Steady-state Kinetic Mechanism of PDK1*

PDK1 catalyzes phosphorylation of Thr in the conserved activation loop region of a number of its downstream AGC kinase family members. In addition to the consensus sequence at the site of phosphorylation, a number of PDK1 substrates contain a PIF sequence (PDK1-interacting fragment), which binds and activates the kinase domain of PDK1 (PDK1(ΔPH)). To gain further insight to PIF-dependent catalysis, steady-state kinetic and inhibition studies were performed for His6-PDK1(ΔPH)-catalyzed phosphorylation of PDK1-Tide (Tide), which contains an extended “PIF” sequence C-terminal to the consensus sequence for PDK1 phosphorylation. In two-substrate kinetics, a large degree of negative binding synergism was observed to occur on formation of the active ternary complex (\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\alpha}K_{d}^{\mathrm{ATP}}=40{\ }{\mu}\mathrm{M}\) \end{document} and \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\alpha}K_{d}^{\mathrm{Tide}}=80{\ }{\mu}\mathrm{M}\) \end{document}) from individual transitory binary complexes (\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(K_{d}^{\mathrm{ATP}}=0.6{\ }{\mu}\mathrm{M}\) \end{document} and \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(K_{d}^{\mathrm{Tide}}=1{\ }{\mu}\mathrm{M}\) \end{document}). On varying ATP concentrations, the ADP product and the (T/E)-PDK1-Tide product analog (p′Tide) behaved as competitive and noncompetitive inhibitors, respectively; on varying Tide concentrations, ADP and p′Tide behaved as noncompetitive and competitive inhibitors, respectively. Also, negative binding synergism was associated with formation of dead-end inhibited ternary complexes. Time progress curves in pre-steady-state studies under “saturating” or kcat conditions showed (i) no burst or lag phenomena, (ii) no change in reaction velocity when adenosine 5′-O-(thiotriphosphate) was used as a phosphate donor, and (iii) no change in reaction velocity on increasing relative microviscosity (0 ≤ η/η0 ≤ 3). Taken together, PDK1-catalyzed trans-phosphorylation of PDK1-Tide approximates a Rapid Equilibrium Random Bi Bi system, where motions in the central ternary complex are largely rate-determining.

The common ability of PDK1 to catalyze phosphorylation of the activation loop of its numerous protein targets, but with varying degrees and mechanisms of regulation, has been explained from the intriguing perspective that PDK1 has the ability to "sense the conformation" of many of its substrates (24). PDK1 and other AGC kinases possess a "PIF (PDK1-interacting fragment) pocket" on the catalytic kinase domain (25,26). In contrast to other AGC kinases, PDK1 does not possess a hydrophobic motif C-terminal to its catalytic domain. Therefore, the PIF pocket of PDK1 is accessible for interaction with the phosphorylated hydrophobic motifs of its target kinases. Such intermolecular interaction promotes activation of PDK1, enabling PDK1-catalyzed phosphorylation of target kinases at the activation loop. Upon phosphorylation of the activation loop, the phosphorylated C-terminal hydrophobic motif of the target kinase is released from the PIF pocket on PDK1, and it forms an intramolecular interaction with its own PIF pocket, which fully stabilizes an active conformation (24). Both in vivo and in vitro studies indicated the important role of intermolecular PIF interactions in activating PDK1-catalyzed phosphorylation of S6K, RSK, and SGK (27)(28)(29).
To further investigate the role of PIF interactions, a model "PIF-Tide" was synthesized to contain the C-terminal hydrophobic motif region of protein kinase C-related kinase-2. The PIF region in protein kinase C-related kinase-2 contains high sequence homology to the PIF regions of PDK1 protein substrates, except that the Ser/Thr phosphorylation site is replaced by a negatively charged Asp residue (Fig. 1B) (25,30). Surface plasmon resonance and competition measurements yielded K d PIF values of ϳ0.8 -1.5 M, indicating a strong binary complex between PIF-Tide and PDK1 (30). In addition, PIF-Tide was found to activate PDK1-catalyzed phosphorylation of the small T308-Tide, which represents the consensus motif near the site of phosphorylation in PKB␣ (Fig. 1B) (25). By conjugating the PIF-Tide to the C terminus of T308-Tide, the PDK1-Tide was generated ( Fig.  1B) (25). PDK1-Tide remains the prevailing model PDK1 substrate, as it undergoes phosphorylation at a rate Ͼ100fold than T308-Tide, and its K m of ϳ80 M is significantly lower than the K m of Ͼ10 mM estimated for T308-Tide.
