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, k3, was calculated using early transient time domain data, which are difficult to obtain experimentally. The technique used an iterative approach to calculate k3 with a pair of data and the value of k3 could be retrieved with 35% error. The second technique calculated k3 using stationary domain data and the value of k3 could be retrieved with less than 5% error. This second technique also offered internal consistency in the calculation of k3 by calculating k3 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 k3 from simulated data to the changes in the reaction rate constants (k1, k2, and k3) and the initial concentration of enzyme used for simulation. It was found that the second technique generally worked well in the estimation of k3 except for the simulated data for fast substrate conversions such as in the large k3 and [E]0 cases . This latter method, thus, shows promise for the use of late time experimental substrate/product concentration data to obtain k3. Exclusively using late time data avoids the need for difficult and expensive rapid early time measurement techniques for estimating k3. Once a reasonable estimate for k3 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 k3 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.
Highlights
The reactions between an enzyme and a substrate are usually analyzed by using the substrate and product concentrations measured over time under isothermal conditions
The simplest and most often used enzyme substrate model is the reaction scheme with one substrate, one intermediate, and one product with the recovery of the enzyme (Equation 1) and this model reaction is sufficient to describe the behavior of many enzyme-substrate systems (Bernhard, S.,1968)
The difference with the known value increased for higher k3 values, reaching, for instance, 80 % for k3 equal to 1 (Figure 5), showing that the method becomes significantly less accurate at high k3 values. An explanation for this breakdown in the estimations is that there is the lack of data in the stationary state domain for these cases with high k3 values and this leads to large fitting errors
Summary
The reactions between an enzyme and a substrate are usually analyzed by using the substrate and product concentrations measured over time under isothermal conditions. FIGURA 1 - Simulated concentrations of substrate and product for a reaction medium containing [S]0 = 1, [E]0 = 0.1 relative normalized molar units with rate constants of ki = 1 (i = 1,2,3). It is difficult to obtain the early time product formation rates since enzyme-substrate reactions are generally too fast, and there are typically only one or two data points taken (at best) in the transient period.
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