Kinetic analysis of a general model of activation of aspartic proteinase zymogens.

Starting from a simple general reaction mechanism of activation of aspartic proteinase zymogens involving an uni- and a bimolecular simultaneous route, the time course equation of the concentration of the zymogen and of the activated enzyme have been derived. From these equations, an analysis quantifying the relative contribution to the global process of the two routes has been carried out for the first time. This analysis suggests a way to predict the time course of the relative contribution as well as the effect of the initial zymogen and activating enzyme concentrations, on the relative weight. An experimental design and kinetic data analysis is suggested to estimate the kinetic parameters involved in the reaction mechanism proposed. Finally, we apply some of our results to experimental data obtained by other authors in experimental studies of the activation of some aspartic proteinase zymogens.

The influence of product instability on slow-binding inhibition.

We present a kinetic study of an enzyme reaction that takes place with slow-binding inhibition where the immediate product undergoes a spontaneous or induced process of decomposition. A kinetic study of an enzyme process, in which a slow-binding inhibition process and a decomposition of the immediate product of the reaction take place simultaneously is performed. The corresponding explicit concentration-time equations were obtained. Using the analytical solutions obtained, which were tested numerically, we suggest a procedure that allows the discrimination between the particular cases considered and the evaluation of the principal kinetic parameters of the reaction.

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.

Evidence of quasi-linear gas transport through sperm whale myoglobin.

The diffusion of molecular oxygen or its isosteric analogue, carbon monoxide, from the surface of myoglobin to its deeply imbedded haem appears to represent one of the simplest protein functions. Hence, it was chosen for the study of the possible role of a global controlling effect like an attractor. However, whereas the six statistical criteria of the classical non-linear dynamic analysis for the existence of an attractor in myoglobin were fulfilled and invariant to the Fourier transformation, the properties of this attractor were not as simple as anticipated. The parameters were tested and confirmed by alternative approaches, the interpoint distance method of Judd and Fourier transformation. If the diffusion were approximately linear, the order of the attractor would be expected to be near one. However, a clearly higher value, 1.46+/-0.03, was found, indicating the existence of additional steps. Later, the latter were identified as a 90 degrees rotation of CO followed by a translocation by 0.4 A to a transient pocket. These additional steps may explain the high number of regulatory factors found, 10+/-1. The autocorrelation function was damped with a correlation length of at least 20 residues. The Poincaré plot showed a dense domain compatible with the cross-section of a quasi-spherical attractor. The first Lyapunov exponent, lambda(1), was clearly positive. The Hurst fractal coefficient was 1.90+/-0.22, indicating a clear departure from simple linear diffusion.

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.

Kinetic analysis of enzyme systems with suicide substrate in the presence of a reversible competitive inhibitor, tested by simulated progress curves.

The use of suicide substrates remains a very important and useful method in enzymology for studying enzyme mechanisms and designing potential drugs. Suicide substrates act as modified substrates for the target enzymes and bind to the active site. Therefore the presence of a competitive reversible inhibitor decreases the rate of substrate-induced inactivation and protects the enzyme from this inactivation. This lowering on the inactivation rate has evident physiological advantages, since it allows the easy acquisition of experimental data and facilitates kinetic data analysis by providing another variable (inhibitor concentration). However despite the importance of the simultaneous action of a suicide substrate and a competitive reversible inhibition, to date no corresponding kinetic analysis has been carried out. Therefore we present a general kinetic analysis of a Michaelis-Menten reaction mechanism with double inhibition caused by both, a suicide substrate and a competitive reversible inhibitor. We assume rapid equilibrium of the reversible reaction steps involved, while the time course equations for the reaction product have been derived with the assumption of a limiting enzyme. The goodness of the analytical solutions has been tested by comparison with the simulated curves obtained by numerical integration. A kinetic data analysis to determine the corresponding kinetic parameters from the time progress curve of the product is suggested. In conclusion, we present a complete kinetic analysis of an enzyme reaction mechanism as described above in an attempt to fill a gap in the theoretical treatment of this type of system.

The kinetic effect of product instability in a Michaelis-Menten mechanism with competitive inhibition.

