B.H. Havsteen

The biochemistry and medical significance of the flavonoids

Flavonoids are plant pigments that are synthesised from phenylalanine, generally display marvelous colors known from flower petals, mostly emit brilliant fluorescence when they are excited by UV light, and are ubiquitous to green plant cells. The flavonoids are used by botanists for taxonomical classification. They regulate plant growth by inhibition of the exocytosis of the auxin indolyl acetic acid, as well as by induction of gene expression, and they influence other biological cells in numerous ways. Flavonoids inhibit or kill many bacterial strains, inhibit important viral enzymes, such as reverse transcriptase and protease, and destroy some pathogenic protozoans. Yet, their toxicity to animal cells is low. Flavonoids are major functional components of many herbal and insect preparations for medical use, e.g., propolis (bees glue) and honey, which have been used since ancient times. The daily intake of flavonoids with normal food, especially fruit and vegetables, is 1-2 g. Modern authorised physicians are increasing their use of pure flavonoids to treat many important common diseases, due to their proven ability to inhibit specific enzymes, to simulate some hormones and neurotransmitters, and to scavenge free radicals.

Transient phase of enzyme reactions. Time course equations of the strict and the rapid equilibrium conditions and their computerized derivation.

In this contribution, we present the derivation, from the strict transient phase equations of enzyme reactions, of the transient phase equations under the usual assumptions that one or more of the reversible steps involved in the mechanism of the enzyme reaction are assumed to be in rapid equilibrium. Moreover, we present the transient phase equations of all of the species in a general enzyme system model, valid for the partial or total rapid equilibrium conditions, as well as the particular case of the strict transient phase equations. In the case of the rapid equilibrium assumptions, the equations may be given either as functions of the individual rate constants in the reversible steps assumed in rapid equilibrium or as functions of the corresponding equilibrium constants. The steady state equations are easily obtained from the transient phase equations by setting the time --> infinity. We have implemented a computer program, easy to use and with a user-friendly format for the input of data and output of results, which allows the user to derive the symbolic strict transient phase equations and/or those corresponding to the assumption that one or more of the reversible reaction steps are in rapid equilibrium.

A new principle of enzyme catalysis: Coupled vibrations facilitate conformational changes

The coupling between the molecular vibrations in chymotrypsinogen, alpha-chymotrypsin and tosyl-alpha-chymotrypsin, as expressed by the temperature factors of individual amino acid sidechains and by a flexibility parameter calculated from the masses and co-ordinates of the atoms, has been analyzed by calculation of the integral correlation coefficient, the autocorrelation coefficient, the Poincaré projection, the first Liapunov coefficient and the power spectra. The agreement between the results obtained with the temperature factors and the flexibility parameter as well as the correct display by the latter of known structural features support the validity of the approach. The localization and extent of the conformational change in the enzyme following its binding of a specific substrate is detected in the difference plot between the enzyme and the acylenzyme of the distribution of the flexibility parameter over the peptide chain. As many as about 70% of the aminoacids participate in this rearrangement. An attractor of low dimensionality, two, i.e. a limit cycle, is detected both in the total enzyme and in its domain which is mobilized by the specific substrate. A simple model based on a known prominent structural feature, which is common to the trypsin family of serine proteases, two extensive coaxial halfcylinders of beta-sheets, to which previously no mechanistic function could be assigned, is proposed to account for the role of the attractor in the catalytic process: (1) control of the entry of a specific substrate to the catalytic site by co-ordinated disentanglement of the interlocking sidechains; (2) correct positioning of the functional groups in the active site; (3) lowering of the activation energy of the formation of the transition state complex.

Protein kinase activity of the intracellular but not of the membrane-associated form of the KI-1 antigen (CD30)

