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The Cyclin-dependent Kinases cdk2 and cdk5 Act by a Random, Anticooperative Kinetic Mechanism*

Open AccessPublished:December 21, 2001DOI:https://doi.org/10.1074/jbc.M102034200
      cdk2·cyclin E and cdk5·p25 are two members of the cyclin-dependent kinase family that are potential therapeutic targets for oncology and Alzheimer’s disease, respectively. In this study we have investigated the mechanism for these enzymes. Kinases catalyze the transfer of phosphate from ATP to a protein acceptor, thus utilizing two substrates, ATP and the target protein. For a two-substrate reaction, possible kinetic mechanisms include: ping-pong, sequential random, or sequential ordered. To determine the kinetic mechanism of cdk2·GST-cyclin E and cdk5·GST-p25, kinase activity was measured in experiments in which concentrations of peptide and ATP substrates were varied in the presence of dead-end inhibitors. A peptide identical to the peptide substrate, but with a substitution of valine for the phosphoacceptor threonine, competed with substrate with a K i value of 0.6 mm. An aminopyrimidine, PNU 112455A, was identified in a screen for inhibitors of cdk2. Nonlinear least squares and Lineweaver-Burk analyses demonstrated that the inhibitor PNU 112455A was competitive with ATP with a K i value of 2 μm. In addition, a co-crystal of PNU 112455A with cdk2 showed that the inhibitor binds in the ATP binding pocket of the enzyme. Analysis of the inhibitor data demonstrated that both kinases use a sequential random mechanism, in which either ATP or peptide may bind first to the enzyme active site. For both kinases, the binding of the second substrate was shown to be anticooperative, in that the binding of the first substrate decreases the affinity of the second substrate. For cdk2·GST-cyclin E the kinetic parameters were determined to be K m, ATP = 3.6 ± 1.0 μm, K m, peptide = 4.6 ± 1.4 μm, and the anticooperativity factor, α = 130 ± 44. For cdk5·GST-p25, theK m, ATP = 3.2 ± 0.7 μm, K m, peptide = 1.6 ± 0.3 μm, and α = 7.2 ± 1.8.
      MAPK
      mitogen-activated protein kinase
      MEK
      MAPK/extracellular signal-regulated kinase kinase
      cdk
      cyclin-dependent kinase
      GST
      glutathione S-transferase
      AD
      Alzheimer's disease
      NFT
      neurofibrillary tangles
      Rb
      retinoblastoma
      AIC
      Akaike's information criterion
      EGF
      epidermal growth factor
      PEST
      proline (P), glutamic acid (E), serine (S), threonine (T)
      PKV
      PKVPKKAKKL peptide
      Kinases are a major component of the signal transduction pathways involved in cellular regulation. In addition to their role in maintaining normal homeostasis, there is increasing evidence implicating these enzymes in various diseases, such as cancer, neurodegeneration, and inflammation. Increased levels of enzymatic activity can lead to pathway deregulation, as exemplified by a number of oncogenic kinases, including Akt, Src, and Raf. The important role of kinases in health and disease has led to the suggestion that kinases may be good therapeutic targets (for review, see Refs.
      • Hudkins R.L.
      ,
      • Cohen P.
      ). In fact, inhibitors of several kinases, such as protein kinase C and p38 MAPK,1 are in clinical development as cancer and inflammation therapeutics, respectively (
      • Kaubisch A.
      • Schwartz G.K.
      ,
      • Lee K.-Y.
      • Qi Z., Yu, Y.P.
      • Wang J.H.
      ). Two members of the cyclin-dependent kinase family, cdk2 and cdk5, have been implicated in cancer and Alzheimer's disease, respectively, and inhibitors of these kinases may prove to be clinically useful.
      cdk2 is a member of the cyclin-dependent kinase family, which binds cyclins A and E and regulates cell cycle progression (for review, see Refs.
      • Morgan D.
      ,
      • Johnson D.G.
      • Walker C.L.
      ). Disruption of the normal cell cycle is a hallmark of cancer, and deregulation of the cyclin·cdk complexes is associated with the disease (
      • Sandhu C.
      • Slingerland J.
      ,
      • Meijer L.
      • Jezequel A.
      • Ducommun B.
      Progress in Cell Cycle Research.
