Computer fittings

Figure 10.24a and the allosteric model in Figure 10.24b. The circled data points were changed very slightly to cause an F-test to prefer either model for each respective model, illustrating the fallacy of relying on computer fitting of data and statistical tests to determine molecular mechanism. As discussed in Chapter 7, what is required to delineate orthosteric versus allosteric...

FIGURE 10.24 Simulation data set fit to an allosteric model (Equation 7.6 panel a) and to an orthosteric model (Equation 6.31 panel b). The data points circled with the dotted line were altered very slightly to cause the sum of squares for computer fit of the points to the model to favor either the allosteric or orthosteric model. It can be seen that very small differences can support either model even though they describe completely different molecular mechanisms of action. 

Only a few quantitative data are available on copolymerization of methacrylates. Direct determination of the cross-propagation constants is readily achieved in living polymer systems whenever the absorption spectra of the two propagating species are different. Unfortunately, this is not the case in the methacrylate series. A new approach to this problem was developed by Muller 43). A mixture of two monomers is copolymerized, the reaction is interrupted at various times, and the concentrations of the residual monomers are determined as functions of time. The pertinent differential equations include 4 constants ku, k12, k21, and k22. Since kn and k22 were independently determined, the remaining cross-propagation constants are obtained by computer fitting the experimental conversion curves to the calculated ones. 

Table II. MCssbauer Spectral Parameters Obtained from Computer Fitting Spectra of Figure 1...

Fig. 8.4 Fe Mossbauer spectra of [Fe(2-pic)3]Cl2 C2H50H as a function of temperature source Co/Cu at room temperature). The outer two lines represent the quadrupole doublet of the T2 (HS) state, the inner two lines that of the Aj (LS) state. The solid lines are obtained by a least-squares computer fit of Lorentzian lines to the experimental spectra (from [11])...

Figure 2. Hel photoelectron spectra of Mo2(TFA)k (left) and W2(TFA)k (right). The spectra have been computer fitted to combination Lorentzian-Gaussian peaks. (Reproduced with permission from Ref. 4. Copyright 1982, The Royal Society of Chemistry.)...

For other cases, such as La3+ where more detail is required about the nature of the species present in solution, titration data can be computer fit to more complicated multi-equilibrium models containing Mx 1 v( OR)v forms whose stoichiometry is suggested by information gained from independent spectroscopic or kinetic techniques. One must be mindful of the pitfalls of simply fitting the potentiometric data to complex multi-component models for which there is no independent evidence for the various species. Without some evidence for the species put into the fit, the procedure simply becomes an uncritical mathematical exercise of adding and removing various real and proposed components until the goodness of fit is satisfactory. 

The EXAFS study on Ru-Cu/Si02 of Sinfelt et al. [39] is one of the few examples where conclusions can be drawn on a qualitative base without the need to construct computer fits to the data. The following example illustrates EXAFS as a quantitative tool in a study of particle sizes. 

Fig. 58 Computer fit of the Nemst equation to the rotating disk electrode electrochemistry, at 121 rpm, of [100] (5 X 10-4 mol dm-3) in CH2C12 with BuJNBF4 (0.1 mol dm-3) as supporting electrolyte.

We also examined the effects of various heat treatments in both reducing and oxidizing atmospheres. An indochinite reduced for 12 hours in a hydrogen atmosphere at 950 °C. yielded the Mossbauer spectrum displayed in Figure 5. The curve shown is the result of the computer fit the data points are not given, but the closeness of fit is about the same as in the other spectra. The spectrum clearly shows that a certain amount of the original tektite remains the two broad lines at —0.11 and 1.83 mm./sec. match the original tektite lines closely. There is also clear evidence of the presence of metallic iron since the six narrow... 

The positions, widths, and heights of the lines were determined by least-squares computer fits to the sum of four Lorentzian lines with no restrictions connecting these 12 parameters. The criterion for a good fit was the sum of the squared deviations divided by the number of data points, and statistically it was reasonably satisfactory in all cases. The general trends in Tables XI and XII are clear. The discrepancies are probably caused in part by the inadequacies of the fitting procedure, especially the lack of provision for the evident peak height asymmetry... 

The pharmacokinetics of hyperforin have been studied in rats and humans (Biber et ai. 1998). In rats, after a 300 mg/kg orai dose of hypericum extract (WS 5572, containing 5% hyperforin), maximum piasma ieveis of 370 ng/mi (690 nM) are achieved at 3 hours. The haif-iife of hyperforin is 6 hours. Humans given a 300 mg tabiet of hypericum (containing 14.8 mg hyperforin) showed maximum piasma ieveis of 150 ng/mi (280 nM) at 3.5 hours. The haif-iife is 9 hours, and mean residence time is 12 hours. Pharmacokinetics of hyperforin are iinear up to 600 mg, and no accumuiation occurs after repeated doses. By comparison, effective and safe piasma ieveis of paroxetine and fluoxetine vary between 40 and 200 ng/mi (Preskorn 1997). The effective piasma concentration of hyperforin predicted from computer-fit data is approximateiy 97 ng/mi (180 nM), which couid be easiiy monitored (Biber et ai. 1998). There is a iinear correiation between orai dose of hyperforin and piasma ieveis, and steady-state concentrations of 100 ng/mi (180 nM) couid be achieved with three-times-daiiy dosing. 

Drago and co-workers Introduced an empirical correlation to calculate the enthalpy of adduct formation of Lewis acids and bases ( 5). In 1971, he and his co-workers expanded the concept to a computer-fitted set of parameters that accurately correlated over 200 enthalpies of adduct formation ( ). These parameters were then used to predict over 1200 enthalpies of interaction. The parameters E and C are loosely Interpreted to relate to the degree of electrostatic and covalent nature of the Interaction between the acids and bases. This model was used to generalize the observations involved in the Pearson hard-soft acid-base model and render it more quantitatively accurate. 

We thank Professor Bruce Robinson for valuable discussions on EPR measurements and Professor Alvin Kwiram for use of his EPR instrument. Michael Russell provided computer fitting routines and Eric Shank I and provided purified samples. This research was supported in part by NSF grant DMR-7823958. 

Computer Fit of a nmr Spectrum Using Method of Conditional Probabilities... 

Since steric effects of the F-strain variety are not an inherent property of the acid or base, but a function of the geometry of the adduct, we would not expect our parameters to incorporate this effect. When this data is included in an attempted computer fit, large deviations between experimental and calculated values are observed for these systems. Consequently, in attempting to obtain meaningful parameters, data in... 

The correlation coefficients generated for mono-, bi- and triexponential fits obtained by nonlinear regression analyses are summarized in Table 1. Wilson el al. [8] reported that the rate of tobramycin release from Simplex PMMA beads could be fitted to monoexponential and power functions however, they obtained r2 values<0.9 for both fits. Our results show that, although the monoexponential fit is poor, both biexponential and triexponential fits provided r2 values>0.9. Since the biexponential relationship in equation (2) is proposed to fit our physical model, this approach was adopted in analysis of computer fits to release data. The rate constants, a and P, represent an initial, rapid surface release and a prolonged matrix diffusion-controlled release respectively. 

In order to clarify in detail the appearance of this new peak, the carbonyl carbon region and the Ca, Cp and Cy carbon region in the spectrum of the PLA/PLV blend, with a mixture ratio of 50/50, were expanded as shown in Fig. 6. By computer-fitting the observed spectrum was decomposed to a sum of Lorentzian lines, and then the components of the a-helix and p-sheet forms for PLA and PLV were determined. 

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