Wednesday, June 22, 2011

Convex Geometry, Stoichiometry and Combinatorial Chemistry

While on Twitter, I came across this arxiv entry on approaching chemistry through linear algebra: Convex Geometry and Stoichiometry by Jer-Chin (Luke) Chuang. The abstract reads:

We demonstrate the benefits of a convex geometric perspective for questions on chemical stoichiometry. We show that the balancing of chemical equations, the use of "mixtures" to explain multiple stoichiometry, and the half-reaction for balancing redox actions all yield nice convex geometric interpretations. We also relate some natural questions on reaction mechanisms with the enumeration of lattice points in polytopes. Lastly, it is known that a given reaction mechanism imposes linear constraints on observed stoichiometries. We consider the inverse question of deducing reaction mechanism consistent with a given set of linear stoichiometric restrictions.

I see many things here that I did not appreciate before about chemistry. With the lens of compressive sensing, I see underdetermined systems, larger than rank one nullspaces ( a good thing when looking for sparsest solutions), polytopes and convex geometry. And then there is this issue of combinatorial chemistry where I  wonder aloud whether if my initial dislike of chemistry is not grounded in rules and conventions that maybe are the sparsest solution of a combinatorial problem. Maybe it's time to talk to a chemist ?