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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
Proteins. Author manuscript; available in PMC 2017 May 1.
Published in final edited form as:
Published online 2016 March 9. doi:  10.1002/prot.25018
PMCID: PMC4840055
NIHMSID: NIHMS760353

Mechanism and Rate Constants of the Cdc42 GTPase Binding with Intrinsically Disordered Effectors

Abstract

Intrinsically disordered proteins (IDPs) are often involved in signaling and regulatory functions, through binding to cellular targets. Many IDPs undergo disorder-to-order transitions upon binding. Both the binding mechanisms and the magnitudes of the binding rate constants can have functional importance. Previously we have found that the coupled binding and folding of any IDP generally follows a sequential mechanism that we term dock-and-coalesce, whereby one segment of the IDP first docks to its subsite on the target surface and the remaining segments subsequently coalesce around their respective subsites. Here we applied our TransComp method within the framework of the dock-and-coalesce mechanism to dissect the binding kinetics of two Rho-family GTPases, Cdc42 and TC10, with two intrinsically disordered effectors, WASP and Pak1. TransComp calculations identified the basic regions preceding the GTPase binding domains (GBDs) of the effectors as the docking segment. For Cdc42 binding with both WASP and Pak1, the calculated docking rate constants are close to the observed overall binding rate constants, suggesting that basic-region docking is the rate-limiting step and subsequent conformational coalescence of the GBDs on the Cdc42 surface is fast. The possibility that conformational coalescence of the WASP GBD on the TC10 surface is slow warrants further experimental investigation. The account for the differences in binding rate constants among the three GTPase-effector systems and mutational effects therein yields deep physical and mechanistic insight into the binding processes. Our approach may guide the selection of mutations that lead to redesigned binding pathways.

Keywords: intrinsically disordered proteins, coupled binding and folding, dock-and-coalesce mechanism, transient-complex theory, binding kinetics

INTRODUCTION

A significant portion of cellular proteins is now recognized as intrinsically disordered or as containing intrinsically disordered regions (IDPs/IDRs)1,2. Many IDPs/IDRs play signaling or regulatory roles, through binding with target proteins (or other domains of the IDR-containing proteins)3. Upon binding the IDPs often become ordered on the surfaces of the target proteins. The conformational ensembles of unbound IDPs47, structures of the bound IDPs814, and binding thermodynamics1517 have been intensely characterized. In comparison, the kinetics and mechanisms of the coupled folding and binding of IDPs have been less scrutinized, even though the binding pathways as well as the magnitudes of binding rate constants can be functionally important. Both experimental1824 and computational studies2532 have suggested that the structures of IDPs bound to their targets accrue sequentially on the latters’ surfaces (hence cane be termed induced fit). More specifically, we have proposed dock-and-coalesce as a common mechanism for the coupled folding and binding, whereby one segment of the IDP first docks to its subsite on the target surface and the remaining segments subsequently coalesce around their respective subsites33. A number of questions then arise. What distinguish the “docking” segment from the “coalescing” segments? What physical properties dictate the magnitudes of the rate constants of the docking and coalescing steps, and therefore their relative contributions to the overall binding rate constant? Here we use computation to address these questions for the binding of the intrinsically disordered effectors of Cdc42 to this GTPase.

Cdc42, along with Rac1, belongs to the Rho family of p21 GTPases, which regulates actin cytoskeleton organization through interacting with various effectors. In particular, upon activation by GTP-loaded Cdc42, WASP, the protein associated with the immune disorder Wiskott–Aldrich syndrome, stimulates Arp2/3-mediated nucleation of actin polymerization3440. The 502-residue WASP comprises a WASP-homology-1 domain (WH1), a basic region (BR; residues 230–237), a GTPase binding domain (GBD; residues 238–288) containing a Cdc42/Rac1 interactive binding motif (CRIB; residues 238–251), a proline-rich region, and the VCA domain (V: verprolin-homology region; C: cofilin-homology region; and A: acidic-rich region) (Fig. 1a). Unbound WASP is autoinhibited, with the VCA domain trapped through intramolecular binding with the GBD34. In Cdc42-bound WASP, the BR and GBD are engaged in intermolecular interactions10, thereby releasing the VCA domain for interacting with Arp2/3 (Fig. 1b).

