Prion diseases: dynamics of the infection and properties of the bistable transition.

Prion diseases are thought to result from a pathogenic, conformational change in a cellular protein, the prion protein. The pathogenic isoform seems to convert the normal isoform in an autocatalytic process. In contrast to the conditions used for in vitro studies of enzyme kinetics, the concentration of the catalyst is not much lower than that of the substrate in the course of infection. This feature may endow the system with a time-hierarchy allowing the pathogenic isoform to relax very slowly in the course of infection. This may contribute to the long incubation periods observed in prion diseases. The dynamic process of prion propagation, including turnover of the cellular prion protein, displays bistable properties. Sporadic prion diseases may result from a change in one of the parameters associated with metabolism of the prion protein. The bistable transition observed in sporadic disease is reversible, whereas that observed in cases of exogenous contamination is irreversible. This model is consistent with the occurrence of rare, sporadic forms of prion diseases. It may also explain why only some individuals of a cohort develop a prion disease following transient food contamination.

Multistability: a major means of differentiation and evolution in biological systems.

Very simple biochemical systems regulated at the level of gene expression or protein function are capable of complex dynamic behaviour. Among the various patterns of regulation associated with non-linear kinetics, multistability, which corresponds to a true switch between alternate steady states, allows a graded signal to be turned into a discontinuous evolution of the system along several possible distinct pathways, which can be either reversible or irreversible. Multistability plays a significant role in some of the basic processes of life. It might account for maintenance of phenotypic differences in the absence of genetic or environmental differences, as has been demonstrated experimentally for the regulation of the lactose operon in Escherichia coli. Cell differentiation might also be explained as multistability.

Species barrier in prion diseases: a kinetic interpretation based on the conformational adaptation of the prion protein.

Prion diseases are thought to result from the conformational change of the normal cellular prion protein to a pathogenic protease-resistant isoform. However, brain extracts not containing the protease-resistant isoform of the prion protein can be infectious following interspecies transmission. The 'protein-only' hypothesis of pathogenesis is extended to provide possible explanations which could be interpreted in terms of a different infectious agent. It is proposed that normal cellular protein (PrPC) may be transformed into a form (PrP*) that is conformationally distinct from the host-specific abnormal isoform (PrPSc). In infection from a heterologous donor, the dimeric forms of heterologous PrPSc, which may catalyse the formation of host PrP* from PrPC, host PrP* and host PrPSc are all considered to be capable of catalysing, to some extent, the conversion of PrPC into PrPSc. However, depending on the species involved, PrP* may, or may not, be pathogenic, and may, or may not, be sensitive to proteolysis. It is shown, by numerical integration of the differential rate equations derived from this model, that a strain may be stabilized after two or three passages through a different species and that transmission might occur in the absence of detectable protease-resistant prion protein. The natural transmission of scrapie to cattle is discussed in relation to the model.

Coordination of catalytic activities within enzyme complexes.

If two enzymes are physically and permanently associated as a bi-enzyme complex and if these enzymes catalyze non-consecutive chemical reactions, either of these reactions may inhibit or activate the other. If these reactions belong to two different metabolic cycles, the functioning of one of these cycles will control the fine tuning of the other. Thus simple kinetic considerations lead to the conclusion that, owing to the spatial organization of enzymes as multimolecular complexes, a fine tuning and a coordination of different metabolic networks, or cycles, may be exerted. It thus appears that channelling of reaction intermediates within a multienzyme complex does not represent the only functional advantage brought about by this type of spatial molecular organization.

Dynamics aspects of long distance functional interactions between membrane-bound enzymes.

The aim of this mini review is to study how an organized charged milieu, such as a membrane, may alter functional long-distance interactions between bound enzymes. Two questions are more specifically considered. The first is to know whether the overall response of a bound enzyme is dependent upon the degree of spatial order of fixed charges and enzymes molecules. The second is to determine whether electric interaction between the fixed charges of the matrix and the charged substrate may generate hysteresis loop of substrate concentration as well as oscillations of this concentration at the surface of the membranes. These effects that have been shown to occur at the surface of membranes, are not the result of intrinsic properties of enzymes. They appear as the consequence of the interplay between functional long-distance interactions between bound enzyme systems and electric repulsion effects of mobile ions. They may be viewed as supramolecular devices that allow storing information from the external milieu.