The Hodgkin-associated Ki-1 antigen (CD30) consists of a 120-kDa membrane-associated glycosylated phosphoprotein (Ki-1/120) and a 57-kDa non-glycosylated phosphoprotein (Ki-1/57) which only occurs intracellularly. Both molecules are phosphorylated at serine residues. An analysis of the peptide fragments resulting from staphylococcal V8-protease digestion of the Ki-1/57 molecule revealed identical bands irrespective of the cell source. Only a few bands of the Ki-1/57 digests appeared among the peptide fragments of the Ki-1/120 membrane antigen. The protein kinase activity was tested for both forms of the Ki-1 antigen. The Ki-1/120, devoid of the Ki-1/57 molecule, was immunoprecipitated from cell lysates of Hodgkin-analogous cell lines L428 or L540, which had been loaded with the Ki-1 or the Ki-1-analogous antibodies Ber-H2, HSR-1, -2 and -3 (method 1). These other antibodies reacted with the Ki-1/120, but not with the Ki-1/57 antigen. The latter, devoid of the Ki-1/120, was isolated from L540 cells after removal of the membrane form by method 1 or from U266/Bl myeloma or Raji Burkitt lymphoma cells which only contain the smaller form. Effects of non-specific adsorption were eliminated by various control precipitates. The Ki-1/57 intracellular antigen showed autophosphorylation and could phosphorylate histones as well. In contrast, a protein kinase activity of the membrane-associated Ki-1/120 could not be demonstrated.

Mean residence times in linear compartmental systems. Symbolic formulae for their direct evaluation

A complete analysis has been performed of the mean residence times in linear compartmental systems, closed or open, with or without traps and with zero input. This analysis allows the derivation of explicit and simple general symbolic formulae to obtain the mean residence time in any compartment of any linear compartmental system, closed or open, with or without traps, as well as formulae to evaluate the mean residence time in the entire system like the above situations. The formulae are given as functions of the fractional transfer coefficients between the compartments and, in the case of open systems, they also include the excretion coefficients to the environment from the different compartments. The relationship between the formulae derived and the particular connection properties of the compartments is discussed. Finally, some examples have been solved.

Time course equations of the amount of substance in a linear compartmental system and their computerized derivation.

In this contribution, we present the symbolic time course equations corresponding to a general model of a linear compartmental system, closed or open, with or without traps and with zero input. The steady state equations are obtained easily from the transient phase equations by setting the time --> infinity. Special attention has been given to the open systems, for which an exhaustive kinetic analysis has been developed to obtain important properties. Besides, the results have been particularized to open systems without traps and an alternative expression for the distribution function of exit times has been provided. We have implemented a versatile computer program, that is easy to use and with a user-friendly format of the input of data and the output of results. This computer program allows the user to obtain all the information necessary to derive the symbolic time course equations for closed or open systems as well as for the derivation of the distribution function of exit times.

Evaluation of the kinetic parameters of the activation of trypsinogen by trypsin.

Kinetic analysis of the mechanism of trypsinogen activation by trypsin under rapid equilibrium conditions and certain relationships between the rate constants are presented. The kinetic equations are valid from the beginning of the reaction. In addition, we suggest a procedure, based on the above equations, for the evaluation of the kinetic parameters of the reaction. This procedure is applied to a set of experimental data collected during the activation of bovine trypsinogen by trypsin at 30 degrees C (pH 8.1) in 0.01 M CaCl2. In this system, the amount of active enzyme increases exponentially, as expected from an autocatalytic process. The apparent rate constant, delta, governing this increase would vary linearly with the trypsinogen concentration, [Z]0, if no Michaelis complex was detectable. However, the increase in delta with [Z]0 is clearly non-linear and fits a hyperbola (delta = k2[Z]0/(Kz + [Z]0)) well.

Kinetics of the trypsinogen activation by enterokinase and trypsin.

A global kinetic analysis of the mechanisms of the trypsinogen activation by enterokinase and trypsin is presented. The kinetic equations of both the transient-phase and the steady-state of these mechanisms are presented. In addition, we here derive the corresponding kinetic equations for the case in which the condition of rapid equilibrium prevails and we propose a kinetic data analysis. The significance of this approach to the treatment of other zymogen activation processes is discussed.

General linear compartment model with zero input: I. Kinetic equations

The derivation of kinetic equations is described for n-compartment linear models, in which the substance may be simultaneously introduced into one or more compartments at t = 0 and eliminated from any compartment. For a given zero-input, general formulas are derived which describe the amount of tracer in any of the compartments as a function of time and the model parameters. New algorithms have been developed which allow the expression of the kinetic equations.

Kinetics of the transient-phase and steady-state of the monocyclic enzyme cascades

We present a kinetic analysis of the whole course of the reaction, that is, of both the transient-phase and steady-state, of monocyclic enzyme cascade systems. The equations for the rapid equilibrium conditions are obtained as a particular case of the general transient-phase equations. An analysis of the kinetic data allows the determination of the equilibrium and the rate constants if adequate experimental results are available. Finally, our results for the steady-state are compared with those obtained by other authors.