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Inversion formulae for ellipsoid of revolution macromolecular shape functions
1National Centre for Macromolecular Hydrodynamics, University of Nottingham, Sutton Bonington, United Kingdom.
Analytical Biochemistry
|June 10, 1995
Summary
This study introduces polynomial expansions to easily calculate ellipsoid shape parameters (a/b) from various measurements. This method replaces complex graphical or tabular interpolations, simplifying data analysis in scientific research.
Area of Science:
- Physical Chemistry
- Polymer Science
- Biophysics
Background:
- Established relationships link ellipsoid shape parameters to axial ratios (a/b).
- Direct inversion of these functions is mathematically impossible, necessitating interpolation methods.
- Graphical and tabular methods have historically been used for axial ratio determination.
Purpose of the Study:
- To develop a simplified method for determining axial ratios (a/b) from shape parameters.
- To provide polynomial expansion coefficients for direct calculation.
- To overcome limitations of graphical and tabular interpolation.
Main Methods:
- Utilized simple, unconstrained polynomial expansions.
- Derived coefficients for hydration-dependent and independent shape functions.
- Covered axial ratio ranges: 1.1 < a/b < 2.0, 2 < a/b < 10, and 10 < a/b < 100.
Main Results:
- Polynomial coefficients provide an excellent fit to real data values.
- The method is applicable to shape functions P, v, beta, R, Lambda, and Pi.
- Exceptions were noted for four insensitive shape functions.
Conclusions:
- Polynomial expansions offer a direct and accurate alternative to interpolation for ellipsoid shape analysis.
- This approach simplifies the determination of axial ratios from experimental data.
- The provided coefficients enhance the practical application of shape parameter analysis.