Computer analysis of enzyme-substrate-inhibitor kinetic data with automatic model selection using IBM-PC compatible microcomputers

A weighted nonlinear least-squares curve-fitting program, implemented in compiled BASIC for the IBM-PC is described to estimate the parameters of enzyme kinetics obeying Michaelis-Menten kinetics and seven inhibition models. The effects of the inhibitor on the maximal velocity (Vm) and the Michaelis-Menten constant (Km) are used to select automatically the most plausible model of inhibition and to calculate initial estimates of parameters. The program is used to demonstrate that the inhibition of carbamyl-phenylalanine hydrolase by the product phenylalanine is consistent with the pure mixed noncompetitive model.     

A semi-integrated method for the determination of enzyme kinetic parameters and graphical representation of the Michaelis-Menten equation

A semi-integrated method for the determination of the enzyme kinetics parameters (Km and V) and graphical representation of the Michaelis-Menten equation is proposed as a variation of determination of initial reaction rate (v) as a function of initial substrate concentration ([S]0). The method is based on the determination of the time required to exhaust half of the initial substrate concentration as a function of the initial substrate concentration. The advantages and limitations of this method are discussed.     

Optimization of urease immobilization onto non-porous HEMA incorporated poly(EGDMA) microbeads and estimation of kinetic parameters.

Jack bean urease (urea aminohydrolase, EC 3.5.1.5) was immobilized onto modified non-porous poly(ethylene glycol dimethacrylate/2-hydroxy ethylene methacrylate), (poly(EGDMA/HEMA)), microbeads prepared by suspension copolymerization for the potential use in hemoperfusion columns, not previously reported. The conditions of immobilization; enzyme concentration, medium pH, substrate and ethylene diamine tetra acetic acid (EDTA) presence in the immobilization medium in different concentrations, enzyme loading ratio, processing time and immobilization temperature were investigated for highest apparent activity. Immobilized enzyme retained 73% of its original activity for 75 days of repeated use with a deactivation constant kd = 3.72 x 10(-3) day(-1). A canned non-linear regression program was used to estimate the intrinsic kinetic parameters of immobilized enzyme with a low value of observable Thiele modulus (phi < 0.3) and these parameters were compared with those of free urease. The best-fit kinetic parameters of a Michaelis-Menten model were estimated as Vm = 3.318 x 10(-4) micromol/s mg bound enzyme protein, Km = 15.94 mM for immobilized, and Vm = 1.074 micromol NH3/s mg enzyme protein, Km = 14.49 mM for free urease. The drastic decrease in Vm value was attributed to steric effects, conformational changes in enzyme structure or denaturation of the enzyme during immobilization. Nevertheless, the change in Km value was insignificant for the unchanged affinity of the substrate with immobilization. For higher immobilized urease activity, smaller particle size and concentrated urease with higher specific activity could be used in the immobilization process.     

On true and apparent Michaelis constants in enzymology. III. Is it linear dependence between apparent michaelis constant and limiting rate and is it possible to determine the substrate constant value using this dependence?

The Slater-Bonner method which is used for graphic determination of substrate constant (Ks) by linear dependence of apparent Michaelis constant (Km(app)) on the limiting rate (V(app)) of enzyme-catalysed reactions with activator participation has been critically analysed. It has been shown that although it is possible to record the mechanisms of such reactions as a scheme similar to Michaelis-Menten model which allow to find correlation Km(app) and V(app) as equation Km(app) = Ks + V(app)/k1[E]0 ([E]0 is a total enzyme concentration, k1 is a rate constant of enzyme-substrate complex formation from free enzyme and substrate) in order to calculate Ks and individual rate constants (k1, k(-1)), but this approach for investigation of all reactions with activator participation ought not to be used. The above equation is not obeyed in general, it may be true for some mechanisms only or under certain ratios of kinetic parameters of enzyme-catalysed reactions.     

Structure and function of the two heads of the myosin molecule. IV. Physiological functions of various reaction intermediates in myosin adenosinetriphosphatase, studied by the interaction between actomyosin and 8-bromoadenosine triphosphate.