Molecular organization and clustering of cell-wall-bound enzymes as a source of kinetic apparent co-operativity.

When fixed charges and enzyme molecules are not homogeneously distributed in a matrix, the degree of organization of charges, of enzyme molecules and of charges with respect to enzyme molecules modulate the enzyme reaction rate. The overall reaction velocity of the bound enzyme system may be expressed in terms of monovariate moments of the charge density distribution and of the bivariate moments of the charge and enzyme density distributions. With respect to the situation where fixed charges and enzyme molecules are randomly distributed in the matrix, the molecular organization, as expressed by the monovariate and bivariate moments results in an increase or a decrease, of the overall reaction rate, as well as in the appearance of a kinetic cooperativity. The degree of spatial organization of objects may be expressed quantitatively through the concept of minimal spanning tree. This concept may thus be applied to the quantification of the degree of order that may exist in the bidimensional distribution of enzyme molecules in a charged matrix. Primary walls of isolated plant cells in sterile culture behave as a polyanion and contain different enzymes. The spatial distribution in sycamore cell walls of an acid phosphatase has been studied through the concept of minimal spanning tree and shown to be non-randomly distributed in the polyanionic matrix, but clustered in that matrix. This spatial organization results in a modulation of the reaction rate of the cell-wall-bound phosphatase reaction. Both the theoretical and experimental results presented in this study leave little doubt as to the validity of the idea that in situ the organization of fixed charges and enzyme molecules modulate the overall dynamics of enzyme reactions.

Spatial order as a source of kinetic cooperativity in organized bound enzyme systems.

When enzyme molecules are distributed within a negatively charged matrix, the kinetics of the conversion of a negatively charged substrate into a product depends on the organization of fixed charges and bound enzyme molecules. Organization is taken to mean the existence of macroscopic heterogeneity in the distribution of fixed charge density, or of bound enzyme density, or of both. The degree of organization is quantitatively expressed by the monovariate moments of charge and enzyme distributions as well as by the bivariate moments of these two distributions. The overall reaction rate of the bound enzyme system may be expressed in terms of the monovariate moments of the charge density and of the bivariate moments of charge and enzyme densities. The monovariate moments of enzyme density do not affect the reaction rate. With respect to the situation where the fixed charges and enzyme molecules are randomly distributed in the matrix, the molecular organization, as expressed by these two types of moments, generates an increase or decrease of the overall reaction rate as well as a cooperativity of the kinetic response of the system. Thus both the alteration of the rate and the modulation of cooperativity are the consequence of a spatial organization of charges with respect to the enzyme molecules. The rate equations have been derived for different types of organization of fixed charges and enzyme molecules, namely, clustered charges and homogeneously distributed enzyme molecules, clustered enzyme molecules and homogeneously distributed charges, clusters of charges and clusters of enzymes that partly overlap, and clusters of enzymes and clusters of charges that are exactly superimposed. Computer simulations of these equations show how spatial molecular organization may modulate the overall reaction rate.

Analysis of progress curves for a highly concentrated Michaelian enzyme in the presence or absence of product inhibition.

Methods are given for analysing the time course of an enzyme-catalysed reaction when the concentration of the enzyme itself is high, a situation which is often found in vivo. (1) The integrated form of the kinetic equation for a concentrated Michaelian enzyme in absence of product inhibition is given. Parameters are shown to be calculated easily using non-linear fitting procedures. (2) A general algorithm to analyse progress-curve data in more complex cases (i.e. when the analytical form of the integrated rate equation is not known or is exceedingly complex) is proposed. This algorithm may be used for any enzyme mechanism for which the differential form of the kinetic equation may be written analytically. We show that the method allows differentiation between the main types of product inhibition which may occur in the case of a highly concentrated Michaelian enzyme.

Apparent co-operativity for highly concentrated Michaelian and allosteric enzymes.

The effect of high enzyme concentration on velocity curves is analysed quantitatively for both Michaelian and simple allosteric enzymes. The general principles and practical approaches developed here are applicable to other models and may provide information on enzyme function in vivo. At physiological enzyme concentrations. Michaelian enzymes display amplification properties of the same magnitude as those observed for allosteric enzymes. In terms of apparent co-operativity, this corresponds to Hill coefficients that are locally much larger than the number of interacting or non-interacting binding sites. However, compared to the Michaelian case, allosteric interactions are needed to provide a combination of both positive and negative apparent co- operativities . These effects are important for understanding the biological significance of intersubunit cooperation in oligomeric enzymes.

