This research project is focused on understanding the mechanisms of biological pattern formation. The formation of appropriate patterns of cells, tissues, and organs is critical for proper development in multicellular organisms. In this project, we study how cell types are patterned in the root epidermis of the plant Arabidopsis thaliana. This is a simple and useful model tissue because it consists of a single cell layer with only two cell-types that are morphologically distinct (hair cells and non-hair cells), it forms rapidly and continuously after seed germination, and the cell types arise in a predictable position-dependent pattern. To date, several genes have been identified that influence the specification and/or patterning of the root epidermal cells. Many of these genes encode transcription factors that appear to participate in a complex regulatory network, which includes positive and negative transcriptional feedback loops acting within and between adjacent cells. These findings provide a molecular genetic framework for students to become engaged in both experimental and mathematical research.

Experimental Component: Our current knowledge of this system suggests that, at its core, the epidermal cell pattern relies on transcription factors to achieve lateral inhibition and local self-enhancement of cell identities. The key transcription factors appear to be of two types: a transcriptionally active, but less-mobile type (WER and MYB23) and a transcriptionally inactive, mobile type (CPC, TRY, and ETC1). The students will help define the precise role of these and other elements of the gene regulatory network by creating mutation (knock-out) lines and overexpression lines, and they will study the effect of these perturbations on the cell patterning process. They will spend at least one semester in the lab, which will enable them to learn and use these molecular biology and genetic methods and to obtain experimental data that they can use in their modeling exercises.

Mathematical Component: The experimental findings that we have uncovered in this gene regulatory patterning process have become sufficiently complex so as to preclude intuitive understanding. As a result, we have necessarily begun developing a mathematical model to help depict these dynamic regulatory interactions and to provide predictions and hypotheses for biological testing. The students will begin with the standard kinetic type models pioneered by Hans Meinhardt and then will proceed to more involved models. The students will develop the appropriate mathematical model and will learn how to apply mathematical identifiability, selection, and sensitivity to test the modelsÕ robustness and correctness to fit the biological data. These models are expected to be more advanced than the reaction-diffusion type models with kinetic dynamics. They will be multiscale models that address the impact of each of the gene types on the cellular patterning mechanism.

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