The kinetic properties of the hydrolyses of 8-Br ATP and 8-SCH3 ATP by myosin [EC 3.6.1.3] and actomyosin were compared with those of ATP, and the following results were obtained. The Ca-NTPase activities of myosin using these two ATP analogs as substrates were smaller than that of ATPase, and the NTPase activities toward these analogs were strongly suppressed by EDTA. The Mg-NTPase activities toward these analogs were higher in a medium of high ionic strength than in a medium of low ionic strength, in contrast to the activity of Mg-ATPase. These analogs did not produce any initial burst of Pi liberation, activation of myosin NTPase by F-actin, or superprecipitation of actomyosin. The interactions between 8-Br ATP and HMM, acto-HMM, actomyosin, and myofibrils were studied in detail in the presence of Mg2+ in medium of low ionic strength. The Michaelis constant, Km, and the maximum rate, Vm, of 8-Br ATPase of HMM were 27 muM and 21 min-1, respectively. The fluorescence change of HMM induced by 8-Br ATP also followed the Michaelis-Menten equation, and the Michaelis constant, Kf1, was as low as 4 muM. Acto-HMM and acto-S-1 were fully dissociated by the addition of 8-Br ATP. The relation between the extent of dissociation of acto-HMM and the concentration of 8-Br ATP followed the Michaelis-Menten equation, and the apparent dissociation constant, Kd, was 22 muM. This Kd value is almost equal to the Km value of 8-Br ATPase of HMM described above. Myofibrillar contraction was not supported by 8-Br ATP. It was concluded that in the myosin NTPase reaction with 8-Br ATP as a substrate, M2NTP but not MNDPP is formed in route (1), while MNTP is formed in route (2). It was also concluded that the key intermediate for the actomyosin NTPase reaction is MNDPP, and that dissociation of acto-HMM is induced by the formation of M2NTP and MNTP in routes (1) and (2), respectively.     

Malate Dehydrogenase and NAD Malic Enzyme in the Oxidation of Malate by Sweet Potato Mitochondria

Over a range of concentrations from less than 0.1 mm to more than 70 mm, sweet potato root mitochondria display a bimodal substrate saturation isotherm for malate. The high affinity portion of the isotherm has an apparent Km for malate of 0.85 mm and fits a rectangular hyperbolic function. The low affinity portion of the isotherm is sigmoid in character and gives an apparent S(0.5) of 40.6 mm and a Hill number of 3.7.Extracts of sweet potato mitochondria contain both malate dehydrogenase and NAD malic enzyme. The malate dehydrogenase, assayed in the forward direction at pH 7.2, shows typical Michaelis-Menten kinetics with a Km for malate of 0.38 mm. The NAD malic enzyme shows pronounced sigmoidicity in response to malate with a Hill number of 3.5 and an S(0.5) of 41.6 mm.On the basis of the normal kinetics, the Km, and the fact that oxaloacetate production from malate by mitochondria appears most active at low malate concentrations, the high affinity portion of the malate isotherm with mitochondria is attributed to malate dehydrogenase. The low affinity portion of the malate isotherm with mitochondria is thought, on the basis of the similarity of S(0.5) values, the Hill numbers, and the greater production of pyruvate from malate at high malate concentrations, to represent the activity of the NAD malic enzyme.     

A microscopic model of enzyme kinetics.

Many in vivo enzymatic processes, such as those of the tissue factor pathway of blood coagulation, occur in environments with facilitated substrate delivery or enzymes bound to cellular or lipid surfaces, which are quite different from the ideal fluid environment for which the Michaelis-Menten equation was derived. To describe the kinetics of such reactions, we propose a microscopic model that focuses on the kinetics of a single-enzyme molecule. This model provides the foundation for macroscopic models of the system kinetics of reactions occurring in both ideal and nonideal environments. For ideal reaction systems, the corresponding macroscopic models thus derived are consistent with the Michaelis-Menten equation. It is shown that the apparent Km is in fact a function of the mechanism of substrate delivery and should be interpreted as the substrate level at which the enzyme vacancy time equals the residence time of ES-complexes; it is suggested that our microscopic model parameters characterize more accurately an enzyme and its catalytic efficiency than does the classical Km. This model can also be incorporated into computer simulations of more complex reactions as an alternative to explicit analytical formulation of a macroscopic model.     

