Crossing over...Markov meets Mendel.

Chromosomal crossover is a biological mechanism to combine parental traits. It is perhaps the first mechanism ever taught in any introductory biology class. The formulation of crossover, and resulting recombination, came about 100 years after Mendel's famous experiments. To a great extent, this...

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Main Author: Saad Mneimneh
Format: Article
Language:English
Published: Public Library of Science (PLoS) 2012-01-01
Series:PLoS Computational Biology
Online Access:http://europepmc.org/articles/PMC3355070?pdf=render
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spelling doaj-cb529962fe694ec38fa137b0ea0af62a2020-11-24T23:48:47ZengPublic Library of Science (PLoS)PLoS Computational Biology1553-734X1553-73582012-01-018511210.1371/journal.pcbi.1002462Crossing over...Markov meets Mendel.Saad MneimnehChromosomal crossover is a biological mechanism to combine parental traits. It is perhaps the first mechanism ever taught in any introductory biology class. The formulation of crossover, and resulting recombination, came about 100 years after Mendel's famous experiments. To a great extent, this formulation is consistent with the basic genetic findings of Mendel. More importantly, it provides a mathematical insight for his two laws (and corrects them). From a mathematical perspective, and while it retains similarities, genetic recombination guarantees diversity so that we do not rapidly converge to the same being. It is this diversity that made the study of biology possible. In particular, the problem of genetic mapping and linkage-one of the first efforts towards a computational approach to biology-relies heavily on the mathematical foundation of crossover and recombination. Nevertheless, as students we often overlook the mathematics of these phenomena. Emphasizing the mathematical aspect of Mendel's laws through crossover and recombination will prepare the students to make an early realization that biology, in addition to being experimental, IS a computational science. This can serve as a first step towards a broader curricular transformation in teaching biological sciences. I will show that a simple and modern treatment of Mendel's laws using a Markov chain will make this step possible, and it will only require basic college-level probability and calculus. My personal teaching experience confirms that students WANT to know Markov chains because they hear about them from bioinformaticists all the time. This entire exposition is based on three homework problems that I designed for a course in computational biology. A typical reader is, therefore, an instructional staff member or a student in a computational field (e.g., computer science, mathematics, statistics, computational biology, bioinformatics). However, other students may easily follow by omitting the mathematically more elaborate parts. I kept those as separate sections in the exposition.http://europepmc.org/articles/PMC3355070?pdf=render
collection DOAJ
language English
format Article
sources DOAJ
author Saad Mneimneh
spellingShingle Saad Mneimneh
Crossing over...Markov meets Mendel.
PLoS Computational Biology
author_facet Saad Mneimneh
author_sort Saad Mneimneh
title Crossing over...Markov meets Mendel.
title_short Crossing over...Markov meets Mendel.
title_full Crossing over...Markov meets Mendel.
title_fullStr Crossing over...Markov meets Mendel.
title_full_unstemmed Crossing over...Markov meets Mendel.
title_sort crossing over...markov meets mendel.
publisher Public Library of Science (PLoS)
series PLoS Computational Biology
issn 1553-734X
1553-7358
publishDate 2012-01-01
description Chromosomal crossover is a biological mechanism to combine parental traits. It is perhaps the first mechanism ever taught in any introductory biology class. The formulation of crossover, and resulting recombination, came about 100 years after Mendel's famous experiments. To a great extent, this formulation is consistent with the basic genetic findings of Mendel. More importantly, it provides a mathematical insight for his two laws (and corrects them). From a mathematical perspective, and while it retains similarities, genetic recombination guarantees diversity so that we do not rapidly converge to the same being. It is this diversity that made the study of biology possible. In particular, the problem of genetic mapping and linkage-one of the first efforts towards a computational approach to biology-relies heavily on the mathematical foundation of crossover and recombination. Nevertheless, as students we often overlook the mathematics of these phenomena. Emphasizing the mathematical aspect of Mendel's laws through crossover and recombination will prepare the students to make an early realization that biology, in addition to being experimental, IS a computational science. This can serve as a first step towards a broader curricular transformation in teaching biological sciences. I will show that a simple and modern treatment of Mendel's laws using a Markov chain will make this step possible, and it will only require basic college-level probability and calculus. My personal teaching experience confirms that students WANT to know Markov chains because they hear about them from bioinformaticists all the time. This entire exposition is based on three homework problems that I designed for a course in computational biology. A typical reader is, therefore, an instructional staff member or a student in a computational field (e.g., computer science, mathematics, statistics, computational biology, bioinformatics). However, other students may easily follow by omitting the mathematically more elaborate parts. I kept those as separate sections in the exposition.
url http://europepmc.org/articles/PMC3355070?pdf=render
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