The Case for Algebraic Biology: from Research to Education

Area of Science:

• Mathematical Biology
• Algebraic Biology

Background:

• Linear algebra is fundamental to mathematical biology, but polynomial algebra's role is less recognized.
• Multivariate polynomials are central to several biological problems, forming the basis of algebraic biology.

Purpose of the Study:

• To provide an overview of four diverse biological problems where multivariate polynomials are essential.
• To summarize the historical development of discrete and algebraic structures in mathematical biology.
• To discuss the current role and resources of algebraic biology in education.

Main Methods:

• Exploration of biochemical reaction networks.
• Analysis of Boolean models for gene regulatory networks.
• Application of algebraic statistics in genomics.
• Investigation of place fields in neuroscience.

Main Results:

• Demonstration of multivariate polynomials' central role in biochemical networks, gene regulation, genomics, and neuroscience.
• Historical overview tracing algebraic structures in mathematical biology from the 1960s to present.
• Discussion of educational integration, literature, and software for algebraic biology.

Conclusions:

• Algebraic biology offers a powerful framework for understanding complex biological systems.
• The field has a rich history and growing importance in modern biological research and education.
• Accessible resources and software are available to facilitate learning and application.