Figure 1
Structure and activation of WASP. (a) Domain organization of WASP. (b) Autoinhibition of WASP and activation by Cdc42. (c) Structure of Cdc42-bound WASPfrag comprising the BR (residues 230–237; blue), the CRIB (residues 238–251; yellow), ...

The WASP fragment containing the BR and GBD (residues 230–288; hereafter WASPfrag) undergoes disorder-to-order transition upon binding Cdc42. On the Cdc42 surface, the BR and CRIB adopt extended conformations while downstream residues of the GBD form a compact subdomain comprising a β hairpin and an α-helix (Fig. 1c)10. The four basic residues in the BR (Fig. 1d) interact with acidic residues (Glu49 and Glu178) in the β2-β3 turn and α5 helix of Cdc42, respectively, while the CRIB is accommodated in the groove between α1/α5 and β2 of Cdc42. Experimental characterization of the WASPfrag-Cdc42 binding kinetics20 showed very fast association, with an association rate constant (ka) of 2.2×107 M−1s−1 (at an ionic strength of 95 mM). Mutation of the K230KK232 motif in the BR to an oppositely charged EEE motif resulted in a ~250-fold decrease in ka, while the charge reversal double mutation E49K/E178K on Cdc42 resulted in a ~35-fold decrease in ka. These data suggest that electrostatic attraction between the BR and its subsite on Cdc42 makes a strong contribution to ka. Significant salt effects also support the important role of electrostatic interactions in the fast WASPfrag-Cdc42 association. However, the ability of kinetic experiments alone to achieve further mechanistic dissection is limited.

Another Cdc42 effector involved in mediating actin cytoskeleton dynamics is Pak1, the founding member of p21-actived kinases. Like WASP, unbound Pak1 is autoinhibited, by dimerization (through residues 81–87) and interaction of the inhibitory switch domain (residues 88–136) and kinase inhibitory segment (residues 137–149) with the kinase domain (residues 249–545)41. Binding to GTP-loaded Cdc42 activates Pak1, by dissociating the dimer and freeing the kinase domain from the inhibitory switch domain and kinase inhibitory segment. The freed kinase domain then initiates a signal transduction cascade, leading to decreased depolymerization of F-actin42.

Pak1 also contains a CRIB (residues 75–88), and the shortest fragment that binds Rac1 with high affinity extends to residue 118, with a modest increase in affinity provided by the N-terminal extension to residue 7043. Thus Cdc42/Rac1 activation of Pak1 can be explained by the partial overlap of the latter’s GDB (residues 75–118) and the dimerization segment and inhibitory switch domain. On the N-terminal and C-terminal sides of the CRIB, Pak1 and WASP residues that potentially interact with Cdc42 show moderate to weak sequence identity (Fig. 1d). The N-terminal BR of Pak1 contains four basic residues along with three acidic residues, so the net charge is less positive than in the Cdc42 BR. Correspondingly, less intense interaction between the Pak1 BR and Cdc42 can be anticipated, but no experimental structural information is available for this interaction. The structure of the Pak1 GBD bound to Cdc42 has been determined44, and reveals a similar interaction pattern as the WASP GBD, with the CRIB adopting an extended conformation while downstream residues of the GBD forming a compact subdomain comprising a β hairpin and an α-helix (Fig. 1d and Supplementary Fig. S1a). The charge reversal double mutation E49K/E178K on Cdc42 resulted in a ~5-fold decrease in ka for binding a Pak1 fragment containing the BR and GBD (hereafter Pak1frag)20, consistent with a modest effect on affinity by a 5-residue extension N-terminal to the CRIB43 and supporting less intense electrostatic attraction of Cdc42 with the Pak1 BR than with the WASP BR.

