Estimating the turnover number in enzyme kinetic reactions using transient and stationary state data

Abstract

Substrate and product concentration data obtained by simulating enzyme-substrate reaction rate equations were used to test two proposed kinetic rate constant estimation techniques in this study. In the first technique, the turnover number, k 3 , was calculated using early transient time domain data, which are difficult to obtain experimentally. The technique used an iterative approach to calculate k 3 with a pair of data and the value of k 3 could be retrieved with 35% error. The second technique calculated k 3 using stationary domain data and the value of k 3 could be retrieved with less than 5% error. This second technique also offered internal consistency in the calculation of k 3 by calculating k 3 both from the intercept and the slope of the linear plot derived in this study. A series of sensitivity analyses was conducted to understand the robustness of the second technique in estimating k 3 from simulated data to the changes in the reaction rate constants (k 1 , k 2 , and k 3 ) and the initial concentration of enzyme used for simulation. It was found that the second technique generally worked well in the estimation of k 3 except for the simulated data for fast substrate conversions such as in the large k 3 and [E] 0 cases . This latter method, thus, shows promise for the use of late time experimental substrate/product concentration data to obtain k 3 . Exclusively using late time data avoids the need for difficult and expensive rapid early time measurement techniques for estimating k 3 . Once a reasonable estimate for k 3 is obtained, the initial enzyme value can easily be determined from the maximum velocity constant established from fitting the Michaelis-Menten or Briggs-Haldane equations to substrate and product stationary state domain (late time) data. While the first technique can estimate k 3 with only one point in the transient domain, it is suggested that the second method generally be favored since it only requires late-time stationary domain data and appears to be more accurate. Uniterms:Enzyme. Kinetics/rate constant. Enzyme reactions.Dados de concentração de substrato e de produto obtidos por simulação de equações de velocidade de reação enzima-substrato foram usados neste estudo para testar duas técnicas para estimar constantes cinéticas. Na primeira técnica, a constante, k 3 , foi calculada utilizando os dados de domínio do tempo inicial de transição, que são difíceis de serem obtidos experimentalmente. A técnica usou uma aproximação iterativa para calcular k 3 cujo valor pôde ser estimado com erro de 33%. A segunda técnica calculou k 3 usando dados de domínio no estado estacionário e o valor de k 3 pôde ser estimado com erro de 5%. Esta segunda técnica também ofereceu uma consistência interna no cálculo de k 3 , por calculá-lo tanto pela intersecção quanto pela inclinação da reta derivada deste estudo. Uma série de análises de sensibilidade foi realizada para avaliar a robustez da segunda técnica na estimativa de k 3 utilizando dados que foram simulados quanto às mudanças nas constantes de t...