Computational Methods Used to Explore Transport Events in Biological Systems

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.

ACES: Optimized Alchemically Enhanced Sampling

We present an alchemical enhanced sampling (ACES) method implemented in the GPU-accelerated AMBER free energy MD engine. The methods hinges on the creation of an "enhanced sampling state" by reducing or eliminating selected potential energy terms and interactions that lead to kinetic traps and conformational barriers while maintaining those terms that curtail the need to otherwise sample large volumes of phase space. For example, the enhanced sampling state might involve transforming regions of a ligand and/or protein side chain into a noninteracting "dummy state" with internal electrostatics and torsion angle terms turned off. The enhanced sampling state is connected to a real-state end point through a Hamiltonian replica exchange (HREMD) framework that is facilitated by newly developed alchemical transformation pathways and smoothstep softcore potentials. This creates a counterdiffusion of real and enhanced-sampling states along the HREMD network. The effect of a differential response of the environment to the real and enhanced-sampling states is minimized by leveraging the dual topology framework in AMBER to construct a counterbalancing HREMD network in the opposite alchemical direction with the same (or similar) real and enhanced sampling states at inverted end points. The method has been demonstrated in a series of test cases of increasing complexity where traditional MD, and in several cases alternative REST2-like enhanced sampling methods, are shown to fail. The hydration free energy for acetic acid was shown to be independent of the starting conformation, and the values for four additional edge case molecules from the FreeSolv database were shown to have a significantly closer agreement with experiment using ACES. The method was further able to handle different rotamer states in a Cdk2 ligand identified as fractionally occupied in crystal structures. Finally, ACES was applied to T4-lysozyme and demonstrated that the side chain distribution of V111χ1 could be reliably reproduced for the apo state, bound to p-xylene, and in p-xylene→ benzene transformations. In these cases, the ACES method is shown to be highly robust and superior to a REST2-like enhanced sampling implementation alone.

Comparison of umbrella sampling and steered molecular dynamics methods for computing free energy profiles of aromatic substrates through phospholipid bilayers

Understanding the permeation of molecules through lipid membranes is fundamental for predicting the cellular uptake of solutes and drug delivery mechanisms. In molecular simulations, the usual approach is to compute the free energy (FE) profile of a molecule across a model lipid bilayer, which can then be used to estimate the permeability of the molecule. Umbrella Sampling (US), which involves carrying out a series of biased simulations along a defined reaction coordinate (usually the bilayer normal direction), is a popular method for the computation of such FE profiles. However, US can be challenging to implement because the results are dependent on the strength of the biasing potential and the spacing of windows along the reaction coordinate, which, in practice, are usually optimized by an inefficient trial and error approach. The Steered Molecular Dynamics implementation of the Jarzynski Equality (JE-SMD) has been identified as an alternative to equilibrium sampling methods for measuring the FE change across a reaction coordinate. In the JE-SMD approach, equilibrium FE values are evaluated from the average of rapid non-equilibrium trajectories, thus avoiding the practical issues that come with US. Here, we use three different corrections of the JE-SMD method to calculate the FE change for the translocation of two aromatic substrates, phenylalanine and toluene, across a lipid bilayer and compare the accuracy and computational efficiency of these approaches to the results obtained using US. We show evidence that when computing the free energy profile, the JE-SMD approach suffers from insufficient sampling convergence of the bilayer environment and is dependent on the characteristic of the aromatic substrate itself. We deduce that, despite its drawbacks, US remains the more viable approach of the two for computing the FE profile.

Exploration of Free Energy Surfaces Across a Membrane Channel Using Metadynamics and Umbrella Sampling

To reach their site of action, it is essential for antibiotic molecules to cross the bacterial outer membrane. The progress of enhanced sampling techniques in molecular dynamics simulations enables us to understand these translocations at an atomic level. To this end, calculations of free energy surfaces for these permeation processes are of key importance. Herein, we investigate the translocation of a variety of anionic solutes through the outer membrane pore OprO of the Gram-negative bacterium Pseudomonas aeruginosa using the metadynamics and umbrella sampling techniques at the all-atom level. Free energy calculations have been performed employing these two distinct methods in order to illustrate the difference in computed free energies, if any. The investigated solutes range from a single atomic chloride ion over a multiatomic monophosphate ion to a more bulky fosmidomycin antibiotic. The role of complexity of the permeating solutes in estimating accurate free energy profiles is demonstrated by performing extensive convergence analysis. For simple monatomic ions, good agreement between the well-tempered metadynamics and the umbrella sampling approaches is achieved, while for the permeation of the monophosphate ion differences start to appear. In the case of larger molecules such as fosmidomycin it is a tough challenge to achieve converged free energy profiles. This issue is mainly due to neglecting orthogonal degrees of freedom during the free energy calculations. Nevertheless, the freely driven metadynamics approach leads to clearly advantageous results. Additionally, atomistic insights of the translocation mechanisms of all three solutes are discussed.