The fast association between Cdc42 and WASPfrag appears to be functionally essential, as another member of the Rho family of p21 GTPases, TC10, with 66.7% sequence identity (Fig. 1e) and a nearly identical dissociation rate constant but an apparent three orders of magnitude lower association rate constant, only minimally stimulated actin polymerization20. A yeast two-hybrid assay found that TC10 did not interact with WASP, suggesting that the latter is not an endogenous effector of TC1045. The sequence alignment between Cdc42 and TC10 (Fig. 1e) shows that the two acidic Cdc42 residues, Glu49 and Glu178, important for electrostatic interactions with the WASP BR, are replaced by oppositely charged and neutral TC10 residues (Lys63 and Thr192), respectively. However, mutating both Lys63 and Thr192 in TC10 to Glu (Fig. S1b) yielded only partial rescue of the rate constant for binding WASPfrag, reducing the ka gap between Cdc42 and TC10 apparently from three to two orders of magnitude20. The remaining ka gap could suggest different rate-limiting steps for the binding of these two GTPases with WASPfrag. Accounting for the differences in ka among the three GTPase-effector systems and mutational effects therein, as done here, will yield deep physical and mechanistic insight into the binding processes.

MATERIALS AND METHODS

Rate constants were calculated by the TransComp method28,29. This method requires only the structure of the native complex as input, and the method of calculation is equivalent to producing 4,000 trajectories in which the translational and rotational diffusion of the subunits is simulated. In such Brownian dynamics simulations, the steric interactions as well as long-range electrostatic interactions between the subunits are calculated, but the solvent is treated implicitly using the Poisson-Boltzmann model. The subunit molecules are treated as rigid; in essence, the internal conformational changes are assumed to be rapid so the molecules can quickly adapt to the native conformations when they reach the native complex by translational and rotational diffusion. The foregoing Brownian dynamics simulation based approach is well established and widely used46,47.

TransComp is based on the same general approach. Besides explicitly defining the concept of transient complex and prescribing its specification, a significant technical advance is the treatment of the long-range electrostatic interactions48. We found that, to a very high accuracy, the effect of the long-range electrostatic interactions during the Brownian dynamics simulations can be captured by the Boltzmann factor of the electrostatic interaction energy ΔGel in the transient complex49. Therefore in our Brownian dynamics simulations, the electrostatic interactions are turned off, yielding the basal rate constant kD0, and the electrostatic contribution is recouped by calculating ΔGel. The overall diffusion-limited binding rate constant is then

kD=kD0exp(-ΔGel/kBT)
(1)

Using TransComp for the binding kinetics of IDPs requires further adaption28,29. In particular, the TransComp calculation is done using the docking segment of an IDP as one subunit and the target protein as the other subunit. That is, we assume that the docking segment undergoes rapid conformational exchange, such that it adopts the native conformation when it approaches its subunit on the target surface. During this approach, the remaining segments can stay in nonnantive conformations but are assumed to minimally affect the interaction between the docking segment and the target protein (Fig. 2). Based on the latter assumption, the remaining segments are completely removed in the TransComp calculation.

Figure 2
The dock-and-coalesce mechanism, illustrated on Cdc42-WASPfrag binding. The WASP BR (blue) first docks to the Cdc42 surface (gray), with rate constant kD. The resulting docked complex may subsequently either undock (with rate constant k−D) or ...

Below some details on modeling the native complexes and the components of TransComp calculations are described.

Structural modeling of the TC10-WASPfrag complex

The TC10-WASPfrag complex was modeled after the Cdc42-WASPfrag complex (Protein Data Bank (PDB) entry 1CEE10), with Cdc42 replaced by TC10 using their sequence alignment from the Dali server50 (Fig. 1e). Both Lys63 and Thr192 in TC10 were mutated to the corresponding Glu residues in Cdc42, so the modeled complex was for the TC10 K63E/T192E mutant bound with WASPfrag. After removal of steric clash by standard energy minimization in Amber, the WASP BR was relaxed manually to release the N-terminus from being trapped and refined again by energy minimization (Fig. S1b).

