# Is there a model for (quality of) two-component-polymerization (dependent on e.g. concentration)?

Sadly my chemistry background is only from high school (I'm a roboticist), but I try my best to explain the problem:

Situation: Lets say I have two water based solutions/suspensions. One contains cells with A-hooks and one contains proteins with B-hooks. Now i mix those two liquids and then the As will attach to the Bs. And so they will form sort of a polymer (not sure if this is the right phrase here)

Question: Now is there a model that tells me how "well" the polymerization works, dependent on the concentration of the two solutions, temperature, affinity of A to B, whatever other parameters there might be. I think a good measure for "good polymerization" would be the distribution of lengths of the chains or connectivity or some other graph metric.

The Background is the idea to build a 3D tissue printer without support structures. A and B refers to Biotin and Streptavidin

Clarifications:

• each cell will have several 100 A-hooks, the proteins can be engineered to have an arbitrary number of B-hooks (we would like to optimize that)
• to make it work we obviously need to connect each cell with as many different individual proteins as possible and vice versa.
• The Carothers equation springs to mind, but from what i read here en.wikipedia.org/wiki/Streptavidin, this here is not exactly a polymerisation. Streptavidin simply makes tetramers with biotin, which precipitate?
– Karl
Oct 3 '16 at 20:43
• @Karl Thanks a lot, this Carothers equation looks like a good part of the solution to my Problem. Concerning the tetramer/polymer issue I will clarify my question in a minute Oct 4 '16 at 17:10
• en.wikipedia.org/wiki/Flory-Stockmayer_Theory seams to be another related model, but it's still not general enough Oct 5 '16 at 15:23