Statistical mechanics of protein sequences.

Area of Science:

• Statistical mechanics
• Computational biology
• Biophysics

Background:

• Biological macromolecules like proteins and RNA possess complex structures crucial for their function.
• Understanding the relationship between a molecule's sequence and its 3D structure is a fundamental challenge in molecular biology.
• Current models often treat sequence and configuration independently, which may not fully capture their interdependence.

Purpose of the Study:

• To develop a statistical mechanical framework that integrates sequence information as an internal coordinate for biological macromolecules.
• To investigate the interplay between polymer configuration and sequence composition in determining macromolecular structure.
• To explore whether sequence information alone is sufficient to determine macromolecular structure.

Main Methods:

• Utilizing a path integral representation to calculate the canonical partition function.
• Decomposing the partition function into polymer configurational and sequence walk path integrals.
• Analyzing the sequence-dependent configurational potential that couples these two path integrals.
• Examining the dimensionality and Markovian nature of the sequence walk in proteins and RNA.

Main Results:

• The canonical partition function can be expressed as a product of two interacting path integrals: one for polymer configuration and one for sequence walk.
• The sequence composition directly influences the potential energy of inter-subunit interactions, causing the path integrals to be non-separable.
• For proteins and RNA, the sequence walk occurs in dimensions greater than three, behaving as an ideal polymer.
• The Markovian nature of the sequence walk implies that all structural information is contained within the sequence.

Conclusions:

• The developed statistical mechanical model provides a novel way to treat biological macromolecules by incorporating sequence as an internal coordinate.
• The interdependence of sequence and configuration is mediated by a sequence-dependent potential, highlighting a key aspect of macromolecular behavior.
• The high dimensionality of the sequence walk in proteins and RNA suggests that their structural information is inherently encoded in their sequences, irrespective of biological optimization.