Unpacking “ESTEEM”

• Excel: ubiquitous, easy, flexible, non-intimidating

• Exploratory: apply to real-world data; extend & improve

• Experiential: students engage directly with the math

The ESTEEEM Project Homepage

• 55 modules:Broad range of topicsand data sets

• Go to Island Biogeography

http://bioquest.org/esteem

Module Main Page

• Screenshots &brief description

• Mathematical expression

• Research articles& primary data

• User manual & curriculum materials(in progress)

• DownloadableExcel sheet

Population genetics

Population growth Bioinformatics

Operon function

PhylogeneticsEpidemiology

Protein structureEnzyme kinetics

Three Boxes

Black box:Hide the model

? y = axb

Glass box:Study the model

y = axb

No box:Build the model!

How do students interact with the mathematical model underlying the biology?

Copyleft

• download• use• modify• share

Users may freely the software, w/proper attribution

More info available at Free Software Foundation website

Continuous Growth ModelsBiological Goals:

• Explore the growth of microbial populations

• Discriminate among alternate hypotheses

Quantitative Goals:

• Distinguish between absolute & relative, limited & unlimited growth

• Gain hands-on experience with selecting & fitting models

Continuous Growth Models1. Wet lab portion

• Inoculate bread

• Take digital pictures at 1-day intervals

• Calculate mold area using ImageJ (Mac) or Scion Image (PC) — or have students estimate area!

Prediction:What pattern of growth will you see?

Continuous Growth Models2. Computational portion

• Open "Continuous Growth Models" workbook

• Go to "Data" tab

• Enter observed data

• Go to "Plots—Size" tab to view three diff. models of mold population growth

Linear growth:Constant absolute growth rate (e.g., 20 mm2 / day)

Exponential growth:Constant relative growth rate (e.g., 20% / day)

Logistic growth:Relative growth rate as pop. size (e.g., 0% / day at 700 mm2)

Which model, & what parameter values, can best explain the observed data?

• Go to “Plots—Growth” tab

• These graph the same models & data as before:How do they differ from the previous graphs?

Epidemiological Model

Goal: Introduce students to the process of modeling a biological system

Hook: Predict the outbreak and course of a specific epidemic; model the efficacy of different intervention strategies

Epidemiological Model

1. Building formulas in Excel2. Setting parameters and variables3. Translating biology into math4. Implementing a mathematical model in Excel5. Visualizing & interpreting results

Five-step process:

Epidemiological Model

• Open “SIR Model”

• Simple model: 3 variables, 2 parameters

• From this information, how would you calculate the initial # Susceptible, Infected, Recovered?

• Go to View menu, choose “Formula Bar”

• In Cells B2-D2, enter formulas tocarry out those calculations

Biological Knowledge Mathematical Equations

S I R• How do individuals move from one category to another?

• Write “word equations”; for example:

The # of Susceptibles at

Time 1=

The # of Susceptibles at

Time 0±

The # of newly infected

Susceptibles? ?

• Write formulas for: # newly infected Susceptibles# newly recovered Infecteds

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Future Directions

• More thorough documentation on biology, math, Excel

• Pre-built curricular resources: “I need something NOW!”

• More modules & improvements to current ones:share resources among community of ESTEEM users