Summary Degradation of ssrA‐tagged proteins is a central feature of protein‐quality control in all bacteria. In Escherichia coli , the ATP‐dependent ClpXP and ClpAP proteases are thought to participate in this process, but their relative contributions to degradation of ssrA‐tagged proteins in vivo have been uncertain because two adaptor proteins, ClpS and SspB, can modulate proteolysis of these substrates. Here, intracellular levels of these protease components and adaptors were determined during exponential growth and as cells entered early stationary phase. Levels of ClpA and ClpP increased about threefold during this transition, whereas ClpX, ClpS and SspB levels remained nearly constant. Using GFP‐ssrA expressed from the chromosome as a degradation reporter, the effects of altered concentrations of different protease components or adaptor proteins were explored. Both ClpXP and ClpAP degraded GFP‐ssrA in the cell, demonstrating that wild‐type levels of SspB and ClpS do not inhibit ClpAP completely. Upon entry into stationary phase, increased levels of ClpAP resulted in increased degradation of ssrA‐tagged substrates. As measured by maximum turnover rates, ClpXP degradation of GFP‐ssrA in vivo was significantly more efficient than in vitro . Surprisingly, ClpX‐dependent ClpP‐independent degradation of GFP‐ssrA was also observed. Thus, unfolding of this substrate by ClpX appears to enhance intracellular degradation by other proteases.
Switch I and II are key active site structural elements of kinesins, myosins, and G-proteins. Our analysis of a switch I mutant (R210A) in Drosophila melanogaster kinesin showed a reduction in microtubule affinity, a loss in cooperativity between the motor domains, and an ATP hydrolysis defect leading to aberrant detachment from the microtubule. To investigate the conserved arginine in switch I further, a lysine substitution mutant was generated. The R210K dimeric motor has lost the ability to hydrolyze ATP; however, it has rescued microtubule function. Our results show that R210K has restored microtubule association kinetics, microtubule affinity, ADP release kinetics, and motor domain cooperativity. Moreover, the active site at head 1 is able to distinguish ATP, ADP, and AMP-PNP to signal head 2 to bind the microtubule and release mantADP with kinetics comparable with wild-type. Therefore, the structural pathway of communication from head 1 to head 2 is restored, and head 2 can respond to this signal by binding the microtubule and releasing mantADP. Structural modeling revealed that lysine could retain some of the hydrogen bonds made by arginine but not all, suggesting a structural hypothesis for the ability of lysine to rescue microtubule function in the Arg210 mutant.
Conventional kinesin is a highly processive, plus-end-directed microtubule-based motor that drives membranous organelles toward the synapse in neurons. Although recent structural, biochemical, and mechanical measurements are beginning to converge into a common view of how kinesin converts the energy from ATP turnover into motion, it remains difficult to dissect experimentally the intermolecular domain cooperativity required for kinesin processivity. We report here our pre-steady-state kinetic analysis of a kinesin switch I mutant at Arg210 (NXXSSRSH, residues 205–212 in Drosophila kinesin). The results show that the R210A substitution results in a dimeric kinesin that is defective for ATP hydrolysis and a motor that cannot detach from the microtubule although ATP binding and microtubule association occur. We propose a mechanistic model in which ATP binding at head 1 leads to the plus-end-directed motion of the neck linker to position head 2 forward at the next microtubule binding site. However, ATP hydrolysis is required at head 1 to lock head 2 onto the microtubule in a tight binding state before head 1 dissociation from the microtubule. This mechanism optimizes forward movement and processivity by ensuring that one motor domain is tightly bound to the microtubule before the second can detach. Conventional kinesin is a highly processive, plus-end-directed microtubule-based motor that drives membranous organelles toward the synapse in neurons. Although