The intent of this project is to develop new and improve existing instrumentation and to develop new experimental and data analysis methods for the characterization of biological macromolecules and the study of their interactions with special emphasis on the thermodynamic analysis of these interactions. In the area of the analysis of the data from analytical ultracentrifugation, further refinements have been made in the application of L-1 regression for the fitting of ultracentrifugal light absorbance data, which has an error distribution that is a logarithmically-skewed Cauchy-type distribution. These fall in the category of """"""""fat-tailed"""""""" distributions, so called because of the relatively large distribution of deviations in the tails when compared to those in the central portion of the total distribution. Data with distributions of this type are better fit by L-1 (robust) regression. This method utilizes minimization of the sum of the absolute values of the deviations of the data points with the reciprocal of the standard error of each point as its weight. L-1 regression has the further virtue of being singularly insensitive to data """"""""outliers,"""""""" when compared to non-linear least-squares regression. The application of L-1 regression to absorbance data from the analytical ultracentrifuge, where the standard error is a function of radial position, is singularly rapid and easy and has yielded such outstandingly superior results that it is now the fitting technique of choice in this laboratory. L-1 regression does not provide the means of parameter error estimation normally used with non-linear least-squares regression. However, we have been able to develop algorithms for performing a balanced bootstrap procedure for the estimation of the standard errors of the fitting parameters obtained by L-1 regression. This method also yields superior error estimates for non-linear least-squares regression. We have also investigate the effect of systematic error on the values of the natural logarithm of the equilibrium constant obtained by ultracentrifugal analysis, Surprisingly, rotor temperature error as large as one degree Celsius has very little effect on the obtained thermodynamic parameters, but it was no surprise to discover that failure to attain ultracentrifugal equilibrium following a temperature change was the dominant and a marked source of error. Steps to minimize non-equilibrium error have been defined. An invited chapter describing this work has been published by the Royal Society of Chemistry in a book on analytical ultracentrifugation. The objective of these methodological studies has been to obtain the best possible data for the temperature dependence of the values of the natural logarithms of the equilibrium constants for the molecular interactions we are studying. From these we can calculate the values of the standard Gibbs free energy changes (delta G) as a function of temperature. Using standard thermodynamic functions, the value of delta G as a function of temperature can be described in terms of the standard values of the changes of enthalpy (delta H), entropy (delta S), heat capacity (delta C-sub-P), and the first derivative of the heat capacity with respect to temperature, all at a reference temperature. If the reference temperature is taken as fixed (usually the mid-point of the temperature range) then the function is linear with respect to the parameters and linear least-squares fitting gives optimized values for the parameters and their standard errors, but only if the function is orthogonal. This is not the case for this function and as a result the parameter cross-correlation coefficients and the dependency values are very large and the model is very mathematically ill-conditioned, since changes in any of the parameter values can be quite well compensated by changes in the other parameters. We have developed a method for making this function almost orthogonal with parameter cross-correlation coefficients and dependency values, which are small enough that the function is well-behaved and good and meaningful values for the parameters and their standard errors can be obtained. As an alternative to this method we have modified a procedure first devised by Holladay. With this method we rewrite the fitting function in two forms: one where the value of delta H is zero at a specific reference temperature; the other where the value of delta S is zero at a different specific temperature. We then fit each of these functions to the data in order to obtain the different specific reference temperature. If these can be obtained and lie essentially within the temperature range of interest and have standard errors of less than 1 %, then we can fix the values of the specific reference temperatures and globally fit the two functions to the data. The parameter values at the two different reference temperatures are then corrected to what they would be at the normal reference temperature. The results obtained by this global model, provided it is appropriate for the criteria given above, are virtually identical to the values obtained by the orthogonal model procedure. The global model has the advantage of being much easier and rapid in application, but is not suitable for all cases, specifically, where either delta H or delta S is not zero within an appropriate temperature range or where the errors in the specific reference temperatures are too large. In such cases, the orthogonal model still gives good results. This work has also been published as a chapter in the Royal Society of Chemistry book (reference 2). Future research is being directed to further optimization of thermodynamic analysis so that the obtained parameter values can be correlated to the nature of the mechanism(s) of the molecular interaction(s) and to the structure and function of the reactants and their complexes.
| Lewis, Marc S; Reily, Michael M (2004) Estimation of weights for various methods of the fitting of equilibrium data from the analytical ultracentrifuge. Methods Enzymol 384:232-42 |
| Lebowitz, Jacob; Lewis, Marc S; Schuck, Peter (2002) Modern analytical ultracentrifugation in protein science: a tutorial review. Protein Sci 11:2067-79 |
| Dimitriadis, E K; Lewis, M S (2000) Optimal data analysis using transmitted light intensities in analytical ultracentrifuge. Methods Enzymol 321:121-36 |
| Kar, S R; Kingsbury, J S; Lewis, M S et al. (2000) Analysis of transport experiments using pseudo-absorbance data. Anal Biochem 285:135-42 |
