Construction of models
The pathway diagrams of the Rho GTPase cycle and their simulation programs were described using CellDesigner (Systems Biology Institute, Tokyo, Japan) [50], and were simulated by SOSLib in CellDesigner. All kinetic reactions in the pathway diagrams in Figure 1 were described by ordinary differential equations based on mass-action kinetics (reactions 1, 2, 3, 6, 7, and 8) or Michaelis–Menten kinetics (reactions 4 and 5) [51,52].
In the canonical model (Figure 1A), we used a typical Michaelis–Menten kinetic model to describe the promoting activities of GEFs (reaction 4 in Figure 1A and C) and GAPs (reaction 5 in Figure 1A and D) towards the Rho GTPases. GDIs inhibit the activities of GEFs and GAPs only by sequestering Rho GTPases.
The majority of Rho GTPases exist in biologically inactive cytosolic complexes with GDIs and the dissociation of GTPases from GDIs is hypothesized to be a prerequisite for activation by GEFs. However, it has been suggested that βPIX (GEF), Rac1, and RhoGDIα form a ternary complex [27] and that Bcr (GAP), Rac, and RhoGDIα also form a ternary complex [26]. Furthermore, several studies have shown that GDIs directly interact with both GEFs [25] and GAPs [26]. These observations suggest that GDIs and Rho GTPases can simultaneously bind GEFs or GAPs, and form ternary complexes. According to these observations, we constructed a model of the Rho GTPase cycle (Figure 1B, left) in which GDIs inhibit the activities of GEFs and GAPs by interacting with them as well as by sequestering Rho GTPases. We used the non-competitive inhibition model of Michaelis–Menten kinetics to describe the reactions in which GDIs inhibit the actions of GEFs (reaction 4 in Figure 1B and D) and GAPs (reaction 5 in Figure 1B and C), because in the non-competitive inhibition model the inhibitor and substrate can simultaneously bind the enzyme. The processes of GTPase cycling between membrane and cytosol are very important for understanding Rho activation dynamics. However, in the present study we focused on the interaction of GDIs and GEFs/GAPs and address how GDIs regulate GTPase activity through these interactions. Therefore, to simplify the model we did not consider the membrane localization of Rho GTPases and their regulators in our models.
Parameters and equations in the models are listed in Tables S1 and S2 (Additional file 1). The kinetic parameters and initial concentrations of molecules were determined based on previous studies [24,28,53-56] or arbitrary values. The activation levels of GTPases were defined as the concentrations of the GTP-Rho/Effector complex. Model files are provided as .xml files (Additional files 2 and 3) in the supplementary materials and can be viewed using CellDesigner [50].