recent structural, biochemical, and mechanical measurements are beginning to converge into a common view of how kinesin converts the energy from ATP turnover into motion, it remains difficult to dissect experimentally the intermolecular domain cooperativity required for kinesin processivity. We report here our pre-steady-state kinetic analysis of a kinesin switch I mutant at Arg210 (NXXSSRSH, residues 205–212 in Drosophila kinesin). The results show that the R210A substitution results in a dimeric kinesin that is defective for ATP hydrolysis and a motor that cannot detach from the microtubule although ATP binding and microtubule association occur. We propose a mechanistic model in which ATP binding at head 1 leads to the plus-end-directed motion of the neck linker to position head 2 forward at the next microtubule binding site. However, ATP hydrolysis is required at head 1 to lock head 2 onto the microtubule in a tight binding state before head 1 dissociation from the microtubule. This mechanism optimizes forward movement and processivity by ensuring that one motor domain is tightly bound to the microtubule before the second can detach. Kinesin is a highly processive, dimeric mechanoenzyme that travels along microtubules toward their plus-ends in discrete 8-nm steps, each step tightly coupled to a single ATP turnover (1.Howard J. Hudspeth A.J. Vale R.D. Nature. 1989; 342: 154-158Crossref PubMed Scopus (749) Google Scholar, 2.Schnitzer M.J. Block S.M. Nature. 1997; 388: 386-390Crossref PubMed Scopus (646) Google Scholar, 3.Hua W. Young E.C. Fleming M.L. Gelles J. Nature. 1997; 388: 390-393Crossref PubMed Scopus (281) Google Scholar). Recent evidence from a variety of experimental approaches has focused our attention to the proposal presented by Rice et al. (4.Rice S. Lin A.W. Safer D. Hart C.L. Naber N. Carragher B.O. Cain S.M. Pechatnikova E. Wilson-Kubalek E.M. Whittaker M. Pate E. Cooke R. Taylor E.W. Milligan R.A. Vale R.D. Nature. 1999; 402: 778-784Crossref PubMed Scopus (650) Google Scholar) that ATP binding induces a pronounced conformational change in the neck linker region, which docks the neck linker onto the catalytic core and propels the unattached kinesin head forward to find the next binding site on the microtubule. This model is based on a disorder-to-order transition in the neck linker region for monomeric kinesin constructs. The neck linker of the Mt·K 1The abbreviations used are: Mt·Kmicrotubule-kinesin complexMtmicrotubuleK401-wtkinesin heavy chain construct containing the N-terminal 401 amino acids of theDrosophila kinesin heavy chain genemantADP2′(3′)-O-(N-methylanthraniloyl)adenosine 5′-diphosphatemantATP2′(3′)-O-(N-methylanthraniloyl)adenosine 5′-triphosphateAMP-PNP5′-adenylyl imidodiphosphateATPγSadenosine 5′-O-(thiotriphosphate) complex was shown to be mobile in the presence of ADP, existing in an equilibrium with two predominant conformations trapped by cryo-electron microscopy. However, upon the addition of ATP or nonhydrolyzable ATP analogs to the Mt·K complex, the neck mobility ceased with the neck linker element tightly associated with the catalytic core. This ordered state was reversed by the addition of ADP or loss of nucleotide. In addition, the cryo-electron microscopy of this proposed ATP state revealed a single discrete orientation of the neck linker with the carboxyl terminus of the motor domain directed toward the plus-end of the microtubule (4.Rice S. Lin A.W. Safer D. Hart C.L. Naber N. Carragher B.O. Cain S.M. Pechatnikova E. Wilson-Kubalek E.M. Whittaker M. Pate E. Cooke R. Taylor E.W. Milligan R.A. Vale R.D. Nature. 1999; 402: 778-784Crossref PubMed Scopus (650) Google Scholar). microtubule-kinesin complex microtubule kinesin heavy chain construct containing the N-terminal 401 amino acids of theDrosophila kinesin heavy chain gene 2′(3′)-O-(N-methylanthraniloyl)adenosine 5′-diphosphate 2′(3′)-O-(N-methylanthraniloyl)adenosine 5′-triphosphate 5′-adenylyl imidodiphosphate adenosine 5′-O-(thiotriphosphate) Xing et al. (5.Xing J. Wriggers W. Jefferson G.M. Stein R. Cheung H.C. Rosenfeld S.S. J. Biol. Chem. 2000; 275: 35413-35423Abstract Full Text Full Text PDF PubMed Scopus (34) Google Scholar) have reported for a monomeric kinesin motor domain two discrete structural transitions induced by ADP binding and another produced by ATP binding. These three conformations revealed by fluorescence resonance energy transfer were consistent with the results reported by Rice et al. (4.Rice S. Lin A.W. Safer D. Hart C.L. Naber N. Carragher B.O. Cain S.M. Pechatnikova E. Wilson-Kubalek E.M. Whittaker M. Pate E. Cooke R. Taylor E.W. Milligan R.A. Vale R.D. Nature. 