This heading broadly covers all of my current research projects and is a collaboration with the Maharbiz and Arkin groups. We investigate the interplay between the structure of biological networks and their spatial and temporal dynamical behavior. Motivated by naturally occurring developmental processes where specific genes are activated in specific regions in the embryo, our goal is to design gene networks that have the ability to generate patterns with a robust set of parameters.
-- Master's Thesis: Exploration of Turing Phenomena in Quenched Oscillator Systems
-- Ph.D. Dissertation: Design and Engineering of Pattern Formation in Gene Expression in Escherichia coli.
Macroscopic organisms are composed of cells, usually from a common genetic parent, differentiated through environmentally sensitive genetic programs. At its most fundamental level, multicellularity arises when cells come together and find means to couple their internal states in such a way that the connections result in emergent behavior - generally with improved fitness for a set of problems - that arises from the collective of cells. Our goal is to design a system that depends on the presence of two separate populations for survival. Possible applications include the programmed death of one species in the absence of the other (i.e. bio-security) or the reduced susceptibility to invading cells or mutation.
Lateral inhibition is a mechanism where cell-to-cell signaling induces neighboring cells to compete and diverge into sharply contrasting fates, enabling developmental processes such as segmentation or boundary formation. The best-known example of lateral inhibition is the Notch pathway in Metazoans where membrane-bound Delta ligands bind to the Notch receptors on the neighboring cells. This binding releases the Notch intracellular domain in the neighbors, which then inhibits their Delta ligand production. Because of the limited range of communication of the ligands and receptors, this particular type of lateral inhibition is referred to as contact-dependent inhibition (CDI). Despite the vigorous research on elucidating natural pathways such as Notch, a synthetic lateral inhibition system for pattern formation has not been developed. We have developed a graph theoretic approach to analyzing potentially large contact networks for the existence and stability of "fine-grained" patterns. In place of an actual contact-based system, we propose a synthetic circuit we call a "compartmental lateral inhibition" system that used diffusible molecules to demonstrate these types of patterns.
A particularly well-studied mechanism for pattern formation is diffusion-driven instability, originally proposed by Alan Turing in 1952, where a homogeneous steady state is destabilized in the presence of diffusion. To date, there have been no experimental demonstrations of a robust, tunable system which can break symmetry and spontaneously generate predictable gene expression patterns (spatiotemporal inhomogeneities) as in the Turing mechanism. In the synthetic biology community, efforts to achieve spontaneous generation of spatial patterns in gene expression have been centered around networks similar to the one originally proposed by Turing: two diffusible species (usually termed an activator and an inhibitor) interact with each other via chemical reactions that produce positive and negative interactions. Our investigations have led to a new a class of networks that we call "quenched oscillator" systems. These systems consist of a primary feedback loop that serves as an oscillator, and a secondary feedback loop that quenches the oscillations and incorporates a diffusible molecule. Diffusion releases the quenching effect in higher spatial frequencies, thus generating patterns.
Research project for the class "Control and Optimization of Distributed Systems and Partial Differential Equations" in the Spring of 2007. Worked under the graduate student Edgar Lobaton to help model and simulate bacterial motion in environments with low Reynolds number. Framed as an adjoint optimization problem over the elasticities of the spring connecting the particles that made up the model of the flagellum. Continued work on this project through the Summer of 2007. Acknowledged in the resulting paper.