The Case for Algebraic Biology: from Research to Education
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The Case for Algebraic Biology: from Research to Education Matthew Macauley1
· Nora Youngs2
Received: 29 February 2020 / Accepted: 3 August 2020 © Society for Mathematical Biology 2020
Abstract Though it goes without saying that linear algebra is fundamental to mathematical biology, polynomial algebra is less visible. In this article, we will give a brief tour of four diverse biological problems where multivariate polynomials play a central role—a subfield that is sometimes called algebraic biology. Namely, these topics include biochemical reaction networks, Boolean models of gene regulatory networks, algebraic statistics and genomics, and place fields in neuroscience. After that, we will summarize the history of discrete and algebraic structures in mathematical biology, from their early appearances in the late 1960s to the current day. Finally, we will discuss the role of algebraic biology in the modern classroom and curriculum, including resources in the literature and relevant software. Our goal is to make this article widely accessible, reaching the mathematical biologist who knows no algebra, the algebraist who knows no biology, and especially the interested student who is curious about the synergy between these two seemingly unrelated fields. Keywords Algebraic biology · Algebraic statistics · Biochemical reaction network · Boolean model · Combinatorial neural code · Computational algebra · Finite field · Gröbner basis · Mathematics education · Polynomial algebra · Pseudomonomial · Phylogenetic model · Place field · Neural ideal Mathematics Subject Classification 92B05 · 14-01 · 13P25 · 12-08 · 97M60
Matthew Macauley is partially supported by Simons Foundation Grant #358242. Nora Youngs is supported by the Clare Boothe Luce Program.
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Matthew Macauley [email protected] Nora Youngs [email protected]
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School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC 29634, USA
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Department of Mathematics and Statistics, Colby College, Waterville, ME 04901, USA 0123456789().: V,-vol
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M. Macauley, N. Youngs
1 Introduction Nobody would dispute the fundamental role that linear algebra plays in applied fields such as mathematical biology. Systems of linear equations arise both as models of natural phenomena and as approximations of nonlinear models. As such, it is not hard to surmise that systems of nonlinear polynomials can also arise from biological problems. Despite this, it still may come as a surprise to mathematicians and biologists alike when they first hear the term “algebraic biology.” The reaction may be that of inquisitive curiosity, skepticism, or cynicism, as mathematicians have earned a reputation for occasionally making questionable abstractions and constructing frameworks that are perhaps too detached from reality to be more than just amusement. Some people who work in this field avoid the term “algebraic biology” for precisely this reason. Ironically, it actually might seem more reasonable to biologists, since most people without a degree in
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