Figure 1.
Reaction Scheme of the Small GTPase Cycle
The three forms of the GTPase (RD, RT, and nucleotide-free R) (middle layer) form complexes with a GEF (E) (bottom layer) and a GAP (A) (top layer). Solid arrows indicate the main reaction fluxes. All reactions except GTP hydrolyses (2 → 1, 6 → 8, 5 → 3) are reversible. Numbering of the species is consistent with the reaction rate constants listed in Table 3. Free GTP (T), GDP (D), GEF, and GAP are not shown for simplicity.
Figure 2.
GTPase Cycling in the GEF-Only System
The values of the GTPase activity (A), recovery time (B), and performance index (C) are shown as functions of the total concentrations of the GTPase (R0) and GEF (E0). The model predicts that in the physiologically relevant range of the GTPase concentrations (R0 ≤ 10 mM) all three characteristics do not depend on R0. Roman numerals on the contour plot of the performance index P denote three regions with distinct GTPase cycling regimes: (I) effectively control-free, (II) processive (P > 0.1, highlighted in light grey), and (III) futile cycling within the complex with the GEF. Numbers on the contour lines indicate the levels of P.
Figure 3.
Concentrations of GEF and GAP Define the Efficiency of the GTPase Cycling
The profiles of the GTPase activity (A), recovery time (B), and performance index (C) are plotted as contour lines. While activity remains largely a function of the GEF concentration, the recovery time is determined mostly by the GAP concentration. Performance maximum with the activity 85% and recovery time ∼3 min is attained at E0 = 0.78 mM and A0 = 0.66 μM. Further increase in the turnover rate can be achieved at the expense of activity. Numbers on the contour lines indicate the levels of the respective characteristics. Total GTPase concentration is R0 = 1 mM.
Figure 4.
The GTPase Activity and the Overall Cycling Performance Are Improved by the Introduction of a GEF-Activating GTPase Effector S
The profiles of the GTPase activity (A), recovery time (B), and performance index (C) are plotted as contour lines. Note the increase in the area of the optimal control and its shift toward lower GEF concentrations in comparison with Figure 3C.
Table 1.
Performance of the M–GEF Control Module with the Scaffold-Effector Depends on the Total GTPase Concentration
Table 2.
Model Equations
Table 3.
Reaction Rate Constants Used in the Model Simulations
Figure 5.
Simulation of the Yeast cdc42p Cycling In Vitro
(A) Kinetics of GDP dissociation from [3H]GDP-bound cdc42p after mixing with GTP. Comparison of the model simulations and experimental results [59] is shown as groups a and b for the reactions with and without GEF cdc24p, respectively. Concentrations of cdc42p, cdc24p, and GTP were 90 μM, 28 μM, and 100μM.
(B) Simulation of GAP-stimulated GTP hydrolysis by cdc42p. Experimental data are for the yeast GAP Bem3 [60]. GTP hydrolysis was essayed by measuring phosphate (Pi) release over 5 min. Initial concentration of [γ-32P]GTP-bound cdc42p was 0.1 μM. Simulation results are shown by solid lines.
Figure 6.
Comparison of the Complete and Reduced Models for the GEF–GAP Cycling Control Module
The Euclidean distance between the flux vectors of complete and reduced models was computed as described in Methods and normalized by the magnitude of the flux vector for the complete model. The profile of the normalized distance is shown by thick solid contour lines. The profile of the performance index P (same as Figure 3C) is shown by a thin line for comparison. Note that in the parameter region where the GTPase cycles with a high activity and turnover rate, the difference between the complete and reduced models is 5% or less.
Figure 7.
Flux Diagrams for the Reduced Models of GEF–GAP (A) and M–GAP (B) Modules
Activation of RD by the GEF or by the GEF-effector complex (E*) is denoted as J1. Inactivation of RT by the GAP and its spontaneous hydrolysis are represented by fluxes J2 and J3, correspondingly. Activation of RD by M is represented by J4 in (B).
Figure 8.
Comparison of the Numerically Computed and Analytically Estimated Cycling Characteristics
The activity (upper row) and the recovery time (bottom row) profiles of GTPase are plotted versus the total concentrations of GEF and GAP. Results shown in (A) and (C) were numerically simulated using the complete model, while those shown in (B) and (D) were calculated based on the analytical estimates derived from the reduced model. Note the good match between the simulated and analytically estimated results in a broad domain of parameter values.