Self-organization and dynamics of an open futile cycle

The dynamic behaviour of an open futile cycle composed of two enzymes has been investigated in the vicinity of a steady-state. A necessary condition required for damped or sustained oscillations of the system is that enzyme E₂, which controls recycling of the substrate S₂, be inhibited by an excess of this substrate. In order for the system to be neutrally stable and therefore to exhibit sustained oscillations, it is not necessary for antagonist enzyme E₁ to be activated by its product S₂. If it is enzyme E₁ which is inhibited by an excess of its substrate S₁, the system has a saddle point. Other conditions for stability or instability of the system have been determined. If the enzyme E₁, which is not inhibited by the substrate, exhibits a slow conformational transition of the mnemonical type, this transition dramatically alters the stability behavior of the system. If the mnemonical enzyme E₁ were exhibiting a positive kinetic co-operativity, decreasing the rate of the conformational transition of the mnemonical enzyme will increase the stability of the whole system and will tend to damp the oscillations in the vicinity of the steady-state. If conversely the mnemonical enzyme E₁ were exhibiting a negative kinetic co-operativity, decreasing the rate of the enzyme conformational transition will decrease the stability of the system and will tend to create or amplify oscillations of the system taken as a whole. If these results may be extended to more complex metabolic cycles, involving more than two enzymes, it may be tentatively considered that positive co-operativity associated with slow transition has emerged in the course of evolution in order to limit temporal instabilities of metabolic cycles. Alternatively one may speculate that the “biological function” of negative co-operativity is to create or amplify these temporal instabilities.     

Subunit coupling and kinetic co-operativity of polymeric enzymes. Amplification, attenuation and inversion effects

The principles of structural kinetics, as applied to dimeric enzymes, allow us to understand how the strength of subunit coupling controls both substrate-binding co-operativity, under equilibrium conditions, and kinetic co-operativity, under steady state conditions. When subunits are loosely coupled, positive substrate-binding co-operativity may result in either an inhibition by excess substrate or a positive kinetic co-operativity. Alternatively, negative substrate-binding co-operativity is of necessity accompanied by negative kinetic co-operativity. Whereas the extent of negative kinetic co-operativity is attenuated with respect to the corresponding substrate-binding co-operativity, the positive kinetic co-operativity is amplified with respect to that of the substrate-binding co-operativity. Strong kinetic co-operativity cannot be generated by a loose coupling of subunits. If subunit is propagated to the other, the dimeric enzyme may display apparently surprising co-operativity effects. If the strain of the active sites generated by subunit coupling is relieved in the non-liganded and fully-liganded states, both substrate-binding co-operativity and kinetic co-operativity cannot be negative. If the strain of the active sites however, is not relieved in these states, negative substrate-binding co-operativity is accompanied by either a positive or a negative co-operativity. The possible occurrence of a reversal of kinetic co-operativity, with respect to substrate-binding co-operativity, is the direct consequence of quaternary constraints in the dimeric enzyme. Moreover, tight coupling between subunits may generate a positive kinetic co-operativity which is not associated with any substrate-binding co-operativity. In other words a dimeric enzyme may well bind the substrate in a non co-operative fashion and display a positive kinetic co-operativity generated by the strain of the active sites.     

Enzyme memory. Effect of glucose 6-phosphate and temperature on the molecular transition of wheat-germ hexokinase LI.