Urea-aromatic interactions in biology

Noncovalent interactions are key determinants in both chemical and biological processes. Among such processes, the hydrophobic interactions play an eminent role in folding of proteins, nucleic acids, formation of membranes, protein-ligand recognition, etc.. Though this interaction is mediated through the aqueous solvent, the stability of the above biomolecules can be highly sensitive to any small external perturbations, such as temperature, pressure, pH, or even cosolvent additives, like, urea-a highly soluble small organic molecule utilized by various living organisms to regulate osmotic pressure. A plethora of detailed studies exist covering both experimental and theoretical regimes, to understand how urea modulates the stability of biological macromolecules. While experimentalists have been primarily focusing on the thermodynamic and kinetic aspects, theoretical modeling predominantly involves mechanistic information at the molecular level, calculating atomistic details applying the force field approach to the high level electronic details using the quantum mechanical methods. The review focuses mainly on examples with biological relevance, such as (1) urea-assisted protein unfolding, (2) urea-assisted RNA unfolding, (3) urea lesion interaction within damaged DNA, (4) urea conduction through membrane proteins, and (5) protein-ligand interactions those explicitly address the vitality of hydrophobic interactions involving exclusively the urea-aromatic moiety.

Proton Control of Transitions in an Amino Acid Transporter

Amino acid transport into the cell is often coupled to the proton electrochemical gradient, as found in the solute carrier 36 family of proton-coupled amino acid transporters. Although no structure of a human proton-coupled amino acid transporter exists, the crystal structure of a related homolog from bacteria, GkApcT, has recently been solved in an inward-occluded state and allows an opportunity to examine how protons are coupled to amino acid transport. Our working hypothesis is that release of the amino acid substrate is facilitated by the deprotonation of a key glutamate residue (E115) located at the bottom of the binding pocket, which forms part of the intracellular gate, allowing the protein to transition from an inward-occluded to an inward-open conformation. During unbiased molecular dynamics simulations, we observed a transition from the inward-occluded state captured in the crystal structure to a much more open state, which we consider likely to be representative of the inward-open state associated with substrate release. To explore this and the role of protons in these transitions, we have used umbrella sampling to demonstrate that the transition from inward occluded to inward open is more energetically favorable when E115 is deprotonated. That E115 is likely to be protonated in the inward-occluded state and deprotonated in the inward-open state is further confirmed via the use of absolute binding free energies. Finally, we also show, via the use of absolute binding free energy calculations, that the affinity of the protein for alanine is very similar regardless of either the conformational state or the protonation of E115, presumably reflecting the fact that all the key interactions are deep within the binding cavity. Together, our results give a detailed picture of the role of protons in driving one of the major transitions in this transporter.

Ligand Pathways in Nuclear Receptors

Nuclear receptors (NRs) are ligand-inducible transcription factors that play an essential role in a multitude of physiological processes as well as diseases, rendering them attractive drug targets. Crystal structures revealed the binding site of NRs to be buried in the core of the protein, with no obvious route for ligands to access this cavity. The process of ligand binding is known to be an often-neglected contributor to the efficacy of drug candidates and is thought to influence the selectivity and specificity of NRs. While experimental methods generally fail to highlight the dynamic processes of ligand access or egress on the atomistic scale, computational methods have provided fundamental insight into the pathways connecting the buried binding pocket to the surrounding environment. Methods based on molecular dynamics (MD) and Monte Carlo simulations have been applied to identify pathways and quantify their capability to transport ligands. Here, we systematically review findings of more than 20 years of research in the field, including the applied methodology and controversies. Further, we establish a unified nomenclature to describe the pathways with respect to their location relative to protein secondary structure elements and summarize findings relevant to drug design. Lastly, we discuss the effect of NR interaction partners such as coactivators and corepressors, as well as mutations on the pathways.