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NCTS PDE & Analysis Seminar
15:30 - 16:30, December 21, 2017 (Thursday)
Room 440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Applications of Mathematics in Biology: Somite Formation, Cancer Immunotherapy, G Protein Signaling
Kang-Ling Liao (Tamkang University)


In this talk, I will give you three examples: somite formation in zebrafish, cancer immunotherapy, and G protein signaling in plant cells, to show you how mathematical analysis, modeling, and simulation can help solve real-word problems.
There are many interesting dynamics taking place during somite formation, such as synchronized oscillatory gene expression in the tail bud, oscillation arrest in the anterior part of embryo, and traveling waves within these two regions. For these interesting dynamics, I will show you how we used analytical methods, such as delay Hopf bifurcation theory, center manifold theory, and sequential-contracting techniques to derive conditions for synchronous oscillatory gene expression and oscillation arrest dynamics. Moreover, combining these two analytical results and numerical simulation, we provided suitable gradients of the parameter set to generate the traveling wave pattern in the middle part of embryo to generate normal somite pattern.
In cancer immunotherapy, I will show you the treatment involved blocking CD200-D200R complex on macrophages. This treatment has some controversial issues due to different kinds of macrophages. To clarify this issue, we constructed a PDE model to develop a hypothesis that the different treatment results are caused by different binding affinities of macrophages. We further used this model to provide an approach to determine whether we should use this treatment according to different types of cancers.
In the third part, I will use a basic experiment on plant cells to show you how mathematical modeling and simulation can really help design experiments. In this project, I constructed an ODE model to investigate how plant cells react and detect fluctuations in light intensity. My model predicts that there is a duration threshold of this reaction. We also performed experiments to demonstrate my model prediction. Based on our results, we proposed that this property determines when to adjust photosynthetic efficiency in an environment where light intensity changes abruptly caused by moving shadows on top of a background of light changing gradually from sun rise to sun set and fluctuating light such as that caused by fluttering leaves.


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