Pair distribution functions in small systems: implications for protein structure analysis
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Updated: Aug 12, 2026

Investigating Protein Sequence-structure-dynamics Relationships with Bio3D-web
Published on: July 16, 2017
1Department of Physiology and Biophysics, University of California, Irvine 92717.
Abstract:
A general formula is derived for the relation between the pair correlation function and the histogram of interparticle distances in small nonuniform systems. The formula is applied to random packings of spheres in a spherical container, which are generated by a Monte Carlo method. When measured properly, the resultant correlation functions are very similar to ones in bulk systems with the same volume fraction of particles. In contrast, the density is very nonuniform as a function of distance from the center of the container. The variation is an order of magnitude for the number density of particle centers, or severalfold for the occupied volume fraction. It is described how these results can be used to analyze the forces that determine protein structure.
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