Characterization of the cyclic AMP-dependent protein kinase from rat pancreas, further purification of the catalytic subunit, substrate specificity, effect of the pancreatic heat stable inhibitor.

In order to investigate the sequence of events triggered by cyclic AMP and cyclic GMP in exocrine pancreatic cells, the identification of the various protein kinases possibly present in this tissue is of major interest. Further analysis of the two cyclic AMP-dependent protein kinases previously reported [11] suggests that KI is a degraded form of KII. It is therefore likely that a single holoenzyme is present in exocrine cells. In addition no protein kinase, specifically stimulated by cyclic GMP, has been detected in any fraction obtained in the course of purification of the cyclic AMP-dependent protein kinase. A faster and more efficient method than the one previously described [11] allows the purification (5000 times) of the protein kinase catalytic subunit. Analysis of the subunit by sodium dodecyl sulphate polyacrylamide gel electrophoresis indicates a molecular weight of 40 000 +/- 1 000. The enzyme phosphorylates specifically histone H2B (Vm = 236 min(-1), Km = 1.15 10(-5) M) and to a lesser extent H2A, H5 and H1 (Vm = 55--77 min(-1), Km 5--25 10(-5) M). Histones H3 and H4 are not phosphorylated. The effect of the heat stable inhibitor, extracted from rat pancreas, on the phosphorylation of H2B has been investigated. The inhibition is of the non competitive type with respect to ATP. The inhibition at various histone concentrations cannot be described by the Michaelis-Menten equation.     

蒸汽爆破玉米秸秆酶解动力学

为了掌握蒸汽爆破玉米秸秆的酶解特性,研究了不同底物浓度、酶浓度、温度对反应速率的影响。运用米氏方程对酶解动力学过程进行拟合,结果表明,纤维素酶对该玉米秸秆的水解反应在反应前3 h符合一级反应,可用米氏方程对其进行拟合。在转速为120 r/min、酶浓度为1.2 FPU/mL、pH 5.0、温度为45 ℃时米氏常数Km为11.71 g/L,最大反应速率Vm为1.5 g/(L·h)。确立了包括底物浓度、酶浓度、温度在内的酶解动力学模型,该模型适合温度为30 ℃~50 ℃。     

Validation and characterization of uninhibited enzyme kinetics performed in multiwell plates

Several systematic errors may occur during the analysis of uninhibited enzyme kinetic data using commercially available multiwell plate reader software. A MATLAB program is developed to remove these systematic errors from the data analysis process for a single substrate-enzyme system conforming to Michaelis-Menten kinetics. Three experimental designs that may be used to validate a new enzyme preparation or assay methodology and to characterize an enzyme-substrate system, while capitalizing on the ability of multiwell plate readers to perform multiple reactions simultaneously, are also proposed. These experimental designs are used to (i) test for enzyme inactivation and the quality of data obtained from an enzyme assay using Selwyn's test, (ii) calculate the limit of detection of the enzyme assay, and (iii) calculate Km and Vm values. If replicates that reflect the overall error in performing a measurement are used, the latter two experiments may be performed with internal estimation of the error structure. The need to correct for the systematic errors discussed and the utility of the proposed experimental designs were confirmed by numerical simulation. The proposed experiments were conducted using recombinant inducible nitric oxide synthase preparations and the oxyhemoglobin assay.     

基因工程菌1016氨基酰化酶的酶学性质研究

研究了基因工程菌 1 0 1 6所产的氨基酰化酶的酶学特性。该酶的拆分速率符合米氏方程 ,且在 0 .5mol/L的高底物浓度下 ,无底物抑制现象。 37℃时的米氏常数和最大反应速率分别为 0 .0 4 8mmol/L和 2 .1 78mmol/L·h。最适反应温度为 5 5℃。5 5℃时 ,Km为 0 .0 37mmol/L ,Vmax为 2 .5 5 8mmol/L·h。最适底物为乙酰蛋氨酸 ;热稳定性好。     

