Kinetic co-operativity of monomeric mnemonical enzymes. The significance of the kinetic Hill coefficient

The expression of the kinetic Hill coefficient for a two-substrate, two-product mnemonical enzyme has been derived. Its relation with the gamma coefficient, that is the slope of the reciprocal plots for 1/[A]----O, has been established. The variation of this Hill coefficient, as a function of the second substrate and product concentrations, has been studied theoretically. Whereas the gamma coefficient does not vary as a function of the substrate and first product concentrations, the kinetic Hill coefficient does. If the enzyme is positively co-operative, the Hill coefficient increases upon increasing the second substrate concentration and decreases if the first product concentration is increased. The converse is expected to occur if the enzyme displays a negative co-operativity. The last product may either reverse a positive co-operativity into a negative one or, alternatively, strengthen an already negative co-operativity. The co-operativity generated by the mnemonical model has been compared to the kinetic behaviour of a random model. These two models have been shown to be discriminated on the basis of the departure they show with respect to the Michaelis-Menten behaviour. These theoretical considerations have been applied to previously published data, obtained with wheat germ hexokinase LI. This monomeric enzyme has a negative co-operativity with respect to the preferred substrate, glucose. The Hill coefficient decreases with MgATP concentration, increases with MgADP concentration and decreases with glucose-6-phosphate concentration. This is exactly what is to be expected on the basis of the above theory of kinetic co-operativity.     

On the optimal control of fed-batch reactors with substrate-inhibited kinetics

The optimal feed rate profiles, for fed-batch fermentation that maximizes the biomass production and accounts for time, are analyzed. The solution can be found only if the final arc of the optimal control is a batch arc, since in this case the final concentrations of substrate and biomass can be determined by ulterior conditions on the mass balance and on the final growth rate of biomass and thus it is possible to solve the resulting time optimal problem by using Green's theorem. This evidences the "turnpike property" of the solution, which tries to spend the maximum time on or at least near the singular arc along which the substrate concentration is maintained constant. The optimality of the final batch arc is related to the time operational cost in the performance index. The sequence of the control depends on the initial conditions for which six different regions, with the respective patterns, have been identified, in case the performance index allows the control sequence to have a final batch.     

The metalloproteolytic activity of the anthrax lethal factor is substrate-inhibited

The anthrax lethal factor (LF) is a Zn2+ endopeptidase specific for mitogen-activated protein kinase kinases (MAPKKs), which are cleaved within their N termini. Here, the proteolytic activity of LF has been investigated using novel chromogenic MAPKK-derived peptide substrates, which allowed us to determine the kinetic parameters of the reaction. LF displayed maximal proteolytic activity at the pH and temperature values of the cell cytosol, which is its site of action. LF undergoes substrate inhibition, in keeping with the non-productive binding geometry of the MAPPK-2 N terminus to LF.     

Hill coefficient for estimating the magnitude of cooperativity in gating transitions of voltage-dependent ion channels

A frequently used measure for the extent of cooperativity in ligand binding by an allosteric protein is the Hill coefficient, obtained by fitting data of initial reaction velocity (or fractional binding saturation) as a function of substrate concentration to the Hill equation. Here, it is demonstrated that the simple two-state Boltzmann equation that is widely used to fit voltage-activation data of voltage-dependent ion channels is analogous to the Hill equation. A general empiric definition for a Hill coefficient (n(H)) for channel gating transitions that is analogous to the logarithmic potential sensitivity function of Almers is derived. This definition provides a novel framework for interpreting the meaning of the Hill coefficient. In considering three particular and simple gating schemes for a voltage-activated cation channel, the relation of the Hill coefficient to the magnitude and nature of cooperative interactions along the reaction coordinate of channel gating is demonstrated. A possible functional explanation for the low value of the Hill coefficient for gating transitions of the Shaker voltage-activated K(+) channel is suggested. The analogy between the Hill coefficients for ligand binding and for channel gating transitions further points to a unified conceptual framework in analyzing enzymes and channels behavior.     

