# Direct Measurement of Protein Pair Interaction Potential

## TL;DR

This paper introduces a direct experimental method to measure how proteins interact with each other, without relying on assumptions or complex calculations.

## Contribution

A novel method is introduced to directly measure protein pair interaction potentials using cryo-ET data, validated against multiple experimental techniques.

## Key findings

- Cryo-ET-derived structure factors match those from small-angle X-ray scattering.
- Cryo-ET-based Kirkwood–Buff integrals align with analytical ultracentrifugation results.
- The method works across various proteins and experimental conditions without assuming protein shape or interaction form.

## Abstract

A direct and unambiguous method for obtaining the pair
interaction
potential (PIP) of proteins does not currently exist. All existing
approaches require solving an inverse problem, which always allows
for alternative solutions. Here, we report a straightforward method
for obtaining the PIP directly from experimentally determined three-dimensional
spatial distributions of proteins. The approach is based on improvements
to a recently developed method for determining the potential of mean
force for nanoparticles using cryogenic electron tomography (cryo-ET).
For the protein PIP, we find good agreement between the structure
factor computed from cryo-ET positions and that obtained from small-angle
X-ray scattering of protein solutions. We apply a novel subvolume
method to compute Kirkwood–Buff integrals and show that the
second virial coefficients calculated from the cryo-ET tomograms closely
match those obtained experimentally from analytical ultracentrifugation.
Both results validate our approach for deriving the PIP and indicate
that the vitrified state matches the solution state. The generality
of our validated approach is demonstrated for several small proteins
with different structures and molecular weights, and under various
experimental conditions, including changes in salt concentration,
temperature, and pH. Our method does not require assumptions about
protein shape or the analytical form of the interaction potential.