Bias-Exchange Metadynamics Simulation of Membrane Permeation of 20 Amino Acids

Quantifying Induced Dipole Effects in Small Molecule Permeation in a Model Phospholipid Bilayer

The cell membrane functions as a semipermeable barrier that governs the transport of materials into and out of cells. The bilayer features a distinct dielectric gradient due to the amphiphilic nature of its lipid components. This gradient influences various aspects of small molecule permeation and the folding and functioning of membrane proteins. Here, we employ polarizable molecular dynamics simulations to elucidate the impact of the electronic environment on the permeation process. We simulated eight distinct amino-acid side chain analogs within a 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayer using the Drude polarizable force field (FF). Our approach includes both unbiased and umbrella sampling simulations. By using a polarizable FF, we sought to investigate explicit dipole responses in relation to local electric fields along the membrane normal. We evaluate molecular dipole moments, which exhibit variation based on their localization within the membrane, and compare the outcomes with analogous simulations using the nonpolarizable CHARMM36 FF. This comparative analysis aims to discern characteristic differences in the free energy surfaces of permeation for the various amino-acid analogs. Our results provide the first systematic quantification of the impact of employing an explicitly polarizable FF in this context compared to the fixed-charge convention inherent to nonpolarizable FFs, which may not fully capture the influence of the membrane dielectric gradient.

MemCross: Accelerated Weight Histogram method to assess membrane permeability

Passive permeation events across biological membranes are determining steps in the pharmacokinetics of xenobiotics. To reach an accurate and rapid prediction of membrane permeation coefficients of drugs is a complex challenge, which can efficiently support drug discovery. Such predictions are indeed highly valuable as they may guide the selection of potential leads with optimum bioavailabilities prior to synthesis. Theoretical models exist to predict these coefficients. Many of them are based on molecular dynamics (MD) simulations, which allow calculation of permeation coefficients through the evaluation of both the potential of mean force (PMF) and the diffusivity profiles. However, these simulations still require intensive computational efforts, and novel methodologies should be developed and benchmarked. Free energy perturbation (FEP) method was recently shown to estimate PMF with a significantly reduced computational cost compared to the adaptive biasing force method. This benchmarking was achieved with small molecules, namely short-chain alcohols. Here, we show that to estimate the PMF of bulkier, drug-like xenobiotics, conformational sampling is a critical issue. To reach a sufficient sampling with FEP calculations requires a relatively long time-scale, which can lower the benefits related to the computational gain. In the present work, the Accelerated Weight Histogram (AWH) method was employed for the first time in all-atom membrane models. The AWH-based protocol, named MemCross, appears affordable to estimate PMF profiles of a series of drug-like xenobiotics, compared to other enhanced sampling methods. The continuous exploration of the crossing pathway by MemCross also allows modeling subdiffusion by computing fractional diffusivity profiles. The method is also versatile as its input parameters are largely insensitive to the molecule properties. It also ensures a detailed description of the molecule orientations along the permeation pathway, picturing all intermolecular interactions at an atomic resolution. Here, MemCross was applied on a series of 12 xenobiotics, including four weak acids, and a coherent structure-activity relationship was established.

Calculation of the permeability coefficients of small molecules through lipid bilayers by free-energy reaction network analysis following the explicit treatment of the internal conformation of the solute

