Spin analogs of proteins: scaling of "folding" properties

TL;DR

This paper investigates the analogy between protein folding and spin system ground states, analyzing how folding times and characteristic temperatures scale with system size, revealing similarities and differences with real proteins.

Contribution

It introduces a model of spin systems that mimics protein folding, analyzing the scaling of folding times and temperatures, highlighting both parallels and distinctions from biological proteins.

Findings

Folding times scale as a power law with system size.

Characteristic temperatures show different scaling behavior than in proteins.

Folding properties deteriorate as system size increases.

Abstract

Reaching a ground state of a spin system is analogous to a protein evolving into its native state. We study the ``folding'' times for various random Ising spin systems and determine characteristic temperatures that relate to the ``folding''. Under optimal kinetic conditions, the ``folding'' times scale with the system size as a power law with a non-universal exponent. This is similar to what happens in model proteins. On the other hand, the scaling behavior of the characteristic temperatures is different than in model proteins. Both in the spin systems and in proteins, the folding properties deteriorate with the system size.