Search PubMed⌕ Search

Biomedical subjects

Joel Tellinghuisen

Publications and source records attributed to Joel Tellinghuisen.

12 recordsLinked to original sources
PubMed2006

Calibration in isothermal titration calorimetry: heat and cell volume from heat of dilution of NaCl(aq).

An isothermal titration calorimeter of the perfusion type (MicroCal model VP-ITC) is calibrated using the heat of dilution of NaCl in water. The relative apparent molar enthalpy function (L(phi)) for NaCl(aq) varies strongly and nonlinearly with concentration in the low-concentration region (<0.2M) that is sampled easily and extensively in a single program of injections of NaCl solution into water. This nonlinearity makes it possible to calibrate with respect to two quantities: the measured heat and the active cell volume. The heat factor is determined with typical standard error 0.003; its value in the current case is 0.987. The cell volume factor is 0.93 but is quite sensitive to possible systematic errors in the temperature and in the literature values for L(phi). Both correction factors are closely tied to the delivered volume from the injection syringe, which required a correction factor of 0.973, attributed to an instrumental gear ratio error. Temperature calibration of the instrument showed a small offset of 0.12K at the temperature 25 degrees C of the experiments, but the error increased to more than 1K at 46 degrees C. The experiments were not able to distinguish clearly between mixing algorithms that assume instantaneous mixing on injection and those that assume instantaneous injection followed by mixing; however, examination of these algorithms has revealed an error in a program widely used to analyze isothermal titration calorimetry data.

Algorithms↗
PubMed2005

Van't Hoff analysis of K degrees (T): how good...or bad?

Binding constant data K degrees (T) are commonly subjected to van't Hoff analysis to extract estimates of DeltaH degrees, DeltaS degrees, and DeltaCP degrees for the process in question. When such analyses employ unweighted least-squares fitting of lnK degrees to an appropriate function of the temperature T, they are tacitly assuming constant relative error in K degrees. When this assumption is correct, the statistical errors in DeltaG degrees, DeltaH degrees, DeltaS degrees, DeltaCP degrees, and the T-derivative of DeltaCP degrees (if determined) are all independent of the actual values of K degrees and can be computed from knowledge of just the T values at which K degrees is known and the percent error in K degrees. All of these statistical errors except that for the highest-order constant are functions of T, so they must normally be calculated using a form of the error propagation equation that is not widely known. However, this computation can be bypassed by defining DeltaH degrees as a polynomial in (T-T0), the coefficients of which thus become DeltaH degrees, DeltaCP degrees, and 1/2 dDeltaCP degrees/dT at T=T0. The errors in the key quantities can then be computed by just repeating the fit for different T0. Procedures for doing this are described for a representative data analysis program. Results of such calculations show that expanding the T range from 10-40 to 5-45 degrees C gives significant improvement in the precision of all quantities. DeltaG degrees is typically determined with standard error a factor of approximately 30 smaller than that for DeltaH degrees. Accordingly, the error in TDeltaS degrees is nearly identical to that in DeltaH degrees. For 4% error in K degrees, the T-derivative in DeltaCP degrees cannot be determined unless it is approximately 10 cal mol-1 K-2 or greater; and DeltaCP degrees must be approximately 50 cal mol-1 K-1. Since all errors scale with the data error and inversely with the square root of the number of data points, the present results for 4% error cover any other relative error and number of points, for the same approximate T structure of the data.

Calorimetry↗
PubMed2005

Optimizing experimental parameters in isothermal titration calorimetry.

In isothermal titration calorimetry, the statistical precisions with which the equilibrium constant (K) and reaction enthalpy (DeltaH degrees ) can be estimated from data for 1:1 binding depend on a number of quantities, key among them being the products c identical with K[M](0) and h identical with DeltaH degrees [M](0), the stoichiometry range (R(m)(), ratio of total titrant X to total titrate M after the last injection), and the number of injections of titrant. A study of the statistical errors as functions of these quantities leads to the following prescription for optimizing throughput and precision: (1) Make 10 injections of titrant. (2) Set the concentrations in accord with the empirical equation R(m)() = 6.4/c(0.2) + 13/c (but no smaller than 1.1). (3) Make the starting concentration [M](0) as large as possible within the large-signal limits of the instrumentation but limited to c < 10(3) for estimating K. With this procedure, both K and [M](0) are predicted to have relative standard errors <1% over large ranges of K. Systematic errors in the concentrations, [X](0) and [M](0), are fully compensated by the "site number" or stoichiometry parameter (n). On the other hand, altering and freezing any of the fit parameters leads to a deterioration of the fit quality and to predictable changes in the other parameters. Fit divergence at very small c is avoidable through a simple redefinition of the fit parameters; however, unless n can be fixed from other information, DeltaH degrees may be statistically ill-defined in this region.

Journal Article↗
PubMed2005

Statistical error in isothermal titration calorimetry: variance function estimation from generalized least squares.

