July 30-August 2, 2008
Society for Mathematical Biology Conference

hosted by the Centre for Mathematical Medicine, Fields Institute
held at University of Toronto, Medical Sciences Bldg


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Primary Organizer: Timothy D. Comar Associate Professor of Mathematics, Department of Mathematics, Benedictine University
Olcay Akman, Associate Professor, Department of Mathematics, Illinois State University, Normal
Mike Martin, Department of Mathematics, Johnson County Community College

Summary: New undergraduate courses and programs in mathematical biology have recently developed in response to the Bio 2010 and Math & Bio 2010 reports. It is important to ensure that students in these courses are prepared for graduate programs in mathematical and computational biology and have the opportunity to participate in research activities as undergraduates. This minisymposium presents a variety of courses, research experiences, and other pedagogical activities designed to prepare and engage undergraduate students in research in mathematical biology at wide range of institutions. Talks will discuss new course projects and undergraduate research activities including the use of Boolean networks, neural networks and genetic algorithms. The presentations address activities for a wide range of undergraduate students from students in introductory courses to advanced undergraduate students.

Purpose: This minisymposium is designed to discuss the issues of the preparation of undergraduates for biomathematical research and the implementation of undergraduate research activities at different types of institutions. As many potential future researchers in mathematical and computational biology attend teaching oriented undergraduate institutions, it is important to include perspectives from these institutions in addition to the undergraduate activities that occur at research oriented universities. The collection of talks promotes the discussion about preparation expectations among faculty at all types of institutions that educate undergraduate students and exemplifies current discussion and activity in this area. This minisymposium nicely fits into the undergraduate mathematical biology education strand for the conference. Additionally, as this conference is primarily a research conference, this minisymposium provides the opportunity for discussion between researchers and those preparing students in the undergraduate environment.

Audience: Mathematicians and biologists interested in undergraduate mathematical biology education, involving undergraduates in research, and designing courses to support current and future undergraduate student research; researchers interested in participating in the discussion about appropriate undergraduate training for future graduate students in mathematical and computational biology


1. Raina Robeva, Department of Mathematical Sciences, Sweet Briar College, with Terrell Hodge and Reinhard Laubenbacher

Top-down and bottom-up models of the lac operon network dynamics
The lac operon allows E coli bacteria to utilize extracellular lactose as a nutrient source by transporting it into the cell and metabolizing it into glucose. As the first gene network, its discovery in 1961 resulted in a Nobel Prize for F. Jacob and J. Monod in 1965. Since then, many mathematical models have been constructed for this network, which remains an object of active research. This system is particularly attractive for pedagogical purposes because the variety of different models that have been constructed cover broad areas such as systems of nonlinear differential equations, Boolean networks, and stochastic methods. While modeling with differential equations is now routinely taught in conventional courses in mathematics in mathematical biology, the Bollean networks approach has not achieved equal popularity even though the mathematical concepts it are fully accessible to undergraduates with the proper use of specialized software. The talk will focus on describing, comparing, and contrasting the Boolean networks and the differential equations models of the lac operon.

