Implementation of Telescoping Boxes in Adaptive Steered Molecular Dynamics

Improving the Computational Efficiency of the Adaptive Biasing Force Sampling by Leveraging the Telescopic-Solvation Scheme

The number of solvent molecules present in the system during molecular dynamics is the balancing act between the need to remove the boundary effects present in the system and the computational cost. Application of the telescopic-solvation box scheme during the estimation of the potential of mean force (PMF) can be advantageous in situations where the contribution of solvent far from the site of interest toward the whole PMF is negligible, as previously demonstrated in the case of adaptive steered molecular dynamics and umbrella sampling. This work explores the application of the telescopic-solvation box scheme during enhanced sampling by the stratified adaptive biasing force (ABF) family of methods, including ABF, extended ABF, well-tempered-metadynamics extended ABF, and multiwalker extended ABF. During this scheme, the number of water molecules differed in each stratified window, whose number depended on the value of the collective variable being sampled in that window. Two systems were used to verify the viability of the telescopic scheme: unfolding (Ala)10 peptide in water and insertion of α-tocopherol in a bilayer membrane. In the first system, the 1D and 2D PMFs obtained by the telescopic-solvation scheme matched well with the benchmark PMFs estimated with a standard solvation box. The minimal energy path connecting the α-helical and extended conformational states revealed that the unfolding process of (Ala)10 in water involved multiple closely spaced metastable states. As for the second system, the PMF, equilibrium location of α-tocopherol, and the free energy associated with the desorption and flipping of α-tocopherol obtained within the scope of the telescopic-solvation box scheme agreed with their standard solvation box values. Enhanced sampling with ABF and its variants in conjunction with the telescopic-solvation scheme results in a similar quality of the estimated PMF compared to sampling with a standard solvation box, albeit with reduced computational cost.

Probing the stability and interdomain interactions in the ABC transporter OpuA using single-molecule optical tweezers

Transmembrane transporter proteins are essential for maintaining cellular homeostasis and, as such, are key drug targets. Many transmembrane transporter proteins are known to undergo large structural rearrangements during their functional cycles. Despite the wealth of detailed structural and functional data available for these systems, our understanding of their dynamics and, consequently, how they function is generally limited. We introduce an innovative approach that enables us to directly measure the dynamics and stability of interdomain interactions of transmembrane proteins using optical tweezers. Focusing on the osmoregulatory ATP-binding cassette transporter OpuA from Lactococcus lactis, we examine the mechanical properties and potential interactions of its substrate-binding domains. Our measurements are performed in lipid nanodiscs, providing a native-mimicking environment for the transmembrane protein. The technique provides high spatial and temporal resolution and allows us to study the functionally relevant motions and interdomain interactions of individual transmembrane transporter proteins in real time in a lipid bilayer.

Tertiary Plasticity Drives the Efficiency of Enterocin 7B Interactions with Lipid Membranes

The ability of antimicrobial peptides to efficiently kill their bacterial targets depends on the efficiency of their binding to the microbial membrane. In the case of enterocins, there is a three-part interaction: initial binding, unpacking of helices on the membrane surface, and permeation of the lipid bilayer. Helical unpacking is driven by disruption of the peptide hydrophobic core when in contact with membranes. Enterocin 7B is a leaderless enterocin antimicrobial peptide produced from Enterococcus faecalis that functions alone, or with its cognate partner enterocin 7A, to efficiently kill a wide variety of Gram-stain positive bacteria. To better characterize the role that tertiary structural plasticity plays in the ability of enterocin 7B to interact with the membranes, a series of arginine single-site mutants were constructed that destabilize the hydrophobic core to varying degrees. A series of experimental measures of structure, stability, and function, including CD spectra, far UV CD melting profiles, minimal inhibitory concentrations analysis, and release kinetics of calcein, show that decreased stabilization of the hydrophobic core is correlated with increased efficiency of a peptide to permeate membranes and in killing bacteria. Finally, using the computational technique of adaptive steered molecular dynamics, we found that the atomistic/energetic landscape of peptide mechanical unfolding leads to free energy differences between the wild type and its mutants, whose trends correlate well with our experiment.

Shocker─A Molecular Dynamics Protocol and Tool for Accelerating and Analyzing the Effects of Osmotic Shocks

The process of osmosis, a fundamental phenomenon in life, drives water through a semipermeable membrane in response to a solute concentration gradient across this membrane. In vitro, osmotic shocks are often used to drive shape changes in lipid vesicles, for instance, to study fission events in the context of artificial cells. While experimental techniques provide a macroscopic picture of large-scale membrane remodeling processes, molecular dynamics (MD) simulations are a powerful tool to study membrane deformations at the molecular level. However, simulating an osmotic shock is a time-consuming process due to slow water diffusion across the membrane, making it practically impossible to examine its effects in classic MD simulations. In this article, we present Shocker, a Python-based MD tool for simulating the effects of an osmotic shock by selecting and relocating water particles across a membrane over the course of several pumping cycles. Although this method is primarily aimed at efficiently simulating volume changes in vesicles, it can also handle membrane tubes and double bilayer systems. Additionally, Shocker is force field-independent and compatible with both coarse-grained and all-atom systems. We demonstrate that our tool is applicable to simulate both hypertonic and hypotonic osmotic shocks for a range of vesicular and bilamellar setups, including complex multicomponent systems containing membrane proteins or crowded internal solutions.

