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Mathematical biology modules based on modern molecular biology and modern discrete mathematics - PubMed

Mathematical biology modules based on modern molecular biology and modern discrete mathematics

Raina Robeva et al. CBE Life Sci Educ. 2010 Fall.

Abstract

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.

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Figures

Figure 1.
Figure 1.

(A) lac repressor protein in action. The lac repressor protein binds the lac operon at the operator, preventing transcription of the lac operon mRNA. The operon is OFF. (B) Binding of allolactose to the lac repressor causes a conformational change in the repressor, preventing it from binding at the operator. Transcription of the lac operon mRNA can proceed. The operon is ON.

Figure 2.
Figure 2.

Wiring diagram (A) and the state space diagram (B) for the Boolean dynamical system in the example. Graphs produced with DVD (

http://dvd.vbi.vt.edu

).

Figure 3.
Figure 3.

Wiring diagram for the minimal model. E denotes the lacZ polypeptide, M denotes the mRNA, and L denotes internal lactose. Le and Ge denote external lactose and glucose, respectively. The square nodes in the shaded rectangle represent model variables, whereas the round notes outside represent model parameters. Directed links represent influences between the variables: a positive influence is indicated by an arrow; a negative influence is depicted by a circle.

Figure 4.
Figure 4.

State space for the Boolean model of the lac operon for all possible combinations of parameter values. When external glucose is present, the operon is OFF. When external glucose is unavailable and external lactose is present, the operon is ON. Graphs obtained using DVD (

http://dvd.vbi.vt.edu

).

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