Algebraic systems biology, Fall 2024

Class essentials

• Course syllabus
• Course flyer

Course content

• Part I. Biochemical reaction networks, gene regulation, and ODE models
  1. Biochemical reaction networks.
  2. Gene regulation by operons.
  3. Delay differential equation models.

• Part II. Boolean models of molecular networks
  1. Basic Boolean models.
  2. Boolean models of operons.
  3. Advanced features in Boolean models.
  4. Reduction of Boolean models.

  Part III. Algebraic models and methods
  1. Algebraic models and finite dynamical systems.
  2. Reverse engineering the wiring diagram.
  3. Reverse engineering the model space.

Books

• Mathematical Concepts and Methods in Modern Biology: using modern discrete models, edited by Raina Robeva and Terrell Hodge. Academic Press, 2013. Freely available with ScienceDirect subscription.
• Algebraic and Discrete Mathematical Methods for Modern Biology, edited by Raina Robeva. Academic Press, 2015. Freely available with ScienceDirect subscription.
• Algebraic and Combinatorial Computational Biology, edited by Raina Robeva and Matthew Macauley. Academic Press, 2018. Freely available with ScienceDirect, subscription.
• Probabilistic Boolean Networks: The Modeling and Control of Gene Regulatory Networks, by Ilya Shmulevich and Edward R. Dougherty. SIAM, 2010.
• Biological Feedback, by René Thomas and Thomas D'Ari. CRC Press, 1990 (updated 2006).
• Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, by David A. Cox, John Little, and Donal O'Shea. Springer, 2015 (4th edition).
• Foundations of Chemical Reaction Network Theory, by Martin Feinberg. Springer, 2019.

Papers

• M. Macauley and N. Youngs. The case for algebraic biology: from research to education. Bull. Math. Biol., 82(115), 2020.
• R. Laubenbacher and B. Sturmfels. Computer algebra in systems biology. Amer. Math. Monthly. 116(10): 882-891, 2009.
• B. Sturmfels. Can biology lead to new theorems? Annual report of the Clay Mathematics Institute, 2005, 13-26.
• M. Macauley and R. Robeva. Algebraic models, pseudomonomials, and inverse problems in algebraic biology. Lett. Biomath. 7(1):81-104, 2020.
• A. Veliz-Cuba and B. Stigler. Boolean models can explain bistability in the lac operon. J. Comput. Biol. 18(6): 783-794, 2011.
• A. Dickenstein. Biochemical reaction networks: an invitation for algebraic geometers. Mathematical Congress of the Americas. Contemp. Math. 656: 65-83, 2015.

Software

• The "Cyclone" program for computing the phase space of an algebraic model, on GitHub.
• Macaulay2: free open-source software for computational algebraic geometry and commutative algebra. Can be downloaded or run online.
• Analyze Boolean models with the BoolNet library [paper | documentation | vignette] in RStudio.
• Singular: free open-source computer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebra, algebraic geometry, and singularity theory. Can be downloaded or run online.
• Sage: free open-source mathematics software. Can be downloaded or run online.
• GINsim (Gene Interaction Network simulation), a computer tool for modeling and simulation of Boolean and logical networks.