Before revision:  We found that the signal flow of the system, defined as the activation rate of target protein, shows the following non-trivial variations against the change in the 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.
After revision:  We found that the signal flow of the system, defined as the activation rate of target protein, shows the following non-trivial variations against the change in the volume fraction of molecules on the membrane becomes so large that the excluded volume of the molecules for the reaction and diffusion dynamics cannot be negligible. We find that such excluded volume effects of the molecules induce non-trivial variations of the signal flow, defined as the activation frequency of target proteins, as follows. 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.