Iterative method kinetic data analysis

A class of statistical methods frequently used to analyze kinetic and thermodynamic data. Most of these methods require a preliminary estimate of the constants followed by cycles of iterative calculations that converge on a final value(s). Cleland has presented a protocol for the statistical estimation of kinetic data. A nonlinear analysis has also been applied to progress curves. ... 

The Iterative Method and Linear Least-Squares Regression Analysis of Kinetic Data... 

Under the same reaction conditions, the equilibrium method can determine Ame for ethanol below 0.20 mmol/L after reaction for 50 min. For kinetic analyses of such reaction curves, the lag time for steady-state reaction is estimated to be over 40 s and is used to select data of steady-state reaction for analysis. Using the equilibrium method as the reference method, the best steady-state Caid for data of 6.0-min reaction is obtained for consistency of A k with Ame at each tested ethanol level from 10 tmol/L to 0.17 mmol/L. After dilution and determination by the equilibrium method, Ame for each tested ethanol level from 0.17 mmol/L to 0.30 mmol/L is also available. Consequently, an exponential additive function is obtained to apvproximate the correlation of the best Caid for predicting Amk consistent with Ame (Fig. 9). This special correlation function for Caid and Amk is used as a restriction function to iteratively adjust Caid for predicting Amk namely, iterative kinetic analysis of reaction curve with Caid predicted from the restriction function using previous Amk finally gives the desired Amk- Such an artificial intelligence approach to the steady-state Caid for kinetic analysis of reaction curve can hardly be found in publications. 

The mathematical solution of the pharmacokinetic model depicted by Figure 5 Is described by Equation 5, where K12 and K23 are first order rate constants analogous to Ka and Ke, respectively. This solution was applied to the data and "best fit" parameters estimated by Iterative computational methods. The "fit" of the data to the kinetic model was analyzed by least squares nonlinear regression analysis ( ). 

The approach to a correct model through kinetic investigations is an iterative process preliminary experiments result in a proposed model. Simulation of this model allows predictions to be tested with further experiments. These experiments result in alterations or refinements of the model and so on (hopefully not ad infinitum). Methods for simulations of models and the least square analysis of experimental and simulated data, are discussed in chapter 2. Jencks (1989) gives the warning that models can take on a life of their own. He points out that mathematical models which explain all the data can be physically unrealistic. A bon mot attributed to Francis Crick is if a theory explains all the facts it is likely to be wrong because some of the facts will be wrong . 

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