Regression Analysis for Nucleation-Elongation Model of Supramolecular Assembly: How To Determine Nucleus Size

Nucleation-elongation is known to give satisfactory descriptions of many supramolecular polymerization systems in thermal equilibrium. Its key feature is the necessity to form a "nucleus" consisting of a certain number of monomer units before being able to grow into a longer polymer chain. The size of the nucleus has significant implications for the understanding of the supramolecular polymerization mechanism. Here we investigate how experiments can give information on the nucleus size by regression analysis of various types of measurements. The measurements of free monomer concentrations, diffusion coefficients, and calorimetric response as functions of concentration or temperature are considered. The nucleation-elongation model with a general value for the nucleus size is used to provide mathematical expressions for these experimental observables. Numerical experiments are performed where experimental errors are simulated by computer-generated random numbers, and it is investigated whether least-squares fitting analyses can give the correct values of the nucleus size in the presence of experimental errors. It is recommended that the calorimetric measurements such as differential scanning calorimetry (DSC) or isothermal titration calorimetry (ITC) be performed under various conditions to correctly determine the nucleus size experimentally.