Specific interactions of 3-phosphoglyceroyl-glyceraldehyde-3-phosphate dehydrogenase with coenzymes.

The binding of oxidized and reduced coenzyme (NAD+ and NADH) to 3-phosphoglyceroyl-glyceraldehyde-3-phosphate dehydrogenase has been studied spectrophotometrically and fluorimetrically. The binding of NAD+ to the acylated sturgeon enzyme is characterized by a significant quenching of the enzyme fluorescence (about 25%) and the induction of a difference spectrum in the ultraviolet absorbance region of the enzyme. Both of these spectroscopic properties are quantitatively distinguishable from those of the corresponding binary enzyme-NAD+ complex. Binding isotherms estimated by gel filtration of the acylated enzyme are in close agreement to those obtained by spectrophotometric and fluorimetric titrations. Up to four NAD+ molecules are bound to the enzyme tetramer. No anticooperativity can be detected in the binding of oxidized coenzyme, which is well described on the basis of a single class of four binding sites with a dissociation constant of 25 muM at 10 degrees C, pH 7.0. The binding of NADH to the acylenzyme has been characterized spectrophotometrically. The absorption band of the dihydronicotinamide moiety of the coenzyme is blue-shifted to 335 nm with respect to free NADH. In addition, a large hypochromicity (23%) is observed together with a significant increase of the bandwidth at half height of this absorption band. This last property is specific to the acylenzyme-DADH complex, since it disappears upon arsenolysis of the acylenzyme. The binding affinity of NADH to the acylated enzyme has been estimated by performing simultaneous spectrophotometric and fluorimetric titrations of the NADH appearance upon addition of NAD+ to a mixture of enzyme and excess glyceraldehyde 3-phosphate. In contrast to NAD+, the reduced coenzyme NADH appears to be relatively strongly bound to the acylated enzyme, the dissociation constant of the acylenzyme-NADH complex being estimated as 2.0 muM at 25 degrees C. In addition a large quenching of the NADH fluorescence (about 83%) is observed. The comparison of the dissociation constants of the coenzyme-acylenzyme complexes and the corresponding Michaelis constants suggests a reaction mechanism of the enzyme in which significant formation and dissociation of NAD+-acylenzyme and NADH-acylenzyme complexes occur. Under physiological conditions the activity of the enzyme can be regulated by the ratio of oxidized and reduced coenzymes. Possible reasons for the lack of anticooperativity in coenzyme binding to the acylated form of the enzyme are discussed.

Sturgeon glyceraldehyde-3-phosphate dehydrogenase.

The formation of binary complexes between sturgeon apoglyceralddhyde-3-phosphate dehydrogenase, coenzymes (NAD+ and NADH) and substrates (phosphate, glyceraldehyde 3-phosphate and 1,3-bisphosphoglycerate) has been studied spectrophotometrically and spectrofluorometrica-ly. Coenzyme binding to the apoenzyme can be characterized by several distinct spectroscopic properties: (a) the low intensity absorption band centered at 360 nm which is specific of NAD+ binding (Racker band); (b) the quenching of the enzyme fluorescence upon coenzyme binding; (c) the quenching of the fluorescence of the dihydronicotinamide moiety of the reduced coenzyme (NADH); (D) the hypochromicity and the red shift of the absorption band of NADH centered at 338 nm; (e) the coenzyme-induced difference spectra in the enzyme absorbance region. The analysis of these spectroscopic properties shows that up to four molecules of coenzyme are bound per molecule of enzyme tetramer. In every case, each successively bound coenzyme molecule contributes identically to the total observed change. Two classes of binding sites are apparent at lower temperatures for NAD+ Binding. Similarly, the binding of NADH seems to involve two distinct classes of binding sites. The excitation fluorescence spectra of NADH in the binary complex shows a component centered at 260 nm as in aqueous solution. This is consistent with a "folded" conformation of the reduced coenzyme in the binary complex, contradictory to crystallographic results. Possible reasons for this discrepancy are discussed. Binding of phosphorylated substrates and orthophosphate induce similar difference spectra in the enzyme absorbance region. No anticooperativity is detectable in the binding of glyceraldehyde 3-phosphate. These results are discussed in light of recent crystallographic studies on glyceraldehyde-3-phosphate dehydrogenases.