Enzymatic reaction of silent substrates: kinetic theory and application to the serine protease chymotrypsin

Investigating the selectivity that an enzyme expresses toward its substrates can be technically challenging if reaction of these substrates is not accompanied by a conveniently monitored change in some physicochemical property. In this paper, we describe a simple method for determining steady-state kinetic parameters for enzymatic turnover of such "silent" substrates. According to this method, silent substrate S is allowed to compete for enzymic reaction with signal-generating substrate S*, whose conversion to product can be conveniently monitored. Full reaction progress curves are collected under conditions of [S*](o) < K(m)* and [S](o) >or= 3K(m). Progress curves collected under these conditions are characterized by an initial lag phase of duration tau that is followed by the pseudo-first-order reaction of S. Steady-state kinetic parameters for the silent substrate can be obtained by one of two methods. One method combines least-squares fitting with numerical integration of appropriate rate equations to analyze the progress curves, while the other method relies on direct graphical analysis in which K(m) is the value of [S](o) that reduces the control velocity by a factor of 2 and V(max) is shown to simply equal the ratio [S](o)/tau. We use these methods to analyze the alpha-chymotrypsin-catalyzed hydrolysis of silent substrate Suc-Ala-Phe-AlaNH(2) with signal generator Suc-Ala-Phe-pNA. From the curve-fitting method, k(c) = 0.9 +/- 0.2 s(-1) and K(m) = 0.4 +/- 0.1 mM, while by direct graphical analysis, k(c) = 1.1 +/- 0.1 s(-1) and K(m) = 0.51 +/- 0.03 mM. As validation of this new method, we show agreement of these values with those determined independently by HPLC analysis of the hydrolysis of Suc-Ala-Phe-AlaNH(2) by alpha-CT, where k(c) = 1.1 +/- 0.1 s(-1) and K(m) = 0.5 +/- 0.1 mM.     

Progress curves analysis as an alternative for exploration of activation-inhibition phenomena in cholinesterases

The kinetic behaviour of insect acetylcholinesterases deviates from the Michaelis-Menten pattern. These deviations are known as activation or inhibition at various substrate concentrations and can be more or less observable depending on mutations around the active site of the enzyme. Most kinetic studies on these enzymes still rely on initial rate measurements. It is demonstrated here that according to this method one of the deviations can be overlooked. We attempt to point out that in such cases a detailed step-by-step progress curves analysis is successful. The study is focused on two different methods of analysing progress curves: (i) the first one is based on an integrated initial rate equation which can sufficiently fit truncated progress curves under corresponding conditions; and (ii) the other one precludes the algebraic formulae, but uses numerical integration for searching a non analytical solution of ordinary differential equations describing a kinetic model. All methods are tested on three different acetylcholinesterase mutants from Drosophila melanogaster. The results indicate that kinetic parameters for the E107K mutant with highly expressive activation and inhibition can be well evaluated applying any analysis method. It is quite different for E107W and E107Y mutants where latent activation is present, but discovered only using one or the other progress curves analysis methods.     

Progress Curves Analysis as an Alternative for Exploration of Activation-inhibition Phenomena in Cholinesterases

The kinetic behaviour of insect acetylcholinesterases deviates from the Michaelis-Menten pattern. These deviations are known as activation or inhibition at various substrate concentrations and can be more or less observable depending on mutations around the active site of the enzyme. Most kinetic studies on these enzymes still rely on initial rate measurements. It is demonstrated here that according to this method one of the deviations can be overlooked. We attempt to point out that in such cases a detailed step-by-step progress curves analysis is successful. The study is focused on two different methods of analysing progress curves: (i) the first one is based on an integrated initial rate equation which can sufficiently fit truncated progress curves under corresponding conditions; and (ii) the other one precludes the algebraic formulae, but uses numerical integration for searching a non analytical solution of ordinary differential equations describing a kinetic model. All methods are tested on three different acetylcholinesterase mutants from Drosophila melanogaster. The results indicate that kinetic parameters for the E107K mutant with highly expressive activation and inhibition can be well evaluated applying any analysis method. It is quite different for E107W and E107Y mutants where latent activation is present, but discovered only using one or the other progress curves analysis methods.     