      ). For example, increased cdk2 kinase activity was detected in tumor tissues in a mouse mammary tumor model. In addition, cyclin E protein levels were increased in the tumor tissue, and a number of variant cyclin E isoforms also were detected in tumor, but not in normal tissues (
      • Said T.K.
      • Medina D.
      ). In human tissues, cyclin E levels have been shown to be increased in some breast, colon, and leukemic cancers. The inhibitory proteins p21, p27, and p16 are deleted or mutated in some tumor types, further supporting the idea that deregulation of cdk activity may contribute to oncogenesis (
      • Loden M.
      • Nielsen N.H.
      • Roos G.
      • Emdin S.O.
      • Landberg G.
      ,
      • Slingerland J.
      • Pagano M.
      ,
      • Buolamwini J.K.
      ). Taken together, these results have led to the hypothesis that the cell cycle checkpoints are good points for therapeutic intervention. In fact, a number of cdk inhibitors currently are in phase I and phase II development as cancer therapeutics (
      • Garrett M.D.
      • Fattaey A.
      ,
      • Sielecki T.M.
      • Boylan J.F.
      • Benfield P.A.
      • Trainor G.L.
      ,
      • Senderowicz A.M.
      • Headlee D.
      • Sinson S.F.
      • Lush R.M.
      • Kalil N.
      • Villalba L.
      • Hill K.
      • Steinberg S.M.
      • Figg W.D.
      • Tompkins A.
      • Arbuck S.G.
      • Sausville E.A.
      ).
      cdk5 is a unique member of the cdk family of kinases involved in neuronal function (for review, see Refs.
      • Lee K.-Y.
      • Qi Z., Yu, Y.P.
      • Wang J.H.
      ,
      • Tang D.
      • Lee K.-Y.
      • Qi Z.
      • Matsuura I.
      • Wang J.H.
      ). Although the cdk5 protein is widely expressed in many tissues and cells, cdk5 kinase activity is restricted to neuronal cells. This tissue specificity is the result of the cdk5 activator proteins (p35, p25 (an N-terminally truncated form of p35), and p39), which are expressed only in brain (
      • Tang D.
      • Yeung J.
      • Lee K.-Y.
      • Matsushita M.
      • Matsui H.
      • Tomizawa K.
      • Hatase O.
      • Wang J.H.
      ,
      • Tsai L.H.
      • Delalle I.
      • Caviness Jr., V.S.
      • Chae T.
      • Harlow E.
      ,
      • Xiong W.
      • Pestell R.
      • Rosner M.R.
      ,
      • Zheng M.
      • Leung C.L.
      • Liem R.K.H.
      ). Results from a number of studies, including dominant negative mutant forms of cdk5 and knock-out mice, demonstrate that the cdk5·p35 complex plays an essential role in neurite outgrowth and neuronal differentiation (
      • Nikolic M.
      • Dudek H.
      • Kwon Y.T.
      • Ramos Y.F.M.
      • Tsai L.-H.
      ,
      • Ohshima T.
      • Ward J.M.
      • Huh C.-G.
      • Longenecker G.
      • Veeranna F.G
      • Pant H.C.
      • Brady R.O.
      • Martin L.J.
      • Kulkarni A.B.
      ).
      Increased cdk5·p35 kinase activity has been implicated in Alzheimer’s disease. Hyperphosphorylated tau protein is the major component of the neurofibrillary tangles (NFTs) found in Alzheimer’s disease (AD) brain, and in vitro experiments have demonstrated that cdk5·p35 phosphorylates sites on tau that are also phosphorylated on NFT tau (
      • Baumann K.
      • Mandelkow E.-M.
      • Biernat J.
      • Piwnica-Worms H.
      • Mandelkow E.
      ). Immunocytochemical experiments have shown that cdk5 co-localizes with NFT-tau in pretangle neurons (
      • Pei J.-J.
      • Grundke-Iqbal I.
      • Igbal K.
      • Bogdanovic N.
      • Winblad B.
      • Cowburn R.F.
      ), and cdk5 enzyme activity in AD brain is increased ∼2-fold compared with tissue from age-matched controls (
      • Lee M.-S.
      • Kwon Y.T.
      • Li M.
      • Peng J.
      • Friedlander R.M.
      • Tsai L.-H.
