Experiments in Stochastic Self Assembly

The reaction rate equations of chemical kinetics provide a useful model for molecular self assembly, which can be exhibited as a continuous-time, continuous-space limit under the LLN (law of large numbers) scaling. The model takes the form of a set of first order, usually nonlinear ODEs describing the concentrations of the various reactants. With explicit solutions in mind, these systems have rarely been tractable; even numerical approaches have been limited within the parameter spaces of practical systems. Thus, studies of algorithmic self-assembly have turned to experimental tools based on discrete-event simulation. This paper presents such a model argued from first principles and elementary collision theory. We prove first that in the hydrodynamic limit the equations underlying the discrete model become reaction rate equations; and second, we verify by a number of experiments that the accuracy of our experimental results is strikingly good, even for systems that are very small, i.e., with a relatively small population of molecules.