1999; 402: 778-784Crossref PubMed Scopus (650) Google Scholar). Furthermore, biochemical studies of dimeric kinesin have demonstrated that ATP binding (or nonhydrolyzable analogs of ATP) to one of the two kinesin heads will trigger ADP release from the other (6.Hackney D.D. Proc. Natl. Acad. Sci. 1994; 91: 6865-6869Crossref PubMed Scopus (307) Google Scholar, 7.Ma Y.Z. Taylor E.W. J. Biol. Chem. 1997; 272: 724-730Abstract Full Text Full Text PDF PubMed Scopus (166) Google Scholar, 8.Gilbert S.P. Moyer M.L. Johnson K.A. Biochemistry. 1998; 37: 792-799Crossref PubMed Scopus (154) Google Scholar). These pre-steady-state kinetics were the basis of the alternating site ATP hydrolysis model for kinesin motility. Another important contribution to our understanding of kinesin stepping was advanced by a molecular force clamp study that revealed a load-dependent isomerization that followed ATP binding (9.Schnitzer M.J. Visscher K. Block S.M. Nat. Cell Biol. 2000; 2: 718-723Crossref PubMed Scopus (470) Google Scholar). These results eliminated models in which ATP hydrolysis triggered the major conformational change for the 8-nm step and most loose coupling models, which predict that the ATP coupling ratio will decline with load. Therefore, the results from a variety of experimental approaches are converging into a model for kinesin plus-end directed motility and processivity. However, these studies have provided information predominantly for ATP-induced structural transitions. The results presented here focus on the role of ATP hydrolysis for motor domain coordination and tight coupling of ATP turnover with kinesin stepping. We present the kinetics of a dimeric kinesin motor construct in which the target amino acid, switch I Arg210, has been mutated to an alanine. The mutant kinesin motor, R210A, can be expressed and purified; therefore, we can evaluate the importance of Arg210 for ATP-dependent interactions that are required for ATP turnover and coordination of the motor domains. The results presented here show that the steady-state ATPase kinetics are dramatically reduced, yet ATP binding is comparable with wild type. R210A is defective for ATP hydrolysis, and the dissociation kinetics suggest that this mutant cannot detach from the microtubule, a step essential for microtubule-based movement. We propose a model in which ATP hydrolysis at the rearward head is required for the leading head to bind tightly to the microtubule, and this tight binding state of the forward head is required for rearward head dissociation. This strategy ensures forward motion of kinesin stepping and tight coupling of ATP turnover to movement. Radiolabeled ATP ([α-32P]ATP, >3000 Ci/mmol) was purchased from PerkinElmer Life Sciences, Paclitaxel (taxol, Taxus brevifolia) from Sigma, polyethyleneimine-cellulose F TLC plates (20 × 20 cm, plastic-backed; EM Science of Merck) from VWR Scientific (West Chester, PA). ATP, GTP, DEAE-Sephacel, and S-Sepharose from Amersham Biosciences. MantATP and mantADP were synthesized and characterized as described previously (8.Gilbert S.P. Moyer M.L. Johnson K.A. Biochemistry. 1998; 37: 792-799Crossref PubMed Scopus (154) Google Scholar, 10.Foster K.A. Gilbert S.P. Biochemistry. 2000; 39: 1784-1791Crossref PubMed Scopus (47) Google Scholar, 11.Woodward S.K.A. Eccleston J.F. Geeves M.A. Biochemistry. 1991; 30: 422-430Crossref PubMed Scopus (135) Google Scholar). The steady and pre-steady-state kinetic experiments were performed in ATPase buffer (20 mmHepes, pH 7.2, with KOH, 5 mm magnesium acetate, 0.1 mm EGTA, 0.1 mm EDTA, 50 mmpotassium acetate, 1 mm dithiothreitol) at 22–25 °C. All concentrations reported are final concentrations after mixing. The R210A kinesin mutant plasmid was constructed by introducing a single amino acid change in the K401-wt plasmid (12.Gilbert S.P. Johnson K.A. Biochemistry. 