The geometry of shape space: application to influenza

Area of Science:

• Computational immunology
• Mathematical psychology
• Biophysics

Background:

• Shape space is a conceptual model for antibody-antigen binding, representing molecules as points with physico-chemical properties.
• Distances in shape space correlate with binding affinity, but coordinates were previously implicit.

Purpose of the Study:

• To develop algorithms for constructing explicit, quantitative coordinates in shape space from experimental affinity data.
• To enable precise quantification of molecular similarities and binding affinities.

Main Methods:

• Adapted metric and ordinal multidimensional scaling algorithms from mathematical psychology.
• Utilized experimental data, such as hemagglutination inhibition assays, to derive shape space coordinates.

Main Results:

• Successfully generated explicit, quantitative coordinates for shape space representation.
• Determined the dimensionality of shape space for influenza virus to be approximately five dimensions.
• Demonstrated new methods for quantifying antibody-antibody, antigen-antigen, and antibody-antigen similarities and affinities.

Conclusions:

• The developed algorithms provide a quantitative framework for analyzing molecular interactions in shape space.
• This approach offers significant potential for applications like influenza vaccine strain selection and general binding assay analysis.