Question

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...

PS

related questions:

http://mathoverflow.net/questions/94907/applications-of-group-theory-to-math-biology-pharmacology

http://mathoverflow.net/questions/94840/any-applications-integrable-systems-pde-ode-q-to-math-biology-pharmakin

http://mathoverflow.net/questions/94931/graphical-models-and-gene-finding-and-diagnosis-of-diseases

http://mathoverflow.net/questions/95065/applications-of-the-knot-theory-to-biology-pharmacology

Answer 1

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/

Answer 2

Pointers to questions on mathoverflow which contain directly relevant material, or describe how algebraic geometry diffuses through the soil nourrishing scientists' thinking:

http://mathoverflow.net/questions/62866/recent-applications-of-mathematics/62876#62876

http://mathoverflow.net/questions/84003/are-there-some-original-papers-or-books-related-to-applications-of-algebraic-topo

http://mathoverflow.net/questions/29271/algebraic-geometry-used-externally-in-problems-without-obvious-algebraic-struc

http://mathoverflow.net/questions/77195/how-has-modern-algebraic-geometry-affected-other-areas-of-math

http://mathoverflow.net/questions/62677/applications-of-commutative-algebra

http://mathoverflow.net/questions/36471/facts-from-algebraic-geometry-that-are-useful-to-non-algebraic-geometers

http://mathoverflow.net/questions/2556/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.)