The concentration-dependence of macromolecular parameters

Area of Science:

• Physical Chemistry
• Biophysics
• Polymer Science

Background:

• Understanding macromolecule behavior in dilute solutions is crucial for various scientific disciplines.
• Existing theories on concentration-dependence of sedimentation and diffusion coefficients present some ambiguities.
• Clarifying these ambiguities is essential for accurate interpretation of experimental data.

Purpose of the Study:

• To compare and discuss theories on the concentration-dependence of sedimentation and diffusion coefficients for macromolecules.
• To address the uncertainty regarding the correction of sedimentation coefficients for solvent versus solution density.
• To derive a general thermodynamic expression for the concentration-dependence of diffusion.

Main Methods:

• Theoretical comparison of existing models for sedimentation and diffusion coefficients.
• Thermodynamic derivation of a general expression for diffusion concentration-dependence.
• Mathematical analysis to demonstrate equivalence between different theoretical frameworks.

Main Results:

• Identified that sedimentation corrected for solvent or solution density yield the same extrapolation limit but different concentration-dependencies.
• Related these different concentration-dependencies.
• Derived a general thermodynamic expression for diffusion concentration-dependence, incorporating sedimentation coefficients corrected from solution density.
• Showed equivalence of the derived expression to Batchelor's (1976) for rigid spheres.

Conclusions:

• The study provides a unified thermodynamic framework for understanding the concentration-dependence of diffusion coefficients.
• It resolves ambiguities in the literature regarding sedimentation coefficient corrections.
• The findings contribute to a more accurate determination of macromolecular properties from solution-based measurements, including apparent molecular weights.