Results

Interaction of GDI with GAP sustains Rho activation
A Rho GTPase switch can be regulated by three classes of regulators: GEFs, GAPs, and GDIs. In the canonical model of the Rho GTPase cycle (Figure 1A, left), GEFs promote GDP/GTP exchange, thereby activating Rho GTPases. In contrast, GAPs promote GTP hydrolysis, thereby inactivating Rho GTPases. GDIs sequester GDP-bound GTPases from GEFs and keep them inactive; however, GDIs can also sequester GTP-bound GTPases from GAPs and keep them active. In this model, the Rho GTPase cycle functions as a simple ON/OFF switch and Rho activation is transiently elevated upon stimulation (Figure 1A, right).
Figure 1  Representation of the models of Rho GTPase cycle regulation (left) and simulations of their Rho activation dynamics (right). The activation levels of GTPases were defined as the concentration of the GTP-Rho/Effector complex. A) The canonical model of the Rho GTPase cycle in which GDIs inhibit the activities of GEFs and GAPs by sequestering GTPase. B) The GDI-integrated model of the Rho GTPase cycle in which GDIs inhibit the activities of GEFs and GAPs not only by sequestering GTPase but also by interacting with GEFs and GAPs. C) GDI/GEF interaction was removed from the GDI-integrated model. D) GDI/GAP interaction was removed from the GDI-integrated model. All parameters and reactions in the models are shown in Additional file 1: Tables S1 and S2. Reaction numbers (re#) correspond to the reaction numbers in Additional file 1: Table S2.
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 GDI and Rho GTPase can simultaneously bind GEF or GAP and form a ternary complex (GEF/GDI/Rho GTPase or GAP/GDI/Rho GTPase) [25-27]. 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 physically interacting with them as well as by sequestering Rho GTPases (see Methods). We designated this model the ‘GDI-integrated model’ because the activation dynamics and ultimate output of GEFs and GAPs are integrated by GDIs to regulate Rho activity. Rho activation is sustained for a longer period of time in this model (Figure 1B, right), compared with the canonical model (Figure 1A, right).
To clarify which interaction of GDIs with GEFs or GAPs participates in this sustained Rho activation, we further modified our GDI-integrated model. When the interaction of GDIs with GEFs was removed (Figure 1C, left), similar Rho activation dynamics, with a two-fold increase in the overall level, were obtained (Figure 1C, right). In contrast, when the interaction of GDIs with GAPs was removed (Figure 1D, left), Rho activation level decreased and was not sustained (Figure 1D, right). These results therefore suggest that GDIs sustain Rho activation through interaction with GAPs.

Influence of free (non-GTPase-complexed) GDI levels on Rho activation dynamics
To confirm the contribution of GDIs in sustaining Rho activation, we simulated Rho activation dynamics in the presence of various cellular concentrations of free GDIs, i.e., GDIs not complexed with GTPases. Based on the literature [28], we calculated the concentration of free RhoGDIα to be 0.7 μM (Additional file 1: Table S1). We used a range of concentrations of free GDIs close to this value to simulate the Rho activation dynamics. The canonical model predicted that an increase in free GDIs would simply lead to an overall decrease in Rho activation (Figure 2A). However, in our GDI-integrated model, while the increase of free GDIs also led to an overall decrease in Rho activation, this did not negate the sustained Rho activation (Figure 2B). Unexpectedly, the presence of free GDIs sustained the Rho activation level beyond 1,800 min after stimulation, in contrast to the cessation observed at this time point in the absence of free GDIs (Figure 2C).
Figure 2  Free (non-GTPase-complexed) GDI concentration affects the prolongation of Rho activation in the GDI-integrated model. Rho activation dynamics were simulated at various concentration of free GDI. A) 600 min after stimulation in the canonical model. B) 600 min after stimulation in the GDI-integrated model. C) 1,800 min after stimulation in the GDI-integrated model. The activation levels of GTPases were expressed as the concentration of GTP-Rho/Effector complex.

Influence of GDI affinity for GEF and GAP and the concentration of GEF and GAP on Rho activation dynamics
Phosphorylation affects the affinity of GDIs for various Rho GTPases [29-33] and affects the function of GEFs [34,35] and GAPs [36-38]. Therefore, phosphorylation may modify the regulation of Rho signaling by GDIs, GEFs and GAPs. To examine how the affinity of GDIs for GEFs (KmGEF/GDI) and GAPs (KmGAP/GDI) affects the ability of GDIs to sustain Rho activation, we simulated the Rho activation dynamics at 0.01, 0.1, and 1.0 μM of KmGEF/GDI and KmGAP/GDI in our model. The decrease of KmGEF/GDI resulted in overall decrease of Rho activation at all the tested concentrations of KmGAP/GDI (Figure 3A). The Rho activation was markedly sustained at 0.01 and 0.1 μM of KmGAP/GDI and decreasing KmGEF/GDI did not negate the sustained Rho activation (Figure 3A). Conversely, as the KmGAP/GDI value became smaller, the Rho activation was sustained to a greater degree at all KmGEF/GDI (Figure 3B). These results indicate that the sustained Rho activation can primarily be attributed to the interaction between GAPs and GDIs, and the higher affinity of GDIs for GAPs promotes sustained Rho activation.
Figure 3  Prolongation of Rho activation in the GDI-integrated model is dependent on K mGAP/GDI and the GAP concentration. Rho activation dynamics were simulated at various K mGEF/GDI values (A), K mGAP/GDI values (B), GEF concentration (C), and GAP concentrations (D) in the GDI-integrated model. The activation levels of GTPases were expressed as the concentration of GTP-Rho/Effector complex.
It was also suggested that the local concentration of GEFs and GAPs defined the modes of Rho GTPase signaling [22]. We examined how the concentration of GEFs and GAPs affected the ability of GDIs to sustain Rho activation. We simulated the Rho activation dynamics at 0.1, 0.3, and 0.9 μM concentrations of GEFs and GAPs in our model. The decrease of GEF concentration resulted in overall decrease of Rho activation at all of the tested GAP concentrations (Figure 3C). The sustained Rho activation was apparent only at 0.1 μM of GAP and the decrease of GEF concentration did not negate this sustained Rho activation (Figure 3C). However, at all of the tested GEF concentrations, as the GAP concentrations became smaller, Rho activation was sustained to a higher degree, and increasing GAP concentration negated this sustained Rho activation (Figure 3D). These results indicate that the sustained Rho activation is dependent on the concentration of GAPs, and a lower GAP concentration sustains Rho activation. Finally, we compared the Rho activation dynamics at 0.01, 0.1, and 1.0 μM KmGAP/GDI under various concentrations of free GDI. A decrease in the KmGAP/GDI value enhanced the prolongation of Rho activation regardless of free GDI concentration (Figure 4A). Surprisingly, at 0.01 μM KmGAP/GDI, Rho activation was sustained for a significant period of time, longer than 12,000 min (8.3 days), after stimulation in the presence of free GDI (Figure 4B). However, the overall levels of Rho activation markedly decreased in association with an increase in free GDI. These results suggest that GDIs enable extremely long-term retention of the activated state of the Rho GTPases.
Figure 4  GDI enables extremely long-term retention of the activation state of Rho GTPases. Simulation of Rho activation dynamics at K mGAP/GDI = 0.01, 01, and 1.0 μM in the presence of various free GDI concentrations (0–2.4 μM) in the GDI-integrated model. A) 600 min after stimulation. B) 12,000 min after stimulation. The activation levels of GTPases were expressed as the concentration of GTP-Rho/Effector complex.