Mechanisms of passive ion permeation through lipid bilayers: insights from simulations

Designing Reaction Coordinate for Ion-Induced Pore-Assisted Mechanism of Halide Ions Permeation through Lipid Bilayer by Umbrella Sampling

Ion permeation mechanism through lipid membranes helps to understand cellular processes. We propose new reaction coordinates that allow ions to permeate according to their water affinity and interaction with the hydrophilic layer. Simulations were done for three different halides (F-, Cl-, and I-) in two different lipid bilayers, 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and 1,2-dinervonoyl-sn-glycero-3-phosphocholine (DNPC). It is found that the involvement of the water molecules decreases the free energy barrier. The ions were found to follow different pathways for permeation. Formation of proper pores required a collaboration effort of the hydration shell water molecules and the hydrophilic lipid layer, which was favored in the case of Cl- ions. The optimum charge density and good water affinity of Cl- with respect to F- and I- ions helped to form the pore. The effect was prominently seen in the case of DNPC membrane because of its higher hydrophobic thickness. The umbrella sampling results were compared with other methods such as the Markov state model (MSM) and well-tempered metadynamics (WT-metaD).

Evidence for long-term potentiation in phospholipid membranes

Biological supramolecular assemblies, such as phospholipid bilayer membranes, have been used to demonstrate signal processing via short-term synaptic plasticity (STP) in the form of paired pulse facilitation and depression, emulating the brain's efficiency and flexible cognitive capabilities. However, STP memory in lipid bilayers is volatile and cannot be stored or accessed over relevant periods of time, a key requirement for learning. Using droplet interface bilayers (DIBs) composed of lipids, water and hexadecane, and an electrical stimulation training protocol featuring repetitive sinusoidal voltage cycling, we show that DIBs displaying memcapacitive properties can also exhibit persistent synaptic plasticity in the form of long-term potentiation (LTP) associated with capacitive energy storage in the phospholipid bilayer. The time scales for the physical changes associated with the LTP range between minutes and hours, and are substantially longer than previous STP studies, where stored energy dissipated after only a few seconds. STP behavior is the result of reversible changes in bilayer area and thickness. On the other hand, LTP is the result of additional molecular and structural changes to the zwitterionic lipid headgroups and the dielectric properties of the lipid bilayer that result from the buildup of an increasingly asymmetric charge distribution at the bilayer interfaces.

Quantum Mechanical Aspects in the Pathophysiology of Neuropathic Pain

Neuropathic pain is a challenging complaint for patients and clinicians since there are no effective agents available to get satisfactory outcomes even though the pharmacological agents target reasonable pathophysiological mechanisms. This may indicate that other aspects in these mechanisms should be unveiled to comprehend the pathogenesis of neuropathic pain and thus find more effective treatments. Therefore, in the present study, several mechanisms are chosen to be reconsidered in the pathophysiology of neuropathic pain from a quantum mechanical perspective. The mathematical model of the ions quantum tunneling model is used to provide quantum aspects in the pathophysiology of neuropathic pain. Three major pathophysiological mechanisms are revisited in the context of the quantum tunneling model. These include: (1) the depolarized membrane potential of neurons; (2) the cross-talk or the ephaptic coupling between the neurons; and (3) the spontaneous neuronal activity and the emergence of ectopic action potentials. We will show mathematically that the quantum tunneling model can predict the occurrence of neuronal membrane depolarization attributed to the quantum tunneling current of sodium ions. Moreover, the probability of inducing an ectopic action potential in the axons of neurons will be calculated and will be shown to be significant and influential. These ectopic action potentials are generated due to the formation of quantum synapses which are assumed to be the mechanism behind the ephaptic transmission. Furthermore, the spontaneous neuronal activity and the emergence of ectopic action potentials independently from any adjacent stimulated neurons are predicted to occur according to the quantum tunneling model. All these quantum mechanical aspects contribute to the overall hyperexcitability of the neurons and to the pathogenesis of neuropathic pain. Additionally, providing a new perspective in the pathophysiology of neuropathic pain may improve our understanding of how the neuropathic pain is generated and maintained and may offer new effective agents that can improve the overall clinical outcomes of the patients.