Structural modeling of the basic region of Cdc42-bound Pak1

Using Modeller51 on the sequence alignment of Fig. 1d, an initial conformation of the Pak1 BR was modeled after the WASP BR, after superimposing the GBD Cα atoms in their respective complexes with Cdc42 (PDB entries 1E0A44 and 1CEE, respectively). The Pak1 BR was then relaxed manually and refined by energy minimization (Fig. S1a).

kD calculation by the TransComp method

TransComp and the associated parameters have undergone thorough validation,28,29,47,48 and were used here without modification. Each TransComp calculation consists of three components: identification of the transient complex by mapping the inter-subunit interaction energy landscape around the native complex, determination of the basal rate constant kD0 by Brownian dynamics simulations, and computation of the electrostatic interaction energy ΔGel in the transient complex by solving the Poisson-Boltzmann equation.

In identifying the transient complex, the interaction energy is simply modeled by the number of contacts (both native and nonnative), Nc, between the apposing binding sites on the two subunits in any clash-free configuration. A total of 107 such configurations were generated by randomly sampling the six degrees of relative translational/rotational freedom in and around the bound-state energy well. As illustrated in Fig. 3a, the bound state is characterized by configurations with high Nc but a very restricted accessible range of the relative rotation angle χ, as indicated by small standard deviations, σχ, of χ calculated among configurations at a given Nc. When the two subunits move out of the bound-state energy well, there is a sharp increase in σχ. We fit the dependence of σχ on Nc to a function used for modeling two-state protein denaturation, and identify the midpoint, where Nc is designated Nc*, of this fit as the transient complex. That is, configurations with Nc = Nc* comprise the transient-complex ensemble, and configurations with Nc > Nc* fall in the bound-state well.

Figure 3
Calculation of the rate constant for the WASP BR (residues 230–236) docking to Cdc42. (a) Sharp transition from the unbound regime characterized by large relative translational/rotational freedom (i.e., high standard deviation, σχ ...

The basal rate constant kD0 is calculated from Brownian dynamics simulations in which electrostatic interactions are turned off. Each Brownian dynamics trajectory starts from the bound-state well (i.e., from a configuration with Nc > Nc*) and is propagated in the translational/rotational space. At each time step where the protein pair is in the bound-state well, it is given a certain rate γ to form the native complex. If that happens, the trajectory is terminated. All trajectories are otherwise terminated at a cutoff time. The survival fraction of 4,000 trajectories as a function of time, upon extrapolating to infinite γ, allows kD0 to be calculated52.

The electrostatic interaction energy ΔGel in the transient complex is calculated by numerically solving the Poisson-Boltzmann equation. We randomly choose 100 configurations from the transient-complex ensemble, calculate the electrostatic interaction energy for each at the desired ionic strength, and take the average to yield ΔGel. Finally the diffusion-limited rate constant is calculated according to Equation 1.

To obtain kD for a mutant, the basal rate constant kD0 was assumed to be unaltered and only the electrostatic interaction energy ΔGel was recalculated after molecular modeling of the mutation. Mutations were introduced by Pymol (www.pymol.org) and refined by side-chain energy minimization.

RESULTS

Framework for modeling the binding kinetics of IDPs

The extended conformation of WASPfrag formed on the Cdc42 surface (Fig. 1c) typifies the bound structures of IDPs, with stability largely arising from intermolecular (rather than intramolecular) interactions distributed over elongated interfaces. In the binding process, different regions of an IDP are unlikely to form contact with the target protein all at once. Instead the binding may proceed via parallel pathways, each with a different region of the IDP acting as the initial docking segment, followed by structural consolidation on the target surface. Presumably, for a given IDP, a single such dock-and-coalesce pathway, or a very small number of them, yield much higher binding rate constants than alternative pathways, hence make the dominant contribution to the overall rate of the productive formation of the native complex.

