For this prerequisite, the first and the last points of data in a reaction curve for analysis should be carefully selected. The first point should exclude data within the lag time of steady-state reaction. The last point should ensure data for analyses to have substrate concentrations high enough for steady-state reaction. Namely, substrate concentrations should be much higher than the concentration of the active site of the enzyme (Dixon & Webb, 1979). The use of special weighting functions for NLSF can mitigate the contributions of residual squares at low substrate levels that potentially obviate steady-state reaction.
The fourth prerequisite is that the enzyme should be stable to validate Equ.(2), or else the inactivation kinetics of the enzyme should be included in the kinetic model. Enzyme stability should be checked before kinetic analysis of reaction curve. When the inactivation kinetics of an enzyme is included in a kinetic model for kinetic analysis of reaction curve, the integrated rate equation is usually quite complex or even inaccessible if the inactivation kinetics is too complex. For kinetic analysis of reaction curve of complicated kinetics, numerical integration to produce calculated reaction curves for NLSF to a reaction curve of interest, instead of NLSF with Equ.(4), can be used to estimate parameters (Duggleby, 1983, 1994; Moruno-Davila, et al., 2001; Varon, et al., 1998; Yang, et al., 2010).
The fifth prerequisite is that there should be negligible inhibition/activation of activity of an enzyme by products/substrates, or else such inhibition/activation on the activity of the enzyme by its substrate/product should be included in an integrated rate equation for kinetic analysis of reaction curve (Zhao, L.N., et al., 2006). For validating Equ.(2), any substrate that alters enzyme activity should be preset at levels low enough to cause negligible alterations; any product that alters enzyme activity can be scavenged by proper reactions. When such alterations are complex, numerical integration of differential rate equations for NLSF to a reaction curve of interest can be used (Duggleby, 1983, 1994; Moruno-Davila, et al., 2001; Varon, et al., 1998).
Obviously, the first three prerequisites are mandatory for the inherent reliability of parameters estimated by kinetic analysis of reaction curve; the later two prerequisites are required for the validity of Equ.(2) or its equivalency for kinetic analysis of reaction curve.
2.2 Realization of NLSF and limitation on parameter estimation
To estimate parameters by kinetic analysis of reaction curve based on NLSF, the main concerns are the satisfaction to the prerequisites for the quality of data under analysis, the procedure to realize NLSF, and the reliability of parameters estimated thereby.
For the estimation of parameters by kinetic analysis of reaction curve, there are two general prerequisites for the quality of data under analysis: (a) there should be a minimum number of the effective data whose changes in signals are over three times the random error; (b) there should be a minimum consumption percentage of the substrate in such effective data for analysis. In general, at least two parameters like $V_m$ and $S_0$ should be estimated; the minimum number of the effective data should be no less than 7 (Atkins & Nimmo, 1973; Baywenton, 1986; Miller, J. C. & Miller, J. N., 1993). The minimum consumption percentage of the substrate can be about 40% if only $V_m$ and $S_0$ are estimated while other parameters are fixed as constants. In general, the estimation of more parameters requires higher consumption percentages of the substrate in the effective data for analysis.