      ). Neurons from the brain tissue of AD patients have increased levels of p25, the truncated form of p35, and the p25·cdk5 complex shows increased tau phosphorylation, compared with the p35·cdk5 complex (
      • Patrick G.N.
      • Zukerberg L.
      • Nikolic M.
      • Monte S.
      • Dikkes P.
      • Tsai L.-H.
      ). Cell death induced by amyloid β-peptide was inhibited both by a cdk inhibitor and a calpain inhibitor, suggesting that abnormal accumulation of p25 may contribute to cell death and AD pathology (
      • Lee M.-S.
      • Kwon Y.T.
      • Li M.
      • Peng J.
      • Friedlander R.M.
      • Tsai L.-H.
      ).
      The role of cdk2 and cdk5 in proliferation and neuronal function has led to the idea that these kinases may be good therapeutic targets (
      • Martin-Castellanos C.
      • Moreno S.
      ,
      • Meijer L.
      ,
      • Senderowicz A.M.
      • Sausville E.A.
      ). However, a detailed understanding of the kinetic mechanisms by which these enzymes act is an important step in the rational design of inhibitors, but it has not been previously reported. A number of studies have been carried out identifying the kinetic mechanisms of various kinases (
      • Cook P.F.
      • Neville M.E.
      • Vrana K.E.
      • Hartl F.T.
      • Roskoski R.
      ,
      • Stein B.
      • Yang M.X.
      • Young D.B.
      • Janknecht R.
      • Hunter T.
      • Murray B.W.
      • Barbosa M.S.
      ,
      • Lograsso P.V.
      • Frantz B.
      • Rolando A.M.
      • O'Keefe S.J.
      • Hermes J.D.
      • O'Neill E.A.
      ). The results of these studies have been varied, and no one mechanism has emerged for all kinases. The majority of the kinases appear to act via a sequential and not a ping-pong mechanistic pathway, although both sequential random and sequential ordered mechanisms have been reported. In this study we have determined the mechanistic pathway for cdk2·cyclin E and cdk5·p25. As with other kinases, these enzymes utilize two substrates, ATP and protein (peptide). We show that both enzymes act via a random sequential mechanism, and furthermore, that the two substrates bind in an anticooperative fashion.

      RESULTS

      The cdk2 and cdk5 substrate consensus sequence for phosphorylation is Ser/Thr-Pro-X-Arg/Lys (
      • Songyang Z.
      • Blechner S.
      • Hoagland N.
      • Hoekstra M.F.
      • Piwnica-Worms H.
      • Cantley L.C.
      ,
      • Songyang Z.
      • Lu K.P.
      • Kwon Y.T.
      • Tsai L.-H.
      • Filhol O.
      • Cochet C.
      • Brickey D.A.
      • Soderling T.R.
      • Bartleson C.
      • Graves D.J.
      • DeMaggio A.J.
      • Hoekstra M.F.
      • Blenis J.
      • Hunter T.
      • Cantley L.C.
      ). A number of peptides have been shown to serve as substrates for cdk2 and cdk5, and a peptide derived from histone H1, PKTPKKAKKL, was chosen for use in these studies (
      • Ando S.
      • Ikuhara T.
      • Kamata T.
      • Sasaki Y.
      • Hisanaga S.
      • Kishimoto T.
      • Ito H.
      • Inagaki M.
      ,
      • Higashi H.
      • Suzuki-Takahashi I.
      • Taya Y.
      • Segawa K.
      • Nishimura S.
      • Kitagawa M.
      ,
      • Tang D.
      • Wang J.H.
      ). This peptide contains only one amino acid available for phosphorylation, which is desirable for kinetic experiments because the presence of multiple phosphorylation sites complicates the interpretation of results. Using the histone-derived substrate peptide and purified complexes of cdk2·GST-cyclin E and cdk5·GST-p25, time course experiments at 37 °C were carried out to establish the linear range of the assays. All subsequent assays were conducted at 37 °C for 20 min, which was within the linear range for the chosen enzyme concentration (data not shown).
      To determine the kinetic mechanism for the enzymes, replot analysis, as well as dead-end inhibitors were used. The two substrates, ATP and peptide, were varied within a single experiment, and the activities of cdk2·GST-cyclin E (Fig. 1 A) and cdk5·GST-p25 (Fig. 2 A) were measured. Each data set first was analyzed using equations describing ping-pong, random, and ordered mechanisms. The rapid equilibrium velocity equations describing these mechanisms are mathematically distinct with respect to their denominators (see “Experimental Procedures”), however, they cannot be used to discriminate between random and steady-state ordered pathways.
