#### Consortium for Mathematics and its Applications

Product ID: Biomath
Textbook
High School

# Evolution By Substitution : Amino Acid Changes Over Time (Student)

### Author: Published by COMAP, Inc. in conjunction with DIMACS, Rutgers University.

What is the BioMath Connection (BMC) Project?

BMC was a pioneering project linking biology and mathematics in the high schools. It provided an opportunity for high school teachers, writers, researchers, and others to get in on the ground floor of developing innovative classroom materials. The materials consist of 20 modules that can be flexibly adapted for use in a variety of courses at a variety of grade levels in both biology and mathematics. The project was run by DIMACS at Rutgers University in collaboration with the Consortium for Mathematics and its Applications (COMAP) and Colorado State University (CSU).

This unit introduces students to the Central Dogma of Biology. In short, DNA, or deoxyribonucleic acid, carries the code for life and that code directs the making of proteins that will carry out the organism's functions. Proteins are made from twenty different amino acids and the number and order of those amino acids will determine the properties and function of the protein. Any alterations in the sequence of amino acids may have an effect on the function of the protein. The protein may not function as well, may lose all function, or may possibly function better. It is also possible that the substitution may not affect the function of the protein at all. Mathematical analysis of similar proteins in different organisms based on the sequence of amino acids may give insight into their possible evolutionary history and perhaps even that of the organisms that contain those proteins. Such analysis may also lead to explanations of the mechanisms of evolution, which resulted in the natural selection of these proteins.

Topics
Biology: Changes in DNA may result in amino acid substitutions in proteins that may then be used to study evolutionary relationships.
Mathematics: Single and multi-stage probability events, disjoint and independent events, matrices, matrix multiplication, powers of matrices.

Prerequisites
Biology: The unit deals primarily with evolution as the result of amino acid changes over time. It does not assume any prior knowledge about biology.
Mathematics: Decimal multiplication and percentage calculations. Other mathematics topics in this unit are not assumed as prior knowledge, and are developed in such a way that students can learn it for the first time or refresh their prior knowledge of those topics. The materials in the unit give teachers options about how much emphasis to place on the development of the mathematical content.

Length
This unit consists of 4 lessons and a project and will take 5-7 class periods (45 minutes each) if the majority of the work is done during class. Length will vary depending on the number of additional practice and extension problems done.

BioMath Student Edition
42 pages

Various

Biology

#### Prerequisites:

Various

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