Fixman compensating potential for general branched molecules.

Area of Science:

• Computational chemistry
• Molecular dynamics simulations
• Biophysics

Background:

• Constraining high-frequency molecular motion enhances simulation efficiency and conformational sampling.
• However, these constraints introduce systematic biases in statistical properties by stiffening molecular models.
• The Fixman potential was proposed to correct these biases but was limited to simple systems.

Purpose of the Study:

• To develop and validate a general algorithm for calculating the Fixman potential and its gradient.
• To enable the application of the Fixman potential to constrained dynamics simulations of branched molecules.
• To assess the algorithm's accuracy and computational cost for complex systems like proteins.

Main Methods:

• Development of a spatial operator algebra-based algorithm for Fixman potential calculation.
• Application of the algorithm to molecular dynamics simulations of systems with varying complexity.
• Numerical validation by comparing constrained and unconstrained simulations.

Main Results:

• The algorithm accurately calculates the Fixman potential and its gradient for branched molecules.
• Recovery of the dihedral angle probability distribution function was demonstrated across diverse molecular structures.
• The Fixman potential successfully corrected biases, recovering the free energy surface of a polymer model.

Conclusions:

• The developed algorithm effectively removes biases introduced by constraining molecular motion in simulations.
• This work extends the application of the Fixman potential to general branched systems, including macromolecules.
• The method offers a computationally efficient way to improve the accuracy of constrained molecular dynamics simulations.