2. John R. Jungck, Department of Biology, Beloit College,

Linking A Life to Life
Reasoning about spatial, temporal, and phylogenetic patterns are crucial to many areas in biology. Recent advances in computer graphics involving computational geometry and graph theory have revolutionized our ability to visualize complex patterns in nature. How can biologists take advantage of these revolutions in helping them not only comprehend causal forces generating these patterns as well as rigorously testing hypotheses about these causal mechanisms? We have developed two such software packages: "3D FractaL Tree" and "Ka-me': Voronoi Image Analyzer" (see <http://www.bioquest.org/BQLibrary/>) that enable users to analyze two diverse sets of three-dimensional and two-dimensional natural patterns. The "3D FractaL Tree" package encourages users to take explicit measurements on actual trees such as branching angles, phyllotactic angles, relative lengths and diameters of successive branches, and the number of iterative bifurcations along a branch. Realistic three dimensional trees are generated from these measures and graph re-writing grammars (Lindenmeyer systems) that can be rotated, translated, and zoomed on a computer screen. Users can easily see the power of simple fractal generation rules in the development of complex, realistic images as well as investigate self-shading, relationships of canopy area to trunk area, and stochasticity due to environmental variation. The "Ka-me': Voronoi Image Analyzer" package enable users to test whether such diverse biological patterns as fish nests on a sandy lake bottom, canopy gaps between trees in mature rain forests, packing of coral colonies, and cell membranes of epithelial cell tessellations result from nearest neighbor, local or long-range, global interactions. A specific case of analyzing the difference between cancerous and non-cancerous tissue patterns will be presented as an example of what has been termed "cellular sociology" in order to illustrate the diagnostic power of using such mathematical abstractions in a specific biological context. General conclusions about enabling user communities to develop new languages and iconography for interpreting visual data will be shared.

3. Mike Martin, Department of Mathematics, Johnson County Community College,

Quantitative & Computational Literacy: Observations & Implementations for Mathematical Biology
A characteristic for STEM initiatives is often an integrated, interdisciplinary curriculum. This talk will feature resources and observations for models, modules, and media aimed at increasing the quantitative and computational literacy of undergraduate students early in their study of both the mathematical and the life sciences. The aim is to attract mathematically-talented students through exposure to rich learning materials and to enrich awareness for those pursuing careers in the life sciences. Topics range mathematically from college algebra through differentials equations and statistics and are scattered throughout the life sciences. In addition to existing resources, project outcomes from recent MAA-PREP biomath workshops and the CALC for BIO TRUST will be exhibited.

4. Glenn Ledder, Department of Mathematics, University of Nebraska

A Terminal Post-Calculus I Mathematics Course for Biology Students
BIO2010 lays out an ambitious mathematics agenda for future research biologists. To see most of these topics in math courses, a student would need to take three semesters of calculus and one each of probability/statistics, differential equations, and linear algebra. Omission of any one of the latter three would significantly decrease the value of the whole. However, only the most dedicated biology major can find room for six mathematics courses in the crowded biology curriculum. The problem is worse than it needs to be because of all the topics in those six courses that are not high priority for biology. At the University of Nebraska, we set out to follow calculus I with a single course that includes the most important topics in probability/statistics, differential equations, and linear algebra, each geared specifically to the needs of biologists. Students who have room for a third course can then take a more advanced mathematical biology course. The challenges have, of course, been to make a wise choice of topics and to learn how to present them at a lower pedagogical level than customary. In this talk, we will focus our attention on the list of topics in our course and the methods we use to teach these topics.

5. Timothy D. Comar, Department of Mathematics, Benedictine University

Activities Designed to Prepare Undergraduates for Research in Mathematical Biology
The second semester biocalculus course at Benedictine University serves as a hybrid between a second semester calculus course and course designed to prepare students to partake in undergraduate research activities in mathematical biology or other quantitatively oriented areas of the biological sciences. Project activities in this course are designed to integrate mathematics, biology, and the use of computational software to investigate biological models. This presentation will highlight several of the weekly computer laboratory projects and one extended project. The extended project requires students to read original literature, implement a biological mathematical model in a computational platform, prepare a written summary of the mathematics and biology surrounding the particular model, and give an oral presentation of their work. This particular project enables students delve more deeply into a particular model than they can do through a weekly assignment and also develop skills that will be useful in an interdisciplinary research environment.

6. Olcay Akman, Department of Mathematics, Illinois State University

Mathematics and Biology Student Engagement on Biomathematics Research Projects
We started implementing student research by teaming graduate and undergraduate students of biology and mathematics respectively about two years ago. The hope was that the biology graduate students get the mathematical and computing-intensive methods based research help while they gain mentoring experience. On the other hand the undergraduate mathematics students gain valuable insight on biological research problems while they get involved in active research with an almost-peer advisor. In this talk we will report the outcomes of recent research teams and offer comparison with prior research activities.

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