Scaling Laws for Protein Folding under Confinement.

Area of Science:

• Biophysics
• Computational Biology
• Protein Science

Background:

• Spatial confinement, such as that provided by chaperones, is crucial for correct protein folding.
• The quantitative impact of confinement on protein folding dynamics remains largely unexplored.

Purpose of the Study:

• To investigate and quantify the effect of spatial confinement on protein folding transition temperature.
• To establish scaling laws that describe the relationship between confinement size and folding behavior.

Main Methods:

• Observing scaling laws between the variation in folding transition temperature and confinement size.
• Analyzing the influence of protein topology and folding cooperativity on scaling exponents.
• Developing a novel scaling argument to predict the behavior of the scaling exponent.

Main Results:

• A scaling law was identified: (Tf - Tfbulk)/Tfbulk ∼ L⁻ᵛ, where Tf is the folding transition temperature and L is the confinement size.
• The scaling exponent (v) is significantly affected by protein topology and folding cooperativity.
• Increased folding cooperativity reduces v due to heightened sensitivity of unfolded state energy to cage size.
• Protein topological complexity, indicated by contact order and nonlocal contacts, positively correlates with v.

Conclusions:

• The study establishes quantitative scaling laws for protein folding under spatial confinement.
• Protein topology and folding cooperativity are key determinants of how confinement affects folding thermodynamics.
• A theoretical framework was developed, predicting a scaling exponent range of 5/3 ≤ ν ≤ 10/3, consistent with simulation findings.