rates with expanded linear ranges and practical analysis efficiency. This integration strategy is effective at substrate concentrations from one-eighth of $K_m$ to three-fold of $K_m$ (Li, et al., 2011; Liao, et al., 2009; Liu, et al., 2009; Yang, et al., 2011). The integration strategy for enzyme initial rate assay uses a special method to convert $V_m$ into initial rates so that the indexes of enzyme activities by both methods become the same; it is applicable to enzymes suffering strong inhibition by substrates/products (Li, et al., 2011). Walsh et al. proposed an integration strategy to measure enzyme initial rate but they employed Equ.(9) that requires substrate levels below 10% of $K_m$ (Walsh, et al. 2010). Our integration strategy is valid at any substrate level to satisfy Equ.(2) and hence can be a universal approach to common enzymes of different $K_m$. The principles and applications of the integration strategy to one enzyme reaction systems and enzyme-coupled reaction systems are discussed below.
As for one enzyme reaction systems, kinetic analysis of reaction curve can be realized with an integrated rate equation after data transformation; the integration strategy for enzyme initial rate assay requires enzyme kinetics on single substrate and an integrated rate equation with the predictor variable of reaction time (Liao, et al., 2003a, 2005a, Zhao, L.N., et al., 2006). Moreover, the integration strategy should solve the following challenges: (a) there should be an overlapped range of enzyme activities measurable by both methods with consistent results; (b) there should be consistent slopes of linear response for enzyme activities to enzyme quantities by both methods (Figure 1). After these two challenges are solved, the linear segment of response by the classical initial rate method is an extended line of the linear segment of response by kinetic analysis of reaction curve (Liu, et al., 2009).
To solve the first challenge, a practical $S_0$ and reasonable duration to monitor reaction curve for favourable analysis efficiency are required as optimized experimental conditions. By mathematic derivation and simulation analyses to solve the first challenge, it is demonstrated that a ratio of $S_0$ to $K_m$ from 0.5 to 2.5, the duration of 5.0 min to monitor reaction curves at intervals no longer than 10 s can solve the first challenge for most enzymes, any ratio of $S_0$ to $K_m$ smaller than 0.5 or larger than 2.5 requires longer duration to monitor reaction curves. The use of $S_0$ about one-eighth of $K_m$ requires no shorter than 8.0 min to monitor reaction curves at 10-s intervals to solve the first challenge (Li, et al., 2011; Liu, et al., 2009). When $S_0$ is too much larger than three times $K_m$, reaction time to record reaction curves for analysis to solve the first challenge should be much longer than 5 min. Clearly, the first challenge can be solved with practical $S_0$ for favourable analysis efficiency.
To solve the second challenge, $K_m$ and other parameters should be optimized and fixed as constants to estimate $V_m$ by kinetic analysis of reaction curve, and a preset substrate concentration (PSC) should be optimized to convert $V_m$ into initial rates according to the differential rate equation. In theory, a reliable $V_m$ should be independent of ranges of data when they are reasonably restricted, and CVs for estimating parameters by enzymatic analysis are usually about 5%. Hence, the estimation of $V_m$ with variations below 3% for the changes of substrate consumption percentages from 60% to 90% can be a criterion to select the optimized set of preset parameters. For converting $V_m$ into initial rates, the optimized PSC is usually about 93% of $S_0$ and can be refined for different enzymes (Li, et al., 2011; Liao, et al., 2009; Liu, et al., 2009; Yang, et al., 2011). Optimized $K_m$ and PSC to solve the second challenge are parameters for data processing while optimized $S_0$ and reaction duration to solve the first challenge are experimental conditions. The concomitant solution of the two challenges provides feasibility and potential reliability to the integration strategy.