In most kinetic studies it is assumed that both the reactant and the products are stable. However, under certain conditions spontaneous decomposition or deterioration caused by one of the participating species occurs. Studies, in which a species (the free enzyme, the enzyme-substrate complex, an inhibitor or the product of the reaction) is unstable, have appeared in the literature. However, to our knowledge, the enzymatic systems, in which a competitive inhibition and a decomposition or transformation of the products take place simultaneously, have not been studied so far. In this paper, we present a kinetic analysis of an enzyme reaction that follows a Michaelis-Menten mechanism, in which the free enzyme suffers a competitive inhibition simultaneously with the decomposition of the immediate product. In this study, we have linearised the differential equations that describe the kinetics of the process. Under the assumption of limiting concentration of enzyme, we have obtained and tested the explicit equation describing the time dependence of the product concentration using numerical calculus. With this equation and the experimental progress curve of the product, we constructed an easy procedure for the evaluation of the principal kinetic parameters of the process.

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.

An esterolytic antibody with vibrational properties of a catalytic H-chain and a non-catalytic L-chain.

An analysis of the temperature factors of an abenzyme has been performed to gain information on the possible role of deterministic chaos in the catalytic mechanism of such artificial proteins. The H-chain displayed a regular attractor of the dimension 3.0 +/- 0.3, whereas the L-chain showed one of = 7.5 +/- 0.5. The abenzyme also displayed a stochastic attractor of the dimension ca. 0.9. The H-chain attractor has one dimension more than those of the native hydrolases chymotrypsin and lysozyme. The additional degree of freedom of the abenzyme offers a likely explanation of the low specific catalytic activities of these artificial enzymes. The dimension of the attractor in the L-chain falls in the range found for other antibodies. Hence, a clear dichotomy seems to rule in this abenzyme; the H-chain displays the vibrational properties of an enzyme and the L-chain those of an antibody. The new data supports the hypothesis of an important role of attractors in biochemical mechanisms by reduction of the number of degrees of freedom (entropy) of reaction partners. A hierarchy of attractors is associated with specific protein functions.

Attractor control of the redox reactions of bovine cytochrome c.

Although the conformational changes accompanying the oxidation of ferrocytochrome c by the transfer of an electron to cytochrome a are small, they may contribute to the regulation of the electron transfer by transient storage of the liberated energy as strain and atomic vibrations. Both the electron transfer and the conformational changes seem to be controlled by an attractor, i.e. by a manifestation of a deterministic chaos. The putative attractor is regular and is, for the reaction involving the inner monomer of ferricytochrome c (I), of the order of 3.03 +/- 0.03. The conformational changes involving the outer monomer of ferricytochrome c (O) seem also to be controlled by a regular attractor, but its order is 4.2 +/- 0.2. The low order of the coupled reactions of electron transfer and conformational change suggests that it is essential to the electron transfer process in the respiratory chain. Since the order of attractors of other proteins correlates with the vectorial description of the function (1.0 for myoglobin, 2.0 for chymotrypsin and lysozyme, 3.0 for an abenzyme), the value for cyt. c indicates that not only the electron transfer, but also an additional reaction, e.g. the conformational change, are essential for the function of this protein. Hence, the study of protein attractors may yield information on important details, which could not be obtained by other methods.

Kinetics of enzyme systems with unstable suicide substrates.

This paper deals with kinetic studies of enzyme reaction mechanisms with enzyme inactivation induced by an unstable suicide substrate. An initial steady-state of the catalytic route is assumed and the time course equations for the total active enzyme forms and the reaction product have been derived. The goodness of the analytical solutions has been tested by comparison with the simulated curves obtained by numerical integration. A kinetic data analysis to determine the corresponding kinetic parameters is suggested and the time course equations of an important reaction mechanisms involving a stable suicide substrate and which can be regarded as particular case of that under study has also been derived from the corresponding equations. The simplicity of our method allows its systematic application to more complex mechanisms.

Elucidation of a new biological function of an old protein: unique structure of the cobra serum albumin controls its specific toxin binding activity.