Biomembrane permeation represents a major barrier to pharmacokinetics. During preclinical drug discovery, the coefficients of the permeation of molecules through lipid bilayers account for a valuable property of such molecules. Therefore, the control of the permeation of molecules through lipid bilayers is an essential factor in drug design, and the estimation of the permeation phenomena is a crucial study in pharmacy. Thus, there are many published studies on the theoretical estimations of permeation coefficients. Here, we propose a molecular dynamics (MD) simulation method for estimating the permeation of small molecules through lipid bilayers based on the free-energy reaction network (FERN) analysis. In this method, the collective variables (CVs) of the free energy calculations explicitly include the conformational changes in the rotational bonds of the solute molecules. The advantages of the present method over the other method are that it is possible to estimate reaction pathways and their reaction rates, i.e., permeation coefficients or passage times, in multidimensional space spanned by CVs though conventional methods such as the umbrella sampling method and target MDs often dealt with a few degrees of freedom. To demonstrate the efficacy of our method, we calculate the coefficients of the permeation of three small aromatic peptides, namely N-acetylphenylalanineamide (Ac-Phe-NH2 or NAFA), N-acetyltyrosineamide (Ac-Tyr-NH2 or NAYA), and N-acetyltryptophanamide (Ac-Trp-NH2 or NATA), through a 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) lipid bilayer. In these cases we adopted one CV for the permeation direction and four CVs for the internal rotational coordinates. The results reveal that the permeation coefficients of NAFA, NAYA, and NATA are 1.7 × 10^-2, 0.51 × 10^-4, and 5.7 × 10^-4 cm s^-1, respectively. Compared with the experimental data, our simulation results followed the same trend, i.e., NAFA > NATA > NAYA. By analyzing the structures of metastable points of the solute molecules, our simulation result reveals that the aforementioned trend is caused by the differences in stability among their rotamers. Furthermore, we evaluate the statistical fluctuation of the rotamers, and the time scale of flipping the side chain reveals that the structures rigidify as the ligand moves deeper into the membrane.

Analysis of Charged Peptide Loop-Flipping across a Lipid Bilayer Using the String Method with Swarms of Trajectories

The hydrophobic core of the lipid bilayer is conventionally considered a barrier to the translocation of charged species such that the translocation of even single ions occurs on long time scales. In contrast, experiments have revealed that some materials, including peptides, proteins, and nanoparticles, can translocate multiple charged moieties across the bilayer on experimentally relevant time scales. Understanding the molecular mechanisms underlying this behavior is challenging because resolving corresponding free-energy landscapes with molecular simulation techniques is computationally expensive. To address this challenge, we use atomistic molecular dynamics simulations with the swarms-of-trajectories (SOT) string method to analyze charge translocation pathways across single-component lipid bilayers as a function of multiple collective variables. We first demonstrate that the SOT string method can reproduce the free-energy barrier for the translocation of a charged lysine amino acid analogue in good agreement with the literature. We then obtain minimum free-energy pathways for the translocation, or flipping, of charged peptide loops across the lipid bilayer by utilizing trajectories from prior temperature-accelerated molecular dynamics (TAMD) simulations as initial configurations. The corresponding potential of mean force calculations reveal that the protonation of a central membrane-exposed aspartate residue substantially reduces the free-energy barrier for flipping charged loops by modulating the water content of the bilayer. These results provide new insight into the thermodynamics underlying loop-flipping processes and highlight how the combination of TAMD and the SOT string method can be used to understand complex charge translocation mechanisms.

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.

Molecular Dynamics Simulation of Small Molecules Interacting with Biological Membranes

Cell membranes protect and compartmentalise cells and their organelles. The semi-permeable nature of these membranes controls the exchange of solutes across their structure. Characterising the interaction of small molecules with biological membranes is critical to understanding of physiological processes, drug action and permeation, and many biotechnological applications. This review provides an overview of how molecular simulations are used to study the interaction of small molecules with biological membranes, with a particular focus on the interactions of water, organic compounds, drugs and short peptides with models of plasma cell membrane and stratum corneum lipid bilayers. This review will not delve on other types of membranes which might have different composition and arrangement, such as thylakoid or mitochondrial membranes. The application of unbiased molecular dynamics simulations and enhanced sampling methods such as umbrella sampling, metadynamics and replica exchange are described using key examples. This review demonstrates how state-of-the-art molecular simulations have been used successfully to describe the mechanism of binding and permeation of small molecules with biological membranes, as well as associated changes to the structure and dynamics of these membranes. The review concludes with an outlook on future directions in this field.

Interplay of hydrophobic and hydrophilic interactions in sequence-dependent cell penetration of spontaneous membrane-translocating peptides revealed by bias-exchange metadynamics simulations