      Figure thumbnail gr1
      Figure 1Data plots for cdk2·GST-cyclin E. A, Michaelis-Menten plot of velocity versus ATP in assay. Five data sets were combined and normalized to generate this plot. The data from each set are shown, and the lines are from the combined data are fitted to the rapid equilibrium random/steady-state ordered model. Peptide concentrations: ■, 100 μm; ▪, 75 μm; ▿, 50 μm; ▾, 25 μm; ○, 5 μm; ●, 1 μm.B and C, replot analysis showing data from one data set.
      Figure thumbnail gr2
      Figure 2Data plots for cdk5·GST-p25. A, Michaelis-Menten plot of velocity versus ATP in assay. One data set was used to generate this plot. A second experiment gave identical results. The lines are from the combined data fitted to the rapid equilibrium random/steady-state ordered model. Peptide concentrations: ▪, 100 μm; ▿, 50 μm; ▾, 25 μm; ○, 5 μm;●, 1 μm. B and C, replot analysis.
      Nonlinear least squares analysis was used to determine the most probable pathway (Table I). In comparing the kinetic mechanisms, the most significant fit was determined through the use of sum of squares, the F test, and Akaike’s information criterion (AIC) (
      • Yamaoka K.
      • Tanigawara Y.
      • Nakagawa T.
      • Uno T.
      ,
      • Motulsky H.J.
      • Ransnas L.A.
      ,
      • Akaike H.
      ,
      • Yamaoka K.
      • Nakagawa T.
      • Uno T.
      ). As shown by the very low sum of squares, 1.2, the random mechanism clearly gave the best fit to the data. However, because the velocity equation describing this mechanism contains one additional parameter as compared with the other pathways, the low sum of squares value alone is not sufficient as a basis for choosing the best fit model. The AIC is useful for distinguishing between models with differing numbers of parameters. In general, when comparing models with differing numbers of parameters the model with the least positive AIC is superior. The AIC for the random pathway ranged from 2- to 4-fold lower in the case of cdk2·GST-cyclin E and 4- to 8-fold lower in the case of cdk5·GST-p25, compared with the other pathways. On the basis of this comparison the random model was the most probable kinetic pathway for both cdk2·GST-cyclin E and cdk5·GST-p25. Finally, we applied an F test comparison of the random model to each of the other models. As can be seen by the very lowp values, in each case less than 0.01, the random pathway kinetic model fits the data for both cdk2·GST-cyclin E and cdk5·GST-p25 significantly better than either the ordered or ping-pong models.
      Table ISummary of statistical analysis of kinetic mechanisms
      EnzymeKinetic mechanismSum of squaresAICF testp value
      Cdk2·cyclin ERandom or steady-state ordered1.243
      Rapid equilibrium ordered, ATP binds first2.8200<0.01
      Rapid equilibrium ordered, peptide binds first6.9360<0.01
      Ping-pong2.6190<0.01
      Cdk5·p25Random or steady-state ordered3.047
      Rapid equilibrium ordered, ATP binds first160180<0.01
      Rapid equilibrium ordered, peptide binds first49140<0.01
      Ping-pong9.083<0.01
      Replots of the data graphically demonstrate the mathematical differences between the velocity equations representing the three considered pathways. A plot ofK m/V max versus 1/[ATP] will have a slope of zero for a ping-pong pathway and a positive slope for a sequential system (either ordered or random). A plot of 1/V max versus 1/[ATP] will have a slope of zero for a rapid equilibrium ordered pathway and a positive slope for a random or a ping-pong system. Replots ofK m/V max versus 1/[ATP] and 1/V max versus 1/[ATP] for both cdk2·GST-cyclin E and cdk5·GST-p25 all had positive slopes, which are consistent with both enzymes acting by a random ordered substrate binding mechanism (Figs. 1 B,1 C, 2 B, and 2 C).