Importantly, this dock-and-coalesce mechanism also provides a framework for quantitatively modeling the binding kinetics of IDPs28,29,33 (Fig. 2). In the docking step, the docking segment approaches its subsite on the target protein by translational/rotational diffusion, and simultaneously undergoes rapid conformational exchange to reach a docked complex in which the docking segment is bound but the remaining segment(s) of the IDP are still loose. This step is likely to be rate-limited by the diffusional approach, which in turn can be sped up enormously by long-range electrostatic attraction of the target protein47. In the subsequent coalescing step, the remaining segments evolve toward their bound conformations, with energy barriers lowered by interactions with surface residues of the target protein27. If the rate constants are kD and k−D, respectively, for the docking step and the its reverse process, i.e., the undocking step, and kC for the coalescing step, then the overall association rate constant is

ka=kDkCk-D+kC
(2)

For any diffusion-limited binding event, including the docking step of an IDP, we have developed a transient-complex theory for predicting the binding rate constant48. The transient complex refers to an on-pathway late intermediate in which the two binding partners have near-native separation and relative orientation, but have not yet formed most of the stereospecific short-range interactions. Note that the focus in this paragraph is the docking step, not the whole binding process of the IDP (Fig. 2). The binding partners are thus the docking segment and its subsite on the target surface. Correspondingly the transient complex here occurs intermediately before the successful docking of the docking segment only; the coalescing step is to occur subsequently. Once the docking segment and its subsite diffuse to the transient complex, located at the outer boundary of an energy well created by the native interactions between the two binding partners, they rapidly fall into it to generate the docked complex.

We have developed an automated implementation of the transient-complex theory, known as TransComp, and adapted it for IDP binding28. From our understanding of the determinants for the wide variation in association rate constants47, we predict the dominant binding pathway to be the one where the docking step is rate-enhanced by electrostatic attraction and close to being rate-limiting for the overall binding process. By applying the TransComp method to different fragments of the IDP complexed with the target protein, we can identify the docking segment of the dominant pathway and predict the rate constant of the docking step, which serves as an upper bound for the rate constant of the overall binding process (see Equation 2). This approach has yielded rate constants in good agreement with experimental results for a number of IDPs28,29,33, and is used below to account for the differences in ka among the three GTPase-effector systems and mutational effects therein.

Cdc42-WASPfrag binding

TransComp prediction of the diffusion-limited docking rate constant kD starts with identification of the transient complex using the native complex as input28,29. As the two binding partners approach each other to form the docked complex, they abruptly lose relative translational/rotational freedom (as represented by the standard deviation, σχ, in the relative rotation angle χ) but gain intermolecular contacts (Nc) (Fig. 3a). The transient complex is located at the mid-point of this transition (Fig. 3a, b). In line with the assumption that rapid conformational exchange allows the docking segment of the IDP to achieve its bound conformation during the docking step, in the TransComp calculation the docking segment, like the target protein, takes the bound conformation. However, if the docking segment were extended to include coalescing segments, then binding would no longer be a single-step process. TransComp identifies this situation by a large gap in Nc, as occurs when the full WASPfrag bound with Cdc42 (PDB entry 1CEE) was used for kD prediction (Fig. S2a).

We broke WASPfrag into three segments for separate TransComp runs in order to identify the likely docking segment. With the BR segment comprising residues 230–236 (Fig. 3a, b), the predicted docking rate constant kD is 3.3×107 M−1s−1 (at an ionic strength of 95 mM). This segment was selected for its highest kD among all the segments starting at residue 230 and ending successively at residues 234 to 255 (Fig. S3a). In comparison, the docking rate constant would be two to three orders of magnitude lower, at 1.7×105 and 1.9×104 M−1s−1, respectively, for the CRIB segment (residues 237–251; Fig. S2b) and the C-terminal segment (residues 252–288; Fig. S2c). With this large separation in predicted docking rate constants, we can identify the BR with high confidence as the docking segment.