Whereas x-ray structural and mutagenesis studies have clearly defined PIF pocket residues important to catalytic activation of PDK1 (25,26), a detailed kinetic study of this process awaits description. Here, we report kinetic and chemical/solution perturbation studies aimed to establish the steady-state kinetic mechanism for PDK1-catalyzed trans-phosphorylation of PDK1-Tide. The results of these studies are best approximated a Rapid Equilibrium Random Bi Bi system, where conformational steps in the central ternary complex are largely rate-determining. Most interesting was the apparently large degree of negative binding synergism exhibited between the peptide and nucleotide substrates/products. Such synergism may derive from conformational transitions important to catalytic turnover.

EXPERIMENTAL PROCEDURES
Materials and General Methods-The catalytic kinase domain of PDK1 (His 6 -PDK1(⌬PH), residues 51-359) (26), containing an N-terminal His 6 tag followed by a PreScission protease recognition sequence prior to residue 51, was expressed using the Bac-to-Bac Baculovirus Expression System (Invitrogen) and His 6 affinity purified as described (31). Protein concentration was estimated using the Bio-Rad Protein Assay Kit with bovine serum albumin as a standard. PDK1-Tide and (T/E)-PDK1-Tide were from 21st Century Biochemicals, Inc. (Marlboro, MA). [␥-32 P]ATP and [␥-35 S]ATP␥S were from MP Biomedical (Irvine, CA). All other chemicals, salts, and buffers were from Sigma.
After 5 min preincubation of a 60-l reaction mixture containing both substrates at 30°C, the assays were initiated by addition of a 5-l amount of a stock concentration of His 6 -PDK1(⌬PH) to yield final enzyme concentrations of 5-30 nM. For kinase assays where both the ATP and PDK1-Tide concentrations were Ն3 M, 20-l aliquots were removed and quenched at three different times (ranging from 5 to 60 min). For kinase assays where either the ATP or PDK1-Tide concentration was Յ1 M, it was necessary to extend some reaction times up to 3 h to obtain the minimal detectable amounts of 32 P-radiolabeled PDK1-Tide (300 -600 cpm) in a 20-l reaction aliquot (ϳ0.6 -1.2 pmol or 30 -60 nM). Each 20-l reaction aliquot was quenched by mixing with 20 l of 50 mM phosphoric acid, which was then applied to P81 phosphocellulose paper (2 ϫ 2 cm). After 30 s, the papers were washed in 50 mM phosphoric acid for 10 min, then rinsed with acetone, and placed in the hood (Յ5 min) to dry. The amount of 32 P-labeled peptide was determined by scintillation counting of the paper in 10 ml of scintillation mixture.
Initial rates for reactions containing Ն1 M of both substrates were measured under conditions where total product formation represented Յ10% of the initial concentration of the limiting substrate. Due to detection limits, initial rates for reactions containing 0.3 M of either substrate were measured under conditions where total product formation (30 -60 nM) represented 10 -20% of the initial limiting substrate concentration. Because it was often necessary to use 30 nM enzyme to catalyze 30 -60 nM product under these limiting conditions, it is important to point out these initial velocities were obtained under pre-steady-state conditions. However, the initial velocities obtained under these conditions approximate those obtained under true steady-state conditions, as demonstrated by more rigorous pre-steady-state experiments described later in this paper, which provide no evidence of burst or lag phenomena. Initial velocities (v, M s Ϫ1 ) were normalized to enzyme concentration to yield apparent first-order rate constants (k, s Ϫ1 ), which better facilitate kinetic comparisons between steady-state and pre-steady-state kinetic results.