Telescoping-Solvation-Box Protocol-Based Umbrella Sampling Method for Potential Mean Force Estimation

Previously, it was shown that the telescoping box scheme, in combination with adaptive steered molecule dynamics (ASMD), can be used to estimate the potential of mean force (PMF) with a decrease in computational cost associated with large solvation boxes. Since ASMD reduces to umbrella sampling (US) in the limit of infinitely slow pulling velocity, a hypothesis was made that the telescoping box scheme can be extended to include the US method. The hypothesis was tested using the unfolding pathway of a polyalanine peptide in a water box and translocation of α-tocopherol through the human membrane. Two different approaches were tried: telescoping US (TELUS), in which the number of solvent molecules was linearly coupled to the reaction coordinate, and Block-TELUS, which was a compromise between the fixed solvation box of the US and the window-wise variable solvation box of TELUS. In the case of polyalanine peptide in a water box, both approaches gave overlapping potential of mean force (PMF) concerning the benchmark US-PMF. Window-wise comparison of properties like root-mean-square inner product, Ramachandran plot, α-helix content, and hydrogen bond formation was used to verify that both approaches captured the same dynamics as the US method. Applying the Block-TELUS protocol in the system with diffusing α-tocopherol through the bilayer resulted in overlapping PMF to its US benchmark. A comparison between the window-wise orientation of the chromanol headgroup also produced almost identical results. This study concluded that with the careful application of telescoping solvation boxes, a less computationally expensive US could be performed for systems where the effect of distant solvent molecules on the configurational space sampled in the window depends on the value of the reaction coordinate.

Correlation between chemical denaturation and the unfolding energetics of Acanthamoeba actophorin

The actin filament network is in part remodeled by the action of a family of filament severing proteins that are responsible for modulating the ratio between monomeric and filamentous actin. Recent work on the protein actophorin from the amoeba Acanthamoeba castellani identified a series of site-directed mutations that increase the thermal stability of the protein by 22°C. Here, we expand this observation by showing that the mutant protein is also significantly stable to both equilibrium and kinetic chemical denaturation, and employ computer simulations to account for the increase in thermal or chemical stability through an accounting of atomic-level interactions. Specifically, the potential of mean force (PMF) can be obtained from steered molecular dynamics (SMD) simulations in which a protein is unfolded. However, SMD can be inefficient for large proteins as they require large solvent boxes, and computationally expensive as they require increasingly many SMD trajectories to converge the PMF. Adaptive steered molecular dynamics (ASMD) overcomes the second of these limitations by steering the particle in stages, which allows for convergence of the PMF using fewer trajectories compared with SMD. Use of the telescoping water scheme within ASMD partially overcomes the first of these limitations by reducing the number of waters at each stage to only those needed to solvate the structure within a given stage. In the PMFs obtained from ASMD, the work of unfolding Acto-2 was found to be higher than the Acto-WT by approximately 120 kCal/mol and reflects the increased stability seen in the chemical denaturation experiments. The evolution of the average number of hydrogen bonds and number of salt bridges during the pulling process provides a mechanistic view of the structural changes of the actophorin protein as it is unfolded, and how it is affected by the mutation in concert with the energetics reported through the PMF.

Free energy and kinetic rate calculation via non-equilibrium molecular simulation: application to biomolecules

Non-equilibrium molecular dynamics (NEMD) simulation has been recognized as a powerful tool for examining biomolecules and provides fruitful insights into not only non-equilibrium but also equilibrium processes. We review recent advances in NEMD simulation and relevant, fundamental results of non-equilibrium statistical mechanics. We first introduce Crooks fluctuation theorem and Jarzynski equality that relate free energy difference to work done on a physical system during a non-equilibrium process. The theorems are beneficial for the analysis of NEMD trajectories. We then describe rate theory, a framework to calculate molecular kinetics from a non-equilibrium process; this theoretical framework enables us to calculate a reaction time-mean-first passage time-from NEMD trajectories. We, in turn, present recent NEMD techniques that apply an external force to a system to enhance molecular dissociation and introduce their application to biomolecules. Lastly, we show the current status of an appropriate selection of reaction coordinates for NEMD simulation.