Calculation of inhibitor Ki and inhibitor type from the concentration of inhibitor for 50% inhibition for Michaelis-Menten enzymes

The use of I50 (concentration of inhibitor required for 50% inhibition) for enzyme or drug studies has the disadvantage of not allowing easy comparison among data from different laboratories or under different substrate conditions. Modifications of the Michaelis-Menten equation for treatment of inhibitors can allow both the determination of the type of inhibition (competitive, noncompetitive, and uncompetitive) and the Ki for the inhibitor. For competitive and uncompetitive inhibitors when the assay conditions are [S] = Km, then Ki = I50/2. For different conditions of [S] there is a divergence between competitive and uncompetitive inhibitors that may be used to identify the type of inhibitor. The equation for Ki also differs. For noncompetitive inhibitors the Ki = I50 and this relationship is valid with changing [S]. The equations developed require a single substrate, reversible-type inhibitors, and kinetics of the Michaelis-Menten type. Examples of the use of the equations are illustrated with experimental data from scientific publications.     

A method for writing enzyme rate equations: application to the estimation of the number and size of key proton families

We develop a method to derive the rate equation for enzyme models that include pH-dependent activation. Our presentation is based on a kinetic model recently described for sucrase, the three-key-proton model of Vasseur and coworkers, which considers the existence, in the acid ionization reaction, of two functionally distinct prototropic groups, respectively responsible for either V-type or K-type kinetic effects. In contrast, as concerns the basic ionization reaction, the model conforms to classical concepts of pH-dependent activation, whereby a single proton participates in either V-type or K-type effects but not in both at the same time. Enzymes with more than three key protons have been described, indicating that, rather than isolated protons, groups of protons should be considered, and therefore the model can be better described as a three-proton-family model, where a proton family is defined as one or several protons that are gained or lost as a block and perform the same kinetic function. The resulting model is treated here as a useful framework upon which other models can be built. To facilitate the writing of the rate equations, we define two new entities: (1) intralevel coefficients, which describe the various combinations of the enzyme with either the substrate(s), the allosteric effector(s), or both at a given protonation level, and (2) interlevel coefficients, which describe the interplay between the various protonation levels. The resulting rate equation can be used in a global fit procedure permitting in a single computer run the estimation of (1) the entire set of dissociation and microscopic ionization constants of the model, (2) the number and kinetic function of proton families characterizing the enzyme under consideration, and (3) the number of key protons constituting each family, which is derived from the derivatives of the kinetic parameters, Vm/Km, Vm, and Km.     

Lack of deviation from Michaelis--Menten kinetics for pig heart fumarase.

Studies of steady-state kinetics of fumarase in the usual substrate-concentration range from 0.1 Km to 10 Km and in the high substrate-concentration range from 10 Km to 200 Km are described. The purpose is to investigate reports of substrate inhibition and oscillatory kinetics. In the normal substrate-concentration range, no deviations from hyperbolic kinetics were found, and in the extended concentration range, up to more than 200 times the Km value, no substrate inhibition was demonstrated. A discussion of the discrepancies between the mentioned reports of deviations from the hyperbolic kinetics and the present findings is given.     

A hypothetical model of the influence of inorganic phosphate on the kinetics of pyruvate kinase

This paper presents a simple solution to the problem of approximating the calculated curve of reaction progress to the measured curve which is usually disturbed by initial oscillation of auxiliary lactate dehydrogenase (LDH) reaction. The experiments leading to the determination of the apparent Km for phosphoenolpyruvate (PEP) and Vm were performed. For precise estimation of kinetic parameters (Km and Vm) of the M1 isozyme of pyruvate kinase (PK), measured by coupling it to LDH reaction, the sequence of Michaelis-Menten for pyruvate kinase and second-order kinetics for lactate dehydrogenase reaction as well as a non-zero initial concentration of lactate was assumed. The functions of apparent Km and Vm of pyruvate kinase with respect to phosphate concentration, computed by an analysis of the total reaction progress curves, indicate that the reaction mixture contains an uncompetitive inhibitor of pyruvate kinase, and that the phosphate binds this inhibitor. The proposed simple mathematical model of pyruvate kinase Km and Vm increase by inorganic phosphate assumes that the pyridine nucleotides (NAD-derivatives) are kinase inhibitors. An approximate dissociation constant for pyridine nucleotides-phosphate complex and true Km of pyruvate kinase for PEP were estimated. The proposed model fits exactly the entire measured reaction process.     