Control assays were carried out in which either the enzyme or PDK1-Tide were omitted; these values were always Յ5% of the activity measured in the presence of both the lower-and upper-bound concentrations of these reagents (0.3 and 300 M [␥-32 P]ATP; 5 and 30 nM enzyme). Control assays containing the enzyme and only the [␥-32 P]ATP substrate were further analyzed to measure ATPase activity. The amount of [ 32 P]inorganic phosphate released from [␥-32 P]ATP was determined by addition of 50 l of the reaction mixture to 100 l of a quench solution containing a 21% suspension of acid-washed (HCl) activated charcoal in 75 mM phosphoric acid. The quenched solution was mixed and placed on ice for 5 min, which provided for effective removal of the [␥-32 P]ATP nucleotide from solution by the charcoal. The charcoal with bound [␥-32 P]ATP was pelleted by centrifugation for 10 min, and a 60-l aliquot of the supernatant was analyzed for [ 32 P]inorganic phosphate. 32 P radioactivity in the supernatant was always Յ5% of the radioactivity measured in the absence of enzyme, indicating that the ATPase activity of His 6 -PDK1(⌬PH) is significantly lower than activity to the PDK1-Tide substrate.
Product and Dead-end Inhibition Steady-state Kinetic Assays-Diagnostic enzyme inhibition studies were carried out for His 6 -PDK1(⌬PH)-catalyzed transphosphorylation of PDK1-Tide exactly as described for two-substrate kinetics. ADP was tested as a product inhibitor and a phospho-PDK1-Tide mimetic in which the number 2 Thr residue that undergoes phosphorylation was replaced by a Glu residue ((T/E)-PDK1-Tide, Fig. 1B)) was used as a dead-end product analog inhibitor. In both cases, initial velocities were measured for varying substrate concentrations (0.3, 1, 3, 10, 30, 100, and 300 M) at different fixed concentrations of the inhibitor (0, 10, 30, 50, 70, and 100 M) at an unsaturating concentration of the other substrate (30 M). Data collection in this manner provided information necessary to construct companion plots for "diagnostic" analysis of the effect of either the ADP or (T/E)-Tide inhibitors on the two different varied substrates.
In contrast to the diagnostic inhibition studies, a full array of data sets was collected for product inhibition with ADP. Initial velocities were measured for varying PDK1-Tide concentrations (0.3, 1, 3, 10, 30, 100, and 300 M) at different fixed concentrations of ADP (0, 1, 3, 10, 30, and 100 M). In this case, ADP product inhibition was also measured at different fixed concentrations of [␥-32 P]ATP (0.3, 1, 3, 10, 30, 100, and 300 M). Data collection in this manner provided all information necessary to construct companion plots for complete kinetic analysis of the effect of ADP on the two different varied substrates.
Pre-steady-state Kinetic Assays-Pre-steady-state kinetic assays were carried out for His 6 -PDK1(⌬PH)-catalyzed transphosphorylation of PDK1-Tide using a KinTek Corporation (Austin, TX) model RQF-3 rapid quench-flow apparatus thermostatted at 30°C. Reaction buffer refers to 50 mM Tris-HCl buffer, pH 7.5, 0.1% 2-mercaptoethanol, 10 mM MgCl 2 , and 0.2 mM sodium vanadate. The left and right drive syringes in the RQF apparatus were filled with reaction buffer, and the middle (quench) syringe was filled with 75 mM phosphoric acid. One sample loop was loaded with 15 l of reaction buffer containing 600 M of both PDK1-Tide and [␥-32 P]ATP; and the other sample loop contained 15 l of varying concentrations of His 6 -PDK1(⌬PH) enzyme (2, 6, and 10 M) in reaction buffer. Thio-substitution effects were determined by equivalent substitution of [␥-35 S]ATP␥S for [␥-32 P]ATP. The phosphorylation reaction was initiated by mixing the contents of the sample loops that was allowed to react for a time t (0.05 Յ t Յ 10 s) before the reaction was acid quenched. For each time point, two 20-l aliquots of each quenched reaction solution were individually applied to P81 phosphocellulose paper (2 ϫ 2 cm), and the amount of PDK1-Tide phosphorylation was quantified as described for the steady-state kinetic assays. The time courses were performed in triplicate and the data points represent averaged values Ϯ S.E.