Peptide Permeation across a Phosphocholine Membrane: An Atomically Detailed Mechanism Determined through Simulations and Supported by Experimentation

Cell-penetrating peptides (CPPs) facilitate translocation across biological membranes and are of significant biological and medical interest. Several CPPs can permeate into specific cells and organelles. We examine the incorporation and translocation of a novel anticancer CPP in a dioleoylphosphatidylcholine (DOPC) lipid bilayer membrane. The peptide, NAF-1^44-67, is a short fragment of a transmembrane protein, consisting of hydrophobic N-terminal and charged C-terminal segments. Experiments using fluorescently labeled NAF-1^44-67 in ∼100 nm DOPC vesicles and atomically detailed simulations conducted with Milestoning support a model in which a significant barrier for peptide-membrane entry is found at the interface between the aqueous solution and membrane. The initial step is the insertion of the N-terminal segment and the hydrophobic helix into the membrane, passing the hydrophilic head groups. Both experiments and simulations suggest that the free energy difference in the first step of the permeation mechanism in which the hydrophobic helix crosses the phospholipid head groups is -0.4 kcal mol^-1 slightly favoring motion into the membrane. Milestoning calculations of the mean first passage time and the committor function underscore the existence of an early polar barrier followed by a diffusive barrierless motion in the lipid tail region. Permeation events are coupled to membrane fluctuations that are examined in detail. Our study opens the way to investigate in atomistic resolution the molecular mechanism, kinetics, and thermodynamics of CPP permeation to diverse membranes.

GABA Receptors Can Depolarize the Neuronal Membrane Potential via Quantum Tunneling of Chloride Ions: A Quantum Mathematical Study

GABA (gamma-aminobutyric acid) receptors represent the major inhibitory receptors in the nervous system and their inhibitory effects are mediated by the influx of chloride ions that tends to hyperpolarize the resting membrane potential. However, GABA receptors can depolarize the resting membrane potential and thus can also show excitatory effects in neurons. The major mechanism behind this depolarization is mainly attributed to the accumulation of chloride ions in the intracellular compartment. This accumulation leads to increase in the intracellular chloride concentration and depolarize the Nernst potential of chloride ions. When the membrane potential is relatively hyperpolarized, this will result in a chloride efflux instead of influx trying to reach their depolarized equilibrium potential. Here, we propose different mechanism based on a major consequence of quantum mechanics, which is quantum tunneling. The quantum tunneling model of ions is applied on GABA receptors and their corresponding chloride ions to show how chloride ions can depolarize the resting membrane potential. The quantum model states that intracellular chloride ions have higher quantum tunneling probability than extracellular chloride ions. This is attributed to the discrepancy in the kinetic energy between them. At physiological parameters, the quantum tunneling is negligible to the degree that chloride ions cannot depolarize the membrane potential. Under certain conditions such as early neuronal development, gain-of-function mutations, stroke and trauma that can lower the energy barrier of the closed gate of GABA receptors, the quantum tunneling is enhanced so that the chloride ions can depolarize the resting membrane potential. The major unique feature of the quantum tunneling mechanism is that the net efflux of chloride ions is attained without the need for intracellular accumulation of chloride ions as long as the energy barrier of the gate is reduced but still higher than the kinetic energy of the chloride ion as a condition for quantum tunneling to take place.

The Quantum Tunneling of Ions Model Can Explain the Pathophysiology of Tinnitus

Tinnitus is a well-known pathological entity in clinical practice. However, the pathophysiological mechanisms behind tinnitus seem to be elusive and cannot provide a comprehensive understanding of its pathogenesis and clinical manifestations. Hence, in the present study, we explore the mathematical model of ions’ quantum tunneling to propose an original pathophysiological mechanism for the sensation of tinnitus. The present model focuses on two major aspects: The first aspect is the ability of ions, including sodium, potassium, and calcium, to depolarize the membrane potential of inner hair cells and the neurons of the auditory pathway. This membrane depolarization is induced via the quantum tunneling of ions through closed voltage-gated channels. The state of membrane depolarization can be a state of hyper-excitability or hypo-excitability, depending on the degree of depolarization. Both of these states aid in understanding the pathophysiology of tinnitus. The second aspect is the quantum tunneling signals between the demyelinated neurons of the auditory pathway. These signals are mediated via the quantum tunneling of potassium ions, which exit to the extracellular fluid during an action potential event. These quantum signals can be viewed as a “quantum synapse” between neurons. The formation of quantum synapses results in hyper-excitability among the demyelinated neurons of the auditory pathway. Both of these aspects augment and amplify the electrical signals in the auditory pathway and result in a loss of the spatiotemporal fidelity of sound signals going to the brain centers. The brain interprets this hyper-excitability and loss of spatiotemporal fidelity as tinnitus. Herein, we show mathematically that the quantum tunneling of ions can depolarize the membrane potential of the inner hair cells and neurons of the auditory pathway. Moreover, we calculate the probability of action potential induction in the neurons of the auditory pathway generated by the quantum tunneling signals of potassium ions.

