Quantitative Assessment of Methods Used To Obtain Rate Constants from Molecular Dynamics Simulations—Translocation of Cholesterol across Lipid Bilayers

Interaction of MRI Contrast Agent [Gd(DOTA)]- with Lipid Membranes: A Molecular Dynamics Study

Contrast agents are important imaging probes in clinical MRI, allowing the identification of anatomic changes that otherwise would not be possible. Intensive research on the development of new contrast agents is being made to image specific pathological markers or sense local biochemical changes. The most widely used MRI contrast agents are based on gadolinium(III) complexes. Due to their very high charge density, they have low permeability through tight biological barriers such as the blood-brain barrier, hampering their application in the diagnosis of neurological disorders. In this study, we explore the interaction between the widely used contrast agent [Gd(DOTA)]- (Dotarem) and POPC lipid bilayers by means of molecular dynamics simulations. This metal complex is a standard reference where several chemical modifications have been introduced to improve key properties such as bioavailability and targeting. The simulations unveil detailed insights into the agent's interaction with the lipid bilayer, offering perspectives beyond experimental methods. Various properties, including the impact on global and local bilayer properties, were analyzed. As expected, the results indicate a low partition coefficient (KP) and high permeation barrier for this reference compound. Nevertheless, favorable interactions are established with the membrane leading to moderately long residence times. While coordination of one inner-sphere water molecule is maintained for the membrane-associated chelate, the physical-chemical attributes of [Gd(DOTA)]- as a MRI contrast agent are affected. Namely, increases in the rotational correlation times and in the residence time of the inner-sphere water are observed, with the former expected to significantly increase the water proton relaxivity. This work establishes a reference framework for the use of simulations to guide the rational design of new contrast agents with improved relaxivity and bioavailability and for the development of liposome-based formulations for use as imaging probes or theranostic agents.

Interaction of Hoechst 33342 with POPC Membranes at Different pH Values

Hoechst 33342 (H33342) is a fluorescent probe that is commonly used to stain the DNA of living cells. To do so, it needs to interact with and permeate through cell membranes, despite its high overall charge at physiological pH values. In this work, we address the effect of pH in the association of H33342 with lipid bilayers using a combined experimental and computational approach. The partition of H33342 to 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) lipid membranes was experimentally quantified using fluorescence spectroscopy and isothermal titration calorimetry (ITC) measurements. Quantum chemical calculations were performed to select the most stable isomer of H33342 for the overall charges 0, +1, and +2, expected to predominate across the 5 < pH < 10 range. The interaction of these isomers with POPC bilayers was then studied by both unrestrained and umbrella sampling molecular dynamics (MD) simulations. Both experimental results and computational free energy profiles indicate that the partition coefficient of H33342 displays a small variation over a wide pH range, not exceeding one order of magnitude. The enthalpy variation upon partition to the membrane suggests efficient hydrogen bonding between the probe and the lipid, namely, for the protonated +2 form, which was confirmed in the MD simulation studies. The relatively high lipophilicity obtained for the charged species contrasts with the decrease in their general hydrophobicity as estimated from octanol/water partition. This highlights the distinction between lipophilicity and hydrophobicity, as well as the importance of considering the association with lipid bilayers when predicting the affinity for biomembranes.

Permeation of a Homologous Series of NBD-Labeled Fatty Amines through Lipid Bilayers: A Molecular Dynamics Study

Permeation through biomembranes is ubiquitous for drugs to reach their active sites. Asymmetry of the cell plasma membrane (PM) has been described as having an important role in this process. Here we describe the interaction of a homologous series of 7-nitrobenz-2-oxa-1,3-diazol-4-yl (NBD)-labeled amphiphiles (NBD-Cn, n = 4 to 16) with lipid bilayers of different compositions (1-palmitoyl, 2-oleoyl-sn-glycero-3-phosphocholine (POPC):cholesterol (1:1) and palmitoylated sphingomyelin (SpM):cholesterol (6:4)), including an asymmetric bilayer. Both unrestrained and umbrella sampling (US) simulations (at varying distances to the bilayer center) were carried out. The free energy profile of NBD-Cn at different depths in the membrane was obtained from the US simulations. The behavior of the amphiphiles during the permeation process was described regarding their orientation, chain elongation, and H-bonding to lipid and water molecules. Permeability coefficients were also calculated for the different amphiphiles of the series, using the inhomogeneous solubility-diffusion model (ISDM). Quantitative agreement with values obtained from kinetic modeling of the permeation process could not be obtained. However, for the longer, and more hydrophobic amphiphiles, the variation trend along the homologous series was qualitatively better matched by the ISDM when the equilibrium location of each amphiphile was taken as reference (ΔG = 0), compared to the usual choice of bulk water.

