Jacques Ricard

Self-organization and dynamics of an open futile cycle

Abstract 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 E 2 , which controls recycling of the substrate S 2 , 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 E 1 to be activated by its product S 2 . If it is enzyme E 1 which is inhibited by an excess of its substrate S 1 , the system has a saddle point. Other conditions for stability or instability of the system have been determined. If the enzyme E 1 , 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 E 1 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 E 1 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.

Kinetic and Equilibrium Studies of Cyanide and Fluoride Binding to Turnip Peroxidases

Abstract A stopped-flow and T-jump kinetic study of cyanide and fluoride binding to turnip peroxidases P 1 and P 7 was done in order to gain information on the ionizable groups located in close vicinity to the heme iron. Cyanide binding to P 1 and P 7 as well as fluoride binding to P 1 , occurs in only one detectable step. However, fluoride binding to P 7 exhibits three distinct steps: a “fast” ligand-binding step followed by two “slow” isomerization processes. These processes certainly correspond to slow conformational changes in the protein. A study of pH effects on ligand binding to P 1 and P 7 was also effected. On the basis of this kinetic analysis, it is impossible to decide whether the anionic or the neutral form of the ligand is the attacking species. Two different ionization processes of the heme protein P 1 are required to explain ligand binding and release. The p K s of the ionizable groups on the free enzyme are, respectively, 6.3 and 3.9. The 6.3 value can be tentatively assigned to a histidine and the 3.9 value to a carboxylate residue. The p K values are, respectively, 9.6 and 6.5 for the enzyme-cyanide complex and 6.9 and 6.2 for the enzyme-fluoride complex. The pH dependence of ligand binding to P 7 cannot be explained by the ionization of only two groups. The minimum models derived from kinetic data involve at least three ionization reactions of the enzyme and of the enzyme-ligand complexes. The ionizable groups of the free enzyme are 3.8, 6.7 and 7. One of the two ionization processes close to neutrality corresponds to that previously shown by potentiometry and tentatively assigned to a distal imidazole. As with heme protein P 1 , cyanide and fluoride binding to P 7 results in a shift of the p K . The p K values are, respectively, 7.3, 8 and 8.8 in the enzymecyanide complex and 5, 7 and 10 in the enzyme-fluoride complex. The above results strengthen the view that turnip peroxidases P 1 and P 7 exhibit profound differences in their catalytic behavior.

The alkaline transition of turnip peroxidases

Received April 23, 1976 A stopped-flow kinetic study of the spectral changes which appear during the transi- tion between the neutral and the alkaline form of two turnip peroxidases P1 and P, was conducted. With P1, the kinetics of the spectral changes present three distinct steps: One is fast while the other two are slow. From the pH dependence of the observed rate constant for the fast step, it is proposed that this step might represent deprotonation by the hydroxide anions of a heme-linked group with a pK of 10.1. For P,, only one step was detected which was fast. In this case, the pH dependence of the observed rate constant indicates that a heme-linked group is deprotonated either by water solvent molecules or by hydroxide anions. The simplest explanation for the observed results is that the groups titrated represent a water molecule in the sixth coordination position of the iron for both peroxidases. The small values of the rate constants found for these deprotonation reactions are explained in terms of hydroxide anion binding to the sixth coordination position of the iron or by the existence of a negatively charged electrostatic gate which prevents negatively charged ligands from entering the heme pocket. A reanalysis of the results reported for a similar study with horseradish peroxidase shows that the alkaline transition of this hemoprotein can also be explained in the same manner as for turnip peroxidases.

Enzymes as biosensors. 2. Hysteretic response of chloroplastic fructose-1, 6-bisphosphatase to fructose 2, 6-bisphosphate

Oxidized chloroplastic fructose-bisphosphatase is almost totally inactive at pH 7.5, that is under pH conditions that prevail in the chloroplast stroma. When preincubated for different time periods with fructose 2,6-bisphosphate and assayed in the absence of this ligand, it displays an activity which is directly related to the duration of the preincubation phase. This implies that fructose 2,6-bisphosphate induces enzyme conformers that appear in sequence and may be competent for catalytic activity. Upon desorption of fructose 2,6-bisphosphate the enzyme may retain its active conformation for a time period whose duration depends on magnesium concentration. It thus appears that reduction of the enzyme is not an obligatory prerequisite for its activity. Fructose 2,6-bisphosphate behaves as a competitive inhibitor of the reduced, active enzyme, with respect to the real substrate. When assayed with the oxidized enzyme, however, it behaves as an activator. Moreover the apparent steady-state rate that may be measured experimentally depends on both fructose 2,6-bisphosphate concentration and the direction of a concentration change. The reaction velocity experimentally measured is thus a meta-steady-state rate and depends on the initial conditions of the system. The fructose-bisphosphatase system thus displays, with respect to fructose 2,6-bisphosphate, a hysteresis loop and may then sense whether the concentration of that ligand is increased or decreased. A model has been proposed which allows one to explain these results. This model is based on the view that the substrate and fructose 2,6-bisphosphate compete for the same site of the enzyme and that this latter ligand stabilizes a conformation competent for enzyme activity. After the ligand has been chased away, the enzyme retains the active conformation for a while and slowly relapses to the initial inactive conformation. The time-scale of this slow relaxation overlaps that of the steady state of product appearance and this generates meta-steady-state kinetics, which is dependent on the initial state and therefore on the history of the system.

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.