Model Reduction on the Wnt Pathway Leads to Biological Adaptation

Complex systems are an unavoidable problem in the field of biology. One of the ways that scientists have tried to overcome this problem is by building mathematical models—manageable representations designed to look at specific physical phenomena. The Wnt Signaling Pathway is a complex system known to regulate cell-to-cell interactions, play a crucial role in Embryonic Development, and has been implicated in the study of cancer. Typically, the Wnt signal is observed through the behavior of a protein called beta-Catenin (β-Catenin). In 2003, Lee et al. built a model of the Wnt pathway which caused β-Catenin to increase over time. However, in 2010, Jensen et al. built a different model of the Wnt pathway which caused β-Catenin to oscillate over time. This project called for model reduction on the Jensen et al. model to identify the phenomenological parameter combinations that determined features of the Wnt oscillations. The method used to reduce the model is called the Manifold Boundary Approximation Method, which is a geometric, parameter-independent method of reducing the model one parameter at a time. Reduction of the model showed that there were 5 variables and 8 parameters which drove the oscillating behavior of the system. After comparing our results to the Lee et al. reduced model of the Wnt pathway done by student Dane Bjork, a minimal model was constructed which predicted a novel class behavior of the Wnt system: biological adaptation

Patent Purchase as a Policy for Pharmaceuticals

We consider a proposal for pharmaceutical patenting policy: namely, for society to grant and purchase the patent of the first of a new class of drug, instead of purchasing the drug, and award no further patents to runner-up drugs, producing or licensing production with price set to maximise welfare subject to cover costs. It is often observed that when the first of a new class of drugs is patented, it does not necessarily halt the development of a second and a third drug of the same class. The result may be a number of rugs with similar efficacy at similar prices well above the production costs. Where this happens, society could substantially reduce the cost of duplicated R&D and the price of the drug by buying the first patent. This would benefit more patients and produce larger health gains. Under this policy social welfare is increased, the winner is fully compensated, while the runner-up firm incurs possible losses - but there are viable conditions under which firms would not lose on average. We take a drug life-cycle approach to the welfare gains of a patent purchase policy. The results are generated based upon a number of stylised facts regarding R&D in the pharmaceutical industry

Stimulating situational interest and student questioning through three types of historical introductory texts

This study investigates questions students ask related to an introductory text about a new topic in the history classroom. The effects of a narrative, problematizing, and expository introductory text on the situational interest of students and the number and type of student-generated questions, are compared. Participants are 174 students in higher secondary education (16 years old). Student-generated questions are categorized in higher -and lower-order questions, in descriptive, explanative, comparative and evaluative questions, and in emotive and non-emotive questions. The type of introductory text had a significant effect on the level of situational interest and type of questions but not on the number of generated questions. Narrative and problematizing texts provoked more situational interest and more emotive questions than the expository text. We found a significant positive correlation between prior topic knowledge, interest in History, situational interest, and number of questions