Fluorescent Probes cis- and trans-Parinaric Acids in Fluid and Gel Lipid Bilayers: A Molecular Dynamics Study

Fluorescence probes are indispensable tools in biochemical and biophysical membrane studies. Most of them possess extrinsic fluorophores, which often constitute a source of uncertainty and potential perturbation to the host system. In this regard, the few available intrinsically fluorescent membrane probes acquire increased importance. Among them, cis- and trans-parinaric acids (c-PnA and t-PnA, respectively) stand out as probes of membrane order and dynamics. These two compounds are long-chained fatty acids, differing solely in the configurations of two double bonds of their conjugated tetraene fluorophore. In this work, we employed all-atom and coarse-grained molecular dynamics simulations to study the behavior of c-PnA and t-PnA in lipid bilayers of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), representative of the liquid disordered and solid ordered lipid phases, respectively. All-atom simulations indicate that the two probes show similar location and orientation in the simulated systems, with the carboxylate facing the water/lipid interface and the tail spanning the membrane leaflet. The two probes establish interactions with the solvent and lipids to a similar degree in POPC. However, the almost linear t-PnA molecules have tighter lipid packing around them, especially in DPPC, where they also interact more with positively charged lipid choline groups. Probably for these reasons, while both probes show similar partition (assessed from computed free energy profiles across bilayers) to POPC, t-PnA clearly partitions more extensively than c-PnA to the gel phase. t-PnA also displays more hindered fluorophore rotation, especially in DPPC. Our results agree very well with experimental fluorescence data from the literature and allow deeper understanding of the behavior of these two reporters of membrane organization.

Interaction of a Homologous Series of Amphiphiles with P-glycoprotein in a Membrane Environment-Contributions of Polar and Non-Polar Interactions

The transport of drugs by efflux transporters in biomembranes limits their bioavailability and is a major determinant of drug resistance development by cancer cells and pathogens. A large number of chemically dissimilar drugs are transported, and despite extensive studies, the molecular determinants of substrate specificity are still not well understood. In this work, we explore the role of polar and non-polar interactions on the interaction of a homologous series of fluorescent amphiphiles with the efflux transporter P-glycoprotein. The interaction of the amphiphiles with P-glycoprotein is evaluated through effects on ATPase activity, efficiency in inhibition of [¹²⁵I]-IAAP binding, and partition to the whole native membranes containing the transporter. The results were complemented with partition to model membranes with a representative lipid composition, and details on the interactions established were obtained from MD simulations. We show that when the total concentration of amphiphile is considered, the binding parameters obtained are apparent and do not reflect the affinity for P-gp. A new formalism is proposed that includes sequestration of the amphiphiles in the lipid bilayer and the possible binding of several molecules in P-gp's substrate-binding pocket. The intrinsic binding affinity thus obtained is essentially independent of amphiphile hydrophobicity, highlighting the importance of polar interactions. An increase in the lipophilicity and amphiphilicity led to a more efficient association with the lipid bilayer, which maintains the non-polar groups of the amphiphiles in the bilayer, while the polar groups interact with P-gp's binding pocket. The presence of several amphiphiles in this orientation is proposed as a mechanism for inhibition of P-pg function.

Modeling Ensembles of Enzyme Reaction Pathways with Hi-MSM Reveals the Importance of Accounting for Pathway Diversity

Conventional quantum mechanical-molecular mechanics (QM/MM) simulation approaches for modeling enzyme reactions often assume that there is one dominant reaction pathway and that this pathway can be sampled starting from an X-ray structure of the enzyme. These assumptions reduce computational cost; however, their validity has not been extensively tested. This is due in part to the lack of a rigorous formalism for integrating disparate pathway information from dynamical QM/MM calculations. Here, we present a way to model ensembles of reaction pathways efficiently using a divide-and-conquer strategy through Hierarchical Markov State Modeling (Hi-MSM). This approach allows information on multiple, distinct pathways to be incorporated into a chemical kinetic model, and it allows us to test these two assumptions. Applying Hi-MSM to the reaction carried out by dihydrofolate reductase (DHFR) we find (i) there are multiple, distinct pathways significantly contributing to the overall flux of the reaction that the conventional approach does not identify and (ii) that the conventional approach does not identify the dominant reaction pathway. Thus, both assumptions underpinning the conventional approach are violated. Since DHFR is a relatively small enzyme, and configuration space scales exponentially with protein size, accounting for multiple reaction pathways is likely to be necessary for most enzymes.

