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), 1522
DOI:10.1007/9783540734338_2

R. Laubenbacher and B. Stigler,
A computational algebra approach to the reverse engineering of gene regulatory
networks,
J. Theor. Biol. 229 (2004), 523537
DOI:10.1016/j.jtbi.2004.04.037
arXiv:qbio/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.inescid.pt/~ines/