The Effect of the Osmotically Active Compound Concentration Difference on the Passive Water and Proton Fluxes across a Lipid Bilayer

The molecular details of the passive water flux across the hydrophobic membrane interior are still a matter of debate. One of the postulated mechanisms is the spontaneous, water-filled pore opening, which facilitates the hydrophilic connection between aqueous phases separated by the membrane. In the paper, we provide experimental evidence showing that the spontaneous lipid pore formation correlates with the membrane mechanics; hence, it depends on the composition of the lipid bilayer and the concentration of the osmotically active compound. Using liposomes as an experimental membrane model, osmotically induced water efflux was measured with the stopped-flow technique. Shapes of kinetic curves obtained at low osmotic pressure differences are interpreted in terms of two events: the lipid pore opening and water flow across the aqueous channel. The biological significance of the dependence of the lipid pore formation on the concentration difference of an osmotically active compound was illustrated by the demonstration that osmotically driven water flow can be accompanied by the dissipation of the pH gradient. The application of the Helfrich model to describe the probability of lipid pore opening was validated by demonstrating that the probability of pore opening correlates with the membrane bending rigidity. The correlation was determined by experimentally derived bending rigidity coefficients and probabilities of lipid pores opening.

Elucidating the Mechanism Behind Sodium-Coupled Neurotransmitter Transporters by Reconstitution

Sodium-coupled neurotransmitter transporters play a fundamental role in the termination of synaptic neurotransmission, which makes them a major drug target. The reconstitution of these secondary active transporters into liposomes has shed light on their molecular transport mechanisms. From the earliest days of the reconstitution technique up to today's single-molecule studies, insights from live functioning transporters have been indispensable for our understanding of their physiological impact. The two classes of sodium-coupled neurotransmitter transporters, the neurotransmitter: sodium symporters and the excitatory amino acid transporters, have vastly different molecular structures, but complementary proteoliposome studies have sought to unravel their ion-dependence and transport kinetics. Furthermore, reconstitution experiments have been used on both protein classes to investigate the role of e.g. the lipid environment, of posttranslational modifications, and of specific amino acid residues in transport. Techniques that allow the detection of transport at a single-vesicle resolution have been developed, and single-molecule studies have started to reveal single transporter kinetics, which will expand our understanding of how transport across the membrane is facilitated at protein level. Here, we review a selection of the results and applications where the reconstitution of the two classes of neurotransmitter transporters has been instrumental.

Molecular Dynamics Simulations Based on Polarizable Models Show that Ion Permeation Interconverts between Different Mechanisms as a Function of Membrane Thickness

Different mechanisms have been proposed to explain the permeation of charged compounds through lipid membranes. Overall, it is expected that an ion-induced defect permeation mechanism, where substantial membrane deformations accompany ion movement, should be dominant in thin membranes but that a solubility-diffusion mechanism, where ions partition into the membrane core with large associated dehydration energy costs, becomes dominant in thicker membranes. However, while this physical picture is intuitively reasonable, capturing the interconversion between these two permeation mechanisms in molecular dynamics (MD) simulations based on atomic models is challenging. In particular, simulations relying on nonpolarizable force fields are artificially unfavorable to the solubility-diffusion mechanism, as induced polarization of the nonpolar hydrocarbon is ignored, causing overestimated free energy costs for charged molecules to enter into this region of the membrane. In this study, all-atom MD simulations based on nonpolarizable and polarizable force fields are used to quantitatively characterize the permeation process for the arginine side chain analog methyl-guanidinium through bilayer membranes of mono-unsaturated phosphatidylcholine lipids with and without cholesterol, resulting in thicknesses spanning from ∼24 to ∼42 Å. With simulations based on a nonpolarizable force field, ion translocation can take place solely through an ion-induced defect mechanism, with free energy barriers increasing linearly from 14 to 40 kcal/mol, depending on the thickness. However, with simulations based on a polarizable force field, ion translocation is predominantly dominated by an ion-induced defect mechanism in thin membranes, which progressively converts to a solubility-diffusion mechanism as the membranes get thicker. The transition between the two mechanisms occurs at a thickness of ∼29 Å, with lipid tails of 22 or more carbon atoms. This situation appears to represent the upper limit for ion-induced defect permeation within the current polarizable models. Beyond this thickness, it becomes energetically preferable for the ion to dehydrate and partition into the membrane core-a phenomenon that cannot be captured using the nonpolarizable models. Induced electronic polarizability therefore leads not just to a shift in permeation energetics but to an interconversion between two strikingly different physical mechanisms. The result highlights the importance of induced polarizability in modeling lipid membranes.