Steroid metabolising enzymes in the determination of brain gender

The neurotrophic effects of oestrogen formed in the brain are important in brain sexual differentiation of the central nervous system and behaviour. Aromatase, converting testosterone to oestradiol-17β, is a key enzyme involved in brain development. In primary cell cultures of foetal hypothalamus, we have found that male neurones consistently have higher aromatase activity than in the female. Using a specific antibody to the mouse aromatase, immunoreactivity was localized in the neural soma and neurites in hypothalamic cultures. Additionally more male foetal hypothalamus neurones express aromatase than in the female. Testosterone increases aromatase activity in parallel with a greater number of aromatase-immunoreactive neurones. Testosterone also increases soma size, neurite length, and branching of cultured hypothalamic neurones. The neuronal aromatase activity appears to be sensitive to the inductive effects of androgen only during the later stages of foetal development. Endogenous inhibitors of the aromatase are also likely to have a regulatory role. This work suggests that regulation of a network of aromatase neurones, sensitive to the hormonal environment of the hypothalamus, may determine when oestrogens are available for neurotrophic effects underlying brain differentiation.     

Microphotometric determination of enzymes in brain sections

Summary An incubation medium was adapted for the microphotometric determination (kinetic and end-point measurements) of the activities of mitochondrial alpha-glycerophosphate dehydrogenase (GPDH) in the rat hippocampus. For comparison, the activities of the cytoplasmic NAD-linked alpha-glycerophosphate dehydrogenase were also measured. The study showed that in the demonstration of both enzymes the use of an exogenous electron carrier is necessary. Both enzymes react to phenazine methosulfate (PMS) which transfers reduction equivalents to the electron acceptor nitroblue tetrazolium chloride (NBT), thus causing a coreaction of GPDH in the demonstration of NAD-GPDH. Therefore, only the NAD-independent GPDH which is stimulated by menadione, can be selectively demonstrated in the histochemical procedure applied. The final incubation medium of GPDH consisted of 15 mMl-glycerol 3-phosphate, 5 mM NBT, 0.4 mM menadione, 7.5% polyvinyl alcohol in 0.05 M Hepes buffer, pH 8; the final pH of the incubation medium was 7.5. A linear response of the reaction lasted about 5 min. There was a linear relationship between section thickness and the formation of reaction product up to a section thickness of 14 microns. The apparent K_m value at 25°C was 0.6 mM. It is concluded that using menadione histochemical methods are suited to determine the mitochondrial GPDH activities in brain sections whereas using PMS a coreaction of GPDH takes place in the demonstration of NAD-GPDH, so that a histochemical quantification of NAD-GPDH cannot be recommended.     

Microphotometric determination of enzymes in brain sections

Summary An incubation medium was established for the microphotometric demonstration of glutamate dehydrogenase (Gldh) in cryostat sections of the rat hippocampus which served as an exemplary brain region. The final incubation medium consisted of 100 mM l-glutamic acid monosodium salt, 5 mM NAD, 10 mM sodium azide (NaN₃), 5 mM ADP, 20 mM sodium chloride, 0.15 mM phenazine methosulfate (PMS), 5 mM nitroblue tetrazolium chloride and 22% polyvinyl alcohol (PVA) in 0.05 M Hepes buffer; the final pH was 7.5. — The study showed that in the histochemical demonstration of Gldh the use of relatively high PVA concentrations were necessary to avoid diffusion artefacts because Gldh seems to be only loosely bound to the mitochondrial matrix. The use of NaN₃ as a blocker of the respiratory chain was indispensible, because without NaN₃ most reduction equivalents were lost through the respiratory chain. With PMS as an exogenous electron carrier, the demonstrable Gldh activities increased significantly indicating that, in the case of Gldh, the endogenous NADH tetrazolium reductase was not sufficiently effective. Furthermore, it was shown that Gldh was affected by many small molecules (e.g. activation by sodium ions, inhibition by magnesium and calcium ions) so that minor variations of the incubation conditions may cause major differences in demonstrable activities. Supported by the Deutsche Forschungsgemeinschaft (Ku 541/2-2)     

Microphotometric determination of enzymes in brain sections

Summary A histochemical procedure was established for the microphotometric determination of hexokinase (HK) in sections of the rat hippocampus, which served as an exemplary brain region. For this quantitative procedure, slides were coated with glucose 6-phosphate dehydrogenase (G6PDH) as an auxiliary enzyme and sections were mounted onto this enzyme film. The sections were then incubated with the following adapted incubation medium: 5 mM d-glucose, 1.5 mM NADP, 7.5 mM ATP, 4 mM nitroblue tetrazolium chloride, 10 mM NaN₃, 10 mM MgCl₂, 0.25 mM phenazine methosulfate, 1 U/ml G6PDH, 22% polyvinyl alcohol in 0.05 M Hepes buffer; the final pH was 7.5. A linear response of the reaction was observed in the initial 10 min of reaction (kinetic and end-point measurements). The relationship between HK activity and section thickness was linear up to 5 m. The need for such thin sections is discussed in relation to the limited penetration of the auxiliary enzyme into the section. It is concluded that the quantitative demonstration of HK in brain sections could be a valuable tool for studying the local metabolic entrance of glucose in the glycolytic pathway.Supported by the Deutsche Forschungsgemeinschaft (Ku 541/2-1, 2-2)     

