Here we quantitatively investigated how the cycling dynamics of a small GTPase are controlled by GEFs and GAPs. Although our model is predominantly based on the Rho family of GTPases, it is mechanism- rather than molecule-specific. Under the assumptions of our model, GTPases can freely cycle and form complexes with effectors and regulatory GEFs and GAPs while remaining anchored to the membrane. According to the existing FRAP data, this “Rho-type” mechanism is exhibited by at least some members of the Rho and Rab families, such as cdc42 [13
], Rac2 [19
], and Rab5 [18
]. Future research will undoubtedly identify more small GTPases that follow this mechanism as well as likely reveal more functional patterns of GTPase cycling, distinct from both “Arf”- and “Rho”-type mechanisms.
To elucidate the individual roles of regulatory proteins as well as their synergistic action, we compared several possible designs of the control module with progressively increasing complexity. Characterizing the stationary activity of the GTPase and its turnover rate as either high or low, one can distinguish up to four qualitatively distinct regimes of cycling. Of these we concentrated on the regime with high activity and high turnover rate since this is the only regime that is relevant for the rapid recovery of fluorescence observed in the FRAP-based studies described here. The fundamental question that we sought to address is how GTPase cycling is controlled so that high activity is achieved in parallel with a rapid turnover.
A convenient baseline for this analysis is provided by the spontaneous cycling of a GTPase in a chemostat with the intracellular concentrations of GTP and GDP. Under these control-free conditions, yeast cdc42p would cycle with the basal activity of ~0.5 and the turnover rate nearly three orders of magnitude lower than the rate observed in the emerging bud [13
]. In vivo, this slow “parasitic” cycling is thought to be prevented by GDIs that sequester the inactive form of the GTPase and block it from shedding the GDP [43
]. Several lines of evidence suggest that GDIs play an important role in the transport of GTPases between cellular compartments [35
]. However, once a GTPase molecule is localized on the membrane, its cycling is not appreciably affected by GDIs [43
], and GDI knockouts often show no changes in GTPase functions [35
]. Since transport processes are left outside the scope of the present analysis, we did not consider the influence of GDIs on GTPase cycling.
Analysis of the three plausible designs of the cycling control module represented by a single GEF, a GEF–GAP module, and its modification with a GEF-activating GTPase effector have revealed a number of common trends. We demonstrated that GEF and GAP play distinct and separable roles in cycling control. While the activity of GTPase in a stationary state is mainly defined by the activity of the GEF, the turnover rate, which is inversely proportional to the GTPase recovery time, is almost entirely a function of the free GAP concentration. Our model shows that in the absence of a GAP, GEF alone can only marginally increase the turnover rate. Combined action of GAP and GEF amplifies the turnover of the GTPase and reduces the recovery time by at least one order of magnitude. The involvement of a scaffold-effector that increases the activity of a GEF can significantly improve the GTPase cycling performance by boosting both the activity and turnover rate. This additional level of control reduces the recovery time by another order of magnitude, bringing it into the range reported in FRAP experiments.
In the field of G protein signaling it has been observed that GAPs accelerate the termination of signaling without reduction of the signal amplitude [24
]. We found that the maximization of the activity and turnover rate of a small GTPase impose conflicting requirements on the GAP concentration. While the activity is always reduced by the GAP, the turnover rate grows proportionally to the GAP concentration. Therefore, to achieve a high activity and turnover rate at once, the concentrations of GEF and GAP should be tightly controlled to remain within the optimal range. Based on the contradictory nature of the requirement for the GAP, we predict that future experiments will reveal two distinct subclasses of the GTPase-controlled systems: optimized for high turnover rate and for high activity. Cycling regimes of a small GTPase are found to be less dependent on its total concentration than the activity of G proteins on the G protein concentration [30
]. For the GEF–GAP module, our model predicts that
, the optimal total concentrations of GEF and GAP, are almost insensitive to the variation of the GTPase concentration, R0
. As R0
increases by three orders of magnitude,
modestly rises ~3.5-fold, while
remains virtually the same. On the contrary, the performance of the modified M–GAP module steadily increases with the GTPase concentration (). This difference can be potentially utilized to experimentally distinguish the two designs of the control module.
Similar to the control of G protein signaling [30
], concentrations of GAP and GEF were identified as the major factors that determine the character of the cycling regime. Our results indicate that for the GEF–GAP module to provide acceptable GTPase activity and turnover rate, the total concentration of the GEF should be on the order of 1 mM. Such high concentrations are possible only within dense protein clusters assembled on the membrane. For comparison, a compact hexagonal packaging of spherical protein complexes with diameter 10 nm would result in an effective 1.93 mM concentration of its components in a 10-nm-thick layer of the cytoplasm above the membrane surface. Reduction of this concentration requirement by an effector-scaffold, which was demonstrated here for the M–GAP module, allows for sparser clusters. It is also tempting to speculate that for certain low-abundant GEFs, the co-option of such effectors may provide a vital mechanism that enables effective control over the respective GTPases despite a low cellular copy number. These hypotheses may offer some insight into why GEF-effector complexes are increasingly found as a recurring motif of the complex-formation control modules [4
]. Thus, apart from the quantitatively characterized cases of intersectin-l and Rabaptin-5, the increase in the GEF activity has been observed in the yeast complexes Sec4p[GTPase]-exocyst[effector]-Sec2p[GEF] [45
] and Ypt7p[GTPase]-Vps/HOPS[effector]-Vps39p[GEF] [46
]. Although all GTPases in the above examples belong to either Rho or Rab families, the phenomenon of a GEF-activating GTPase effector is likely not restricted to these two families only. Thus, Sos is simultaneously an effector and a GEF for Ras GTPase [48
]. In this peculiar case, the roles of the effector and the GEF are performed by two different domains of the same protein. It is conceivable that Sos evolved as a fusion of two originally independent proteins. Regardless of the molecular implementation, the function of all GEF-activating effectors is to provide a positive feedback loop that increases the cooperativity of GTPase activation.
Our results indicate that maintaining optimal concentrations of regulatory proteins in the focus of complex formation is the key factor for achieving efficient GTPase cycling. Since these concentrations are typically several orders of magnitude higher than the respective cytoplasmic concentrations, powerful mechanisms must be in operation to recruit regulatory molecules to the membrane. Several candidate mechanisms based on protein–lipid [49
] and protein–protein interactions [51
] have been identified and require further investigation. These mechanisms often form the basis for positive and negative regulatory feedback loops [53
] and are likely to increase the cooperativity of protein complex formation. The integration of these upstream mechanisms with the GTPase control module will result in more realistic models of GTPase-controlled complex formation and bring a better understanding of a great variety of cellular processes that depend on cycling dynamics of small GTPases.