Modeling Gd3+ Complexes for Molecular Dynamics Simulations: Toward a Rational Optimization of MRI Contrast Agents

The correct parametrization of lanthanide complexes is of the utmost importance for their characterization using computational tools such as molecular dynamics simulations. This allows the optimization of their properties for a wide range of applications, including medical imaging. Here we present a systematic study to establish the best strategies for the correct parametrization of lanthanide complexes using [Gd(DOTA)]^- as a reference, which is used as a contrast agent in MRI. We chose the bonded model to parametrize the lanthanide complexes, which is especially important when considering the study of the complex as a whole (e.g., for the study of the dynamics of its interaction with proteins or membranes). We followed two strategies: a so-called heuristic approach employing strategies already published by other authors and another based on the more recent MCPB.py tool. Adjustment of the Lennard-Jones parameters of the metal was required. The final topologies obtained with both strategies were able to reproduce the experimental ion to oxygen distance, vibrational frequencies, and other structural properties. We report a new strategy to adjust the Lennard-Jones parameters of the metal ion in order to capture dynamic properties such as the residence time of the capping water (τ_m). For the first time, the correct assessment of the τ_m value for Gd-based complexes was possible by recording the dissociative events over up to 10 μs all-atom simulations. The MCPB.py tool allowed the accurate parametrization of [Gd(DOTA)]^- in a simpler procedure, and in this case, the dynamics of the water molecules in the outer hydration sphere was also characterized. This sphere was divided into the first hydration layer, an intermediate region, and an outer hydration layer, with a residence time of 18, 10 and 19 ps, respectively, independent of the nonbonded parameters chosen for Gd³⁺. The Lennard-Jones parameters of Gd³⁺ obtained here for [Gd(DOTA)]^- may be used with similarly structured gadolinium MRI contrast agents. This allows the use of molecular dynamics simulations to characterize and optimize the contrast agent properties. The characterization of their interaction with membranes and proteins will permit the design of new targeted contrast agents with improved pharmacokinetics.

Calculation of Permeability Coefficients from Solute Equilibration Dynamics: An Assessment of Various Methods

Predicting the rate at which substances permeate membrane barriers in vivo is crucial for drug development. Permeability coefficients obtained from in vitro studies are valuable for this goal. These are normally determined by following the dynamics of solute equilibration between two membrane-separated compartments. However, the correct calculation of permeability coefficients from such data is not always straightforward. To address these problems, here we develop a kinetic model for solute permeation through lipid membrane barriers that includes the two membrane leaflets as compartments in a four-compartment model. Accounting for solute association with the membrane allows assessing various methods in a wide variety of conditions. The results showed that the often-used expression Papp= β × r/3 is inapplicable to very large or very small vesicles, to moderately or highly lipophilic solutes, or when the development of a significant pH gradient opposes the solute’s flux. We establish useful relationships that overcome these limitations and allow predicting permeability in compartmentalised in vitro or in vivo systems with specific properties. Finally, from the parameters for the interaction of the solute with the membrane barrier, we defined an intrinsic permeability coefficient that facilitates quantitative comparisons between solutes.

LiPyphilic: A Python Toolkit for the Analysis of Lipid Membrane Simulations

Molecular dynamics simulations are now widely used to study emergent phenomena in lipid membranes with complex compositions. Here, we present LiPyphilic-a fast, fully tested, and easy-to-install Python package for analyzing such simulations. Analysis tools in LiPyphilic include the identification of cholesterol flip-flop events, the classification of local lipid environments, and the degree of interleaflet registration. LiPyphilic is both force field- and resolution-agnostic, and by using the powerful atom selection language of MDAnalysis, it can handle membranes with highly complex compositions. LiPyphilic also offers two on-the-fly trajectory transformations to (i) fix membranes split across periodic boundaries and (ii) perform nojump coordinate unwrapping. Our implementation of nojump unwrapping accounts for fluctuations in the box volume under the NPT ensemble-an issue that most current implementations have overlooked. The full documentation of LiPyphilic, including installation instructions and links to interactive online tutorials, is available at https://lipyphilic.readthedocs.io/en/latest.

