Sampling efficiency of the counting method for permeability calculations estimated with the inhomogeneous solubility-diffusion model

Validation of a Coarse-Grained Martini 3 Model for Molecular Oxygen

Molecular oxygen (O2) is essential for life, and continuous effort has been made to understand its pathways in cellular respiration with all-atom (AA) molecular dynamics (MD) simulations of, e.g., membrane permeation or binding to proteins. To reach larger length scales with models, such as curved membranes in mitochondria or caveolae, coarse-grained (CG) simulations could be used at much lower computational cost than AA simulations. Yet a CG model for O2 is lacking. In this work, a CG model for O2 is therefore carefully selected from the Martini 3 force field based on criteria including size, zero charge, nonpolarity, solubility in nonpolar organic solvents, and partitioning in a phospholipid membrane. This chosen CG model for O2 (TC3 bead) is then further evaluated through the calculation of its diffusion constant in water and hexadecane, its permeability rate across pure phospholipid- and cholesterol-containing membranes, and its binding to the T4 lysozyme L99A protein. Our CG model shows semiquantitative agreement between CG diffusivity and permeation rates with the corresponding AA values and available experimental data. Additionally, it captures the binding to hydrophobic cavities of the protein, aligning well with the AA simulation of the same system. Thus, the results show that our O2 model approximates the behavior observed in the AA simulations. The CG O2 model is compatible with the widely used multifunctional Martini 3 force field for biological simulations, which will allow for the simulation of large biomolecular systems involved in O2's transport in the body.

A methodology of quantifying membrane permeability based on returning probability theory and molecular dynamics simulation

We propose a theoretical approach to estimate the permeability coefficients of substrates (permeants) for crossing membranes from donor (D) phase to acceptor (A) phase by means of molecular dynamics (MD) simulation. A fundamental aspect of our approach involves reformulating the returning probability (RP) theory, a rigorous bimolecular reaction theory, to describe permeation phenomena. This reformulation relies on the parallelism between permeation and bimolecular reaction processes. In the present method, the permeability coefficient is represented in terms of the thermodynamic and kinetic quantities for the reactive (R) phase that exists within the inner region of a membrane. One can evaluate these quantities using multiple MD trajectories starting from phase R. We apply the RP theory to the permeation of ethanol and methylamine at different concentrations (infinitely dilute and 1 mol % conditions of permeants). Under the 1 mol% condition, the present method yields a larger permeability coefficient for ethanol (0.12 ± 0.01 cm s-1) than for methylamine (0.069 ± 0.006 cm s-1), while the values of the permeability coefficient are satisfactorily close to those obtained from the brute-force MD simulations (0.18 ± 0.03 and 0.052 ± 0.005 cm s-1 for ethanol and methylamine, respectively). Moreover, upon analyzing the thermodynamic and kinetic contributions to the permeability, we clarify that a higher concentration dependency of permeability for ethanol, as compared to methylamine, arises from the sensitive nature of ethanol's free-energy barrier within the inner region of the membrane against ethanol concentration.

PyRETIS 3: Conquering rare and slow events without boundaries

We present and discuss the advancements made in PyRETIS 3, the third instalment of our Python library for an efficient and user-friendly rare event simulation, focused to execute molecular simulations with replica exchange transition interface sampling (RETIS) and its variations. Apart from a general rewiring of the internal code towards a more modular structure, several recently developed sampling strategies have been implemented. These include recently developed Monte Carlo moves to increase path decorrelation and convergence rate, and new ensemble definitions to handle the challenges of long-lived metastable states and transitions with unbounded reactant and product states. Additionally, the post-analysis software PyVisa is now embedded in the main code, allowing fast use of machine-learning algorithms for clustering and visualising collective variables in the simulation data.

tICA-Metadynamics for Identifying Slow Dynamics in Membrane Permeation

Molecular simulations are commonly used to understand the mechanism of membrane permeation of small molecules, particularly for biomedical and pharmaceutical applications. However, despite significant advances in computing power and algorithms, calculating an accurate permeation free energy profile remains elusive for many drug molecules because it can require identifying the rate-limiting degrees of freedom (i.e., appropriate reaction coordinates). To resolve this issue, researchers have developed machine learning approaches to identify slow system dynamics. In this work, we apply time-lagged independent component analysis (tICA), an unsupervised dimensionality reduction algorithm, to molecular dynamics simulations with well-tempered metadynamics to find the slowest collective degrees of freedom of the permeation process of trimethoprim through a multicomponent membrane. We show that tICA-metadynamics yields translational and orientational collective variables (CVs) that increase convergence efficiency ∼1.5 times. However, crossing the periodic boundary is shown to introduce artifacts in the translational CV that can be corrected by taking absolute values of molecular features. Additionally, we find that the convergence of the tICA CVs is reached with approximately five membrane crossings and that data reweighting is required to avoid deviations in the translational CV.