The exponential model for a regulatory enzyme: its extension to describe catastrophic changes in function.

The exponential model for a regulatory enzyme (Ainsworth, 1977) is extended to describe catastrophic changes in function (as measured by the apparent association constant for the substrate under investigation) that are brought about by the binding of the substrate itself. The characteristics of the binding function are examined and an example of a protein reaction that might be described by the model is considered.     

Anomeric specificity and kinetics of glucokinase: theoretical unsuitability of the Hill equation

The kinetics of the low-Km hexokinase isoenzymes, which obey the Michaelis-Menten equation, can be established from the Km (Michaelis constant) and Vmax (maximal velocity) values for either equilibrated D-glucose or its alpha- and beta-anomers. In the case of the high-Km glucokinase isoenzyme, however, the sigmoidal substrate dependency and the competition between the two anomers of D-glucose do not allow, theoretically, to assign any meaningful value to either the Km, Vmax or n (Hill number) constants for equilibrated D-glucose. Thus, with equilibrated D-glucose, the concentration dependency fails to display a rectilinear relationship in the Hill plot. These observations illustrate the shortcomings of current biochemical studies in which the anomeric heterogeneity of D-glucose is ignored.     

Control of Growth Rate by Initial Substrate Concentration at Values Below Maximum Rate

The hyperbolic relationship between specific growth rate, mu, and substrate concentration, proposed by Monod and used since as the basis for the theory of steady-state growth in continuous-flow systems, was tested experimentally in batch cultures. Use of a Flavobacterium sp. exhibiting a high saturation constant for growth in glucose minimal medium allowed direct measurement of growth rate and substrate concentration throughout the growth cycle in medium containing a rate-limiting initial concentration of glucose. Specific growth rates were also measured for a wide range of initial glucose concentrations. A plot of specific growth rate versus initial substrate concentration was found to fit the hyperbolic equation. However, the instantaneous relationship between specific growth rate and substrate concentration during growth, which is stated by the equation, was not observed. Well defined exponential growth phases were developed at initial substrate concentrations below that required for support of the maximum exponential growth rate and a constant doubling time was maintained until 50% of the substrate had been used. It is suggested that the external substrate concentration initially present "sets" the specific growth rate by establishing a steady-state internal concentration of substrate, possibly through control of the number of permeation sites.     

Regulation of ketogenesis. Mitochondrial acetyl-CoA acetyltransferase from rat liver: initial-rate kinetics in the presence of the product CoASH reveal intermediary plateau regions

The analysis of the initial-rate kinetics of the liver mitochondrial acetyl-CoA acetyltransferase (acetoacetyl-CoA thiolase) in the direction of acetoacetyl-CoA synthesis under product inhibition was performed. 1. Acetyl-CoA acetyltransferase shows a hyperbolic response of reaction velocity to changes in acetyl-CoA concentrations with an apparent Km of 0.237 +/- 0.001 mM. 2. CoASH is a (non-competitive) product inhibitor with a Kis of 22.6 microM and shifts the apparent Km for acetyl-CoA to the physiological concentration of this substrate in mitochondria (S0.5 = 1.12 mM in the presence of 121 microM CoASH). 3. CoASH causes a transformation of the Michaelis-Menten kinetics into initial-rate kinetics with four intermediary plateau regions. 4. The product analogue desulpho-CoA triggers a negative cooperativity as to the dependence of the reaction velocity on the acetyl-CoA concentration. These product effects drastically desensitize the acetyl-CoA acetyltransferase in its reaction velocity response to the acetyl-CoA concentrations and simultaneously extend the substrate dependence range. Thus a control of acetoacetyl-CoA synthesis by the substrate is established over the physiological acetyl-CoA concentration range. We suggest that this control mechanism is the key in establishing the rates of ketogenesis.