A High-Throughput Steered Molecular Dynamics Study on the Free Energy Profile of Ion Permeation through Gramicidin A (2309.12088v1)

Abstract: Steered molecular dynamics (SMD) simulations for the calculation of free energies are well suited for high-throughput molecular simulations on a distributed infrastructure due to the simplicity of the setup and parallel granularity of the runs. However, so far, the computational cost limited the estimation of the free energy typically over just a few pullings, thus impeding the evaluation of statistical uncertainties involved. In this work, we performed two thousand pulls for the permeation of a potassium ion in the gramicidin A pore by all-atom molecular dynamics in order to assess the bidirectional SMD protocol with a proper amount of sampling. The estimated free energy profile still shows a statistical error of several kcal/mol, while the work distributions are estimated to be non-Gaussian at pulling speeds of 10 {\AA}/ns. We discuss the methodology and the confidence intervals in relation to increasing amounts of computed trajectories and how different permeation pathways for the potassium ion, knock-on and sideways, affect the sampling and the free energy estimation.

• The paper presents a high-throughput SMD approach using 1,000 pulls per direction to evaluate the PMF of potassium ion permeation in Gramicidin A.
• It applies Crooks fluctuation theorem with bootstrapping to reveal non-Gaussian work distributions and two distinct permeation pathways.
• Key results include a binding site at ~8.5 Å, a barrier height of ~14 kcal/mol, and reduced uncertainty with increased sampling.

High-Throughput SMD for Ion Permeation Free Energy

This paper investigates the free energy profile of potassium ion permeation through the gramicidin A (gA) channel using high-throughput steered molecular dynamics (SMD) simulations. The work focuses on assessing the bidirectional SMD protocol with extensive sampling to evaluate statistical uncertainties.

Methodology and System Setup

The PMF is computed using Crooks fluctuation theorem (CFT) via bidirectional SMD. The gA dimer, embedded in a membrane and explicit solvent, is subjected to 1,000 pulls per direction. The reaction coordinate is defined as the z-coordinate of the potassium ion. A harmonic biasing potential drives the ion through the channel. The cumulative work is calculated by integrating the instantaneous forces. Confidence bands are generated using a variable-size bootstrap procedure. The gA dimer is prepared based on the Protein Data Bank entry PDB:1JNO. The system is solvated with TIP3 water molecules and ionized with K$^+$ and Cl$^-$ ions at 150 mM. The CHARMM27 force field is used for equilibration. Production runs are performed using ACEMD, leveraging GPUs for enhanced performance. A distributed computing grid, GPUGRID.net, is utilized to manage the simulations.

Results and Analysis

The Shapiro-Wilk normality test rejects the null hypothesis that the final work values follow normal distributions ($p < 4 \cdot 10^{-7}$ for both the forward and reverse runs), suggesting non-Gaussian behavior at the pulling speed of 10 Å/ns. The PMF exhibits a binding site at $z \simeq 8.5$ Å and a barrier height of approximately 14 kcal/mol. Two distinct permeation pathways are observed: one where the ion exchanges places with the preceding water molecule (H group), and another where the water file is preserved (L group). The H group pathways are associated with the formation of hydrogen bonds between water molecules and carbonyl atoms in the gA backbone. The convergence of PMF estimates is characterized using non-overlapping blocks of trajectories and bootstrapping. The standard deviation of the PMF depth decreases with increasing numbers of trajectories, reaching 1 kcal/mol with 1,000 trajectories. Control simulations at different pulling speeds ($v=10$ and $v=2.5$ Å/ns) show similar PMF profiles.

Discussion and Conclusions

The paper demonstrates the feasibility of high-throughput SMD simulations for computing free energy profiles in biomolecular systems. The extensive sampling reveals statistical uncertainties in PMF estimates, highlighting the importance of sufficient sampling. The observation of two permeation pathways underscores the complexity of ion permeation. The findings suggest that SMD can be more suitable than US for systems where biasing the equilibrium structure significantly alters the system's behavior. Future studies could focus on more complex systems, such as ligand binding, and explore adaptive sampling techniques to enhance efficiency. The results suggest that for gA, performing SMD at $v=10$ Å/ns is more computationally efficient.