Jean-Michel Soulie

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.

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.

The pH-induced dissociation of fructose 1,6-bisphosphatase of spinach chloroplasts

Fructose 1,6-bisphosphatase from higher plants is receiving considerable attention [l-4]. The reason for this interest rests on the belief that this enzyme plays a major role in the control by light of the Calvin cycle [5,6]. Buchanan and his colleagues have suggested [7,8] that thioredoxin, reduced by electrons from photosystem I, reacts with fructose 1,6-bisphosphatase, thus reducing disulfide bonds of this enzyme and leading to a conformation change itself associated with a modulation of its activity. Fructose 1 ,Gbisphosphatase from spinach chloroplasts is a tetramer with apparently identical subunits and a MW of 160 000. Raising the pH from 7.5 to 8.8 results in the dissociation of the enzyme in two equal halves of MW 80 000 121. Whereas the tetramer is active the dimer is almost devoid of activity. Since it is widely accepted that the pH of the chloroplast stroma changes upon illumination [9], it is of interest to study the kinetics of a conformational transition associated with the dissociation reaction and to relate this process to a possible change in the accessibility of sul~ydryl groups, for these groups are believed to play a key role in the activation-deactivation process of the enzyme [2]. This is the aim of the present paper.

Sensing of Chemical Signals by Enzymes

Living systems are able to sense the intensity of chemical signals originating from the external milieu and are able to detect whether this intensity increases or decreases. Chemotaxis of bacteria represents a striking example of these sensory properties defined at a rather simple level (Koshland, l979, 1980ab, 1981). Bound enzyme systems in which diffusion is a limiting process may also display these sensory properties (Engasser & Horvath, 1974, 1976; Ricard, 1987). This implies that the system possesses a memory and that its response is different depending on whether the concentration of a ligand increases or decreases. In other words the response of the system is sensitive to its history. Nucleic acids may display metastable secondary structures upon their titration and therefore may exhibit hysteresis effects (Revzin et al., 1973, Neumann, 1973, Schneider, 1976).

Thermodynamics and Kinetics of the Interactions of Thioredoxin Fb with Fructose Bisphosphatase from Spinach Chloroplast

One of the most important process involved in the photoregulation of chloroplast enzymes is their oxidoreductive modification by protein mediators known as thioredoxins (1). Different molecular species of thioredoxins from Spinach chloroplast have been purified and characterized (2). The reductive activation of fructose bisphosphatase is due to the reduction of two disulfide bridges followed by a conformation change of the protein (3). Very little was known, till recently about molecular interaction occuring between the enzyme and its protein effector. We discuss here the binding properties and the kinetics of inactivation of fructose bisphosphatase (FBPase) by thioredoxin fb.