An intuitive approach to measuring protein surface curvature

Area of Science:

• Computational Biology
• Structural Biology
• Biophysics

Background:

• Measuring protein surface curvature is crucial for understanding protein function and interactions.
• Existing methods for protein surface curvature measurement can be complex and difficult to interpret.
• The least squares fitted (LSF) sphere method offers a conceptually simple approach but presents computational challenges.

Purpose of the Study:

• To develop a novel and interpretable method for measuring protein surface curvature.
• To address the complexities of the least squares fitted (LSF) sphere problem.
• To provide a flexible and physically meaningful measure of protein surface curvature.

Main Methods:

• Utilized geometric inversion to transform the sphere-fitting problem into a plane-fitting problem.
• Developed an approach applicable to arbitrary protein surface patches.
• Adjusted the 'resolution' of the method to analyze features at different scales.

Main Results:

• Successfully solved the LSF sphere problem, yielding a radius of curvature with direct physical interpretation.
• Demonstrated the method's flexibility in analyzing arbitrary surface patches.
• Achieved more pronounced curvature results compared to a commonly used solid-angle curvature method.

Conclusions:

• The geometric inversion approach provides a robust and interpretable method for measuring protein surface curvature.
• This technique enhances the visualization of critical protein features like peptide binding sites.
• The method offers a valuable tool for analyzing protein conformational changes and molecular recognition.