1993; 32: 4677-4684Crossref PubMed Scopus (77) Google Scholar) using the Chameleon Mutagenesis protocol (Stratagene). The arginine to alanine substitution at residue 210 was verified by DNA sequencing. The K401-wt motor contains the first 401 amino acids of the kinesin protein and when expressed is dimeric (13.Correia J.J. Gilbert S.P. Moyer M.L. Johnson K.A. Biochemistry. 1995; 34: 4898-4907Crossref PubMed Scopus (51) Google Scholar). The R210A plasmid was transformed into BL21(DE3)pLysS for expression in Escherichia coli and purification as described previously (14.Brendza K.M. Rose D.J. Gilbert S.P. Saxton W.M. J. Biol. Chem. 1999; 274: 31506-31514Abstract Full Text Full Text PDF PubMed Scopus (63) Google Scholar). The R210A protein concentration was determined by the Bradford method using Bio-Rad Protein Assay with IgG as a protein standard. It was also measured spectrophotometrically at A 280 (12.Gilbert S.P. Johnson K.A. Biochemistry. 1993; 32: 4677-4684Crossref PubMed Scopus (77) Google Scholar) based on the calculated extinction coefficient of 29,240m−1 cm−1 (26,740 protein + 2,500 ADP) and M r = 44,994 for R210A. Microtubules were polymerized from tubulin and stabilized with 20 μm taxol as previously described (12.Gilbert S.P. Johnson K.A. Biochemistry. 1993; 32: 4677-4684Crossref PubMed Scopus (77) Google Scholar). Sedimentation assays followed by SDS-PAGE confirmed that the microtubules were stable as the microtubule polymer. The concentrations of tubulin reported reflect the tubulin assembled into microtubules and stabilized with 20 μm taxol. The active site experiments were based on the binding of [α-32P]ATP (15.Gilbert S.P. Mackey A.T. Methods. 2000; 22: 337-354Crossref PubMed Scopus (67) Google Scholar). R210A (K·ADP) at 5 μm was reacted with trace amounts of [α-32P]ATP, and the reaction was quenched with 5m formic acid at various times ranging from 5 s to 100 min. The products [α-32P]ADP + Pi are separated from [α-32P]ATP by TLC and quantified. Because ADP product release is so slow, each active site under the conditions of the assay retains [α-32P]ADP. The data were fit to a single exponential function, [ADP]=A*exp(−kofft)+CEquation 1 where A is the amplitude and t is time. The rate constant, k off, represents the rate of ADP release from the active site in the absence of microtubules, and the constant term C provides the active site concentration. Steady-state ATPase measurements were determined by following the hydrolysis of [α-32P]ATP to form [α-32P]ADP·Pi as previously described (12.Gilbert S.P. Johnson K.A. Biochemistry. 1993; 32: 4677-4684Crossref PubMed Scopus (77) Google Scholar). These experiments were conducted as described previously (16.Foster K.A. Correia J.J. Gilbert S.P. J. Biol. Chem. 1998; 273: 35307-35318Abstract Full Text Full Text PDF PubMed Scopus (48) Google Scholar). R210A at 2 μm was incubated with 0–20 μm microtubules in the absence of added nucleotides for 30 min, followed by centrifugation. The microtubule pellet was resuspended in ATPase buffer to equal the volume of the supernatant. Gel samples of the supernatant and resuspended pellet were prepared in 5× Laemmli sample buffer and resolved by SDS-PAGE (8% acrylamide, 2 m urea). The gel was stained with Coomassie Blue, analyzed by a Microtek Scan Maker X6EL scanner (Microtek, Redondo Beach, CA), and quantified using NIH Image version 1.62 to determine the fraction of R210A in the supernatant and pellet at each microtubule concentration. In Fig. 3 fractional binding, defined as the ratio of R210A in the pellet to total R210A, is plotted as a function of microtubule concentration. The data were fit to quadratic Equation 2, [Mt·K]/[K]=0.5{([K]+[Mt0]+Kd)−[([K]+[Mt0]+Kd) 2Equation 2 −4([K][Mt0])] 1/2}where [Mt·K]/[K] is the fraction of R210A sedimenting with microtubules, [K] is total R210A, [Mt0] is the total tubulin concentration, and K d is the dissociation constant. These experiments were performed to determine the pre-steady-state kinetics of ATP hydrolysis for the switch I mutant in comparison with K401-wt (17.Gilbert S.P. Johnson K.A. Biochemistry. 