Control assays were carried out in which the PDK1-Tide substrate was omitted for each enzyme concentration in the pres-ence of either [␥-32 P]ATP or [␥-35 S]ATP␥S. The amounts of 32 P or 35 S radioactivity detected on the filter paper were always Յ5% of the measured radioactivity in the presence of PDK1-Tide, indicating that purified active pS241 His 6 -PDK1(⌬PH) catalyzes little or no nonspecific autophosphorylation during reaction times Յ10 s. In addition, the amounts of 32 P or 35 S radioactivity hydrolyzed from either [␥-32 P]ATP or [␥-35 S]ATP␥S during this time period were shown to be negligible by the charcoal filtration assay.
Solution Viscometric Studies-Pre-steady-state assays containing either [␥-32 P]ATP or [␥-35 S]ATP␥S as described above were also carried out in reaction buffer containing varying amounts of either microviscogen (0 -30% (w/v) glycerol or sucrose) or macroviscogen (0 -6.3% (w/v) polyethylene glycol). The relative viscosities (/ 0 ) of reaction buffers containing either a micro-or macroviscogen were calculated at 30°C, using an Ostwald viscometer to measure transit times and correcting for density. Relative solvent viscosities of 1.0 and 3.0 were obtained for buffers containing 0 and 30% sucrose, respectively. The measurements were made in triplicate and did not deviate by more than 3%.
Data Analysis-Initial rates determined in the two-substrate steady-state kinetic studies were globally fitted to Equation 1,  (32).
Initial rates determined in steady-state kinetic dead-end inhibition studies were fitted to the general velocity equations derived for competitive and noncompetitive mechanisms of inhibition, respectively (32). In these equations, values of k cat(app) , K m(app) , and K i(app) were determined for varying substrate and inhibitor concentrations at a single fixed concentration of the other substrate.
Initial rates determined in the complete array of ADP inhibition studies were globally fitted to Equation 6, which is the general velocity equation derived for a Rapid Equilibrium Random Bi Bi system with a dead-end PDK1-ADP-Tide ternary complex (32). In this equation, the parameters are the same as described for Equation 1, but further include K i ADP , the dissociation constant of the ADP product inhibitor, and ␤, the proportionality constant to quantify the degree that the binding of Tide substrate either increases (␤ Ͻ 1) or decreases (␤ Ͼ 1) the affinity of the enzyme for ADP. Values of k cat(app) , K m(app) ATP , K m(app) Tide , and K i(app) ADP that were obtained from fits of individual ADP inhibition data sets were further analyzed by the appropriate secondary expressions derived from Equation 6 (32).
All data were plotted and fitted using the GraFit 4.0 software (Erithacus Software, UK), which utilizes an iterative least squares algorithm (33).

Two-substrate Steady-state Kinetics of His 6 -PDK1(⌬PH)-
As demonstrated in a previous study, the recombinant catalytic domain construct of PDK1 (His 6 -PDK1(⌬PH), residues 51-359) was affinity purified (Ն95%) from Sf9 insect cell lysate in its Ser 241 phosphorylated and catalytically active form (26). Whereas His 6 -PDK1(⌬PH) exhibited detectable activity toward trans-phosphorylation of T308-Tide, we confirmed that His 6 -PDK1(⌬PH), similar to full-length PDK1 (25), exhibits very low affinity for T308-Tide with K m Ն 10 mM. In contrast to T308-Tide, His 6 -PDK1(⌬PH) exhibited significantly higher activity to PDK1-Tide, which contains the extended PIF residues C-terminal to the sequence of T308-Tide (Fig. 1B). Most important, saturating conditions could be approached with PDK1-Tide enabling steady-state kinetic determinations of values for k cat(app) , K m(app) Tide , and K m(app) ATP . Therefore, all kinetic studies and mechanistic depictions are given in reference to PDK1-Tide (Tide) as the substrate for phosphorylation by His 6 -PDK1(⌬PH). Fig. 2 shows all steady-state kinetic data and secondary plots for titration of His 6 -PDK1(⌬PH) with varying concentrations of one substrate at different fixed concentrations of the other substrate. During initial attempts to carry out a full titration analysis, it became apparent that titrations using substrate concentrations spanning two log units (3-300 M) were yielding seemingly parallel lines in double reciprocal plots. Only by spanning substrate concentrations over three log units (0.3-300 M) was it possible to clearly identify points of reciprocal plot intersection, which lie far to the left of the 1/k or y axis and well below the 1/[S] or x axis (Fig. 2, A and B). Such a phenomenon reflects a large negative binding synergism associated between the ATP and Tide substrates. Due to the results obtained in inhibition studies (see below), analysis of these data were best approximated and described for a Rapid Equilibrium Random Bi Bi system (Fig. 2G) (32). Global fitting of the data to  (Fig. 2C) and k cat ϭ 0.346 Ϯ 0.006 s Ϫ1 and ␣K d Tide ϭ 80.7 Ϯ 9.2 M (Fig. 2D). However, the difficulty toward accurate determinations of the dissociation constants of ATP and Tide in each individual binary complex are clearly illustrated by the secondary plots of K m(app) ATP (Fig. 2E, Equation 4) and K m(app) Tide (Fig. 2F, Equation 5 fitting to the equations derived for the Rapid Equilibrium Random Bi Bi system (Fig. 2G).
