Solving buffering problems with Mathematica software.

Determining ionic concentrations in buffered solutions usually reduces to solving a set of simultaneous polynomial equations. Mathematica software offers a convenient method for doing this. Using buffering of Ca2+ by ethylene glycol bis(beta-aminoethyl ether)-N,N,N',N'-tetraacetic acid (EGTA) as an example, we provide a Mathematica script to estimate the apparent association constant. A second example shows how to calculate free ion concentrations when two ligands (Ca2+ and Mg2+) compete for one chelator (EGTA). Finally, the concentrations of all species are determined in a complex mixture containing Ca2+, EGTA, and calmodulin, a protein with four Ca(2+)-binding sites. Modifying the examples presented should allow analysis of most practical buffering problems.