      When rapid equilibrium conditions prevail, the initial velocity equations for ping-pong, random, and ordered mechanisms are mathematically distinct, and the results presented in Table I and Figs.1 and 2 are sufficient for identifying the correct kinetic pathway. However, under a specific set of steady-state conditions the velocity equation describing an ordered mechanism becomes mathematically equivalent to that describing a random mechanism. For this to occur, the first order rate constant for the dissociation of the enzyme·ATP complex would have to be much smaller than the apparentk cat. The apparent k catfor a steady-state ordered mechanism where the concentration of products is zero is defined by the rate constant for the phosphotransferase step and all the rate constants for the enzyme·product dissociation steps. Although it seems unlikely that the dissociation of the enzyme·ATP complex would be significantly slower than the catalytic step and all subsequent product dissociation steps combined, this possibility cannot be ruled out on the basis of initial velocity data using enzymes and substrates alone.
      To differentiate conclusively between a random versus steady-state ordered kinetic mechanism, competitive inhibitors for both substrates (ATP and peptide) were used (
      • Fromm H.J.
      ). PNU 112455A is an aminopyrimidine (Fig. 3 A) identified as a cdk2 inhibitor during screening of the Pharmacia compound collection. The K i of this compound against cdk2·GST-cyclin E was 2.0 ± 0.2 μm (Fig.3 B), and for cdk5·GST-p25, it was 2.0 ± 0.3 μm (Fig. 3 C). Kinase specificity testing was carried out on a limited basis and demonstrated that PNU 112455A showed some selectivity as a cdk inhibitor. When tested at 100 μm, PNU 112455A did not inhibit the c-Met or insulin-like growth-1 receptor tyrosine kinases, or cAMP-dependent kinase. The MAPK family, like the cdks, consists of proline-directed protein kinases. However, no inhibition of ERK2 activity was observed with 100 μm PNU 112455A (data not shown).
      Figure thumbnail gr3
      Figure 3PNU 112455A is an ATP-competitive cdk inhibitor. A, chemical structure of PNU 112455A.B and C, Lineweaver-Burk plots of PNU 112455Aversus ATP with cdk2·GST-cyclin E (B) and cdk5·GST-p25 (C). D and E, Lineweaver-Burk plots of PNU 112455A versus peptide substrate with cdk2·GST-cyclin E (D) and cdk5·GST-p25 (E). PNU 112455A concentrations: ○, 0 μm;●, 1 μm; ▴, 2.5 μm; □, 5 μm; ▪, 10 μm; ▵, 20 μm.
      Experiments were carried out using PNU 112455A with both cdk2·GST-cyclin E and cdk5·GST-p25 to determine the mechanism of kinase inhibition by this compound. The Lineweaver-Burk plots of 1/v versus 1/[ATP] for PNU 112455A inhibition of both kinases converge on the y axis, demonstrating that the compound was competitive with respect to ATP (Fig. 3, B and C). Plots from experiments in which peptide substrate was varied demonstrated that PNU 112455A was a non-competitive inhibitor with respect to peptide (Fig. 3, D and E) for each of the enzymes.
      Crystals of cdk2 were soaked with PNU 112455A, and Fig.4 A shows a ribbon drawing of the least-squares superimposed cdk2 crystal structures containing the natural substrate, ATP, and the inhibitor PNU 112455A. The inhibitor is located in the same aromatic favoring position as the adenine of the ATP·cdk2 structure and of many other inhibitors in co-crystal structures with cdk2 (
      • Schulze-Gahmen H.
      • Brandsen J.
      • Jones H.D.
      • Morgan D.O.
      • Meijer L.
      • Vesely J.
      • Kim S.-H.
      ,
      • DeBondt H.L.
      • Rosenblatt J.
      • Jancarik J.
      • Jones H.D.
      • Morgan D.O.
      • Kim S-H.
      ). Fig. 4 B shows that it also forms hydrogen bonds to residues Glu81 and Leu83 of cdk2, consistent with other co-crystal structures and the adenine moiety of ATP and substrate, thus providing direct structural detail of the ATP-competitive nature of the inhibitor.
      Figure thumbnail gr4
      Figure 4Crystal structure of PNU 112455A bound to cdk2. A, schematic tracing of the cdk2 backbone shown with ATP (brown) (
      • Schulze-Gahmen H.
      • Brandsen J.
      • Jones H.D.
      • Morgan D.O.
      • Meijer L.
      • Vesely J.
      • Kim S.-H.