As critical support of the BR as docking segment, the predicted kD, 3.3×107 M−1s−1, only slightly overestimates the experimental ka, 2.2×107 M−1s−1, for the association of WASPfrag with Cdc4220. The close agreement between the kD and ka suggests that the subsequent coalescing step is fast and has only a modest effect in slowing down the overall binding process. Hereafter we use the docking rate constant as the prediction for ka. The TransComp calculation further teases out the kD, into a basal rate constant of 3.0×105 M−1s−1, and a two orders of magnitude enhancement by a very favorable ΔGel of −2.8 kcal/mol. The latter reflects the strong electrostatic attraction across the binding interface (Figs. 1c and 3c, d).

Given the strong electrostatic rate enhancement, it is not surprising that a significant salt dependence of kD is found. The calculated kD values at six ionic strengths from 45 to 1045 mM agree closely with the experimental results (Table S1). The calculated kD values, 1.3×106 and 2.4×105 M−1s−1, respectively, for the E49K single mutant and the E49K/E178K double mutant of Cdc42 modestly underestimate the measured ka results (Table 1). The discrepancy suggests, with the slowing down of the BR-initiated pathway by the charge reversal, contributions of alternative pathways may become important. For example, adding the contribution of the CRIB-initiated pathway (i.e., 1.7×105 M−1s−1) would nearly double the rate constant of the E49K/E178K mutant and improves the agreement with the experimental result (Table 1).

Table 1
Comparison of calculated (Calc) and experimental (Expt) results for the association rate constants (in μM−1s−1) of wild-type and mutant Cdc42-WASPfrag complexes.

The findings for charge neutralization and reversal mutations in the BR segment are similar (Table 1). Notably, with the charge reversal of K230KK232, the BR-initiated pathway slows down to a kD of 2×103 M−1s−1, and therefore the CRIB-initiated pathway now potentially becomes dominating and accounts largely for the observed association rate constant of 9×104 M−1s−1.

The foregoing TransComp results clearly indicates that Cdc42-WASPfrag binding proceeds with the BR docking, followed by rapid conformational coalescence of the CRIB and C-terminal subdomain of the GBD on the Cdc42 surface (Fig. 2). To examine the generality of this binding mechanism, below we extend the study to the other two related GTPase-effector systems.

TC10-WASPfrag binding

The structure of the TC10-WASPfrag complex is not available in the PDB. Given the high sequence identity between TC10 and Cdc42, we used the structure of the Cdc42-WASPfrag complex to build a model for the TC10-WASPfrag complex. We then relaxed the BR of WASPfrag, and mutated Lys63 and Thr192 in TC10 to the corresponding Glu residues in Cdc42 (Fig. S1b). TransComp calculations were carried out on the latter structure to identify WASP residues 230–239 as constituting the docking segment, with a rate constant of 6.9×106 M−1s−1 for docking to the TC10 K63E/T192E (EE) mutant (Figs. S3b and 4a, b). This value is 30-fold higher than the reported ka for WASPfrag binding with the TC10 EE mutant20.

The high kD can be attributed to strong electrostatic attraction between the docking segment and the TC10 EE mutant (Fig. 4c, d). Indeed, the TC10 EE mutant appears to have a stronger negative electrostatic surface than Cdc42 (Figs. 3c and and4c),4c), with the former’s acidic residue Asp40 and neutral residue Cys167 corresponding to the latter’s neutral residue Asn26 and basic residue Lys153, respectively (Fig. 1e). With ΔGel=-1.3kcal/mol, the electrostatic attraction between the docking segment and the TC10 EE mutant contributes a 8.5-fold enhancement to their docking rate constant. For the K63E single mutant and wild-type TC10, TransComp predicted 2.6- and 16-fold reductions, respectively, in kD. These results somewhat overestimate the 1.2- and 7.9-fold reductions of the reported ka values for these TC10 variants.

Figure 4
Calculation of the rate constant for the WASP BR (residues 230–239) docking to the TC10 K63E/T192E double mutant. (a–d) See Fig. 3 legend.