The effects of the lipid type on the spatial arrangement and dynamics of cholesterol in binary component lipid membranes

Intermolecular interactions between cholesterol and lipids in cell membranes, which play critical roles in cellular processes such as the formation of nano-domains, depend on the molecular structure of the lipids. The diffusion and the spatial arrangement of cholesterol within the lipid membranes also change with the type of lipids. For example, the flip-flop, an important transport mechanism for cholesterol in the membranes, can be facilitated significantly by the presence of unsaturated lipids. However, how the structure of lipids affects the spatial arrangement and the dynamics of cholesterol remains elusive at a molecular level. In this study, we investigate the effects of lipid-cholesterol interactions on the spatial arrangement and the dynamics of cholesterol. We perform molecular dynamics simulations for the binary component membranes of lipids and cholesterol. We employ seven different kinds of lipids by changing either the degree of a saturation level or the length of lipid tails. We find from our simulations that the rate of cholesterol flip-flop is enhanced as the lipids are either less saturated or shorter, which is consistent with previous studies. Interestingly, when the lipid tails are fully saturated and sufficiently long, the center in between two leaflets becomes metastable for cholesterol to stay at. Because the cholesterol at the membrane center diffuses faster than that within leaflets, regardless of the lipid type, such an emergence of the metastable state (in terms of the cholesterol position) complicates the cholesterol diffusion significantly.

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

Permeability is a key property in various fields such as membrane technology for chemical separation and transport of substances through cell membranes. At the molecular scale, the counting method uses the number of membrane crossings in a conventional unbiased molecular dynamics simulation to predict the permeability. This contribution investigates under which conditions the counting method has insufficient statistics. An equation is derived for a compartmental model based on the inhomogeneous solubility-diffusion (Smoluchowski) model, giving insight into how the flux correlates with the solubility of permeants. This equation shows that a membrane crossing is a rare event not only when the membrane forms a large free energy barrier but also when the membrane forms a deep free energy well that traps permeants. Such a permeant trap has a high permeability; yet, the counting method suffers from poor statistics. To illustrate this, coarse-grained MD was run for 16 systems of dipalmitoylphosphatidylcholine bilayer membranes with different permeant types. The composition rule for permeability is shown to also hold for fluxes, and it is highlighted that the considered thickness of the membrane causes uncertainty in the permeability calculation of highly permeable membranes. In conclusion, a high permeability in itself is not an effective indicator of the sampling efficiency of the counting method, and caution should be taken for permeants whose solubility varies greatly over the simulation box. A practical consequence relevant in, e.g., drug design is that a drug with high membrane permeability might get trapped by membranes thus reducing its efficacy.

The importance of intramolecular hydrogen bonds on the translocation of the small drug piracetam through a lipid bilayer

The number of hydrogen bond donors and acceptors is a fundamental molecular descriptor to predict the oral bioavailability of small drug candidates. In fact, the most widely used oral bioavailability rules (such as the Lipinsky's rule-of-five and the Veber rules) make use of this molecular descriptor. It is generally assumed that hydrogen bond donors and acceptors impact on passive diffusion across cell membranes, a fundamental event during drug absorption and distribution. Although the relationship between the number of these motifs and the probability of having good oral bioavailability has been studied and described for more than 20 years, little attention has been given to their spatial distribution in the molecule. In this paper, we used molecular dynamics to describe the effect of intramolecular hydrogen bonding on the passive diffusion of a small drug (piracetam) through a lipid membrane. The results indicated that the formation of an intramolecular hydrogen bond decreases the barrier for translocation by ca. 4 kcal mol-1 and increases the permeability of the tested molecule, partially compensating the desolvation penalty arising from the penetration of the drug into the biological membrane core. This effect was apparent in simulations where the formation of this interaction was prevented with the help of modified potentials, and in simulations with a similar compound to piracetam that was not able to form this intramolecular hydrogen bond due to a larger distance between the hydrogen bond donor and acceptor groups. These results were also supported by coarse-grained methods, which are becoming an important resource for sampling a larger chemical space of molecules, with reduced computational effort. Furthermore, entropy and enthalpy derived profiles were also obtained as the compounds translocated across the membrane, suggesting that, even though the process of formation of internal hydrogen bonds is entropically unfavorable, the enthalpic gain is such that the formation of these interactions is beneficial for the passive diffusion across cell membranes.