Role of Ion-Phospholipid Interactions in Zwitterionic Phospholipid Bilayer Ion Permeation

Despite the central role of Na⁺ and K⁺ in physiological processes, it is still unclear whether they interact or alter the physical properties of simple zwitterionic phospholipid bilayers at physiologically relevant concentrations. Here we report a difference in membrane permeability between Na⁺ and K⁺, as measured with electrical impedance spectroscopy and tethered bilayer lipid membranes. We reveal that the differences in membrane permeability originate from distinct ion coordination by carbonyl oxygens at the phospholipid-water interface, altering the propensity for bilayer pore formation. Molecular dynamics simulations showed differences in the coordination of Na⁺ and K⁺ at the phospholipid-water interface of zwitterionic phospholipid bilayers. The ability of Na⁺ to conscript more phospholipids with a greater number of coordinating interactions causes a higher localized energy barrier for pore formation. These results provide evidence that ion-specific interactions at the phospholipid-water interface can modulate the physical properties of zwitterionic phospholipid bilayers.

An update of the chemiosmotic theory as suggested by possible proton currents inside the coupling membrane

Understanding how biological systems convert and store energy is a primary purpose of basic research. However, despite Mitchell's chemiosmotic theory, we are far from the complete description of basic processes such as oxidative phosphorylation (OXPHOS) and photosynthesis. After more than half a century, the chemiosmotic theory may need updating, thanks to the latest structural data on respiratory chain complexes. In particular, up-to date technologies, such as those using fluorescence indicators following proton displacements, have shown that proton translocation is lateral rather than transversal with respect to the coupling membrane. Furthermore, the definition of the physical species involved in the transfer (proton, hydroxonium ion or proton currents) is still an unresolved issue, even though the latest acquisitions support the idea that protonic currents, difficult to measure, are involved. Moreover, F_oF₁-ATP synthase ubiquitous motor enzyme has the peculiarity (unlike most enzymes) of affecting the thermodynamic equilibrium of ATP synthesis. It seems that the concept of diffusion of the proton charge expressed more than two centuries ago by Theodor von Grotthuss is to be taken into consideration to resolve these issues. All these uncertainties remind us that also in biology it is necessary to consider the Heisenberg indeterminacy principle, which sets limits to analytical questions.

Defect-Assisted Permeation Through a Phospholipid Membrane: Experimental and Computational Study of the Peptide WKW

We investigate membrane permeation by the peptide WKW that is amidated at its C-terminus and therefore carries a positive charge of +2. To facilitate an efficient calculation, we introduce a novel set of simple coarse variables that measure permeation depth and membrane distortion. The phospholipid head groups shift toward the center of the membrane, following the permeating peptide, and create a defect that assists permeation. The Milestoning algorithm was used in the new coarse space to compute the free-energy profile and the mean first passage time. The barrier was lower than expected from a simple continuum estimate. This behavior is consistent with the known behavior of positively charged cell-penetrating peptides, and is explained by a detailed mechanism of defect formation and propagation revealed by the simulations.

Partition of Positively and Negatively Charged Tryptophan Ions in Membranes with Inverted Phospholipid Heads: Simulations and Experiments

A joint experimental and computational study illustrates that the partitioning of positively and negatively charged tryptophan in a phospholipid bilayer is significantly altered by a reversal in the head group dipole arrangement. Experiments were conducted using tryptophan as a fluorescent reporter of its local environment. Based on the experimental design in a recent publication ( Anderson , C. M. ; Cardenas , A. ; Elber , R. ; Webb , L. J. J. Phys. Chem. B 2018 , 123 , 170 - 179 ), we were able to determine that the arrangement of the head group dipole altered the degree of partitioning of charged tryptophan in the lipid bilayer. In parallel, atomically detailed simulations were performed for the two membrane systems. The simulation results are in accord with the experimental findings and support a simple molecular partition mechanism of electrostatic interactions with the head groups, glycerol linkers, and interfacial water dipoles.

