Origin of Scaling Behavior of Protein Packing Density: A Sequential Monte Carlo Study of Compact Long Chain Polymers

TL;DR

This study investigates the scaling behavior of protein packing density, revealing it decreases with chain length and is a generic feature of random polymers, challenging the idea of evolutionary optimization to eliminate voids.

Contribution

Introduces a sequential Monte Carlo algorithm to generate compact long chain polymers and analyzes their packing density scaling behavior.

Findings

Packing density decreases with chain length in proteins.

Alpha contact number characterizes protein packing well.

High packing density is typical only for short chain proteins.

Abstract

Single domain proteins are thought to be tightly packed. The introduction of voids by mutations is often regarded as destabilizing. In this study we show that packing density for single domain proteins decreases with chain length. We find that the radius of gyration provides poor description of protein packing but the alpha contact number we introduce here characterize proteins well. We further demonstrate that protein-like scaling relationship between packing density and chain length is observed in off-lattice self-avoiding walks. A key problem in studying compact chain polymer is the attrition problem: It is difficult to generate independent samples of compact long self-avoiding walks. We develop an algorithm based on the framework of sequential Monte Carlo and succeed in generating populations of compact long chain off-lattice polymers up to length $N=2,000$. Results based on analysis of these chain polymers suggest that maintaining high packing density is only characteristic of short chain proteins. We found that the scaling behavior of packing density with chain length of proteins is a generic feature of random polymers satisfying loose constraint in compactness. We conclude that proteins are not optimized by evolution to eliminate packing voids.