A method for the determination of the molar extinction coefficient of structure-linked chromophores

Synopsis This paper describes a general method for the determination of the molar extinction ceefficient of a chromophore covalently bound to structure-linked groups, without isolating the compound formed. The method is illustrated by the determination of the molar extinction coefficient of the reaction product of 2,4-dinitro-1-fluorobenzene (DNFB) with films of aminoethyl-cellulose (AE-cellulose). The method is based on the relation between the decrease in extinction of a DNFB staining solution and the increase in extinction of the AE-cellulose after staining as measured in a film-spectrophotometer. In addition, the value of the molar extinction coefficient was used in establishing reaction conditions for a quantitative staining procedure for determining amino groups with DNFB and picric acid. Conditions of optimum DNFB staining were determined and the measured extinction was converted into concentration of amino groups using the molar extinction coefficient. The amino group concentration of the same batch of AE-cellulose was also determined, after finding the optimum reaction conditions, by staining with picric acid. The results, when compared, showed a linear relationship with a slope of unity for batches of AE-cellulose of varying amino group concentrations. This is consistent with the same stoichiometry in both cases and indicates that in both procedures one chromophore molecule has reacted with one amino group and that this reaction has proceeded to completion. The general applicability of the method is discussed.     

A convenient automated method for the determination of proteolytic enzymes

An automated method for the assay of proteolytic enzymes is described. The insoluble dye-protein complex, Remazolbrilliant Blue-hide powder, is used as the substrate and is readily digested by trypsin, elastase, subtilisin, thermolysin, chymotrypsin, and to a lesser extent pronase, pepsin, and bacterial collagenase. The proteolytic activity of crude microbial culture preparations is expressed in terms of an equivalent concentration of crystalline trypsin, which itself can be readily determined within the concentration range 0.25–5.0 μg/ml.     

Kinetic study of the enzyme NADPH cytochrome-C (P-450) reductase: non-Michaelian behaviour

1. Contrary to what has been accepted until now, the enzyme exhibits non-Michaelian kinetics both against NADPH and against cytochrome-c as substrates; deviations were detected that have led to the proposition of a rate equation of minimum degree 2:2. 2. A general mechanism is proposed that includes, apart from the binding of the enzyme to NADPH, the formation of an enzyme-cytochrome-c complex, both routes leading to the formation of a ternary-complex NADPH-enzyme-acceptor. 3. From the latter, a series of intermediate steps finally leads to the release of the enzyme in conditions to start a new catalytic cycle. 4. Application of the King-Altman method to this mechanism yields a kinetic equation of degree 2:2 with respect to the cytochrome-c and NADPH, in accordance with our experimental results.     

Potentiometric determination of coenzyme-dependent oxidoreductase enzymes with recycling of the coenzyme

By enzymatically establishing a rapid (essentially equilibrium) coupling of a redox coenzyme such as NAD with the components of the ferrocyanide–ferricyanide half-cell (e.g., using excess diaphorase) the half-cell potential can be used to monitor another enzymatic reaction involving the same coenzyme. This approach provides a general, rapid potentiometric method of assaying coenzyme-dependent oxidoreductase enzymes. We show that these assay systems can be designed for multiple turnover of coenzyme (in our case NAD) during a single assay thereby amplifying the rate of electromotive force (emf) change with a concomitant increase in sensitivity of enzyme assay. This allows the use of small concentrations of coenzyme and extension of the range of enzyme concentrations that may be assayed.     

Classification of stability behavior of bioreactors with wall attachment and substrate-inhibited kinetics

The biodegradation of pollutants in continuous operation when the microbial population exhibits wall attachment is studied. The proposed model for wall attachment assumes two morphological forms of the microbial cell connected by metamorphosis reactions with first order exchange kinetics. An analysis of the stability of the bioreactor, carried out using elementary principles of the singularity theory and continuation techniques, allows for classification in the multidimensional parameter space of the various stability behaviors exhibited by the reactor model, for both substrate-inhibited and Monod kinetics. The analysis also shows the enhanced stability behavior of the bioreactor due to wall attachment.