Dynamics of Self-Assembling Systems: Analogy with Chemical Kinetics

In this article, we propose a new analyzing method for self-assembling systems. Its initial purpose was to predict the yield—the final amount of desired product—of our original self-assembling mechanical model. Moreover, the method clarifies the dynamical evolution of the system. In this method, the quantity of each intermediate product is adopted as state variables, and the dynamics that dominates the state variables is derived. The behavior of the system is reduced to a set of difference equations with a small degree of freedom. The concept is the same as in chemical kinetics or in population dynamics. However, it was never applied to self-assembling systems. The mathematical model is highly abstracted so that it is applicable to other self-assembling systems with only small modifications.