Our experimental results on single-molecule binding kinetics challenge the established theories established during the early 1900s, which have motivated our research projects. For two molecules in a dilute solution to react, they must first overcome the solvent barrier and collide with each other before any chemical reaction can occur. This process is known as diffusion, with a classic example being the Brownian motion of pollen particles on the surface of water.

As illustrated in the figure, the diffusion process differs significantly from the collision of gas molecules in a non-diluted gas reaction. In a neat gas, the time dependence of molecular collisions is linearly proportional to the separation distance because there are no molecules in between them, i.e., a direct flight; while in a dilute solution, it follows a square root dependence, i.e., traveling with many connections. The total traveling time is very different in these two cases with respect to the distances of the target and probe molecules, which are determined by their concentrations in the solution.

This difference means that the typical second-order reaction rate law, based on the concentrations of the reacting molecules, does not hold for reactions involving diffusion, which are all chemical reactions in practice. Just like most professors cannot afford a direct flight to conferences, predicting an average arriving time based on distances linearly doesn't work. Despite this, the second-order dependence is still often presented as a general rule in textbooks, suggesting that this concept may need to be revised.

https://doi.org/10.1063/5.0238119