The order of 4/3 to the concentration of A or B is very surprising yet consistent with the dimension analysis. If the reaction happens on a 2D surface, there will be an extra ½ order, and 1D with be an extra 1 order depending on the concentration. These dependencies are fully consistent with the previously proposed bimolecular fractal reaction kinetics in the literature. Equation 17 is compared with the Smoluchowski rate constant for proteins A and B with molecular weight 20 kDa and the same concentrations in Fig. . The Smoluchowski rate constant is kMS = 7.4×10 9 M -1 s -1 which is consistent with the literature values. The new rate constant kJC has a builtin concentration dependence and the values go down as the solution is more diluted explained by the cartoon in Fig. . About 2 orders of magnitude smaller value than kMS is observed at 1 µM concentration which is closer to the experimental values of protein association and makes more sense. The more diluted the solution, the further apart the molecules, the square proportional longer the time for them to meet each other instead of simply proportional, thus the smaller the rate constant. A reasonable guess of the reactive area being ~3 orders of magnitude smaller than the sum area of the two proteins already brings the values very close to the experimental values 10 4 -10 6 M -1 s -1 . A simulation shows that the reaction kinetic curves of the two models are similar with the JC model reacts slightly slower than the MS model, and the rate constant of the JC model decays over time (Fig. ). The decreasing of rate constant over the concentrations of the reactants in a relatively small range is consistent with the experimental observation of bimolecular reactions in solutions. 17 Smoluchowski rate constant has been successful to predict bimolecular reaction rate in the gas phase. When a typical concentration is at mM level in a gas reaction, JChen rate constant will be in the same order of magnitude. Table shows a comparison of the Smoluchowski and JChen rate constants for an example protein-protein reaction in aqueous solution found in the literature. Both the Smoluchowski and JChen rate constants are 2-5 orders of magnitude larger than the experimental values. The Smoluchowski rate constant can be brought to the region using rotation and orientation correction explained in the literature. The JChen rate constant can be brought to the experimental region by reducing the area A, and/or just the binding area correction factor β ~0.01, which gives ~10 Å 2 out of the ~10 3 Å 2 surface area of the protein, consistent with the area of a typical protein binding site.