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Evolution by Substitution: Amino Acid Changes Over Time BioMath Evolution By Substitution: Amino Acid Changes Over Time Student Edition Funded by the National Science Foundation, Proposal No. ESI-06-28091 This material was prepared with the support of the National Science Foundation. However, any opinions, findings, conclusions, and/or recommendations herein are those of the authors and do not necessarily reflect the views of the NSF. At the time of publishing, all included URLs were checked and active. We make every effort to make sure all links stay active, but we cannot make any guaranties that they will remain so. If you find a URL that is inactive, please inform us at [email protected]. DIMACS Published by COMAP, Inc. in conjunction with DIMACS, Rutgers University. ©2015 COMAP, Inc. Printed in the U.S.A. COMAP, Inc. 175 Middlesex Turnpike, Suite 3B Bedford, MA 01730 www.comap.com ISBN: 1 933223 75 8 Front Cover Photograph: EPA GULF BREEZE LABORATORY, PATHO-BIOLOGY LAB. LINDA SHARP ASSISTANT This work is in the public domain in the United States because it is a work prepared by an officer or employee of the United States Government as part of that person’s official duties. Evolution By Substitution: Amino Acid Changes Over Time 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. Unit Goals and Objectives Goal: Students will experience the excitement of modern biology from both the biological and mathematical point of view. Objectives: Relate DNA changes and resulting amino acid substitutions to evolution. Develop a deeper understanding of evolution through the study of amino acid substitution and matrix multiplication. Goal: Students will explore the connections between the mathematical and biological sciences. Objectives: Identify the probability for single events. Relate the use of a matrix to the probability for compound events and for events repeated over time. Demonstrate a proficiency in multiplying two matrices together and raising a square matrix to a power. Understand the relationship between powers of a matrix and future evolutionary states. Goal: Students will experience how mathematical modeling simulates theoretically behavior of a proposed system. Objectives: Identify state diagrams and their properties. Construct a state diagram to describe changes in a system. Evolution By Substitution Student 1 Lesson 1 Evolutionary Relationships Man has grouped organisms based on physical similarities for hundreds of years. Scientists have used these similarities to determine evolutionary relationships among organisms. For example, a mouse and a rat have many characteristics in common, more than a mouse shares with a chicken. Based on these observations, a mouse and a rat are more closely related to each other than they are to a chicken; therefore, they share a more recent common ancestor. Again based on similarities, a mouse is more closely related to a chicken than it is to a fish. As more and more information is gathered, a tree can be drawn to show these relationships, as shown in Figure 1.1. Figure 1.1: Portion of an evolutionary tree. The study of evolutionary relationships raises many questions. Given two organisms, what is their evolutionary relationship? What was their common ancestor like? How long ago did they diverge from this common ancestor? Biology Background In all living organisms, DNA, or deoxyribonucleic acid, carries the code for life. The code determines the proteins that an organism’s cells will make, and proteins carry out the organism’s functions. Through a series of complex processes, a segment of DNA called a gene may be read and the message in the gene may be used to build a protein from building blocks called amino acids. There are a total of twenty amino acids used to build proteins in living things (see Table 1.1). A protein is a chain of amino acids whose properties are determined by its particular amino acid sequence. In summary, it is differences in DNA that result in different amino acid sequences. Evolution By Substitution Student 2 Changing one amino acid in the sequence can result in a protein that does not function as well or may completely destroy the functioning of the protein altogether. Occasionally the change produces a protein that functions better than its predecessor and improves the fitness of the organism. In such cases, natural selection will result in improved survival rates for the organisms with this protein. Ultimately, nature will determine which proteins function best given a particular environment. Molecular biology today offers new ways to compare organisms. Proteins may be sequenced and compared giving a more detailed comparison of organisms. Today’s scientist can look for evolutionary relationships based on the sequence of amino acids in proteins rather than looking at bone structure or type of teeth. This unit uses mathematics to examine changes over time in the amino acids that make up proteins. Making the BioMath Connection There are twenty amino acids that may be coded for in DNA. Amino acids are all alike in that they have 3 common parts: an amino group (NH2), a carboxyl group (COOH), and an R group all attached to a central carbon. Figure 1.2 shows the characteristic makeup of an amino acid. Figure 1.2: Characteristics of an amino acid. The Amino Acid table on the next page shows each of the amino acids with its unique R group. R groups have different chemical properties. For example, an R group may make an amino acid polar (charged positive or negative) or nonpolar (uncharged), hydrophobic (repelled by water) or hydrophilic (attracted to water). These differences impact the overall functioning of the protein and how it will fold when made from a long string of amino acids with different properties. Some substitutions in amino acids will have greater effects than others. A change from a polar amino acid to another polar amino acid will not affect the protein as much as a change to a nonpolar amino acid. If the change is too great and the protein does not function, then nature would select against that change. One can begin to see how the probability of some selected changes may be greater than other selected changes. The table also shows the common abbreviations used for each amino acid. For example, alanine can be abbreviated ‘Ala’ or represented by the capital letter A. Arginine is Evolution By Substitution Student 3 abbreviated ‘Arg’, but is represented by the letter R since A has already been used. This use of letters is universal and recognized by scientists. Table 1.1: Amino Acids Evolution By Substitution Student 4 When two amino acid sequences are compared, it is possible to consider how recently they shared a common ancestor. Mathematically, two sequences can be aligned to determine their evolutionary relationship. Amino acids are denoted by a capital letter. The two amino acid sequences below illustrate an alignment between two growth hormone proteins. The top is the partial protein from a domesticated cat and the bottom is from a domesticated dog. MAAGPRNSVLLAFALLCLPWPQEVGTFPAMPLSSLFANAVLRAQHLHQLAADTYKEFERA MAASPRNSVLLAFALLCLPWPQEVGAFPAMPLSSLFANAVLRAQHLHQLAADTYKEFERA The alignment below is for the same partial protein from a domesticated chicken and a domesticated dog. As might be expected a dog and a cat share more common amino acids than the dog does with a chicken. If scores were being assigned to show their commonalities, then the dog and cat protein alignment would receive a higher score. MAPGSWFSPLL-IAVVTLGLPQEAAATFPAMPLSNLFANAVLRAQHLHLLAAETYKEFER MAASPRNSVLLAFALLCLPWPQEVGA-FPAMPLSSLFANAVLRAQHLHQLAADTYKEFER Differences in like (homologous) proteins are the result of mutations in the DNA of a common, but perhaps unknown, ancestor. As seen in the first alignment, the amino acid in the 4th position was replaced by another amino acid, but the substitution allowed for functionality of the protein since cats and dogs do quite fine with their growth hormones. In this mathematical model of evolution by examination of amino acids, the assumption is made that amino acids change independently of each other. One evolutionary unit (e.u.) is the average amount of time it takes for 1% of the amino acids to change. Suppose that over a period of one e.u., 3 out of every 1000 amino acids V change into amino acid R. This is denoted as a probability: P(V changes into R) = 3/1000 = .003. Generally we talk about probabilities of events so if E is the event that V changes to R then we say that P(E) = .003. Also, the chance that a certain change takes place is the probability of its occurrence, often stated as a percentage. In this case .003 becomes 0.3%. As stated earlier, substitutions of dissimilar amino acids are less
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