Mathematical expressions describing enzyme velocity and inhibition at high enzyme concentration

ABSTRACTEnzyme behaviour is typically characterised in the laboratory using very diluted solutions of enzyme. However, in vivo processes usually occur at [ST] ≈ [ET] ≈ Km. Furthermore, the study of enzyme action usually involves analysis and characterisation of inhibitors and their mechanisms. However, to date, there have been no reports proposing mathematical expressions that can be used to describe enzyme activity at high enzyme concentration apart from the simplest single substrate, irreversible case. Using a continued fraction approach, equations can be easily derived to apply to the most common cases in monosubstrate reactions, such as irreversible or reversible reactions and small molecule (inhibitor or activator) kinetic interactions. These expressions are simple and can be understood as an extension of the classical Michaelis-Menten equations. A first analysis of these expressions permits to deduce some differences at high vs low enzyme concentration, such as the greater effectiveness of allosteric inhibitors compared to catalytic ones. Also, they can be used to understand catalyst saturation in a reaction. Although they can be linearised following classical approaches, these equations also show some differences that need to be taken into account. The most important one may be the different meaning of line intersection points in Dixon plots. All in all, these expressions may be useful tools for the translation in vivo of in vitro experimental data or for modelling in vivo and biotechnological processes.

Role of a Mutation at Position 167 of CTX-M-19 in Ceftazidime Hydrolysis

ABSTRACT CTX-M-19 is a recently identified ceftazidime-hydrolyzing extended-spectrum β-lactamase, which differs from the majority of CTX-M-type β-lactamases that preferentially hydrolyze cefotaxime but not ceftazidime. To elucidate the mechanism of ceftazidime hydrolysis by CTX-M-19, the β-lactam MICs of a CTX-M-19 producer, and the kinetic parameters of the enzyme were confirmed. We reconfirmed here that CTX-M-19 is also stable at a high enzyme concentration in the presence of bovine serum albumin (20 μg/ml). Under this condition, we obtained more accurate kinetic parameters and determined that cefotaxime (k cat /Km , 1.47 × 106 s−1 M−1), cefoxitin (k cat /Km , 62.2 s−1 M−1), and aztreonam (k cat /Km , 1.34 × 103 s−1 M−1) are good substrates and that imipenem (k +2 /K, 1.20 × 102 s−1 M−1) is a poor substrate. However, CTX-M-18 and CTX-M-19 exhibited too high a Km value (2.7 to 5.6 mM) against ceftazidime to obtain their catalytic activity (k cat). Comparison of the MICs with the catalytic efficiency (k cat /Km ) of these enzymes showed that some β-lactams, including cefotaxime, ceftazidime, and aztreonam showed a similar correlation. Using the previously reported crystal structure of the Toho-1 β-lactamase, which belongs to the CTX-M-type β-lactamase group, we have suggested characteristic interactions between the enzymes and the β-lactams ceftazidime, cefotaxime, and aztreonam by molecular modeling. Aminothiazole-bearing β-lactams require a displacement of the aminothiazole moiety due to a severe steric interaction with the hydroxyl group of Ser167 in CTX-M-19, and the displacement affects the interaction between Ser130 and the acidic group such as carboxylate and sulfonate of β-lactams.

The analysis of metabolite channelling in multienzyme complexes and multifunctional proteins

Multienzyme complexes and multifunctional proteins may confer a kinetic advantage by channelling reaction intermediates between consecutive enzymes and reducing the transient time for the establishment of steady states. A general means for quantitatively assessing the contribution of channelling to the reduction of pool size and transient time is presented. Restrictions to the kinetic advantage are identified, and it is shown that no channelling advantage is obtained at high enzyme concentration or for enzymes which exhibit rapid-equilibrium kinetic behaviour.