Nonlinear Curve Fitting Method Research Articles

Automatic titration by stepwise addition of equal volumes of titrant. Part VIII. Determination of alkalinity and total carbonate in sea water

Previous parts of this series have presented methods for the evaluation of titration data. This paper shows the utility of some of these methods and extensions of them for solving a practical problem, i.e., the determination of alkalinity and total carbonate in sea water. The procedure is based on the solution of a set of linear equations.The method presented has been tested on theoretical and experimental titration data and has given results that compare extremely well with those obtained by using non-linear curve-fitting methods.

A SIMPLIFIED METHOD OF DNA DISTRIBUTION ANALYSIS

Current methods of analysing DNA distributions utilize complex mathematical expressions that require the use of large non-linear curve fitting methods and, consequently, large computers. This paper presents a new method of analysing DNA distributions of asynchronously growing or mildly perturbed cells. The S phase fraction is obtained by fitting a second degree polynomial to that part of the distribution, mid S phase, which is not influenced by either the G1 or the G2 + M peaks. The method is simple and fast, it exceeds the accuracy of other methods and it can be used on a large desk calculator or mini-computer.

River and Cooling Water Temperature Fluctuations

Cooling water discharged from a power plant changes the fluctuating water temperature characteristics of a receiving river in a clearly detectable way. Daily and hourly water temperature data from two power plant sites on the Upper Mississippi River were used to compute for illustration the magnitude of such differences. Extreme value analysis, autocovariance and spectral analysis, and nonlinear curve fitting methods were applied alternatively. Amplitudes of seasonal periodicities, of diurnal periodicities, and of random components were determined. The results indicate that time series analysis of water temperatures measured downstream from an existing cooling water outfall may provide equally or even more realistic and useful information on the size of a cooling water plume than quasi-instantaneous surveys of spatial water temperature distributions.

Nuclear magnetic resonance studies of the acid–base chemistry of amino acids and peptides. III. Determination of the microscopic and macroscopic acid dissociation constants of α,ω-diaminocarboxylic acids

The acid–base chemistry of 2,3-diaminopropionic acid (dap), 2,4-diaminobutyric acid (dab), ornithine (orn), and lysine (lys) has been studied by 13C and proton nmr spectroscopy. Macroscopic acid dissociation constants for titration of the two ammonium groups of each molecule have been calculated from the 13C chemical shift titration curves for the alkyl carbon atoms by nonlinear least squares curve fitting methods. Microscopic acid dissociation constants for the simultaneous titration of the two ammonium groups of protonated orn and lys have been obtained from their proton chemical shift titration curves and from the 13C titration curves for orn and dap. The results indicate that the α-ammonium group of each of these α,ω-diaminocarboxylic acids is more acidic than its ω-ammonium group, but that the difference decreases as the number of carbons separating the ammonium groups decreases so that the acidities of the two ammonium groups of dap are almost identical. Results of pmr studies of the acid–base chemistry of glycyl-L-lysine and L-lysylglycine also are reported.

Kinetics of gonadotropin binding by receptors by the rat testis. Analysis by a nonlinear curve-fitting method

The kinetics of the reaction between human chorionic gonadotropin (hCG) and specific gonadotropin receptors in the rat testis were determined at 24 and 37 degrees, over a wide range of hormone concentrations. Hormone concentrations were corrected for the binding activity of the (-125I)hCG tracer preparations. Analysis of the experimental data was performed with an interactive nonlinear curve fitting program, based upon the second-order chemical kinetic differential equation. The mean values for the association rate constant (k1) were 4.7 x 10-7 M-1 min-1 at 24 degrees, and 11.0 x 10-7 M-1 min-1 at 37 degrees. At both temperatures, the values of kl were independent of hormone concentration. Initial dissociation rates were consistent with first order kinetics, with dissociation rate constant (k2) of 1.7 x 10 minus -3 and 4.6 x 10 minus -3 min minus -1 at 24 and 37 degrees, respectively. When studied over longer periods at 24 degrees, the dissociation process appeared to be multiexponential. The kinetics of degradation of (-125I)hCG and receptors were determined at both temperatures, and a mathematical model was developed by modification of the second-order chemical kinetic differential equation to take these factors into account. The application of such a model to hCG kinetic binding data demonstrated that reactant degradation had little significant effect on the derivation of the association rate constant (k1), but caused significant overestimation of the dissociation rate constant (k2) values derived from association experiments. The model was also applied by computer simulation to a theoretical analysis of the effects of degradation of free hormone and receptor sites upon kinetic and steadystate binding data. By this method, the initial velocities of hormone binding were shown to be less affected by degradation than the steady-state levels of hormone-receptor complex. Also, reactant degradation in simulated steady-state experiments caused an underestimate of the apparent equilibrium association constant, but had relatively less effect on the determination of binding site concentration.