, Selman Sakar, Vijay Kumar, MinJun Kim

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Abstraction of complex hybrid systems and its applications

Hybrid systems are, simply written, systems that demonstrate both discrete and continuous aspects in its dynamics. Typical examples of hybrid systems include embedded systems, where a digital computing device (discrete) interacts with an analog device/environment (continuous). Furthermore, the
engineering and biological systems mentioned in the previous page can also be modeled in the hybrid systems framework.

As engineering systems gain more functionality and complexity, there is a need for sound discipline in their design, development and deployment. In particular, ensuring the safety and correctness of these large and complex systems is becoming increasingly hard. One way to deal with the increasing complexity is by performing consistent abstraction on the system, to get a simpler model. Consistent abstraction means that the simpler model either conserves the original system's properties of interest, or is an approximation of the original system with a quantifiable deviation.

Allowing the abstraction to be an approximation of the original system turns out to be particularly beneficial, as it allows for stronger abstraction. Using the pioneering work Girard and Pappas, I extended the results to the stochastic domain, where I consider hybrid systems with probabilistic dynamics and stochastic noise/disturbance (see references).

We also develop a novel method of approximate abstraction in verification of hybrid systems. Researchers have shown that exact abstraction problem for hybrid systems (by means of bisimulation) is largely undecidable. We provide an elegant way to circumvent this problem, by formalizing a notion of approximate abstraction.

Another application of approximate abstraction is in the robust testing of hybrid systems, where design automatic test generation for hybrid systems that can cover the system in finitely many tests, while at the same time provide a robustness guarantee on the tested property. We develop a novel method for this purpose, and one of its important features is that it is highly parallel. Along this research direction, on behalf of my postdoctoral mentor, I have written an NSF Computer Systems Research grant proposal that received funding (CSR-EHS 0720518). I am also supervising a graduate student (Akshay Rajhans) who is writing a software that implements the robust testing algorithm for hybrid systems.

Visit the STRONG toolbox page.

References:

1. A. Girard and G.J. Pappas, Approximation metrics for discrete and continuous systems, IEEE Trans. Automatic Control, 52(5):782-798, May 2007.

2. A.A. Julius, Approximate abstraction of stochastic hybrid automata, in Hybrid Systems: Computation
and Control, vol. 3927 of LNCS, Springer Verlag, 2006, pp. 318 - 332.

3. A.A. Julius and G.J. Pappas, Approximate abstraction of stochastic hybrid systems. provisionally accepted to the IEEE Trans. Automatic Control, 2007.

4. A. Girard, A.A. Julius, and G.J. Pappas, Approximate simulation relations for hybrid systems. to appear in Int. J. Discrete Event Dynamic Systems, 2008.

5. A.A. Julius, G. Fainekos, M. Anand, I. Lee, and G.J. Pappas, Robust test generation and coverage for hybrid systems, in Hybrid Systems: Computation and Control, vol. 4416 of LNCS, Springer Verlag, 2007, pp. 329 - 342.

Collaborators: George Pappas, Insup Lee, Antoine Girard, Georgios Fainekos, Alessandro d'Innocenzo, Madhukar Anand

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Theoretical research on the interface between systems theory, computer science and systems biology

Breakthroughs in science and engineering often require a significant progress in the underlying theory. As I work in the interface between systems theory, computer science and systems biology, I am also interested in theoretical research, particularly that promotes cross fertilization of ideas across the
disciplines. Here are a couple of examples. The idea of bisimulation, which is traditionally a computer science concept, is applied to more general classes of systems in systems theory (see references). Bisimulation is an important concept of system abstraction. On the other hand, the theory of stability from systems theory, is applied to the approximate equivalence of transition systems (see references).

My doctoral thesis is about behavioral systems theory, which is a general mathematical systems theory that can potentially bridge some theoretical differences between discrete, continuous and hybrid systems. Along this direction, I have worked on the solution of some LTI control problems of designing a controller that has a particular input/output structure.

References:

1. A.A. Julius, J.C. Willems, M.N. Belur, and H.L. Trentelman, The canonical controllers and regular interconnection}, Systems and Control Letters, 54 (2005), pp. 787 - 797.

2. A.A. Julius, J.W. Polderman, and A.J. van der Schaft, Parametrization of the regular equivalences of the canonical controller. to appear in the IEEE Trans. Automatic Control, 2008.

3. P. Tabuada, A. Ames, A.A. Julius, and G.J. Pappas, Approximate reduction of dynamical systems. accepted for publication in Systems and Control Letters, 2007.

4. A.A. Julius, On interconnection and equivalence of continuous and discrete systems: a behavioral perspective, PhD thesis, University of Twente, The Netherlands, February 2005.

Collaborators: Arjan van der Schaft, Jan Willems, Jan Willem Polderman, Madhu Belur, George Pappas, Paulo Tabuada, Aaron Ames

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