Although few proteins have been studies as thoroughly as serum albumin, a new biological property of this evolutionary ancient protein was recently discovered: The ability of cobra serum albumin (CSA) to specifically sequester lethal endogenous toxins. A study of the structural basis of this property is reported in this contribution. Two independent approaches were used to alter the structure of the CSA at defined positions: Directed mutagenesis and limited proteolysis. The conserved pattern of the disulfide linkages in the primary structure of the serum albumins showed in the case of the cobra snake (Naja naja kaouthia) an anomaly at C11 and C502, which suggested the existence of a unique spatial structure in this protein. The two cysteine residues were singly replaced with the consensus residue, i.e. C11-->F and C502-->T. The former substitution increased the specific neurotoxin binding capacity of the CSA by the factor 1.7 +/- 0.2, whereas the latter replacement reduced it to (25 +/- 2)%. The limited proteolysis yielded the large tryptic peptides T60, T40, T30 and T18, which after isolation by PAGE followed by HPLC had retained a strong toxin affinity. The location of these peptides in the amino-acid sequence was identified by Edman degradation and suggested the order of their release. On the basis of these data, a model of the unfolding and of the activity changes of the CSA caused by the structural perturbations was composed and the kinetic parameters associated with the process were evaluated. The results support the hypothesis of the existence of a structure of multiple homologous domains with a disulfide linkage between C11 and C502 in the native CSA that joins the chain ends to form a dense conformation.

Attractor control of the binding of digoxin to a specific antibody.

The characteristics of attractor control of the changes in the molecular vibrations of a protein have previously been detected when an enzyme (chymotrypsin) reacted with a specific substrate and when myoglobin interacted with oxygen. Similar studies have now been carried out on the binding of a hapten, digoxin, to an antibody. The temperature factors of the Fab-fragment of a specific anti-digoxin antibody with and without the bound antigen were used in this analysis. The integral correlation function of the difference in the temperature factor between the free and the loaded state of the antigen binding site indicated the existence of a regular attractor of the dimension 4.0+/-0.1 in the light chain and one of the dimension 5.7+/-0.7 in the heavy chain, the former under the control of 11+/-1 factors and the latter by 12+/-2 factors. This result was corroborated by Poincaré plots showing the cross-section of attractors and by a positive Liapunov exponent. The power spectrum was, as expected, broad, but the autocorrelation function showed only significant damping in the case of the L-chain. The spacing of the temperature factors resembled a "Devil's Staircase" suggesting the operation of a stochastic attractor. Its dimension, which was determined by the methods of the correlation between the step-gag lengths and that of the Farey tree was found to be near one. Repetition of the calculation using data for the second antigen-antibody complex in the unit cell yielded similar results. However, the dimensions of the attractors in the second complex (6.0+/-0.1 for the L- and 7.6+/-0.1 for the H-chain) are somewhat larger than that of the first, probably reflecting the lower degree of order of the latter. In all cases, the saturation of the integral correlation coefficient with increasing number of phase-space dimensions strongly indicates the existence of an attractor. The evidence of attractors in the molecular dynamics of proteins raises doubt about the value of trajectories calculated by integration of equations of atomic movement of the prediction of folding pathways since the stochastic element in the dynamics can eliminate leading equations in the set, thus influencing the folding pathway.

Time-dependent control of metabolic systems by external effectors.

The expression of elasticity coefficients for time-dependent enzyme inhibition/activation by an external effector was initially derived. Only a limited number of restrictive assumptions were used, for example, the enzyme was considered to obey Michaelis-Menten kinetics and effectors were taken to be competitive. Then, a simple metabolic system under the control of a time-dependent effector (inhibitor or activator) was analysed and the expressions of the control coefficients were obtained. In addition, two numerical examples were used to represent the control coefficients as functions of time and effector concentration. The results indicate that the control coefficients vary in a relatively limited range of values; however, for certain intervals of time and of effector concentration local minima or major modifications of the coefficients may be recorded. The physiological importance of non-steady state analysis of metabolic systems controlled by external effectors was also discussed. It was stressed that the non-steady state treatment may contribute to creating a more realistic image of the metabolic control processes.

[The molecular cloning and sequencing of the cobra serum antitoxic protein gene].

In the previous study the authors found at least one peptide of 39 amino acid residues of several purified tryptic-fragments of the cobra serum antitoxic protein (CSAP), whose sequence had shown certain correlation with the rat serum albumin. For further clarification of the toxin-binding activity of CSAP in relation with its corresponding structure, the cDNA gene library of cobra liver cells was established and DNA primers were designed according to the known amino acid sequences of the tryptic peptides of CSAP. The specific probes were prepared and the specific clone was screened out from the library by PCR. Finally, the CSAP cDNA was sequenced from its sub-clones. Then the complete amino acid sequence of CSAP was elucidated. It is a polypeptide chain of 614 amino acid residues with a molecular size of 69.8 KDa. In comparing the whole sequence of CSAP, especially its signal peptide, with mammalian serum albumins, the authors have come to realize that CSAP is just the cobra serum albumin (CSA).

