Before revision:  We found that the reaction rates of two-dimensional systems consistently exhibit a maximum at a high volume fraction of molecules , such that two molecules in the vicinity cannot easily exchange their positions .
After revision:  We found that the reaction rates of two-dimensional systems consistently exhibit a maximum at a high volume fraction of molecules or the affinity of the target protein to the membrane. For example, with an increase in the binding rate of target proteins to the membrane, the signal flow varies in the form i) monotonically increasing, ii) increasing then decreasing in a bell-shaped curve, or iii) increasing, decreasing then, increasing in an S-shaped curve .