Accelerating energy minimization process in charged polymer-biomolecular systems: An enhanced nonlinear conjugate...

Area of Science:

• Computational Chemistry
• Biophysics
• Optimization Algorithms

Background:

• Energy minimization in charged polymer-multi-biomolecule systems is challenging due to nonconvex, ill-conditioned energy landscapes and long-range electrostatic interactions.
• Standard nonlinear conjugate gradient (NCG) methods face difficulties with unstable parameters and gradient oscillations in such complex systems.

Purpose of the Study:

• To develop an enhanced NCG algorithm (Enlong Shang or ELS method) for improved stability and convergence in challenging energy minimization problems.
• To provide a novel convergence proof for the ELS method, demonstrating its global convergence under nonconvex objectives and broad line search parameter applicability.

Main Methods:

• Introduced a modified conjugate gradient coefficient (βkELS) with a tunable parameter (ω) for enhanced stability in regions of poor local curvature.
• Developed a new convergence proof technique to establish the sufficient descent condition for a wide range of line search parameters (σ ∈ (0, 1)).
• Applied the ELS method to energy minimization in complex biomolecular simulations.

Main Results:

• The ELS method demonstrates superior numerical performance compared to existing NCG methods on traditional unconstrained optimization problems.
• Implementation of ELS in biomolecular simulations reduced the time to reach dynamic equilibrium by approximately 60% compared to direct dynamics simulation.
• The ELS method outperformed the mainstream staged minimization strategy in LAMMPS, achieving thermodynamically comparable final conformations with acceptable energy deviation.

Conclusions:

• The ELS method offers a stable and efficient approach for energy minimization in complex biomolecular systems.
• The algorithm provides significant computational savings and comparable accuracy to established simulation techniques.
• The ELS method represents a valuable advancement for large-scale biomolecular simulations and related optimization challenges.