Multibody local approximation: application to conformational entropy calculations on biomolecules.

Area of Science:

• Computational Chemistry
• Statistical Mechanics
• Molecular Dynamics

Background:

• Multibody expansions, such as mutual information expansions, are essential for analyzing large composite systems.
• However, these methods face challenges with high computational costs and non-monotonic truncation errors due to combinatorial explosions.

Purpose of the Study:

• To develop an efficient reformulation of multibody expansions that implicitly captures all-order correlation effects within a defined cutoff.
• To mitigate the limitations of traditional expansion methods, specifically computational cost and error behavior.

Main Methods:

• A novel approach reformulates multibody expansions, leveraging redundancy to avoid combinatorial explosion.
• This cutoff-dependent method implicitly includes all-order correlation effects.
• It combines multibody local entropy estimations with rigid-rotor and harmonic-oscillator contributions.

Main Results:

• The reformulated approach avoids the combinatorial explosion inherent in traditional multibody expansions.
• It provides a cutoff-dependent, rather than order-dependent, analysis.
• For flexible peptides, this method yields a significantly tighter upper bound of absolute conformational entropy than the quasi-harmonic method.

Conclusions:

• The developed reformulation offers a computationally efficient and accurate alternative for analyzing complex systems using multibody expansions.
• This method shows particular promise for calculating the conformational entropy of flexible molecules from molecular dynamics data.
• The approach successfully addresses key limitations of existing expansion techniques, enhancing their applicability.