All-Atom Calculation of the Normal Modes of Bacteriorhodopsin Using a Sliding Block Iterative Diagonalization Method

Area of Science:

• Computational Chemistry
• Molecular Dynamics
• Biophysics

Background:

• Conventional normal-mode analysis necessitates significant computational resources and memory for storing the Hessian matrix, posing challenges for large biological systems.
• Existing methods struggle with the scale of biological molecules, limiting the depth of vibrational analysis possible.

Purpose of the Study:

• To develop and present an efficient iterative block method for full Hessian diagonalization in molecular vibration analysis.
• To overcome the memory limitations associated with conventional Hessian matrix storage for large biological systems.
• To enable the computation of a larger number of vibrational modes without prohibitive memory requirements.

Main Methods:

• An iterative block method based on the conjugate gradient formulation of the Davidson algorithm is employed for simultaneous optimization of multiple roots (L roots, 10 < L < 300).
• The method dynamically expands the search space by adding new orthogonal vectors for converged roots and uses a projector with a read-rewind step for orthonormality.
• Hessian-vector products are computed efficiently on-the-fly using Kp = dgp/dt, where K is the mass-weighted Hessian and gp is the gradient along p.

Main Results:

• The iterative method successfully diagonalizes the Hessian while requiring minimal memory, storing only a few vectors.
• Preliminary analysis of bacteriorhodopsin (bR) reveals normal modes up to 300 cm⁻¹ and in the high-frequency range (2840–3680 cm⁻¹).
• A highly localized, noncollective mode at approximately 1.4 cm⁻¹ was identified in bR, attributed to long-range domain interactions.

Conclusions:

• The developed iterative block method provides a memory-efficient solution for normal-mode analysis of large biological systems.
• This approach allows for the convergence of an arbitrary number of vibrational modes, significantly advancing computational capabilities in molecular dynamics.
• The findings demonstrate the potential for uncovering subtle vibrational behaviors, such as localized modes, crucial for understanding protein function.