NMR for direct determination of K(m) and V(max) of enzyme reactions based on the Lambert W function-analysis of progress curves

(1)H NMR spectroscopy was used to follow the cleavage of sucrose by invertase. The parameters of the enzyme's kinetics, K(m) and V(max), were directly determined from progress curves at only one concentration of the substrate. For comparison with the classical Michaelis-Menten analysis, the reaction progress was also monitored at various initial concentrations of 3.5 to 41.8mM. Using the Lambert W function the parameters K(m) and V(max) were fitted to obtain the experimental progress curve and resulted in K(m)=28mM and V(max)=13μM/s. The result is almost identical to an initial rate analysis that, however, costs much more time and experimental effort. The effect of product inhibition was also investigated. Furthermore, we analyzed a much more complex reaction, the conversion of farnesyl diphosphate into (+)-germacrene D by the enzyme germacrene D synthase, yielding K(m)=379μM and k(cat)=0.04s(-1). The reaction involves an amphiphilic substrate forming micelles and a water insoluble product; using proper controls, the conversion can well be analyzed by the progress curve approach using the Lambert W function.     

Rapid determination of enzyme kinetics from fluorescence: overcoming the inner filter effect

Fluorescence change is convenient for monitoring enzyme kinetics. Unfortunately, it loses linearity as the absorbance of the fluorescent substrate increases with concentration. When the sum of absorbance at excitation and emission wavelengths exceeds 0.08, this inner filtering effect (IFE) alters apparent initial velocities, K(m), and k(cat). The IFE distortion of apparent initial velocities can be corrected without doing fluorophore dilution assays. Using the substrate's extinction coefficients at excitation and emission wavelengths, the inner filter effect can be modeled during curve fitting for more accurate Michaelis-Menten parameters. A faster and simpler approach is to derive k(cat) and K(m) from progress curves. Strategies to obtain reliable and reproducible estimates of k(cat) and K(m) from only two or three progress curves are illustrated using matrix metalloproteinase 12 and alkaline phosphatase. Accurate estimates of concentration of enzyme-active sites and specificity constant k(cat)/K(m) (from one progress curve with [S]相似文献   

Chorismate lyase: kinetics and engineering for stability

By removing the enolpyruvyl group from chorismate, chorismate lyase (CL) produces p-hydroxybenzoate (p-HB) for the ubiquinone biosynthetic pathway. We have analyzed CL by several spectroscopic and chemical techniques and measured its kinetic (kcat=1.7 s(-1), K(m)=29 microM) and product inhibition parameters (K(p)=2.1 microM for p-HB). Protein aggregation, a serious problem with wild type CL, proved to be primarily due to the presence of two surface-active cysteines, whose chemical modification or mutation (to serines) gave greatly improved solution behavior and minor effects on enzyme activity. CL is strongly inhibited by its product p-HB; for this reason activity and inhibition measurements were analyzed by both initial rate and progress curve methods. The results are consistent, but in this case where the stable enzyme-product complex rapidly becomes the predominant form of the enzyme, progress curve methods are more efficient. We also report inhibition measurements with several substrate and product analogs that give information on ligand binding interactions of the active site. The biological function of the unusual product retention remains uncertain, but may involve a mechanism of directed delivery to the membrane-bound enzyme that follows CL in the ubiquinone pathway.     