      ) and PNU 112455A (green). Software in Refs.
      • Kraulis P.
      and
      • Merritt E.A.
      • Bacon D.J.
      was used to generate the figure. B, a close-up view of the ligand and the surrounding cdk2 environment, showing hydrogen bonds (dotted lines) made by PNU 112455A (green and heteroatom colors), and the relationship of this ligand to the ATP binding site determined in Refs.
      • Schulze-Gahmen H.
      • Brandsen J.
      • Jones H.D.
      • Morgan D.O.
      • Meijer L.
      • Vesely J.
      • Kim S.-H.
      and
      • Yamaoka K.
      • Nakagawa T.
      • Uno T.
      (orange and heteroatom colors).
      PKV is a peptide-based inhibitor that corresponds to the peptide substrate with the substitution of valine for the phosphoacceptor threonine. Experiments were carried out with cdk5·GST-p25 and peptide substrate, in the presence of varying amounts of the inhibitor (Fig.5 A). As expected, Lineweaver-Burk plots of this data demonstrated that inhibition by the PKV peptide was competitive with peptide substrate with aK i value of 0.6 ± 0.3 mm. The same competitive inhibition and K i value were observed using cdk2·GST-cyclin E (data not shown). In contrast, in experiments with either kinase in which the concentration of ATP was varied, the PKV peptide was a non-competitive inhibitor of ATP (Fig. 5,B and C). Taken together, the results with PNU 112455A showing non-competitive inhibition with respect to peptide substrate, as well as the PKV inhibitor results, fulfill the criteria for demonstrating that cdk2 and cdk5 both utilize a random kinetic pathway (
      • Fromm H.J.
      ,
      • Segel I.H.
      ).
      Figure thumbnail gr5
      Figure 5PKV is a competitive cdk inhibitor. A, Lineweaver-Burk plot of PKV versus peptide substrate with cdk5·GST-p25. B and C, Lineweaver-Burk plots of PKV versus ATP with cdk2·GST-cyclin E (B) and cdk5·GST-p25 (C). PKV concentrations: ○, 0 mm; ▪, 1 mm; ●, 2 mm; ■, 4 mm; Δ 5 mm.
      Table II lists the dissociation constants for ATP and peptide for both cdk2·GST-cyclin E and cdk5·GST-p25 calculated by simultaneous fits of the random equation to the data.K a and αK a are the dissociation constants for ATP in the absence and presence, respectively, of the peptide substrate in the kinase active site. Similarly,K b and αK b are the dissociation constants for peptide in the absence and presence of ATP in the active site, respectively. The K a for both enzymes is similar, ∼3 μm, which is comparable to that observed for other kinases. The K b value, the peptide dissociation constant, is ∼4 μm for cdk2·GST-cyclin E and ∼2 μm for cdk5·GST-p25. The cooperativity factor, α, is greater than 1 for both enzymes, demonstrating that the binding of one substrate decreases the affinity for the second substrate. The degree of anticooperativity for cdk2·GST-cyclin E was large, with α greater than 100, whereas for cdk5 the value for α was moderate.
      Table IISummary of kinetic constants
      Parametercdk5·GST-p25cdk2·GST-cyclin E
      k cat, s−15.7 ± 0.215.1 ± 5.5
      K a, μm3.2 ± 0.73.6 ± 1.0
      K b, μm1.6 ± 0.34.6 ± 1.4
      α7.2 ± 1.8130 ± 44
      Data are the average ± S.D. Data for cdk5·GST-p25 are from two experiments and from five experiments for cdk2·GST-cyclin E.

      DISCUSSION

      We have investigated the kinetic mechanism of two members of the cyclin-dependent kinase family, cdk2 complexed with cyclin E, and cdk5 complexed with p25. There is increasing interest in these enzymes as therapeutic targets, and thus establishing their mechanism is an important step in the identification of inhibitors. Kinetic analysis has not been reported previously for either of these kinases, and we demonstrate that they utilize a random mechanism for ATP and peptide substrate binding.
      Kinetic mechanisms have been investigated for a number of other kinases, and for most of them a sequential, and not a ping-pong, mechanistic pathway has been reported. For cAMP-dependent kinase Whitehouse et al. (
      • Whitehouse S.
      • Walsh D.A.
      ,
      • Whitehouse S.