Dead-end Inhibition Steady-state Kinetics-The pattern of intersecting lines shown in Fig. 2, A and B, provide little evidence toward the steady-state kinetic mechanism of peptide phosphorylation other than ruling out both (i) Ping-Pong and (ii) Rapid Equilibrium Ordered Bi Bi systems (32). For these mechanisms, respectively, either parallel lines are observed or lines intersect on the y axis for the second binding substrate. Discrimination between other possible mechanisms (e.g. Steady-State Ordered, Steady-State Random, or (Partial) Rapid Equilibrium Random Bi Bi systems) may be achieved by comparing the effects of product (or dead-end) inhibitors in double reciprocal plots constructed for varying each substrate, while the other substrate is fixed at an unsaturated concentration (32).
For His 6 -PDK1(⌬PH), ADP was shown to be (i) competitive with the ATP substrate ( The observation of competitive inhibition exhibited between both (i) the ATP substrate and the ADP product inhibitor and (ii) the Tide substrate and the pЈTide product analog rule out Steady-State Ordered and Steady-State Random Bi Bi systems (32). In a Steady-State Ordered system, competitive inhibition between a given substrate/ product pair would be observed only for the substrate that binds first. In a Steady-State Random system, only mixed-type inhibition patterns would be observed. Thus, the line patterns in Fig. 3 remain consistent with either (i) a Rapid Equilibrium Random Bi Bi system, which can form both E-ADP-Tide and E-ATP-pЈTide types of deadend ternary complexes or (ii) a Theorell-Chance system, which is a special case of an Ordered Bi Bi system (32). In a Theorell-Chance system, only the substrate that binds first can form a stable binary complex, whereas the concentrations of the central substrate and product ternary complexes are essentially zero.
Binding Synergism between ADP and Tide-To distinguish between the Rapid Equilibrium Random and Theorell-Chance Bi Bi mechanisms, the effect of ADP product inhibition was tested for varying one substrate concentration at different fixed concentrations of the other substrate (32). Due to the extensive substrate concentration ranges required in this experiment, the ADP inhibition data are displayed in arrays of individual plots, which permit close inspection of the analyses (supplemental Figs. S2 and S3). Similar to Fig. 3A, ADP was shown to be competitive with ATP as the varied substrate (supplemental Fig.  S2), and values of k cat(app) (Fig. 4A), K m(app) ATP (Fig. 4C), and K i(app) ADP (Fig. 4E) were obtained for different fixed Tide concentrations. Similar to Fig. 3B, ADP was shown to be noncompetitive with Tide as the varied substrate (supplemental Fig. S3), and values FIGURE 1. Sequence alignment of peptide regions that interact with PDK1. A, human AGC kinase family members that have been shown to be substrates for PDK1 show conserved sequences in the segment comprising the VII and VIII subdomains of the catalytic kinase domain, as well as the hydrophobic motif (HM) near the C terminus. Subdomain VIII is known as the activation loop, and the critical threonine residue that undergoes phosphorylation by PDK1 is indicated by the arrowhead. Phosphatidylinositol 3-kinase-dependent phosphorylation of the critical residue in the hydrophobic motif (arrowhead) enhances PDK1 phosphorylation of the activation loop residue. Identical residues are in bold; and they cluster in the region C-terminal to the threonine phosphorylation site, suggesting a potential consensus motif for PDK1 phosphorylation. B, T308-Tide represents the consensus motif found in subdomain VIII of PKB␣, whereby PDK1 phosphorylates T308 (underlined); PIF-Tide represents the consensus hydrophobic motif, which binds the PIF pocket of PDK1 and activates catalysis; PDK1-Tide is generated by joining the T308-Tide and PIF-Tide sequences; and (T/E)-PDK1-Tide is a mutant analog of the phospho-PDK1-Tide product.