Time dependence of activation of muscle AMP-aminohydrolase by substrate and potassium ion

The kinetics of AMP-aminohydrolase, which under steady state conditions shows a typical sigmoid dependence of initial velocities versus substrate concentration, have been examined by rapid mixing methods. Using this technique it was observed that when substrate or substrate plus activator (K(+)) were mixed with enzyme, the rate of appearance of product markedly increased during the first few tenths of a second. The time course of this change in rate was taken to reflect the progress of activation by substrate or by K(+). On the other hand, addition of activator to enzyme prior to mixing with substrate gave process curves for the formation of product consistent with normal Michaelis-Menten behaviour.Under the conditions where the reaction was examined, the enzyme at time zero had less than 10% of the activity of the fully active enzyme. The time course for activation with K(+) followed a first order process with a rate constant of 10.6 sec(-1) at 20 degrees C. A simple mechanism consistent with the data and capable of explaining the sigmoid dependence of initial velocities versus substrate concentrations observed in steady state kinetics was proposed.     

Benzo(a)pyrene activation to 7,8-dihydrodiol 9,10-oxide by rat liver microsomes. Control by selective product inhibition

Metabolism of benzo(a)pyrene (BP) and 7,8-dihydrodiol by 3-methylcholanthrene (MC)-induced rat liver microsomes are both subject to severe inhibition by primary metabolites of BP, which was analyzed by determining individual inhibition constants for all primary BP metabolites for both BP and 7,8-dihydrodiol metabolism. Monooxygenation of 7,8-dihydrodiol was, surprisingly, 5 to 10 times more sensitive than monooxygenation of BP to inhibition by all primary metabolites, even though both reactions require the same enzyme, cytochrome P-450c. Two representative products, 1,6-quinone and 9-phenol, were both strong, competitive inhibitors of BP metabolism with Ki values of 0.12 and 0.74 microM, respectively. The total effect of product inhibition on the overall reactions was determined by fitting progress curves of BP, 7,8-dihydrodiol, and anti-7,8-dihydrodiol 9,10-oxide (determined as 7,10/8,9-tetrol) over a range of BP concentrations to integrated steady-state equations using experimental Vmax and Km values. The effective product inhibition factors for BP and 7,8-dihydrodiol metabolism, determined from progress curve fits, were only 2-fold higher than the corresponding calculated theoretical values. The effective product inhibition factors, obtained from progress curve analysis, confirmed that 7,8-dihydrodiol metabolism was substantially more sensitive to inhibition by primary BP metabolites than BP metabolism itself. This difference probably reflects the much higher affinity of cytochrome P-450c for BP (Kd = 6 nM), as compared to 7,8-dihydrodiol (Kd = 175 nM) that was established spectrophotometrically both for the purified cytochrome and for MC microsomes. The Km for BP metabolism is 50 to 100 times higher than the Kd, while the Km is similar to the Kd for 7,8-dihydrodiol metabolism. The discrepancy for BP between Km and Kd suggests that standard Michaelis-Menten kinetics may be perturbed by either slow substrate or product dissociation.     

The reliability of Michaelis constants and maximum velocities estimated by using the integrated Michaelis–Menten equation

1. Experimental progress curves were simulated for a reaction obeying Michaelis-Menten kinetics. 2. K(m) and V were estimated (a) by fitting the integrated Michaelis-Menten equation to the progress curves, and (b) from the initial slopes of the curves (i.e. from initial velocities). 3. The integrated equation could not be fitted successfully by a non-linear method, so it was transformed and fitted by a linear method. 4. Provided that the initial substrate concentration was greater than K(m) and the data were precise enough, the integrated equation gave parameter estimates which were unbiased and as reliable as those derived from initial velocities although based on fewer experiments. 5. The integrated equation could be used for progress curves of unknown origin.     

Compartment Analysis of Disease Progression in Time. II. Restricted Disease Increase