An analysis of the kinetics of enzymatic systems with unstable species.

We present a general kinetic analysis of the Michaelis-Menten mechanism for the case in which the substrate, the enzyme-substrate complex, and the product are unstable. The equations for the rapid equilibrium conditions are obtained as a particular case of the general equations of the transient-phase. The kinetic data analysis which we suggest is based on the time progress curve of the product of the enzymatic reaction, or on the progress curve of the species into which the immediate product is transformed. This analysis allows the determination of the rate and equilibrium constants if adequate experimental results are available. It assumes, in contrast to most previous treatments of enzyme kinetics, that the concentration of the enzyme is much higher than that of the substrate. Since this condition often is satisfied inside cells, it can be more relevant to physiological problems than the classical assumption, [E] << [S], which sooner pertains to the situation in the laboratory.

A zinc metalloproteinase is responsible for the release of CD30 on human tumor cell lines.

The activation marker CD30 is expressed on the cell surface of the malignant cells in Hodgkin's disease and a few non-Hodgkin lymphomas. We have analyzed the regulation of membrane-bound CD30 and found that the binding of a variety of anti-CD30 antibodies induced down-regulation of CD30 on cell lines. In addition, such down-modulation was also observed after treatment of the cell surface proteins with the sulfhydryl reagent iodoacetamide or after stimulation of the second messenger pathway with phorbol ester or calcium ionophore. This modulation was abolished at 4 degrees C and strongly inhibited by chelators like EDTA or 1,10-phenanthroline, whereas EGTA, a selective inhibitor of Ca(2+)-dependent proteinases and other inhibitors of serine, thiol and acid proteinases, showed no effect. The down-modulation was strengthened by Zn2+ or Cd2+, but not by other divalent cations such as Fe2+, Mn2+, Mg2+, Ca2+ or Co2+, thus indicating the involvement of a zinc metalloproteinase in CD30 modulation which can be activated by protein kinase C and by alkylation of sulfhydryl groups. Pulse-chase experiments, analysis of the CD30 glycosylation and specific measurement of the 90-kDa soluble form of CD30 (sCD30) with a sandwich radioimmunoassay revealed that CD30 down-modulation results from enhanced release of 90-kDa sCD30 by the site-specific cleavage of CD30 accomplished by a zinc metalloproteinase. This release occurs at the cell membrane without prior endocytosis.

Potential linkage disequilibrium between schizophrenia and locus D22S278 on the long arm of chromosome 22.

Locus D22S278 at 22q12 has been implicated in schizophrenia by sib-pair analysis. In order to replicate these results, we performed the transmission test for linkage disequilibrium (TDT) in 113 unrelated schizophrenic patients and their 226 parents. Evidence for potential linkage disequilibrium was obtained between schizophrenia and allele 243 of the marker AFM 182xd12 at the locus D22S278 (P = 0.02). The results of our study suggest a detectable oligogenic gene in a multigene system for schizophrenia closely linked to D22S278 on the long arm of chromosome 22. If confirmed by others, this finding could lead to the identification of a schizophrenia susceptibility gene.

Evidence of the coevolution of a snake toxin and its endogenous antitoxin cloning, sequence and expression of a serum albumin cDNA of the Chinese cobra.

A full-length cDNA of the serum albumin (CSA) of the cobra (Naja naja kaouthia) was cloned from a lambda gt 11 library. It encodes a mature protein of 614 amino-acid residues homologous to the precursor of mammalian serum albumins. The 1 degree and 2 degrees structures of the CSA resemble those of the human variety. The putative toxin binding sites are mainly located in the subdomains IIA and IIIA. The relation between structural homology and function of the serum albumins (SA) is discussed. An analysis of their evolutionary tree revealed that anti-toxicity arose by < 90 amino-acid exchanges. The rate of substitution is much higher in the SA than in cytochrome C, which probably reflects the difference in evolutionary driving forces. The evolutionary period of the SA (6.7 +/- 0.1 M.Y.) significantly exceeds that of hemoglobin (5.8 M.Y.). Eight tripeptides in the nicotinic acetylcholine receptor (ACR), all flanking the putative toxin binding site, are also found in the CSA where they join to form 1 octa-, 1 penta- and 4 tripeptides, thus indicating the concerted evolution of two functionally linked proteins: toxin and antitoxin (CSA).

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.