of k cat(app) (Fig. 4B), K m(app) Tide (Fig. 4D), and K i(app) ADP (Fig. 4F) were obtained for different fixed ATP concentrations. The critical observation whereby the K i(app) ADP increases hyperbolically with increasing fixed [Tide] (Fig. 4E) (32). Thus, the ADP inhibition data can be appropriately analyzed according to equations derived for a Rapid Equilibrium Random Bi Bi system with a E-ADP-Tide dead-end ternary complex (Fig. 4G, Equation 6) (32).     (Fig. 4G). The primary source of error in the global fitted value of ␤ results from deviations of the K i ADP values obtained at the highest fixed concentrations (300 M) of both Tide (Fig. 4E) and ATP (Fig. 4F), where little ADP inhibition was detected (supplemental Figs. S2 and S3, bottom rows). These relatively small upward deviations cause more dramatic effects on the y intercepts, which yield the values of K i ADP (Fig.  4E, inset) and ␤K i ADP (Fig. 4F, inset). Pre-steady-state Thio-substitution Effects-Because the steady-state kinetic and inhibition results were best approximated by a Rapid Equilibrium Random Bi Bi system, it was of great interest to next investigate the nature of the enzymatic step governing the relatively slow turnover rate of k cat ϳ 0.34 s Ϫ1 . Therefore, His 6 -PDK1(⌬PH)-catalyzed peptide phosphorylation reactions were carried out under pre-steady-state conditions ([E] ϭ 1-5 M) with "saturating" amounts (300 M) of both ATP and Tide. By using enzyme concentrations in this range, it was possible to distinguish whether rates of peptide chemical phosphorylation changed on progressing from the initial turnover (i.e. observed velocity includes all steps leading to and including chemical phosphorylation) to subsequent turnovers (i.e. observed velocity further includes product dissociation steps) (34). Fig. 5A shows the time progress curve of phosphopeptide product (pTide) formed during the first three catalytic turnovers using 5 M enzyme. No changes in the velocity of pTide formation (slope) could be detected on transition between the initial and subsequent turnovers. If the rate of release of either ADP or pTide product was significantly slower than chemical phosphorylation, then a burst of pTide formation would have been observed during the first turnover, followed by slower linear accumulation of pTide during subsequent turnovers. The constant velocity (i.e. absence of a "burst" of pTide) observed in this pre-steady-state experiment is further supported by the y intercept, which closely approaches zero (Fig. 5A).
