The kinetic properties of a soybean cell wall phosphatase were studied and compared under different environmental conditions. The native enzyme isolated from the wall exhibits classical Michaelis Menten kinetics. When buried into the cell wall, its natural environment, the enzyme mimics an apparent negative cooperativity. This deviation from hyperbolic dependence of the activity vs. the substrate concentration may result from an heterogeneous distribution of the enzyme molecules between the surface and the inside of the wall, where an electrostatic partition effect takes place. Cell wall fragments compacted on a Millipore-type membrane allow the study of the dual effects of diffusional hindrances and electrostatic interactions on the global kinetic behavior. By increasing the ionic strength, partition effects can be suppressed and therefore diffusional effects alone can be taken into account. On the one hand, diffusion and partition act individually and synergetically to decrease the apparent global affinity of phosphatase with respect to glucose 6-phosphate. On the other hand, product inhibition by inorganic phosphate is subjected to dual effects from diffusion through accumulation and partition through repulsion. A simple diffusion partition reaction model accounts qualitatively and quantitatively for the experimental observations.

The dynamic properties of the glucose/glucose-6-phosphate cycle are studied under conditions where the phosphatase and kinase interconverting enzymes are spatially distributed. A semi-artificial membrane made of compacted plant cell walls bearing active phosphatase in its natural state, separates two compartments, one of these compartments containing soluble hexokinase. Depending only upon the two enzyme activity levels and the initial distribution of the substrates, numerous asymmetrical and vectorial behaviours can be observed, such as facilitated glucose 6-phosphate diffusion, active transport of either glucose or glucose 6-phosphate and sequential (alternative) transport between glucose and glucose 6-phosphate. A diffusion-partition reaction coupling can account for these oriented mass transfers. The possibility of such a coupling in this model system is clearly dictated by the global analog of the Curie principle. These results may provide new insight on (a) the still obscure role played by the cell-wall phosphatase activities, particularly their involvement in the transport of exogenous phosphomonoesters, and (b) the actual in vivo operation of substrate and protein cycles in view of the heterogeneity and anisotropy of the cellular milieu.Cyclic processes are ubiquitous in metabolism. These processes are involved in many activities such as oxidation and synthesis, generation of energy and reducing equivalents. These cycles occur when two opposing metabolic pathways operate in which the reaction(s) in the forward and reverse directions are catalyzed by different enzymes. If the simultaneous operation of these two interconverting enzymes leads to the hydrolysis of an energy-rich compound (e.g. ATP, GTP) with no net flux of metabolites, such cycles are designated as futile. This latter situation is most frequently encountered in the phosphorylatioddephosphorylation cycles involving both low-molecular-mass metabolites (sugars, amino acids, nucleotides) and proteins, including enzymes (with covalent modifications).The role played by cycles (futile or not) in the regulation of metabolism is still a matter of controversy. However, from experimental data and theoretical considerations, it is likely that substrate (protein) cycling is involved in thermogenesis, the orientation of fluxes, the control of concentrations, and the amplification of sensitivity, particularly when organized in cascades [l-71. When dealing with cycles subjected to a destabilizing factor (product activation, substrate inhibition), more sophisticated dynamic behaviours may be observed, such as multistationarity (alternative steady states, reversible or irreversible), sustained oscillations or chaotic motions [8 -121.However, most of these cycles are implicitly supposed to operate under homogeneous and isotropic conditions. Many situations are known where either the enzyme or metabolite partners are spatially (heterogeneously) distributed between cellular compartments. Interconverting catalysts can also be located in or on membrane structures....