Hybrid Control Models and Computational Tools for Biological Regulatory Networks

With funding from NSF, CHESS Director Tomlin is leading a project focused on designing control theoretic mathematical models and associated computational tools for the systems involved in intra- and inter-cellular regulatory circuits in biological developmtent.

The majority of biological research today focuses on single point organisms or diseases. Even in the emerging field of synthetic biology, researchers concentrate on well-characterized components, which when connected in certain ways, yield point solutions. Often these solutions are extremely valuable, such as the discovery of a mechanism which controls segmentation in embryos, or the design of bacteria which cheaply manufacture useful medicines and fuels. Yet we believe that there is a strong need for general purpose models, analysis methods, and software tools to represent, computationally dissect, and understand the processes by which organisms develop. This will lead to a better understanding of genetic defects which cause disease, leading to effective personalized health care, and could help immensely in the engineering of new biological systems. A deeper understanding of the enviable robustness of biological development could also help in complex software systems design.

The focus of this project is on modeling and computation, in collaboration with several biologists. These collaborations are studying a range of developmental mechanisms, from early Drosophila development, to cell polarity determination in developing Drosophila and mice tissues, as well as in cell cultures, to the transition from low grade to high grade lymphoma in both mice and humans.

This project focuses on (i) development, analysis, control, and simulation of stochastic hybrid system models for properties needed for cell regulation; and (ii) design of efficient computational methods for large scale analysis of the corresponding biological cell networks. We use a hierarchy of interconnected models, and a set of computational algorithms, which describe the operation of cells and cell networks from a molecular level to an organismal level. Our approach combines novel new ideas from hybrid systems theory and developmental biology, as well as control theory, stochastic analysis, and numerical analysis.

The figure above shows a simulated representation of the Drosophila wing cells and associated hair growth, shown for an actual wing below (courtesy of Professor Jeffrey Axelrod, Stanford University School of Medicine). A strip of 5 cells in the center of the simulation are mutant for one of the core developmental proteins, and a disruption in polarity in the neighboring cells results. Axelrod and Tomlin are investigating cell polarity through mathematical models and computational tools.

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