1994; 33: 1951-1960Crossref PubMed Scopus (86) Google Scholar). The preformed Mt·R210A complex (syringe concentrations: 16 μm R210A, 30 μm microtubules, 40 μm taxol) was rapidly mixed in a chemical quench-flow instrument (Kintek Corp., Austin, TX) with [α-32P]ATP. The reaction was terminated with 5 m formic acid (syringe concentration) and expelled from the instrument. Radiolabeled ADP + Pi were separated from radiolabeled ATP by TLC, and the data were quantified. The concentration of [α-32P]ADP was determined for each reaction and plotted as a function of time (KaleidaGraph; Synergy Software, Reading, PA). The data were then fit to the burst equation, Product=A*[1−exp(−kbt)]+ksstEquation 3 where A is the amplitude of the pre-steady-state burst phase which represents the formation of [α-32P]ADP·Pi at the active site during the first turnover; k b is the rate constant of the exponential burst phase; t is time in seconds; andk ss is the rate constant of the linear phase (μm ADP·s−1). The rate constantk ss, when divided by enzyme concentration, corresponds to the rate of steady-state turnover at the same ATP and microtubule concentrations. Concentrations reported in the figure legends are final concentrations after mixing. The pre-steady-state kinetics of mantATP binding, mantADP release, R210A binding to microtubules, and detachment of R210A were all conducted using the SF-2001 Kintek stopped-flow instrument in ATPase buffer at 25 °C. For the mantATP and mantADP experiments, excitation was set at 360 nm (Hg arc lamp) with emitted light measured through a 400-nm cut-off filter (mant λem = 450 nm). The mantATP binding data in Fig. 5 A (inset) were fit to the following equation, kobs=k1[mantATP]+koffEquation 4 where k obs is the rate of first exponential increase in fluorescence, k 1 is the second-order rate constant for mantATP binding, andk off obtained from the y intercept is the rate of mantATP dissociation from the Mt·R210A·ATP complex. The microtubule association kinetics (Fig. 4) and the R210A dissociation kinetics (Fig. 7) were monitored by the change in turbidity at 340 nm. The exponential rate constants for microtubule association were plotted as a function of microtubule concentration and fit to Equation 5,kobs=k5[tubulin]+k−5Equation 5 where k obs is the rate of exponential process, k 5 is the second-order rate constant for microtubule association, and k −5 obtained from the y intercept is the rate constant for motor dissociation from the Mt·R210A complex.Figure 7ATP-promoted dissociation kinetics of Mt·R210A in comparison with Mt· K401-wt. A, the Mt·R210A complex (6 μm R210A, 6 μmtubulin) or the Mt·K401 complex (4 μm K401, 3.75 μm tubulin) was rapidly mixed with 1 mm MgATP plus 100 mm KCl. The Mt·K401 wild type data were fit to a double exponential function that provided the observed rate of dissociation at 16.3 ± 0.7 s−1. The R210A transient did not show a significant change in turbidity. B, the Mt·R210A complex (6 μm R210A, 6 μmtubulin) or the Mt·K401 complex (4 μm K401, 3.75 μm tubulin) was rapidly mixed with 1 mm MgATP but in the absence of the additional 100 mm KCl. The dissociation kinetics of K401-wt at 1.14 s−1 indicate that the wild type motor was in association with the microtubule for 0.88 s (transit time = 1/k obs). In contrast, R210A showed only a small turbidity change during the 30-s period of observation.View Large Image Figure ViewerDownload Hi-res image Download (PPT) We began the analysis of R210A by evaluating the mutant motor in the absence of microtubules to determine whether the mutant retained the fundamental enzymatic features of a kinesin: the ability to bind and hydrolyze ATP and to retain ADP tightly bound at the active site (Fig. 1). R210A was incubated with a trace amount of [α-32P]ATP. During the incubation, ADP tightly bound at the active site should be released, followed by the binding and hydrolysis of [α-32P]ATP to yield a stable R210A·[α-32P]ADP intermediate. The results presented in Fig. 1 show that R210A exhibits the ability to bind and hydrolyze ATP. The rate constant of [α-32P]ADP release from the active site was 0.05 s−1, and this rate is somewhat faster than data reported previously for conventional kinesin at 0.006–0.01 s−1 (12.Gilbert S.P. Johnson K.A. Biochemistry. 