To more closely probe the nature of the rate-determining step(s), the pre-steady-state time progress curve was also generated using ATP␥S as an alternative substrate. If the chemical transfer step were (partially) rate-determining, then such "thio-substitution" could lead to either an increased or decreased reaction velocity, depending on the degree of either dissociative or associative character, respectively, which may occur in the chemical step (35). Similar to the ATP reaction (Fig. 5A), pTide showed linear accumulation with time when ATP␥S was the substrate (Fig. 5B). Presteady-state time progress curves were also generated for [enzyme] ϭ 1 and 3 M; and the slopes (⌬v/⌬[E]) determined from plots of the reaction velocities with either the ATP or ATP␥S substrates yielded similar values of k cat ATP ϭ 0.310 Ϯ 0.015 s Ϫ1 and k cat ATP␥S ϭ 0.306 Ϯ 0.017 s Ϫ1 (Fig. 5C). Importantly, these values approximated the k cat values obtained in two-substrate steady-state kinetics ( Table 1 Pre-steady-state Solution Viscometric Effects-As described in Fig. 5, A-C, pre-steady-state kinetic values of both k cat ATP and k cat ATP␥S were also determined in reaction buffers containing increasing amounts of a microviscogen (e.g. glycerol and sucrose). Similar to reaction buffer alone (Fig. 5, A and B), pTide showed linear accumulations with time, which yielded similar reaction velocities for all viscogen-containing buffers. Fig. 5D highlights the similar glycerol-independent val- ues of k cat 0 (buffer with no viscogen) and k cat (buffer with viscogen) for both the ATP and ATP␥S substrates. The observations that all pre-steady-state kinetic time courses remained linear and independent of viscogen indicate that dissociation of both ADP and pЈTide occur significantly faster than the rate-determining step(s). These results remain consistent with the good approximation of the steady-state kinetic results to a Rapid Equilibrium Random Bi Bi system, where motions in the central ternary complex are largely rate-determining (Figs. 2G and 4G).

DISCUSSION
Protein kinases comprise the largest enzyme family, with ϳ500 being encoded by the human genome (36). The large number of cellular protein kinases reflects the large number of signal transduction pathways required in regulating proper cellular growth, survival, and proliferation. The complexity in elucidating cellular signaling networks is compounded by analyses indicating that individual protein kinases may tar-get and phosphorylate numerous different protein substrates (37,38). Thus, the mechanisms by which protein kinases selectively recognize protein substrates are of fundamental interest; and only recently, have detailed kinetic, binding, and mutagenesis studies revealed the importance of proteinprotein docking complexes in regulating protein phosphorylation specificities (39,40).
Strict interpretation of the ␣ value according the Rapid Equilibrium Random Bi Bi system (Fig. 2G) requires that ␣ quantify the degree that the binding of one substrate either increases (␣ Ͻ 1) or decreases (␣ Ͼ 1) the affinity of the enzyme for FIGURE 6. Docking-based substrate recognition by protein kinases. A, Rapid Equilibrium Random Bi Bi kinetic mechanism (K d ATP , K d Tide ) with rapid chemical phosphorylation (k 3 , k Ϫ3 ) and rate-limiting product release (k 4 ), where k Ϫ3 Ͻ k 3 Ͼ k 4 (40). Whereas distal contacts of the protein substrate provide some added binding affinity relative to consensus residues near the site of phosphorylation, the overall affinity of the complex remains weak. However, a fast and highly favorable phosphoryl transfer step can enhance interactions and further increase the apparent affinity according to Equation 9. B, Rapid Equilibrium Random Bi Bi kinetic mechanism (K d ATP , K d Tide ) with a rate-limiting and unfavorable conformational equilibrium (k 3b , k Ϫ3b ) preceding more rapid chemical phosphorylation (k 3b , k Ϫ3b ) and product release steps, where (k 3a Ͻ k 3b Ͻ k Ϫ3a ). In this case, distal contacts of the protein substrate provide very high binding affinity relative to consensus residues near the site of phosphorylation. However, a rate-limiting and unfavorable conformational equilibrium decreases the apparent affinity according to Equation 10. In the case of PDK1, the C-terminal PIF region of the model PDK1-Tide, as well as PDK1 protein substrates, provides a docking site to which PDK1 binds. The docked complex must undergo conformational rearrangement to form a catalytically competent ternary complex. the other substrate (i.e. K d and ␣K d are true dissociation constants). However, recently reported results of transient kinetic studies have revealed that apparent ␣K d values obtained in steady-state kinetic analyses may contain terms related to steps occurring in the central ternary complex. For example, presteady-state kinetic studies of both Csk with Src (␣ Յ 0.25) (42) and Sky1p with nuclear protein localization-3 (␣ ϳ 0.07) (43) showed that a rapid burst of chemical phosphorylation precedes steady-state rate-limiting steps involving release of products. For these cases, Adams and co-workers (39,42,43) demonstrated how fast and favorable phosphoryl transfer can function as a reversible "clamp" that grasps onto the substrate, pulling it toward product and overcoming weak interactions between the enzyme and substrate (Fig. 6A). Under such conditions (k Ϫ3 Ͻ k 3 Ͼ k 4 ), the complex expression relating to the apparent K m (apparent ␣K d ) is reduced to the approximation given by Equation 9 (39,42,43).
