We investigated the influences of the excluded volume of molecules on biochemical reaction processes on two-dimensional surfaces , using the model of signal-transduction processes on biomembranes. We performed simulations of the two-dimensional cell-based model, which describes the reactions and diffusion of the receptors, signaling proteins, target proteins  and crowders on the cell membrane. Here, the signaling proteins are activated by receptors  and these activated signaling proteins activate target proteins , causing that to unbind from the membrane . 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. We further demonstrated that the excluded volume of molecules influences the hierarchical molecular distributions throughout the reaction processes. In particular, when the system exhibits  large signal flow, the signaling proteins tend to surround the receptors  , and the target proteins tend to become distributed around the receptor--signaling protein clusters. This accelerates both types of reactions. To explain these phenomena, we analyzed the stochastic model of the local motions of molecules around the receptor.
We investigate the influences of the excluded volume of molecules on biochemical reaction processes on 2-dimensional surfaces using a model of signal transduction processes on biomembranes. We perform simulations of the 2-dimensional cell-based model, which describes the reactions and diffusion of the receptors, signaling proteins, target proteins , and crowders on the cell membrane. The signaling proteins are activated by receptors , and these activated signaling proteins activate target proteins that bind autonomously from the cytoplasm to the membrane, and unbind from the membrane if activated. If the target proteins bind frequently, 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 , the signal flow varies by i) monotonically increasing ; ii) increasing then decreasing in a bell-shaped curve ; or iii) increasing, decreasing , then increasing in an S-shaped curve. We further demonstrate that the excluded volume of molecules influences the hierarchical molecular distributions throughout the reaction processes. In particular, when the system exhibits a large signal flow, the signaling proteins tend to surround the receptors to form receptor-signaling protein clusters , and the target proteins tend to become distributed around such clusters. To explain these phenomena, we analyze the stochastic model of the local motions of molecules around the receptor.
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