1993; 32: 4677-4684Crossref PubMed Scopus (77) Google Scholar, 18.Hackney D.D. Malik A.-S. Wright K.W. J. Biol. Chem. 1989; 264: 15943-15948Abstract Full Text PDF PubMed Google Scholar, 19.Sadhu A. Taylor E.W. J. Biol. Chem. 1992; 267: 11352-11359Abstract Full Text PDF PubMed Google Scholar, 20.Lockhart A. Cross R.A. McKillop D.F.A. FEBS Lett. 1995; 368: 531-535Crossref PubMed Scopus (36) Google Scholar). This assay permitted the determination of R210A active site concentration at 4.6 μm. Therefore, these results document the ability of mutant R210A to bind and hydrolyze ATP followed by slow ADP release. Thus, in the absence of microtubules, R210A exhibits the characteristics expected of wild-type kinesin. The steady-state kinetics of R210A were determined in comparison with the kinetics of K401-wt (Fig. 2). The steady-state ATPase kinetics for the Mt·R210A complex were significantly altered in comparison with K401-wt as follows: R210A (seven preparations),k cat = 0.12 ± 0.05 s−1(0.07–0.15 s−1), K m(ATP) = 118 ± 62.7 μm (75–211 μm)versus K401-wt, k cat = 20–25 s−1, K m(ATP) = 60–96 μm. There are several hypotheses that can account for the extremely lowk cat of R210A. The first is that there is a defect in ATP turnover. The second hypothesis is that there is a problem with microtubule binding that will affect release of ADP from the active site of the mutant. The third hypothesis is that the protein was inactive and the small amount of ATP hydrolysis seen was due to a few active motors still functioning. However, the third hypothesis appears unlikely based on the results of the active site assay (Fig. 1), which confirmed that R210A was active and exhibited the characteristics of wild type kinesin in the absence of microtubules. The experiments presented below evaluate ATP binding and ATP hydrolysis, microtubule association and detachment, and microtubule-activated product release. One possible explanation for the depressed ATPase activity may be that microtubule binding and therefore Mt·R210A complex formation is aberrant. We evaluated formation of Mt·R210A complex by equilibrium binding (Fig. 3) and the pre-steady-state kinetics of Mt·R210A association (Fig. 4). The relative affinity of R210A for microtubules was determined by equilibrium binding in which R210A was incubated with increasing concentrations of microtubules, followed by centrifugation and analysis by SDS-PAGE. Fig. 3 shows that R210A partitioned with microtubules as a function of tubulin concentration, and the fit of the data provided an apparent K d(Mt) = 0.95 μmtubulin with maximal fractional binding at 92%. The fact that the fractional binding is almost 100% suggests that the mutant motor can bind microtubules. However, the K d at 0.95 μm for R210A is weaker than the K ddetermined for the Mt·K401-wt complex at 37 nm (21.Moyer M.L. Mechanism of the Microtubule Kinesin Motor ATPasePh.D. thesis. Pennsylvania State University, University Park, PA1998Google Scholar). R210A was rapidly mixed with microtubules in the stopped-flow instrument, and the turbidity signal was monitored to quantify Mt·R210A complex formation. The results presented in Fig. 4 show that the rate of microtubule association increased linearly as a function of microtubule concentration with the second-order rate constant,k +5 = 0.8 μm−1s−1 and k −5 = 5.8 s−1(Scheme 1, Table I). The kinetics for K401-wt have been reported at 10–20 μm−1s−1 with no evidence of an off rate (Table I) (22.Gilbert S.P. Webb M.R. Brune M. Johnson K.A. Nature. 1995; 373: 671-676Crossref PubMed Scopus (248) Google Scholar, 23.Moyer M.L. Gilbert S.P. Johnson K.A. Biochemistry. 