Several possibilities can be suggested for the 30-fold discrepancy between the calculated kD and reported ka for WASPfrag binding with the TC10 EE mutant. First of all, the model for the complex built on the structure of the Cdc42-bound counterpart may be incorrect. However, given the high sequence identity, the structural model is unlikely to be grossly wrong and the docking of the BR segment is almost surely rate-enhanced by electrostatic attraction. Secondly, it is possible that, contrary to the case of binding with Cdc42, the coalescing step in binding with TC10 is very slow as to rate-limit the overall binding process. Hemsath et al.20 noted that, among the small number of Cdc42 residues that contact WASPfrag and differ from the corresponding TC10 residues in amino-acid identity, Ile21, Thr24, and Thr25 interact with the CRIB. When the TC10 residues, Met35, Ala38, and Asn39, were substituted into the Cdc42 counterparts, the association rate constant changed little. This observation does not support a significant difference in the coalescing rate constants of Cdc42 binding and TC10 binding.

The third possibility is that the reported ka underestimates the rate constant for WASPfrag binding with the TC10 EE mutant. As support for this contention, the TC10 EE mutant was almost as effective as Cdc42 and more effective than the Cdc42 E49K mutant in stimulating actin polymerization20. If the stimulation activity is a measure of the rate constant for binding WASPfrag, then the ka of the TC10 EE mutant should be bracket by those of wild-type Cdc42 and the E49K mutant, i.e., between 2.2×107 and 3.5×106 M−1s−1. Interestingly, our kD for the TC10 EE mutant, at 6.9×106 M−1s−1, actually falls into this bracket.

Cdc42-Pak1frag binding

Relative to the WASP BR, the increase in acidic residues in the Pak1 BR (Fig. 1d) is expected to weaken its interaction with Cdc42. We modeled the Pak1 BR onto the structure of the Pak1 GBD (residues 75–118) bound with Cdc42 (PDB entry 1E0A), using the WASP BR in PDB entry 1CEE as a guide but loosened the interaction with Cdc42 (Fig. S1a). Based on TransComp calculations on various fragments containing the Pak1 BR (Fig. S3c), the docking segment was identified as comprising residues 66–77 (Fig. 5a, b). The docking rate constant is 5.0×105 M−1s−1, with a modest 2.6-fold rate enhancement by electrostatic attraction ( ΔGel=-0.6kcal/mol; Fig. 5c, d). This calculated kD is in accord with the experimental ka of 6.1×105 M−1s−1.20 Moreover, the reductions in kD by 1.4- and 2.5-fold, respectively, for the E49K and E49KE178K mutants agree reasonably well with the 2.0- and 5.1-fold reductions in experimental ka (Table 2).

Figure 5
Calculation of the rate constant for the Pak1 BR (residues 67–77) docking to Cdc42. (a–d) See Fig. 3 legend.
Table 2
Comparison of calculated (Calc) and experimental (Expt) results for the association rate constants (in μM−1s−1) of wild-type and mutant Cdc42-Pak1frag complexes.

It appears that the binding of Pak1frag, similar to the binding of WASPfrag, largely proceeds through initial docking by the BR, followed by rapid conformational coalescence of the GBD on the Cdc42 surface (Fig. 2). Due to the introduction of acidic residues in the BR, the binding rate constant in this pathway is lower. As a result the contribution of a CRIB-initiated pathway to the overall binding rate constant may not be negligible.

DISCUSSION

We have dissected the binding kinetics of the Cdc42-WASP and other two related GTPase-effector systems within the framework of the dock-and-coalesce mechanism. For Cdc42-WASP binding, our TransComp calculations have identified the BR of WASP as the docking segment, due to its much higher docking rate constant compared to alternatives. Moreover, the predicted docking rate constant is close to the observed association rate constant20. We therefore conclude that the coalescing step involving the GBD is sufficiently fast as to making only a modest contribution to the overall association rate constant. As support of this conclusion, TransComp predictions have rationalized the effects of salt and key mutations on the association rate constant.