Three-compartmenl analysis was performed to describe the disease motion through presporulating (latent), sporulating (infectious) and postsporulating (removal) stages in the general case, where total disease increase is density dependent. A second-order Runge-Kutta method for numerical integration of the system of difterential equations was used to solve the equations. Total and postsporulating disease progress curves are S-shaped while latent and infectious disease progress in the form of optimum curves. The curve of a composite variable defined as total (latent and infectious) inoculum reservoir of the host progresses also in the form of an optimum curve showing a maxi at the total disease level y_t/K = 1 ? 1/iR, where K is the total population of infection sites, i is the infectious period, R the intrinsic infection rate and iR ≥ 1/(1 ? V_o/K). The size of this maxi is a monotone increasing function of the product iR by given initial disease level V_o. Condition iR =1/(1?y_o/K) is a threshold condition for total inoculum to increase over y_o, or alternatively a threshold condition for a rapid disease increase at the start resulting, possibly, in a large epidemic. Condition iR = O is a threshold condition for total disease to increase over initial disease level. Total disease reaches an asymptotic value less than unity if and only if infectious period is linite (existence of removals). In the compartment system there is a consistency regarding the threshold conditions for total disease to increase over initial disease level in the cases with and without a density-dependent factor. Conversely, in the Vanderplankian system of differential-difference equation the threshold conditions are iR = 0 and iR = 1 respectively due to the assumption of an exponential increase of total disease early in the epidemic. The particular cases without latent period and without removals are treated separately. The implications derived from the compartment analysis are compared with those derived from the Vanderplankian system of epidemiological analysis.     

Kinetics of suicide substrates. Practical procedures for determining parameters.

Many clinically important or mechanistically interesting inhibitors react with enzymes by a branched pathway in which inactivation of the enzyme and formation of product are competing reactions. The steady-state kinetics for this pathway [Waley (1980) Biochem. J. 185, 771-773] gave equations for progress curves that were cumbersome. A convenient linear plot is now described. The time (t1/2) for 50% inactivation of the enzyme (this is also the time for 50% formation of product), or for 50% loss of substrate, is measured in a series of experiments in which the concentration of inhibitor, [I]0, is varied; in these experiments the ratio of the concentration of enzyme to the concentration of inhibitor is kept fixed. Then a plot of [I]0 X t1/2 against [I]0 is linear, and the kinetic parameters can be found from the slope and intercept. Furthermore, simplifications of the equations for progress curves are described that are valid when the concentration of inhibitors is high, or is low, or when the extent of reaction is low. The use of simulated data has shown that the recommended methods are not unduly sensitive to experimental error.     

The use of the direct linear plot for determining initial velocities.

A new method is described for estimating initial velocities of enzyme-catalysed reactions. It is simple to apply either graphically or numerically, and is particularly appropriate for experiments in which the initial straight part of the progress curve is very short or non-existent. It requires no more knowledge than is readily available about the details of the system, such as the extent of reaction at equilibrium, the rate of enzyme inactivation, the nature of product inhibition etc., unlike some other methods of analysing progress curves, which are often invalidated by small errors in the defining assumptions.     

Application of logistic curve fitting to cell-mediated cytotoxicity tests

Blood mononuclear cells from 6 healthy adults were examined for LAK activity against 16 cell lines derived from human malignant tumors. The cytotoxicity curves obtained from a linear plot of the log of E/T ratio versus the percentage of the target cells killed were found to well fit the logistic curves. As the logistic distribution is known to approximate to the normal distribution, and the K/2 value is the function value for the representative, the K/2 value is reasonably selected as the % lysis value for the lytic unit calculation. Values of the three parameters, K as the maximum cytotoxicity, A as the scale parameter and B as the shape parameter, were analyzed using the experimental data. Eleven targets had three or more significantly fitted curves. Six among them were selected as highly sensitive cell lines to LAK activity, because the average values for K were higher than 80% (coefficients of variation were from 0.02 to 0.11) and analyzed further. The average values for B were relatively constant (range: 1.09-1.56) and the average values for A varied from 3.5 to 20.3 (conefficients of variation were from 0.26 to 0.71). The shape of the curves were nearly the same. These results indicate that the 6 cell lines are useful as the targets for the LAK activity.     

