A method for writing enzyme rate equations: application to the estimation of the number and size of key proton families

We develop a method to derive the rate equation for enzyme models that include pH-dependent activation. Our presentation is based on a kinetic model recently described for sucrase, the three-key-proton model of Vasseur and coworkers, which considers the existence, in the acid ionization reaction, of two functionally distinct prototropic groups, respectively responsible for either V-type or K-type kinetic effects. In contrast, as concerns the basic ionization reaction, the model conforms to classical concepts of pH-dependent activation, whereby a single proton participates in either V-type or K-type effects but not in both at the same time. Enzymes with more than three key protons have been described, indicating that, rather than isolated protons, groups of protons should be considered, and therefore the model can be better described as a three-proton-family model, where a proton family is defined as one or several protons that are gained or lost as a block and perform the same kinetic function. The resulting model is treated here as a useful framework upon which other models can be built. To facilitate the writing of the rate equations, we define two new entities: (1) intralevel coefficients, which describe the various combinations of the enzyme with either the substrate(s), the allosteric effector(s), or both at a given protonation level, and (2) interlevel coefficients, which describe the interplay between the various protonation levels. The resulting rate equation can be used in a global fit procedure permitting in a single computer run the estimation of (1) the entire set of dissociation and microscopic ionization constants of the model, (2) the number and kinetic function of proton families characterizing the enzyme under consideration, and (3) the number of key protons constituting each family, which is derived from the derivatives of the kinetic parameters, Vm/Km, Vm, and Km.     

Characterization of competent cells and early events of Agrobacterium-mediated genetic transformation in Arabidopsis thaliana

The insertion of foreign DNA in plants occurs through a complex interaction between Agrobacteria and host plant cells. The marker gene β-glucuronidase of Escherichia coli and cytological methods were used to characterize competent cells for Agrobacterium-mediated transformation, to study early cellular events of transformation, and to identify the potential host-cell barriers that limit transformation in Arabidopsis thaliana L. Heynh. In cotyledon and leaf explants, competent cells were mesophyll cells that were dedifferentiating, a process induced by wounding and-or phytohormones. The cells were located either at the cut surface or within the explant after phytohormone pretreatment. In root explants, competent cells were present in dedifferentiating pericycle, and were produced only after phytohormone pretreatment. Irrespective of their origin, the competent cells were small, isodiametric with thin primary cell walls, small and multiple vacuoles, prominent nuclei and dense cytoplasm. In both cotyledon and root explants, histological enumeration and β-glucuronidase assays showed that the number of putatively competent cells was increased by preculture treatment, indicating that cell activation and cell division following wounding were insufficient for transformation without phytohormone treatment. Exposure of explants for 48 h to A. tumefaciens produced no characteristic stress response nor any gradual loss of viability nor cell death. However, in the competent cell, association between the polysaccharide of the host cell wall and that of the bacterial filament was frequently observed, indicating that transformation required polysaccharide-to-polysaccharide contact. Flow cytofluorometry and histological analysis showed that abundant transformation required not only cell activation (an early state exhibiting an increase in nuclear protein) but also cell proliferation (which in cotyledon tissue occurred at many ploidy levels). Noncompetent cells could be made competent with the appropriate phytohormone treatments before bacterial infection: this should aid analysis of critical steps in transformation procedures and should facilitate developing new strategies to transform recalcitrant plants.     

pH-dependent inhibitory effects of tris and lithium ion on intestinal brush-border sucrase

Tris and two of its hydroxylated amine analogs were examined in a metal-free, universal n-butylamine buffer, for their interaction with intestinal brush border sucrase. Our recent three-proton-families model (Vasseur, van Melle, Frangne and Alvarado (1988) Biochem. J., 251, 667-675) has provided the sucrase pK values necessary to interpret the present work. At pH 5.2, 2-amino-2-methyl-l-propanol (PM) causes activation whereas Tris has a concentration-dependent biphasic effect, first causing activation, then fully competitive inhibition. The amine species causing activation is the protonated, cationic form. The difference between the two amines is related to the fact that Tris has a much lower pKa value than PM (respectively, 8.2 and 9.8). Even at pH 5.2, Tris (but not PM) exists as a significant proportion of the free base which, by inhibiting the enzyme fully competitively, overshadows the activating effect of the cationic, protonated amine. Above pH 6.8, both Tris and PM act as fully competitive inhibitors. These inhibitions increase monotonically between pH 6.5 and 8.0 but, above pH 8, inhibition by 2.5 mM Tris tends to diminish whereas inhibition by 40 mM PM increases abruptly to be essentially complete at pH 9.3 and above. As pH increases from 7.6 to 9.0, the apparent affinity of the free amine bases decreases whereas that of the cationic, protonated amines, increases. In this way, the protonated amines replace their corresponding free bases as the most potent inhibitors at high pH. The pH-dependent inhibition by 300 mM Li+ is essentially complete at pH 8, independent of the presence or absence of either 2.5 mM Tris or 40 mM PM. Even at pH 7.6, an excess (300 mM) of Li+ causes significant increases in the apparent Ki value of each Tris, PD (2-amino-2-methyl-1-3-propanediol) and PM, suggesting the possibility of a relation between the effects of Li+ and those of the hydroxylated amines which in fact are mutually exclusive inhibitors. The inhibitory results are interpreted in terms of a mechanistic model in which the free bases bind at two distinct sites in the enzyme's active center. Binding at the glucosyl sub-site occurs through the amine's free hydroxyl groups. This positioning facilitates the interaction between the lone electron pair of the deprotonated amino group with a proton donor in the enzyme's active center, characterized by a pK0 around 8.1. When this same group deprotonates, then the protonated amines acting as proton donors replace the free bases as the species giving fully competitive inhibition of sucrase.