Composition dependence of cholesterol flip-flop rates in physiological mixtures

Unbiased, all-atom simulations of mixtures representative of the inner and outer leaflets of a mammalian red blood cell and a synaptic vesicle reveal many cholesterol flip-flop events over the 5 μsec duration of the simulations. Enough events are observed for a direct estimate of the flip-flop rate. Slower rates are found in more ordered membranes, and faster rates in more disordered membranes, consistent with earlier reports in the literature. However, the rates found here are neither as fast as the fastest nor as slow as the slowest rates obtained by previous simulations. The difference likely stems from the compositions studied here, which unlike previous work include exclusively lipids with differing acyl chains, as observed in mammalian lipidomes.

The Secret Lives of Fluorescent Membrane Probes as Revealed by Molecular Dynamics Simulations

Fluorescent probes have been employed for more than half a century to study the structure and dynamics of model and biological membranes, using spectroscopic and/or microscopic experimental approaches. While their utilization has led to tremendous progress in our knowledge of membrane biophysics and physiology, in some respects the behavior of bilayer-inserted membrane probes has long remained inscrutable. The location, orientation and interaction of fluorophores with lipid and/or water molecules are often not well known, and they are crucial for understanding what the probe is actually reporting. Moreover, because the probe is an extraneous inclusion, it may perturb the properties of the host membrane system, altering the very properties it is supposed to measure. For these reasons, the need for independent methodologies to assess the behavior of bilayer-inserted fluorescence probes has been recognized for a long time. Because of recent improvements in computational tools, molecular dynamics (MD) simulations have become a popular means of obtaining this important information. The present review addresses MD studies of all major classes of fluorescent membrane probes, focusing in the period between 2011 and 2020, during which such work has undergone a dramatic surge in both the number of studies and the variety of probes and properties accessed.

Multiscale Simulations of Biological Membranes: The Challenge To Understand Biological Phenomena in a Living Substance

Biological membranes are tricky to investigate. They are complex in terms of molecular composition and structure, functional over a wide range of time scales, and characterized by nonequilibrium conditions. Because of all of these features, simulations are a great technique to study biomembrane behavior. A significant part of the functional processes in biological membranes takes place at the molecular level; thus computer simulations are the method of choice to explore how their properties emerge from specific molecular features and how the interplay among the numerous molecules gives rise to function over spatial and time scales larger than the molecular ones. In this review, we focus on this broad theme. We discuss the current state-of-the-art of biomembrane simulations that, until now, have largely focused on a rather narrow picture of the complexity of the membranes. Given this, we also discuss the challenges that we should unravel in the foreseeable future. Numerous features such as the actin-cytoskeleton network, the glycocalyx network, and nonequilibrium transport under ATP-driven conditions have so far received very little attention; however, the potential of simulations to solve them would be exceptionally high. A major milestone for this research would be that one day we could say that computer simulations genuinely research biological membranes, not just lipid bilayers.

Rapid diffusion of cholesterol along polyunsaturated membranes via deep dives

Cholesterol regulates the function of membrane proteins either via direct or membrane-mediated effects. Therefore, its ready availability is crucial for many protein-governed cellular processes. Recent studies suggest that cholesterol can partition to the core of polyunsaturated membranes, where cholesterol binding sites of many membrane proteins are also located. This core region is characterized by a lower viscosity. Therefore, we hypothesized that cholesterol partitioning into the membrane interior increases the rate of its diffusion in polyunsaturated membrane environments. We studied the behavior of cholesterol in membranes with increasing level of lipid chain unsaturation using a combination of atomistic and coarse-grained molecular dynamics simulations. Our simulations suggest a strong correlation between entropy-driven enhanced cholesterol partitioning to the membrane core and its faster lateral diffusion, which indicates that the less viscous membrane core indeed provides an efficient means for cholesterol movement in polyunsaturated membrane environments.