1998; 37: 800-813Crossref PubMed Scopus (127) Google Scholar, 24.Mandelkow E. Johnson K.A. Trends Biochem. Sci. 1998; 23: 429-433Abstract Full Text Full Text PDF PubMed Scopus (62) Google Scholar). Therefore, the association kinetics clearly indicate that formation of the Mt·R210A complex is defective. Both the association kinetics and the equilibrium binding results show that the affinity of R210A for microtubules is weaker than observed for K401-wt.Table IMicrotubule-kinesin constantsExperimentally observedComputer simulation: K401-wtRate constants descriptionsR210AK401-wtk 1ATP binding1-aMantATP binding (23).1-bPulse-chase rapid quench (17).0.82 μm−1s−11-aMantATP binding (23).1.1 μm−1s−11-aMantATP binding (23).1-bPulse-chase rapid quench (17).2 μm−1s−11-aMantATP binding (23).1-bPulse-chase rapid quench (17).1-cExperimentally determined rate constants refined by computer simulation (8, 23, 24).Maximumk obs/K 0.5(ATP)81 s−1/9 μmATP1-aMantATP binding (23).200 s−1/65 μm ATP1-bPulse-chase rapid quench (17).k −1ATP dissociation1-bPulse-chase rapid quench (17).200 s−11-bPulse-chase rapid quench (17).120 s−11-bPulse-chase rapid quench (17).1-cExperimentally determined rate constants refined by computer simulation (8, 23, 24).k 2Acid quench<0.2 s−1100 s−1100 s−11-cExperimentally determined rate constants refined by computer simulation (8, 23, 24).k 3ATP-promoted microtubule dissociation1-dTurbidity (22).No dissociation12–16 s−11-dTurbidity (22).50 s−11-cExperimentally determined rate constants refined by computer simulation (8, 23, 24).1-dTurbidity (22).k 4Pirelease1-eN-[2-(1-Maleimidyl)ethyl]-7-(diethylamino)coumarin-3-carboxamide (MDCC)-phosphate-binding protein (22, 23).13 s−11-eN-[2-(1-Maleimidyl)ethyl]-7-(diethylamino)coumarin-3-carboxamide (MDCC)-phosphate-binding protein (22, 23).>150 s−11-cExperimentally determined rate constants refined by computer simulation (8, 23, 24).1-eN-[2-(1-Maleimidyl)ethyl]-7-(diethylamino)coumarin-3-carboxamide (MDCC)-phosphate-binding protein (22, 23).k 5Microtubule association1-dTurbidity (22).0.8 μm−1 s−110–20 μm−1s−11-dTurbidity (22).11 μm−1s−11-cExperimentally determined rate constants refined by computer simulation (8, 23, 24).k 6ADP release both heads1-fMantADP competed with excess unlabeled MgATP, MgAMP-PNP, or MgADP (8, 22, 23, 50).ATP: 57 s−1>200 s−11-fMantADP competed with excess unlabeled MgATP, MgAMP-PNP, or MgADP (8, 22, 23, 50).300 s−11-cExperimentally determined rate constants refined by computer simulation (8, 23, 24).ADP release head 21-fMantADP competed with excess unlabeled MgATP, MgAMP-PNP, or MgADP (8, 22, 23, 50).ATP: 30–42 s−1ATP: >100 s−1200 s−11-cExperimentally determined rate constants refined by computer simulation (8, 23, 24).1-fMantADP competed with excess unlabeled MgATP, MgAMP-PNP, or MgADP (8, 22, 23, 50).AMP-PNP: 30–40 s−1AMP-PNP: 30–40 s−1ADP: 25 s−1ADP: 6 s−1k cat0.07–0.2 s−120–25 s−1K m(ATP)75–210 μm61–96 μmK d(Mt)950 nm37 nm1-gK d(Mt) (21).1-a MantATP binding (23.Moyer M.L. Gilbert S.P. Johnson K.A. Biochemistry. 1998; 37: 800-813Crossref PubMed Scopus (127) Google Scholar).1-b Pulse-chase rapid quench (17.Gilbert S.P. Johnson K.A. Biochemistry. 1994; 33: 1951-1960Crossref PubMed Scopus (86) Google Scholar).1-c Experimentally determined rate constants refined by computer simulation (8.Gilbert S.P. Moyer M.L. Johnson K.A. Biochemistry. 1998; 37: 792-799Crossref PubMed Scopus (154) Google Scholar, 23.Moyer M.L. Gilbert S.P. Johnson K.A. Biochemistry. 1998; 37: 800-813Crossref PubMed Scopus (127) Google Scholar, 24.Mandelkow E. Johnson K.A. Trends Biochem. Sci. 1998; 23: 429-433Abstract Full Text Full Text PDF PubMed Scopus (62) Google Scholar).1-d Turbidity (22.Gilbert S.P. Webb M.R. Brune M. Johnson K.A. Nature. 1995; 373: 671-676Crossref PubMed Scopus (248) Google Scholar).1-e N-[2-(1-Maleimidyl)ethyl]-7-(diethylamino)coumarin-3-carboxamide (MDCC)-phosphate-binding protein (22.Gilbert S.P. Webb M.R. Brune M. Johnson K.A. Nature. 1995; 373: 671-676Crossref PubMed Scopus (248) Google Scholar, 23.Moyer M.L. Gilbert S.P. Johnson K.A. Biochemistry. 1998; 37: 800-813Crossref PubMed Scopus (127) Google Scholar).1-f MantADP competed with excess unlabeled MgATP, MgAMP-PNP, or MgADP (8.Gilbert S.P. Moyer M.L. Johnson K.A. Biochemistry. 1998; 37: 792-799Crossref PubMed Scopus (154) Google Scholar, 22.Gilbert S.P. Webb M.R. Brune M. Johnson K.A. Nature. 1995; 373: 671-676Crossref PubMed Scopus (248) Google Scholar, 23.Moyer M.L. Gilbert S.P. Johnson K.A. Biochemistry. 