In contrast to the thermodynamically coupled systems described above (K m(app) Ͻ K d ), Adams and co-workers (39) further explained how uncoupled fast phosphoryl transfer can either lower or raise K m relative to K d in cases where substrates bind with high intrinsic affinity. However, this explanation cannot account for the observed K m Ͼ K d relationship exhibited by PDK1, because pre-steady-state kinetics showed no evidence of a chemical burst preceding rate-limiting product release (Fig.  5). Furthermore, the absence of both thio-substitution and solution microviscosity effects suggested that a rate-limiting conformational change likely precedes chemical phosphorylation (k 3a Ͻ k 3b ), as depicted in Fig. 6B. Under conditions where the conformational equilibrium is unfavorable (k 3a Ͻ k 3b Ͻ k Ϫ3a ), the complex expression relating to the apparent K m (apparent ␣K d ) is reduced to the approximation given by Equation 10.
(Eq. 10) Thus, the high affinity that PDK1 exhibits for both ATP and PDK1-Tide in individual binary complexes (K d ATP and K d Tide , Table 1) would appear to decrease ϳ70-fold (␣K d ATP and ␣K d Tide , Table 1), because formation of the ternary complex may be coupled to both a rate-limiting and a thermodynamically unfavorable conformational transition preceding chemistry. Such a conformational step has been included for the reaction of ERK2 with ETS⌬138, whereby mutagenesis studies revealed the important role of distal contacts in mediating "proximityinduced" catalysis (40,51,52). In addition, the apparently negative binding synergism observed between ADP and PDK1-Tide (K i ADP Ͻ ␤K i ADP ) may also reflect a thermodynamically unfavorable conformational transition in the dead-end ternary complex.
Similar to the important role of docking interactions exhibited for the catalytic reactions of Csk, Sky1p, p38␣, and ERK2 with their protein substrates, His 6 -PDK1(⌬PH) reactivity was greatly enhanced by PIF docking interactions to the model PDK1-Tide substrate (e.g. where the K m ϳ 70 M observed for PDK1-Tide compared with K m Ն 10 mM for T308-Tide). However, the significant effect of this specific interaction has yet to lower the apparent substrate K m (␣K d ) values to ՅK d values for the individual binary complexes. Thus, the kinetic constants determined for the PDK1 reaction with PDK1-Tide now serve as a benchmark for future comparisons to kinetic constants determined for reactions of PDK1 with protein substrates (Fig.  1A). Of particular interest will be to identify whether other possible "docking" interactions will serve to overcome the ratelimiting unfavorable conformational transition (Fig. 6B), which currently hinders PDK1-Tide phosphorylation.
In conclusion, the results of steady-state kinetic and inhibition studies for PDK1-catalyzed trans-phosphorylation of PDK1-Tide were best approximated by a Rapid Equilibrium Random Bi Bi system. ATP, PDK1-Tide, ADP, and (Thr/Glu)-Tide were shown to form high affinity binary complexes, which significantly decreased upon formation of either catalytically competent or dead-end inhibited ternary complexes. In addition, time progress curves in pre-steady-state kinetic studies under saturating or k cat conditions showed (i) no burst or lag phenomena, (ii) no change in reaction velocity when ATP␥S was used as a phosphate donor, and (iii) no change in reaction velocity on increasing relative microviscosity. Taken together, a reaction mechanism is proposed whereby a rate-limiting and unfavorable conformation transition coupled to substrate recognition could account for the large degree of apparently negative binding synergism. To further address this phenomenon, extensive transient kinetic and equilibrium binding studies of the coupled interactions will be forthcoming.