      • Feramisco J.R.
      • Casnelle J.E.
      • Krebs E.G.
      • Walsh D.A.
      ) reported that the mechanism was ordered, with the nucleotide binding first while Cooket al. (
      • Cook P.F.
      • Neville M.E.
      • Vrana K.E.
      • Hartl F.T.
      • Roskoski R.
      ) reported that MgATP and peptide bind randomly, although initial binding of the nucleotide is preferred. An ordered sequential mechanism has been reported for p38 MAPK (
      • Lograsso P.V.
      • Frantz B.
      • Rolando A.M.
      • O'Keefe S.J.
      • Hermes J.D.
      • O'Neill E.A.
      ), for the vascular endothelial growth factor receptor-2 tyrosine kinase (
      • Parast C.V.
      • Mroczkowski B.
      • Pinko C.
      • Misialek S.
      • Khambatta G.
      • Krzysztof A.
      ) and for the v-Src kinase (
      • Wong T.W.
      • Goldberg A.R.
      ). Both an ordered (
      • Erneux C.
      • Cohen S.
      • Garbers D.L.
      ) and a random pathway (
      • Posner I.
      • Engel M.
      • Levitzki A.
      ) have been reported for the EGF receptor tyrosine kinase. A number of other kinases, including MEK and IκB, have been shown to utilize a random mechanism (
      • Stein B.
      • Yang M.X.
      • Young D.B.
      • Janknecht R.
      • Hunter T.
      • Murray B.W.
      • Barbosa M.S.
      ,
      • Horiuchi K.Y.
      • Scherle P.A
      • Trzaskos J.M.
      • Copeland R.A.
      ,
      • Burke J.R.
      • Miller K.R.
      • Wood M.K.
      • Meyers C.A.
      ). In comparing these results, it is important to note that some of these studies have used a peptide as substrate, as in the present experiments, whereas others have used a full-length protein. Use of a substrate with a single phosphorylation site simplifies the kinetic analysis, however, it is possible that the use of a small peptide, compared with a physiological protein substrate, may affect the results.
      We used two inhibitors to show the random mechanism for cdk2 and cdk5. The PKV peptide was competitive with respect to peptide substrate, whereas PNU 112455A competed with ATP. This compound is equipotent toward both kinases, with a K i of ∼2 μm. The crystal structure of PNU 112455A bound to cdk2 showed that the compound binds in the ATP binding site of the enzyme, with the aminopyrimidine ring oriented in a similar position as the adenine. Crystal structures of either cdk5 alone or of a complex of the compound with cdk5 have not been determined, however, there is a very high degree of sequence identity between cdk2 and cdk5 in the region that binds ATP and the ATP competitive inhibitors. This allows one to predict a reliable model of the three-dimensional structure of cdk5 in this region (
      • Chou K.-C.
      • Watenpaugh K.D.
      • Heinrikson R.L.
      ). Thus, PNU 112455A is expected to bind to cdk5 in the same orientation.
      Among the cdk family members, a kinetic mechanism for cdk4·cyclin D1 was investigated using a peptide derived from the retinoblastoma (Rb) protein as substrate. Using staurosporine as a dead-end inhibitor, it was suggested that ATP binds first followed by the Rb peptide (
      • Konstantinidis A.K.
      • Radhakrishnan R.
      • Gu F.
      • Rao R.N.
      • Yeh W.-K.
      ). It might be expected that all of the cdks would utilize the same kinetic pathway. However, cdk4 differs from the other cdk family members in several respects. For example, olomoucine and roscovitine potently inhibit cdk2 and cdk5 but show little or no inhibition of cdk4. In addition, cdk4 has a narrow substrate specificity compared with cdk2 and cdk5 (
      • Meijer L.
      ). Differences in the kinetic mechanisms may contribute to these differences in substrate specificity and inhibitor sensitivity between cdk4 and cdk2 and cdk5.
      Defining the ways enzyme activity is controlled is an important step toward understanding the roles of cdk2 and cdk5 in vivo. Multiple mechanisms of regulation have been reported for these kinases. In the case of cdk2, activity is regulated via phosphorylation of key residues (Thr14, Tyr15, and Thr160) as well as by the availability of cyclins throughout the cell cycle. In addition, the endogenous inhibitory proteins (KIPs) contribute to the overall level of kinase activity (
      • Morgan D.