Spontaneous Membrane Translocating Peptides (SMTPs) can translocate silently across the bilayer and, thus, have the best potential to improve the delivery of therapeutic molecules to cells without toxicity. However, how their translocation mechanisms are affected by a specific peptide sequence remains poorly understood. Here, bias-exchange metadynamics simulations were employed to investigate the translocation mechanisms of five SMTPs with the same composition of amino acids (LLRLR, LRLLR, LLLRR, RLLLR, and LRLRL). Simulation results yield sequence-dependent free energy barrier using the FESs along the z-directional distance. An in-depth analysis of sequence-dependent interactions in different regions of the bilayers indicates that the free-energy barrier height of a specific sequence is resulted from the accessibility balance of isolated or clustered hydrophobic residues (L) and hydrophilic residues (R) that leads to different levels of resistance for moving of a peptide into the hydrophobic center of the membrane. At the maximal of the free-energy barrier, all peptides have a conformation parallel to the membrane surface with the barrier height determined by their affinity to the hydrophobic region. The appropriate bilayer perturbation and GDM⁺ pairing are beneficial for peptide translocation. These results provide an improved microscopic understanding of how peptide sequence influences the translocation efficiency and mechanism.

Computer simulations of protein-membrane systems

The interactions between proteins and membranes play critical roles in signal transduction, cell motility, and transport, and they are involved in many types of diseases. Molecular dynamics (MD) simulations have greatly contributed to our understanding of protein-membrane interactions, promoted by a dramatic development of MD-related software, increasingly accurate force fields, and available computer power. In this chapter, we present available methods for studying protein-membrane systems with MD simulations, including an overview about the various all-atom and coarse-grained force fields for lipids, and useful software for membrane simulation setup and analysis. A large set of case studies is discussed.

Energy Landscapes of Ligand Motion Inside the Tunnel-Like Cavity of Lipid Transfer Proteins: The Case of the Pru p 3 Allergen

Allergies are a widespread problem in western countries, affecting a large part of the population, with levels of prevalence increasingly rising due to reasons still not understood. Evidence accumulated in recent years points to an essential role played by ligands of allergen proteins in the sensitization phase of allergies. In this regard, we recently identified the natural ligand of Pru p 3, a lipid transfer protein, a major allergen from peach fruit and a model of food allergy. The ligand of Pru p 3 has been shown to play a key role in the sensitization to peach and to other plant food sources that provoke cross-reactivity in a large proportion of patients allergic to peach. However, the question of which is the binding pose of this ligand in its carrier protein, and how it can be transferred to receptors of the immune system where it develops its function as a coadjuvant was not elucidated. In this work, different molecular dynamics simulations have been considered as starting points to study the properties of the ligand–protein system in solution. Besides, an energy landscape based on collective variables that describe the process of ligand motion within the cavity of Pru p 3 was obtained by using well-tempered metadynamics. The simulations revealed the differences between distinct binding modes, and also revealed important aspects of the motion of the ligand throughout its carrier protein, relevant to its binding–unbinding process. Our findings are potentially interesting for studying protein–ligand systems beyond the specific case of the allergen protein dealt with here.

Different effects of cholesterol on membrane permeation of arginine and tryptophan revealed by bias-exchange metadynamics simulations

Experiments have shown that cholesterol influences the membrane permeability of small molecules, amino acids, and cell-penetrating peptides. However, their exact translocation mechanisms under the influence of cholesterol remain poorly understood. Given the practical importance of cell-penetrating peptides and the existence of varied cholesterol contents in different cell types, it is necessary to examine the permeation of amino acids in cholesterol-containing membranes at atomic level of details. Here, bias-exchange metadynamics simulations were employed to investigate the molecular mechanism of the membrane permeation of two amino acids Arg and Trp important for cell-penetrating peptides in the presence of different concentrations of cholesterol. We found that the free energy barrier of Arg+ (the protonated form) permeation increased linearly as the cholesterol concentration increased, whereas the barrier of Trp permeation had a rapid increase from 0 mol. % to 20 mol. % cholesterol-containing membranes and nearly unchanged from 20 mol. % to 40 mol. % cholesterol-containing membranes. Arg0 becomes slightly more stable than Arg+ at the center of the dipalmitoylphosphatidylcholine (DPPC) membrane with 40 mol. % cholesterol concentrations. As a result, Arg+ has a similar permeability as Trp at 0 mol. % and 20 mol. % cholesterol, but a significantly lower permeability than Trp at 40 mol. % cholesterol. This difference is caused by the gradual reduction of water defects for Arg+ as the cholesterol concentration increases but lack of water defects for Trp in cholesterol-containing membranes. Strong but different orientation dependence between Arg+ and Trp permeations is observed. These results provide an improved microscopic understanding of amino-acid permeation through cholesterol-containing DPPC membrane systems.