Capric Acid and Myristic Acid Permeability Enhancers in Curved Liposome Membranes

Liposomes are considered as advanced drug delivery systems for cancer treatment. A generation of pH-sensitive liposomes is being developed that use fatty acids (FAs) as a trigger for drug release in tumor tissues. However, FAs are also known to enhance permeability, and it is unclear whether FAs in liposomes may cause drug leakage or premature drug release. The passive permeability of the drug through the membrane of the liposome is thus a crucial factor for timely drug delivery. To investigate how the curvature and lipid composition of liposomes affect their passive permeability, coarse-grained molecular dynamics were performed. The permeability was determined with a counting method. Flat bilayers and three liposomes with varying diameters were studied, which had varying lipid compositions of dipalmitoylphosphatidylcholine, cholesterol, and deprotonated or neutral saturated FAs. The investigated permeants were water and two other small permeants, which have different free energy profiles (solubility) across the membrane. First, for the curvature effect, our results showed that curvature increases the water permeability by reducing the membrane thickness. The permeability increase for water is about a factor of 1.7 for the most curved membranes. However, a high curvature decreases permeability for permeants with free energy profiles that are a mix of wells and barriers in the headgroup region of the membrane. Importantly, the type of experimental setup is expected to play a dominant role in the permeability value, i.e., whether permeants are escaping or entering the liposomes. Second, for the composition effect, FAs decrease both the area per lipid (APL) and the membrane thickness, resulting in permeability increases of up to 55%. Cholesterol has a similar effect on the APL but has the opposite impact on membrane thickness and permeability. Therefore, FAs and cholesterol have opposing effects on permeability, with cholesterol's effect being slightly stronger in our simulated bilayers. As all permeability values were well within a factor of 2, and with liposomes usually being larger and less curved in experimental applications, it can be concluded that the passive drug release from a pH-sensitive liposome does not seem to be significantly affected by the presence of FAs.

tICA-Metadynamics for Identifying Slow Dynamics in Membrane Permeation

Molecular simulations are commonly used to understand the mechanism of membrane permeation of small molecules, particularly for biomedical and pharmaceutical applications. However, despite significant advances in computing power and algorithms, calculating an accurate permeation free energy profile remains elusive for many drug molecules because it can require identifying the rate-limiting degrees of freedom (i.e., appropriate reaction coordinates). To resolve this issue, researchers have developed machine learning approaches to identify slow system dynamics. In this work, we apply time-lagged independent component analysis (tICA), an unsupervised dimensionality reduction algorithm, to molecular dynamics simulations with well-tempered metadynamics to find the slowest collective degrees of freedom of the permeation process of trimethoprim through a multicomponent membrane. We show that tICA-metadynamics yields translational and orientational collective variables (CVs) that increase convergence efficiency ∼1.5 times. However, crossing the periodic boundary is shown to introduce artefacts in the translational CV that can be corrected by taking absolute values of molecular features. Additionally, we find that the convergence of the tICA CVs is reached with approximately five membrane crossings, and that data reweighting is required to avoid deviations in the translational CV.

Understanding the Role of Caveolae in Oxygen Buffering: The Effect of Membrane Curvature

The "oxygen paradox" can be explained as two opposing biological processes with oxygen (O2) as a reactant. On the one hand, oxygen is essential to aerobic metabolism, powering oxidative phosphorylation in mitochondria. On the other hand, an excess supply of oxygen will generate reactive species which are harmful for the cell. In healthy tissues, the first process must be maximized relative to the second one. We have hypothesized that curved and cholesterol-enriched membrane invaginations called caveolae help maintain the proper oxygen level by taking up oxygen and attenuating its release to the mitochondria. The mechanism by which caveolae may help to buffer the oxygen level in cells is still unclear. Here, we aim to assess how structural aspects of caveolae, the curvature of the membrane, influence the local oxygen abundance and the membrane partitioning. We have modelled a flat bilayer and a liposome composed of dipalmitoylphosphatidylcholine (DPPC), using molecular dynamics simulation. Associated changes in the membrane-level oxygen partition coefficient and free energy profiles will be presented.

Oxygen Storage in Stacked Phospholipid Membranes Under an Oxygen Gradient as a Model for Myelin Sheaths

Axons in the brain and peripheral nervous system are enveloped by myelin sheaths, which are composed of stacked membrane bilayers containing large fractions of cholesterol, phospholipids, and glycolipids. The oxygen availability to the nearby oxygen consuming cytochrome c oxidase in the mitochondria is essential for the well-functioning of a cell. By constructing a rate network model based on molecular dynamics simulations, and solving it for steady-state conditions, this work calculates the oxygen storage in stacked membranes under an oxygen gradient. It is found that stacking membranes increases the oxygen storage capacity, indicating that myelin can function as an oxygen reservoir. However, it is found that the storage enhancement levels out for stacks with a large number of bilayers, suggesting why myelin sheaths consist of only 10-300 membranes rather than thousands. The presence of additional water between the stacked bilayers, as seen in cancer cells, is shown to diminish myelin oxygen storage enhancement.