The method of generalized least squares (GLS) is used to assess the variance function for isothermal titration calorimetry (ITC) data collected for the 1:1 complexation of Ba(2+) with 18-crown-6 ether. In the GLS method, the least squares (LS) residuals from the data fit are themselves fitted to a variance function, with iterative adjustment of the weighting function in the data analysis to produce consistency. The data are treated in a pooled fashion, providing 321 fitted residuals from 35 data sets in the final analysis. Heteroscedasticity (nonconstant variance) is clearly indicated. Data error terms proportional to q(i) and q(i)/v are well defined statistically, where q(i) is the heat from the ith injection of titrant and v is the injected volume. The statistical significance of the variance function parameters is confirmed through Monte Carlo calculations that mimic the actual data set. For the data in question, which fall mostly in the range of q(i)=100-2000 microcal, the contributions to the data variance from the terms in q(i)(2) typically exceed the background constant term for q(i)>300 microcal and v<10 microl. Conversely, this means that in reactions with q(i) much less than this, heteroscedasticity is not a significant problem. Accordingly, in such cases the standard unweighted fitting procedures provide reliable results for the key parameters, K and DeltaH(degrees) and their statistical errors. These results also support an important earlier finding: in most ITC work on 1:1 binding processes, the optimal number of injections is 7-10, which is a factor of 3 smaller than the current norm. For high-q reactions, where weighting is needed for optimal LS analysis, tips are given for using the weighting option in the commercial software commonly employed to process ITC data.

Analysis of Variance↗
PubMed2005

Simple algorithms for nonlinear calibration by the classical and standard additions methods.

In univariate calibration by both the classical method and the standard additions method, calibration data are fitted to a response function y=f(x), from which the amount of an unknown x(0) is estimated by solving an equation of form y(0)=f(x(0)). Most such calibrations are limited to linear response functions f, for which the uncertainty in x(0) can be estimated from well-known expressions. The present work describes and illustrates one-step algorithms, in which x(0) is treated as an adjustable parameter in a nonlinear fit of the calibration data, with its standard error thus obtained numerically as a direct outcome of the fit. The computations are easily implemented with a number of data analysis programs and are illustrated here for a representative one, KaleidaGraph. The methods handle heteroscedastic data as easily as homoscedastic and nonlinear functions as easily as linear, permitting the analyst to experiment with different response functions in the quest for an optimum calibration. The estimates of sigma (x0) are obtained from the variance-covariance matrix V for the fit, so for weighted fitting with commercial programs, it is important to know which V--a priori or a posteriori--is being used.

Algorithms↗
PubMed2004

Calorimetric vs. van't Hoff binding enthalpies from isothermal titration calorimetry: Ba2+-crown ether complexation.

The 1:1 complexation reaction between Ba(2+) and 18-crown-6 ether is re-examined using isothermal titration calorimetry (ITC), with the goal of clarifying previously reported discrepancies between reaction enthalpies estimated directly (calorimetric) and indirectly, from the temperature dependence of the reaction equilibrium constant K (van't Hoff). The ITC thermograms are analyzed using three different non-linear fit models based on different assumptions about the data error: constant, proportional to the heat and proportional but correlated. The statistics of the fitting indicate a preference for the proportional error model, in agreement with expectations for the conditions of the experiment, where uncertainties in the delivered titrant volume should dominate. With attention to proper procedures for propagating statistical error in the van't Hoff analysis, the differences between Delta H(cal) and Delta H(vH) are deemed statistically significant. In addition, statistically significant differences are observed for the Delta H(cal) estimates obtained for two different sources of Ba(2+), BaCl(2) and Ba(NO(3))(2). The effects are tentatively attributed to deficiencies in the standard procedure in ITC of subtracting a blank obtained for pure titrant from the thermogram obtained for the sample.

Barium Compounds↗
PubMed2003

A study of statistical error in isothermal titration calorimetry.

In isothermal titration calorimetry (ITC), the two main sources of random (statistical) error are associated with the extraction of the heat q from the measured temperature changes and with the delivery of metered volumes of titrant. The former leads to uncertainty that is approximately constant and the latter to uncertainty that is proportional to q. The role of these errors in the analysis of ITC data by nonlinear least squares is examined for the case of 1:1 binding, M+X right arrow over left arrow MX. The standard errors in the key parameters-the equilibrium constant Ko and the enthalpy DeltaHo-are assessed from the variance-covariance matrix computed for exactly fitting data. Monte Carlo calculations confirm that these "exact" estimates will normally suffice and show further that neglect of weights in the nonlinear fitting can result in significant loss of efficiency. The effects of the titrant volume error are strongly dependent on assumptions about the nature of this error: If it is random in the integral volume instead of the differential volume, correlated least-squares is required for proper analysis, and the parameter standard errors decrease with increasing number of titration steps rather than increase.

Calorimetry↗
PubMed2002

Lewis acid-promoted Kharasch-Curran additions: a competition kinetics study of bromine atom transfer addition of N-alpha-bromoacetyl-oxazolidinone to 1-hexene.

Lewis acids can efficiently promote free radical atom transfer reactions of an oxazolidinone imide substrate, 1, derived from alpha-bromo acetic acid. Thus, 1 undergoes a radical chain addition to 1-hexene giving the atom transfer addition compound, 6, in the presence of scandium or ytterbium triflate in 1,2-dichloroethane or a cosolvent mixture of 1/9 THF/dichloromethane. In 1,2-dichloroethane the solution is heterogeneous, while the cosolvent mixture gives a homogeneous solution, even at temperatures of -78 degrees C. Competition experiments were carried out in both solvent systems with added carbon tetrachloride to study how Lewis acid affected the product distribution. In the presence of carbon tetrachloride, chloride 7 is formed in addition to 6 and the ratio of these two products depends on the amount of Lewis acid present. In the presence of ytterbium triflate, in the cosolvent system, the reaction rate of bromine atom transfer was enhanced up to 400-fold compared to the reaction without added Lewis acid. Significant rate enhancements were also obtained in the solvent 1,2-dichloroethane, although the analysis of the system is complicated by the heterogeneous nature of the medium. Computation of C-Br bond dissociation energies (BDE) of the complexed and uncomplexed oxazolidinone bromide suggest that complexation lowers the BDE due to the effect of the strong electron-withdrawing group on the C-Br bond dipole.

Alkenes↗