$$ \begin{aligned} C_{p,i+1} = C_{p,i} + V_{1k} \times \Delta t - & \ & V_m \times \frac{\Delta t}{(1 + K_a/C_{n,i} + K_b/C_{p,i} + K_{ab}/(C_{n,i} \times C_{p,i}))} \end{aligned} \quad (11) $$
By simulation with such a new approach for kinetic analysis of enzyme-coupled reaction curve recorded at 1-s intervals, the upper limit of linear response for measuring ALT initial rates is increased to about five times that by the classical initial rate method. This new approach is resistant to reasonable variations in data range for analysis. By experimentation using the sampling intervals of 10 s, the upper limit is about three times that by the classical initial rate method. Therefore, this new approach for kinetic analysis of enzyme-coupled reaction curve is advantageous, and can potentially be a universal approach for kinetic analysis of reaction curve of any system of much complicated kinetics.
The computation time for numerical integration is inversely proportional to the integration step, $\Delta t$; the use of shorter $\Delta t$ is always better but $\Delta t$ of 0.20 s at low cost on computation is sufficient for a desirable upper limit of linear response. This new approach with Celeron 300A CPU on a personal computer needs about 10 min for just 30 data in a LDH-coupled reaction curve, but it consumes just about 5 s with Lenovo Notebook S10e. The advancement of personal computers surely can promote the practice of this approach.
2.4 Integration of kinetic analysis of reaction curve with other methods
Any analytical method should have favourable analysis efficiency, wide linear range, low cost and strong robustness. Kinetic analysis of reaction curve for $V_m$ and $S_0$ assay can have much better upper limit of linear response, but inevitably tolerates low analysis efficiency when wide linear range is required. Based on kinetic analysis of reaction curve, however, our group developed two integration strategies for enzyme initial rate and substrate assay, respectively, with both favourable analysis efficiency and ideal linear ranges.
2.4.1 New integration strategy for enzyme initial rate assay
The classical initial rate method to measure enzyme initial rates requires $S_0$ much higher than $K_m$ to have desirable linear ranges (Bergmeyer, 1983; Dixon & Webb, 1979; Guilbault, 1976; Marangoni, 2003). Due to substrate inhibition, limited solubility and other causes, practical substrate levels are always relatively low and thus the linear ranges by the classical initial rate method are always unsatisfactory (Li, et al., 2011; Morishita, et al., 2000; Stromme & Theodorsen, 1976). As described above, kinetic analysis of reaction curve can measure enzyme $V_m$, and many approaches based on kinetic analysis of reaction curve are already proposed (Cheng, et al., 2008; Claro, 2000; Cornish-Bowden 1975, 1995; Dagys, et al., 1986, 1990; Duggleby, 1983, 1985, 1994; Hasinoff, 1985; Koerber, & Fink, 1987; Liao, et al., 2001; Lu & Fei, 2003; Marangoni, 2003; Walsh, et al. 2010). Such approaches all require substrate consumption percentage over 40% with $K_m$ preset as a constant. As a result, there should be intolerably long reaction duration to monitor reaction curves for samples of low enzyme activities, or else the lower limits of linear response are unfavourable.
The integration of kinetic analysis of reaction curve using proper integrated rate equations with the classical initial rate method gives an integration strategy to measure enzyme initial