      ,
      • Pavletich N.P.
      ). Less is known about the regulation of cdk5 activity. Phosphorylation of the T loop is not required for cdk5 kinase activity, and endogenous inhibitory proteins have not been characterized (
      • Tang D.
      • Lee K.-Y.
      • Qi Z.
      • Matsuura I.
      • Wang J.H.
      ,
      • Poon Y.C.
      • Lew J.
      • Hunter T.
      ). The availability of p35 or p25 protein appears to be an important regulator of activity, and recent evidence suggests that the processing of p35 to p25 may result in increased kinase activity (
      • Lee M.-S.
      • Kwon Y.T.
      • Li M.
      • Peng J.
      • Friedlander R.M.
      • Tsai L.-H.
      ).
      An interesting aspect of the kinetic analysis of cdk2·GST-cyclin E and cdk5·GST-p25 is the demonstration of anticooperativity (α) between the two substrates, which suggests another level of regulation. The α factor values were greater than one for both enzymes, although there was much greater anticooperativity for cdk2, compared with cdk5. These values indicate that binding of the first substrate (either ATP or peptide) greatly increases the effective K m of the second substrate. For example, in the case of cdk2·GST-cyclin E, if the concentration of ATP was very low and held constant, then the apparent K m for the peptide substrate would approach a minimum of 4.6 μm. At high ATP concentrations, such as 1 mm, the apparent K m value for the peptide substrate would be increased almost 100-fold. Conversely, changes in the peptide substrate concentration would have a similar effect on the apparent K m for ATP. This anticooperativity may play an important role in regulating cdk enzyme activity in vivo, because it implies that the enzymatic activity, without reaching saturation, is spread out over a very large substrate concentration range. Our results indicate that the anticooperativity of binding of the substrates may represent another mechanism by which tight control is maintained over the activation state of cdk2 and cdk5.
      Values for α have been calculated for several other kinases acting via a random kinetic mechanism. For MEK, p38–2 MAPK, and Csk, an α factor of 1 has been reported (
      • Stein B.
      • Yang M.X.
      • Young D.B.
      • Janknecht R.
      • Hunter T.
      • Murray B.W.
      • Barbosa M.S.
      ,
      • Horiuchi K.Y.
      • Scherle P.A
      • Trzaskos J.M.
      • Copeland R.A.
      ,
      • Cole P.A.
      • Burn P.
      • Takacs B.
      • Walsh C.T.
      ). These results indicate that, for these kinases, binding of the first substrate does not influence binding of the second substrate. In contrast, for IκB kinase, the value of α is 0.11, indicating that the two substrates bind in a cooperative manner (
      • Burke J.R.
      • Miller K.R.
      • Wood M.K.
      • Meyers C.A.
      ). Posner et al. (
      • Posner I.
      • Engel M.
      • Levitzki A.
      ) analyzed the kinetic mechanism of the EGF receptor tyrosine kinase and showed that for the unactivated receptor, α equals 20, demonstrating anticooperativity. In contrast, for the EGF-activated receptor kinase, α was markedly reduced, with a value of ∼1. The authors suggest that EGF binding to the receptor induces conformational changes, which influence the binding of the substrates to the kinase (
      • Posner I.
      • Engel M.
      • Levitzki A.
      ). These results suggest that the activation state of the kinase is an important determinant in the degree of cooperativity of substrate binding. In the case of our cdk2·cyclin E experiments, the complex was purified from High-Five insect cells, which contain endogenous cdk-activating enzyme activity, resulting in an enzymatically active complex. It is not known whether this activation accurately mimics the conformational changes that occur upon activation in mammalian cells, but it could influence the value of α in our experiments. An additional factor, which may influence substrate cooperativity, is the substrate used in the assay. In our experiments a histone-derived peptide was used as the substrate. Further experiments are necessary to determine whether use of a more physiological protein substrate, such as the retinoblastoma protein for cdk2·cyclin E or the cytoskeletal protein tau for cdk5·p25, influences the anticooperative nature of the substrate binding.

      Acknowledgments

      The helpful suggestions and analyses of the kinetic data by Dr. Ferenc Kezdy and the assistance of Dr. Barry Finzel with the crystallography figures are gratefully acknowledged.

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