A theory is presented that associates burst (orlag) kinetics with the respective concentrations of enzyme initial states X1 and X6 and with the cooperation of a mnemonical enzyme. The theory predicts that for an enzyme with a negative cooperation, decreasing the initial concentration of X1 (or increasing that of X6) tends to increase the induction time. This increase may correspond to a reversal of a burst in a lag. Similarly, if the enzyme has a positive cooperation, decreasing the initial concentration of X6 (or increasing that of X1) increases the induction time. The first case above is expected to apply to wheat germ hexokinase LI, X1 being the form that binds glucose preferentially, and X6 the one that binds glucose 6-phosphate. By changing solely the respective concentrations of the two initial forms, one may expect to modify the pre-steady-state phase but not the steady-state kinetics of the reaction. By jumping the temperature of the enzyme solution from 4 degrees C to 30 degrees C and letting the transconformation ewuilibrium relax for various periods of time before mixing enzyme with the substrates, one can analyse the effect of the relative concentrations of X1 and X6 on the induction time. One can estimate in that way one of the rate constants of the transconformation between the two free enzyme forms. The shorter the incubation time at 30 degrees C then the smaller is the negative induction time (in absolute values). Another possibility of controlling the ratio between the two initial concentrations of the enzyme, is to pre-mix hexokinase with glucose 6-phosphate and to arrange that glucose-6-phosphate concentration, after mixing enzyme and substrates, is held constant whatever the pre-mixing conditions. When wheat germ hexokinase LI is pre-mixed 30 min at 30 degrees C with glucose 6-phosphate before the reaction starts, the burst does not disappear. If, on the other hand, pre-mixing is effected at 4 degrees C the burst is reversed into lag. This result is taken to mean that the equilibrium constant between the two free enzyme forms (the 'circle' and the 'rhombus') is strongly dependent on temperature. A direct study of the effect of glucose 6-phosphate on the conformational equilibrium of wheat germ hexokinase, gives support to this interpretation. If hexokinase is mixed at 4 degrees C with glucose 6-phosphate a slow increase in fluorescence of tryptophanyl residues is observed, which indicates that the 'rhombus' conformation accumulates under these conditions. On the other hand, at 30 degrees C, glucose 6-phosphate does not produce any significant change in the fluorescence of the protein. As expected, these results imply that the equilibrium between the two free enzymes species is freely reversible a 4 degrees C and nearly irreversible at 30 degrees C. The equations derived from the mnemonical model allow fitting or simulation of the experimental results.     

Mammalian beta-D-mannosidase and beta-mannosidosis.

Lysosomal beta-D-mannosidase is the last exoglycosidase involved in the sequential degradation of the N-glycosylproteins glycans. Research on this enzyme was restricted before the discovery of its hereditary deficiency, first in goat (1981) and later in man (1986). We describe the biochemical aspects of these beta-mannosidosis and the properties of the beta-mannosidases of mammalian origin. Our own results concerning human enzyme (from kidney and urine, seminal plasma and blood cells) suggest that, apart from the case of the inherited disease, beta-mannosidase may become a useful tool in other pathologies.     

Simple model of recovery dynamics after mass extinction

Biotic recoveries following mass extinctions are characterized by a complex set of dynamics, including the rebuilding of whole ecologies from low-diversity assemblages of survivors and opportunistic species. Three broad classes of diversity dynamics during recovery have been suggested: an immediate linear response, a logistic recovery, and a simple positive feedback pattern of species interaction. Here we present a simple model of recovery which generates these three scenarios via differences in the extent of species interactions, thus capturing the dynamical logic of the recovery pattern. The model results indicate that the lag time to biotic recovery increases significantly as biotic interactions become more important in the recovery process.     

Isolation and identification of a putative porcine transferrin receptor from Actinobacillus pleuropneumoniae biotype 1.

Each of two affinity isolation methods, the first based on biotinylated porcine transferrin plus streptavidin-agarose, and the second on Sepharose-coupled porcine transferrin, followed by SDS-PAGE, allowed the isolation and identification of two potential porcine-transferrin-binding polypeptides (approximately 64 kDa and 99 kDa) from total membranes of Actinobacillus pleuropneumoniae grown under iron-restricted conditions. Both polypeptides were iron-repressible and were identified as potential receptor candidates as they were not isolated when biotinylated human transferrin was used instead of biotinylated porcine transferrin. The 64 kDa polypeptide was the more easily removed from Sepharose-coupled porcine transferrin and only the 99 kDa polypeptide appeared to be an outer-membrane protein. While these results suggest that the 99 kDa polypeptide represents the porcine transferrin receptor of A. pleuropneumoniae, and that the 64 kDa polypeptide represents an associated protein serving an accessory role, other interpretations are also possible.