The limitations of TransComp calculations, as with the whole Brownian dynamics simulation based approach, should be noted. First, the conformational exchange dynamics of the docking segment is assumed to be fast. In theory, slow conformational exchange can be treated in TransComp (by not extrapolating the exchange rate γ to infinity). However, the value of γ must be supplied. Given that the predicted diffusion-limited rate constant (i.e., assuming infinite γ) is already close to the experimental value for overall binding, it seems likely that fast conformational exchange is not a bad assumption for Cdc42-WASP binding. Second, the effects of solvent and ions are treated not explicitly, but implicitly through the Poisson-Boltzmann model. Although a large body of literature supports the Poisson-Boltzmann model, its use in relation to an explicit solvent treatment for IDP binding kinetics warrants further investigation. There have been many simulations of IDPs in explicit solvent; however, calculating binding rate constants from these simulations remains a significant challenge.

The binding of WASP with TC10 and of Pak1 with Cdc42 also appears to start mostly with the docking of the effector BR. However, in these two cases, due to charge substitutions in either the GTPase or the effector, the docking rate constant of the BR is significantly reduced relative to the WASP case, and hence alternative pathways, including the CRIB-initiated pathway, may come into play. Additionally, after BR docking, conformational coalescence of the WASP GBD on the TC10 surface may possibly slow down the overall binding process, but this possibility warrants further experimental investigation. Overall, through TransComp calculations, account for the differences in ka among the three GTPase-effector systems and mutational effects therein have yielded deeper physical and mechanistic insight into the binding processes.

The prominent role of the effector BRs in initiating the docking step is identified here from studying the binding of the effector fragments that directly interact with the GTPases. A similar role can be suggested for the BRs in the activation of the full-length effectors by GTPases. For WASP, autoinhibition involves the interaction of the GBD with the VCA domain,34 leaving the BR disordered and free from intramolecular interaction (Fig. 1b). As first suggested by Hemsath et al.20, the free BR may initiate the docking with Cdc42. Once docked, Cdc42 can displace the VCA domain and form additional interaction with GBD. For Pak1, Lei et al.41 proposed that activation by Cdc42 begins with attack of the CRIB. We suggest here that an alternative pathway is initiated by docking with the free BR. Once docked, Cdc42 can peel away the CRIB and the rest of the GBD and thereby dissociate the autoinhibited dimer. These examples illustrate that elucidating binding pathways of IDPs can lead to better understanding of their biological functions.

For both WASP and Pak1, the docking step involving the BRs appears to dictate the (high) association rate constants. For Cdc42-WASP binding, the high association rate constant comes about both because of the strong electrostatic attraction between the BR and its subsite on Cdc42 and because of fast conformational coalescence of the GBD on the Cdc42 surface. The rate enhancement of electrostatic attraction is now well understood4648, and, as illustrated here, can be predicted by TransComp calculations. By comparing the calculated docking rate constant with the observed overall association rate constant, we can isolate the coalescing rate constant and begin to characterize the physical determinants of its magnitude, which surely would include the interactions and internal dynamics of the molecular elements involved in the coalescing step. In this regard, valuable information is being generated by kinetic studies involving systematic mutations of interface residues and variations of solvent conditions (e.g., temperature)22,24.

It will be of both fundamental and practical interest to redesign binding pathways, e.g., by switching docking and coalescing segments. The WASP mutant with charge reversal of K230KK232 may be an example with an altered binding pathway (Table 1): the resulting slow down of the BR-initiated pathway potentially allows the CRIB-initiated pathway to become dominant. In general, guided by TransComp calculations, it may be relatively straightforward to introduce charge mutations to change the docking rate constants of two competing pathways in opposite directions, slowing down one and enhancing the other. Using systematic mutations, it may also be possible to tune the coalescing rate constants of the competing pathways in desired directions. Combinations of these mutations may finally lead to a redesigned binding pathway.

Supplementary Material

Supp Info

Acknowledgments

This work was supported by National Institutes of Health Grant GM0585187.

References

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