Adaptive steered molecular dynamics of biomolecules

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.

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.

Conservation and divergence of the G-interfaces of Drosophila melanogaster septins

Septins possess a conserved guanine nucleotide-binding (G) domain that participates in the stabilization of organized hetero-oligomeric complexes which assemble into filaments, rings and network-like structures. The fruit fly, Drosophila melanogaster, has five such septin genes encoding Sep1, Sep2, Sep4, Sep5 and Pnut. Here, we report the crystal structure of the heterodimer formed between the G-domains of Sep1 and Sep2, the first from an insect to be described to date. A G-interface stabilizes the dimer (in agreement with the expected arrangement for the Drosophila hexameric particle) and this bears significant resemblance to its human counterparts, even down to the level of individual amino acid interactions. On the other hand, a model for the G-interface formed between the two copies of Pnut which occupy the centre of the hexamer, shows important structural differences, including the loss of a highly favourable bifurcated salt-bridge network. Whereas wild-type Pnut purifies as a monomer, the reintroduction of the salt-bridge network results in stabilizing the dimeric interface in solution as shown by size exclusion chromatography and thermal stability measurements. Adaptive steered molecular dynamics reveals an unzipping mechanism for dimer dissociation which initiates at a point of electrostatic repulsion within the switch II region. Overall, the data contribute to a better understanding of the molecular interactions involved in septin assembly/disassembly.

Dissociation Rate Calculation via Constant-Force Steered Molecular Dynamics Simulation

Steered molecular dynamics (SMD) simulations are used to study molecular dissociation events by applying a harmonic force to the molecules and pulling them at a constant velocity. Instead of constant-velocity pulling, we use a constant force: the constant-force SMD (CF-SMD) simulation. The CF-SMD simulation employs a constant force to reduce the activation barrier of molecular dissociation, thereby enhancing the dissociation event. Here, we present the capability of the CF-SMD simulation to estimate the dissociation time at equilibrium. We performed all-atom CF-SMD simulations for NaCl and protein-ligand systems, producing dissociation time at various forces. We extrapolated these values to the dissociation rate without a constant force using Bell's model or the Dudko-Hummer-Szabo model. We demonstrate that the CF-SMD simulations with the models predicted the dissociation time in equilibrium. A CF-SMD simulation is a powerful tool for estimating the dissociation rate in a direct and computationally efficient manner.

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.

Implementation of Telescoping Boxes in Adaptive Steered Molecular Dynamics

Long-time dynamical processes, such as those involving protein unfolding and ligand interactions, can be accelerated and realized through steered molecular dynamics (SMD). The challenge has been the extraction of information from such simulations that generalize for complex nonequilibrium processes. The use of Jarzynski's equality opened the possibility of determining the free energy along the steered coordinate, but sampling over the nonequilibrium trajectories is slow to converge. Adaptive steered molecular dynamics (ASMD) and other related techniques have been introduced to overcome this challenge through the use of stages. Here, we take advantage of these stages to address the numerical cost that arises from the required use of very large solvent boxes. We introduce telescoping box schemes within adaptive steered molecular dynamics (ASMD) in which we adjust the solvent box between stages and thereby vary (and optimize) the required number of solvent molecules. We have benchmarked the method on a relatively long α-helical peptide, Ala₃₀, with respect to the potential of mean force and hydrogen bonds. We show that the use of telescoping boxes introduces little numerical error while significantly reducing the computational cost.

Benchmarking Adaptive Steered Molecular Dynamics (ASMD) on CHARMM Force Fields

The potentials of mean force (PMFs) along the end‐to‐end distance of two different helical peptides have been obtained and benchmarked using the adaptive steered molecular dynamics (ASMD) method. The results depend strongly on the choice of force field driving the underlying all‐atom molecular dynamics, and are reported with respect to the three most popular CHARMM force field versions: c22, c27 and c36. Two small peptides, ALA10 and 1PEF, serve as the particular case studies. The comparisons between the versions of the CHARMM force fields provides both a qualitative and quantitative look at their performance in forced unfolding simulations in which peptides undergo large changes in structural conformations. We find that ASMD with the underlying c36 force field provides the most robust results for the selected benchmark peptides.

Picking on Carbonate: Kinetic Selectivity in the Encapsulation of Anions

Supramolecular hosts bind to inorganic anions at a fast rate and select them in proportion with thermodynamic stability of the corresponding [anion⊂host] complexes, forming in a reversible manner. In this study, we describe the action of hexapodal capsule 1 and its remarkable ability to select anions based on a large span of rates by which they enter this host. The thermodynamic affinity of 1 toward eighteen anions extends over eight orders of magnitude (0<K_a <10⁸  M^-1 ; ¹ H NMR spectroscopy). The capsule would retain CO₃ ^2- (K_a =10⁷  M^-1 ) for hours in the presence of eleven competing anions, including stronger binding SO₄ ^2- , HAsO₄ ^2- and HPO₄ ^2- (K_a =10⁷ -10⁸  M^-1 ). The observed selection resulted from 1 possessing narrow apertures (ca. 3×6 Å) comparable in size to anions (d=3.5-7.1 Å) slowing down the encapsulation to last from seconds to days. The unorthodox mode of action of 1 sets the stage for creating hosts that pick anions by their ability to access the host.

Adaptative Steered Molecular Dynamics Study of Mutagenesis Effects on Calcium Affinity in the Regulatory Domain of Cardiac Troponin C

Calcium-dependent cardiac muscle contraction is regulated by the protein complex troponin (cTn) and specifically by the regulatory N-terminal domain (N-cTnC) which contains one active Ca²⁺ binding site (site II). It has been previously shown that cardiac muscle contractility and functionality is affected by mutations in N-cTnC which alter calcium binding affinity. Here, we describe the application of adaptive steered molecular dynamics to characterize the influence of N-cTnC mutations on site II calcium binding affinity. We observed the correct trends for all of the studied calcium sensitizing and desensitizing mutants, in conjunction with loop II perturbations. Additionally, the potential of mean force accuracy was shown to increase substantially with increasingly slower speeds and using fewer trajectories. This study presents a novel approach to computationally estimate the Ca²⁺ binding affinity of N-cTnC structures and is a valuable potential tool to support the design and characterization of novel mutations with potential therapeutic benefits.