Kinetics and active site dynamics of Staphylococcus aureus arsenate reductase

Arsenate reductase (ArsC) encoded by Staphylococcus aureus arsenic-resistance plasmid pI258 reduces intracellular arsenate(V) to the more toxic arsenite(III), which is subsequently extruded from the cell. It couples to thioredoxin, thioredoxin reductase and NADPH to be enzymatically active. ArsC is extremely sensitive to oxidative inactivation, has a very dynamic character hampering resonance assignments in NMR and produces peculiar biphasic Michaelis-Menten curves with two V(max) plateaus. In this study, methods to control ArsC oxidation during purification have been optimized. Next, application of Selwyn's test of enzyme inactivation was applied to progress curves and reveals that the addition of tetrahedral oxyanions (50 mM sulfate, phosphate or perchlorate) allows the control of ArsC stability and essentially eliminates the biphasic character of the Michaelis-Menten curves. Finally, 1H-15N HSQC NMR spectroscopy was used to establish that these oxyanions, including the arsenate substrate, exert their stabilizing effect on ArsC through binding with residues located within a C-X5-R sequence motif, characteristic for phosphotyrosine phosphatases. In view of this need for a tetrahedral oxyanion to structure its substrate binding site in its active conformation, a reappraisal of basic kinetic parameters of ArsC was necessary. Under these new conditions and in contrast to previous observations, ArsC has a high substrate specificity, as only arsenate could be reduced ( Km=68 microM, k(cat)/ Km =5.2 x 10(4 )M-1s-1), while its product, arsenite, was identified as a mixed inhibitor ( K*iu=534 microM, K*ic=377 microM).     

Multiple parameter kinetic studies of the oxidative folding of reduced lysozyme

We have compared the oxidative renaturation of reduced hen egg white lysozyme promoted by Cu(II) + O2 with that promoted by a glutathione redox buffer. The progress curves for protein fluorescence, circular dicroism, thiol oxidation, hydrodynamic volume, and enzymic activity were determined for both regeneration systems. All of these processes were more rapid in the glutathione regeneration than in the copper-catalyzed. Comparison of the two systems was carried out by normalizing the progress curves with a coordinate system where "time" is replaced by "extent of protein thiol oxidation." While similar progress curves were obtained for circular dichroism, the two systems produced distinctly different progress curves for enzymic activity, fluorescence, and gel permeation chromatographic reflection of protein hydrodynamic volume. We infer that all these differences result from differences in relative amounts and/or kind of reaction intermediates. Thus, there are substantial differences between the renaturation mechanisms of the glutathione- and the copper-promoted systems.     

The use of chromogenic reference substrates for the kinetic analysis of penicillin acylases.

Determination of kinetic parameters of penicillin acylases for phenylacetylated compounds is complicated due to the low K(m) values for these substrates, the lack of a spectroscopic signal, and the strong product inhibition by phenylacetic acid. To overcome these difficulties, a spectrophotometric method was developed, with which kinetic parameters could be determined by measuring the effects on the hydrolysis of the chromogenic reference substrate 2-nitro-5-[(phenylacetyl)amino]benzoic acid (NIPAB). To that end, spectrophotometric progress curves with NIPAB in the absence and presence of the phenylacetylated substrates and their products were measured and analyzed by numerical fitting to the appropriate equations for competing substrates with product inhibition. This analysis yielded kinetic constants for phenylacetylated substrates such as penicillin G, which are in close agreement with those obtained in independent initial velocity experiments. Using NIPAB analogs with lower k(cat)/K(m) values, kinetic parameters for the hydrolysis of cephalexin and penicillin V were determined. This method was suitable for determining the kinetic constants of penicillin acylases in periplasmic extracts from Escherichia coli, Alcaligenes faecalis, and Kluyvera citrophila. The use of chromogenic reference substrates thus appears to be a rapid and reliable method for determining kinetic constants with various substrates and enzymes.     

Estimation of the initial velocity of enzyme-catalysed reactions by non-linear regression analysis of progress curves.

