Algebraic systems biology
Algebraic systems biology, Fall 2024
Class essentials
Course content
- Part 0. What is algebraic biology?
- Part I. Biochemical reactions, gene
regulation, and ODE models
- Chemical
reaction networks. 17 pages. Updated Aug 18, 2024.
- Gene
regulation by operons. 15 pages. Updated Sept 5, 2024.
- Delay
differential equation models of gene regulation. 29 pages. Updated
Sept 11, 2024.
- Part II. Boolean models of molecular networks
- Basics of Boolean modeling. 17 pages. Updated
Sept 16, 2024.
- Fixed points of Boolean models. 14
pages. Updated Sept 18, 2024
- Advanced features in Boolean models. 26
pages. Updated Sept 23, 2024.
- Reduction of Boolean models. 21
pages. Updated Oct 4, 2024.
- Part III. Algebraic models and methods
- Algebraic models and finite dynamical systems. 45 pages. Updated Oct 18, 2024.
- The network inference problem. 48
pages. Updated Nov 14, 2024.
- The model space. 28 pages. Updated Oct 30, 2024.
- Part IV. Dynamics of Boolean models
- Random Boolean networks. 33 pages. Updated Nov 18, 2024.
- Biological feedback. 38 pages. Updated Dec 2, 2024.
Homework
- HW 1: pdf |
tex
Topics: Chemical reaction networks and Michaelis-Menden kinetics. Due Friday, September 6, 2024.
- HW 2: pdf |
tex
Topics: Basic Boolean modeling. Due Friday, September 20, 2024.
- HW 3: pdf |
tex
Topics: Bistability in Boolean models. Due Friday, September 27, 2024.
- HW 4: pdf |
tex
Topics: Reduction of Boolean models. Due Friday, October 11, 2024.
- HW 5: pdf |
tex
Topics: Asynchronous automata. Due Friday, October 25, 2024.
- HW 6: pdf |
tex
Topics: Stanley-Reisner theory. Due Friday, November 1, 2024.
- HW 7: pdf |
tex
Topics: Min-sets and model spaces. Due Friday, November 22, 2024.
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
- J.E. Cohen. Mathematics Is biology's next microscope, only better; biology is mathematics' next physics, only better. PloS Biol., 2(12): e439, 2004.
- M.C. Reed. Mathematical biology is good for
mathematics. Notices of the AMS, 62(10):
1172-1176, 2015. [Follow-up to his 2005 paper Why is mathematical biology so hard?]
- B. Sturmfels. Can biology lead to new theorems? Annual report of the Clay Mathematics Institute, 2005, 13-26.
- 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.
- 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.
- T. Helikar, et al. The cell collective: toward an open and collaborative approach to systems biology. BMC Systems Biology 6:1-14, 2012. Online database.
Software
- The "Cyclone" program for computing the phase space of an algebraic model: Web version | 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.
- MaBoSS: Markovian Boolean Stochastic Simulator. C++ software for simulating continuous/discrete time Markov processes on a Boolean network.
Code
- Matlab
- BoolNet
- Cyclone
- The lac
operon toy model with 5 variables, including 2 parameters,
from Chapter 1 of Robeva/Hodge (2013).
- Flawed lac operon model with 5 variables from Chapter 1 of Robeva/Hodge (2013).
- The lac operon model with 13 variables
(including 3 parameters) of Stigler/Veliz-Cuba (2011).
- The tna operon model with 10 variables
(including 3 parameters) of Deal et al (2023).
- Macaulay2