1998; 37: 800-813Crossref PubMed Scopus (127) Google Scholar, 50.Brendza K.M. Sontag C.A. Saxton W.M. Gilbert S.P. J. Biol. Chem. 2000; 275: 22187-22195Abstract Full Text Full Text PDF PubMed Scopus (19) Google Scholar).1-g K d(Mt) (21.Moyer M.L. Mechanism of the Microtubule Kinesin Motor ATPasePh.D. thesis. Pennsylvania State University, University Park, PA1998Google Scholar). Open table in a new tab The kinetics of ATP binding were evaluated by rapidly mixing in the stopped-flow instrument the Mt·motor complex (15 μm tubulin plus 2 μm R210A or K401-wt) with increasing concentrations of the fluorescent ATP analog, mantATP (Fig. 5). The kinetics reveal a biphasic fluorescence enhancement. Because there is an increase in fluorescence as mantATP enters the more hydrophobic environment of the active site, we assume the initial rapid phase of fluorescence enhancement is mantATP binding to the active site. At low mantATP concentrations (<50 μm), the observed rate of the first exponential phase increased linearly as a function of mantATP concentration and provided the second-order rate constant, k +1 = 0.82 μm−1 s−1 with a dissociation rate of 26.9 s−1 (Scheme 1, Table I). For the Mt·K401-wt complex, mantATP binding was reported at 1.1 μm−1 s−1 with a dissociation rate of 9.8 s−1 (23.Moyer M.L. Gilbert S.P. Johnson K.A. Biochemistry. 1998; 37: 800-813Crossref PubMed Scopus (127) Google Scholar). ATP binding for wild type kinesin is believed to involve two steps (Scheme 2) based on our pulse-chase rapid quench kinetics with K401-wt (17.Gilbert S.P. Johnson K.A. Biochemistry. 1994; 33: 1951-1960Crossref PubMed Scopus (86) Google Scholar) and the mantATP binding kinetics reported by Ma and Taylor for human kinesin K379 (25.Ma Y.-Z. Taylor E.W. Biochemistry. 1995; 34: 13242-13251Crossref PubMed Scopus (103) Google Scholar). In the first step, the collision complex is formed (Mt·K·ATP), followed by a rate-limiting conformational change at 200 s−1 to form the Mt·K*·ATP intermediate that proceeds toward ATP hydrolysis. The kinetics for R210A indicate that the required conformational change does occur; however, the rate constant observed is 81 s−1. These data suggest that the ATP-driven structural transition required for ATP hydrolysis is slowed significantly in the mutant. Although the mantATP binding results indicate that the mutant was able to bind ATP effectively, the chemistry step of ATP hydrolysis was clearly aberrant. For the ATP hydrolysis kinetics (Fig. 6), a preformed Mt·R210A complex was rapidly mixed with [α-32P]ATP in the rapid quench instrument, followed by an acid quench to terminate the reaction and release nucleotide at the active site. The kinetics for K401-wt showed the expected, dramatic exponential burst of ADP·Piproduct formation at the active site during the first turnover because ATP binding and hydrolysis are fast steps for kinesin relative to the rate-limiting step in the pathway (17.Gilbert S.P. Johnson K.A. Biochemistry. 1994; 33: 1951-1960Crossref PubMed Scopus (86) Google Scholar, 25.Ma Y.-Z. Taylor E.W. Biochemistry. 1995; 34: 13242-13251Crossref PubMed Scopus (103) Google Scholar). Note that R210
A potential source of uncertainty within multi-objective design problems can be the exact value of the underlying design constraints. This uncertainty will affect the resulting performance of the selected system commensurate with the level of risk that decision-makers are willing to accept. This research focuses on developing visualization tools that allow decision-makers to specify uncertainty distributions on design constraints and to visualize their effects in the performance space using multidimensional data visualization methods to solve problems with high orders of computational complexity. These visual tools will be demonstrated using an example portfolio design scenario in which the goal of the design problem is to maximize the performance of a portfolio with an uncertain budget constraint.
Abstract Acute compartment syndrome of the lower extremity is typically associated with some form of trauma, either fracture or blunt injury. Accurate diagnosis and urgent treatment of this condition is required for preservation of the viability of the limb. We report the case of a 73‐year‐old man who developed an acute compartment syndrome of the leg after diagnostic electromyography. Potential causes and treatment are discussed. Muscle Nerve 27: 374–377, 2003
