University of California, Irvine
UCI - Department of Mathematics
Topic 1:
Non-receptors in Biological Pattern Formation - Frederic Wan
Project Description:
Broadly speaking, there are two basic mechanisms for the formation of biological tissue patterns: The Turing Instability type mechanism and the French Flag type mechanism. For the French Flag mechanism, a signaling protein (called morphogen or ligand) is synthesized continuously (in time) at a localized source and transported away from the source to be bound reversibly to cell membrane bound receptors downstream to form a (degradation mediated) bound morphogen gradient. Cell differentiation results from different concentration of cell-associated morphogen-receptor complexes. Experimental results have shown that the localized morphogen synthesis rate is sensitive to temperature change leading theoretically to a substantially different bound-morphgen gradient.from that before temperature perturbation. Yet biological development is remarkably robust relative to environmental perturbation. One possible reason is the presence of non-receptors that bind with (excessive) morphogens but do not contribute to the signaling morphogen gradient that differentiate cells. In the formation of the wing imaginal disc by the binding of the Dpp (decapentaplegic) morphogen with the Tkv (thickvein) signaling receptors, the presence of Dlp (dally-like) plays the role of non-receptors. The project is to 1) research existing literature on how the synthesis rate of Dlp is increased by an increase in Dpp synthesis (i.e., what is the feedback mechanism), and 2) model the finding mathematically to see if the suggested feedback mechanism in fact leads to robustness.
Topic 2:
Growth Control and Morphogenesis - John Lowengrub
Project Description:
One of the outstanding problems in developmental biology concerns how growth can be controlled to achieve tissues and organs with precise sizes, shapes and cell numbers. For example, in genetically equivalent mice, the size of the brain varies only about 5% from animal to animal. Other organs like the intestine must be highly branched, to facilitate nutrient and waste transfer, while maintaining a strict control on the number of cells. How do such organs develop? And, how can they maintain homeostasis while at the same time protecting themselves against deleterious mutations that could lead to cancer? In this project, we will address these questions using mathematical modeling and numerical simulation. We will develop mathematical models of tissue-specific lineages (e.g., stem cells, committed progenitor cells and terminally differentiated cells), together with feedback signaling among the cells and solve these equations numerically using ordinary differential equation solvers and partial differential equation solvers adapted from our research program. In particular, we will focus on the intestinal epithelium where we have experimental collaborators who will provide data, which we can use to calibrate the models and to test the model predictions. This project is joint with Prof. Arthur Lander (Developmental and Cell Biology; Director of the Center for Complex Biological Systems), Prof. Anne Calof (Anatomy and Neurobiology), and Dr. Robert Edwards (Pathology and Laboratory Medicine).
Topic 3:
Newport Bay Bivalve Population - German Encisco Ruiz
Project Description:
Estuaries are bodies of water connecting the open sea to rivers. Because they connect fresh and salt waters, the habitat conditions vary greatly within estuaries, with quite dramatic changes in factors such as salinity, pH, and temperature as one moves inwards from the sea. In addition to these spatial variations, estuarial habitat conditions vary in time due to a variety of factors, including sunlight, tidal flow, and seasonal changes in flow. These spatial and temporal variations in habitat conditions make for a very delicate ecosystem that is highly sensitive to human factors. At UCI, we are privileged to be near the Newport Bay, which, as one of the last remaining estuaries in Southern California, forms an important stopover for migratory birds. However, anecdotal evidence suggests that the population of bivalves (molluscs that form a critical component of estuarial food webs) has been declining over the last 50 years, and that this decline is likely due to human factors such as pollution, nutrient load, and dredging.
Our project consists of developing mathematical models that explain how the bivalve populations are affected by various natural and human factors, and which will hopefully make predictions as to how to restore the bivalve populations in Newport Bay. We plan to make use of data from field work activities as well as controlled laboratory experiments, the latter being conducted at the Back Bay Science Center and at UCI. The students will help develop mathematical models, implement them computationally, and compare with available data. Ideally the students will also participate in field work and laboratory experiments, hence this project will be quite suitable for students who want to do both mathematical modeling and experimentation.