Most methods for studying the kinetic properties of an enzyme involve the determination of initial velocities. When the reaction progress curve shows significant curvature due to depletion of the substrate, accumulation of inhibitory products or instability of the enzyme, estimation of the initial velocity is a subjective and inexact process. Two methods have been suggested [Cornish-Bowden (1975) Biochem. J. 144, 305-312; Boeker (1982) Biochem J. 203, 117-123] that attempt to eliminate this subjective element. The present study offers a third alternative, which is based on fitting a reparameterized form of the integrated Michaelis-Menten equation to the progress curves by non-linear regression. This method yields estimates and standard errors of the initial velocity and of the time to reach 50% reaction. No prior knowledge of the apparent product concentration at zero time or infinite time is required, since both of these quantities are also estimated from the data. It is shown that this method yields reliable estimates of the initial velocity under a wide range of circumstances, including those where the two previously published methods perform poorly.     

Spectroscopic studies on proteinase K and subtilisin DY. Relation to X-ray models.

Circular dichroic spectroscopy has been used to study the effect of pH, guanidinium hydrochloride concentration and temperature on the conformation of the fungal subtilisin-like proteinase K and the bacterial DY. The ellipticity of the bands in the far ultraviolet region remains almost unchanged in the pH range 3.0-11.0 (PMS-proteinase K) and 5.0-10.0 (PMS-subtilisin DY). The same ranges of pH stability were determined from the pH dependence of the near ultraviolet dichroic spectra. Hence the changes in the tertiary and secondary structure occur in parallel. Proteinase K is considerably more stable at acidic and somewhat more stable at alkaline pH than subtilisin DY. At neutral pH proteinase K is more resistant to denaturation by guanidinium hydrochloride than is subtilisin DY. The midpoints of the denaturation curves were 6.2 M and 3.2 M guanidinium, respectively. The thermal unfolding of proteinase K occurred at a higher temperature than for subtilisin DY, the transition midpoints being 65 degrees and 48 degrees, respectively. Thus proteinase K is overall a much more robust molecule than subtilisin DY, showing greater resistance to all three forms of denaturation. The differences in the stability of the two proteinases can be partly explained by differences in their calcium binding sites.     

Quantitative determination of plasma vitamin K1 by high-performance liquid chromatography coupled to isotope dilution tandem mass spectrometry

Plasma vitamin K1 (phylloquinone) determination is commonly used for the diagnosis of vitamin K deficiency in patients suffering from lipid malabsorption. Moreover, current evidence that adequate vitamin K intake, and correspondingly adequate plasma vitamin K1 concentration, could also be of importance in relation to bone and brain diseases emphasizes the need to improve the current analytical methods. We developed a liquid chromatography coupled to tandem mass spectrometry method using a stable isotope ring-D4-labeled internal standard of vitamin K1 and operating in the multiple reaction monitoring mode by the selection of a precursor and product ions. The atmospheric pressure chemical ionization (APCI) method was shown to be more sensitive than electrospray ionization. After a single-step extraction with cyclohexane, chromatographic separation was performed on a C18 column with an isocratic mobile phase. The linearity was up to 5400 ng/L, and the limit of detection was 14 ng/L. Intra- and interrun precision were 2.4% and 8.3%, respectively, for the lower limit of the reference range. Recovery was better than 98%. The method is simple and reliable, allowing accurate vitamin K1 measurement in plasma samples from healthy subjects and patients suffering from vitamin K deficiency.     

Kinetics of ribulosebisphosphate carboxylase at high protein concentration

Kinetic parameters of ribulos-1,5-bisphosphate carboxylase/oxygenase (RuBP carboxylase) are usually evaluated in dilute solutions (less than 0.1 mg ml-1). Yet, this enzyme occurs in vivo at 100-200 mg ml-1 and a total protein concentration 300-400 mg ml-1. Enzymes can change their catalytic properties upon 'crowding'. Hence it became of interest to determine whether RuBP carboxylase elicits any properties not observable in dilute solution. Pre-steady state progress curves of fully activated enzyme showed an initial burst followed by a slower rate of product formation. The extent of the burst increased as concentration ratios of RuBP and RuBP carboxylase decreased. The burst corresponds to 1/8 turnover per holoenzyme or 1 turnover per active site. No discontinuity in progress curves was observed with partially activated enzyme.