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Are there applications of algebraic geometry/commutative algebra to biology/pharmacology ?

It might be that some Groebner basis technique is used somewhere ? I know there are some applications to robotics - in solving some complicated non-linear equations, may be something similar can happen in biology...


related questions:

Applications of group theory to math. biology (pharmacology) ?

Any applications integrable systems (pde,ode, q-,...) to math. biology (pharmakinetics, pharmadynamics) ?

"Graphical models" and "gene finding and diagnosis of diseases" ?

Applications of the knot theory to biology/pharmacology ?

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Dear Alexander Chervov, I am curious: are all those questions on applications of mathematics related to recent great increases in pressure from granting institutions around the world to justify mathematical research through applications at least to other sciences, to make it more interdisciplinary (or perhaps intradisciplinary)? If so, what institutions do you have in mind in particular? Thanks. –  plm Apr 25 '12 at 7:40
Well I should have read a little more your profile, I see you are greatly concerned about the future of the ITEP. I guess your questions are directed at helping that cause. Perhaps you can explain a little more the situation, the background to your questions. –  plm Apr 25 '12 at 7:43
@plm the questions are not related to that cause. I need to make some presentation which is important for me by the end of the week, so I am asking these questions. It seems to me the questions do not contradict the policies of MO, except may be you may get bored of so many them, I am sorry about this. Any way this is the last question of that kind. –  Alexander Chervov Apr 25 '12 at 8:04
@Alexander Chervov: Thank you. I did not vote your question down if this is what made comment on getting bored. I was sincerely curious. –  plm Apr 25 '12 at 8:25
@plm Thank you for your understanding... –  Alexander Chervov Apr 25 '12 at 8:49

2 Answers 2

up vote 5 down vote accepted

1. René Thom's theory of morphogenesis involves singularities, unfoldings, perturbations of analytic/geometric structures, etc., which, in its turn, involves (or, rather, should involve, as the whole theory is rather sketchy) a good deal of commutative algebra.

2. A conference "Moduli spaces and macromolecules".

3. Some biological models involve systems of boolean equations, or sentences of propositional calculus, which could be interpreted as polynomials over GF(2), with subsequent application of Gröbner basis technique. A (more or less random) sample of possibly relevant papers (I avoid mentioning algebraic statistics which was mentioned many times elsewhere):

  • G. Boniolo, M. D'Agostino, P.P. Di Fiore, Zsyntax: A formal language for molecular biology with projected applications in text mining and biological prediction, PLoS ONE 5 (2010), N3, e9511 DOI:10.1371/journal.pone.0009511
  • A.S. Jarrah and R. Laubenbacher, Discrete models of biochemical networks: the toric variety of nested canalyzing functions, Algebraic Biology, Lect. Notes Comp. Sci. 4545 (2007), 15-22 DOI:10.1007/978-3-540-73433-8_2
  • R. Laubenbacher and B. Stigler, A computational algebra approach to the reverse engineering of gene regulatory networks, J. Theor. Biol. 229 (2004), 523-537 DOI:10.1016/j.jtbi.2004.04.037 arXiv:q-bio/0312026
  • I. Lynce and J.P. Marques Silva, Efficient haplotype inference with boolean satisfiability, AAAI'06, July 2006; SAT in Bioinformatics: making the case with haplotype inference, SAT'06, August 2006; http://sat.inesc-id.pt/~ines/
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Pointers to questions on mathoverflow which contain directly relevant material, or describe how algebraic geometry diffuses through the soil nourrishing scientists' thinking:

Recent Applications of Mathematics

Are there some original papers or books related to applications of algebraic topology and algebraic geometry in complex dynamic systems

Algebraic geometry used "externally" (in problems without obvious algebraic structure).

How has modern algebraic geometry affected other areas of math?

Applications of commutative algebra

Facts from algebraic geometry that are useful to non-algebraic geometers

Real-world applications of mathematics, by arxiv subject area?

In general studying the works of Bernd Sturmfels (and his many outstanding collaborators) will be of great interest if you are looking for applications. But much of algebraic geometry illuminates directly only other areas of mathematics, the "algebraic" structures it treats arise from layers of abstractions and are usually not visible in the real world model without some work. (For instance surfaces do not come with an algebraic structure in nature but all of them admit many, parametrized by moduli spaces, which may be useful when studying dynamics on them, and dynamics of related systems appearing in nature, c.f. here.)

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