Proton leakage across lipid bilayers: Oxygen atoms of phospholipid ester linkers align water molecules into transmembrane water wires

Up to half of the cellular energy gets lost owing to membrane proton leakage. The permeability of lipid bilayers to protons is by several orders of magnitude higher than to other cations, which implies efficient proton-specific passages. The nature of these passages remains obscure. By combining experimental measurements of proton flow across phosphatidylcholine vesicles, steered molecular dynamics (MD) simulations of phosphatidylcholine bilayers and kinetic modelling, we have analyzed whether protons could pass between opposite phospholipid molecules when they sporadically converge. The MD simulations showed that each time, when the phosphorus atoms of the two phosphatidylcholine molecules got closer than 1.6 nm, the eight oxygen atoms of their ester linkages could form a transmembrane 'oxygen passage' along which several water molecules aligned into a water wire. Proton permeability along such water wires would be limited by rearrangement of oxygen atoms, which could explain the experimentally shown independence of the proton permeability of pH, H₂O/D₂O substitution, and membrane dipole potential. We suggest that protons can cross lipid bilayers by moving along short, self-sustaining water wires supported by oxygen atoms of lipid ester linkages.

Ion Permeation through a Phospholipid Membrane: Transition State, Path Splitting, and Calculation of Permeability

We investigate the thermodynamics and kinetics of the permeation of a potassium ion through a phospholipid membrane. We illustrate that the conventional reaction coordinate (the position of the ion along the normal to the membrane plane) is insufficient to capture essential elements of the process. It is necessary to add coarse variables that measure membrane distortion. New coarse variables are suggested, and a two-dimensional coarse-space is proposed to describe the permeation. We illustrate path splitting and two transition states of comparable barrier heights. The alternative pathways differ by the extent of water solvation of the ion-phosphate pairs. The permeation process cannot be described by a local one-dimensional reaction coordinate, and a network formulation is more appropriate. We use Milestoning with Voronoi tessellation in two dimensions to quantify the equilibrium and rate of the permeation of the positively charged ion. The permeation coefficient is computed and compared favorably to experiment.

Molecular Mechanism of Uptake of Cationic Photoantimicrobial Phthalocyanine across Bacterial Membranes Revealed by Molecular Dynamics Simulations

Phthalocyanines are aromatic macrocyclic compounds, which are structurally related to porphyrins. In clinical practice, phthalocyanines are used in fluorescence imaging and photodynamic therapy of cancer and noncancer lesions. Certain forms of the substituted polycationic metallophthalocyanines have been previously shown to be active in photodynamic inactivation of both Gram-negative and Gram-positive bacteria; one of them is zinc octakis(cholinyl)phthalocyanine (ZnPcChol⁸⁺). However, the molecular details of how these compounds translocate across bacterial membranes still remain unclear. In the present work, we have developed a coarse-grained (CG) molecular model of ZnPcChol⁸⁺ within the framework of the popular MARTINI CG force field. The obtained model was used to probe the solvation behavior of phthalocyanine molecules, which agreed with experimental results. Subsequently, it was used to investigate the molecular details of interactions between phthalocyanines and membranes of various compositions. The results demonstrate that ZnPcChol⁸⁺ has high affinity to both the inner and the outer model membranes of Gram-negative bacteria, although this species does not show noticeable affinity to the 1-palmitoyl-2-oleoyl- sn-glycero-3-phosphatidylcholine membrane. Furthermore, we found out that the process of ZnPcChol⁸⁺ penetration toward the center of the outer bacterial membrane is energetically favorable and leads to its overall disturbance and formation of the aqueous pore. Such intramembrane localization of ZnPcChol⁸⁺ suggests their twofold cytotoxic effect on bacterial cells: (1) via induction of lipid peroxidation by enhanced production of reactive oxygen species (i.e., photodynamic toxicity); (2) via rendering the bacterial membrane more permeable for additional Pc molecules as well as other compounds. We also found that the kinetics of penetration depends on the presence of phospholipid defects in the lipopolysaccharide leaflet of the outer membrane and the type of counterions, which stabilize it. Thus, the results of our simulations provide a detailed molecular view of ZnPcChol⁸⁺ "self-promoted uptake", the pathway previously proposed for some small molecules crossing the outer bacterial membrane.

Sequence-Dependent Interfacial Adsorption and Permeation of Dipeptides across Phospholipid Membranes

We investigate permeation of three blocked dipeptides with different side chain polarity across a phospholipid membrane and their behavior at the water-membrane interface by way of molecular dynamics simulations. Hydrophilic serine-serine dipeptide is found to desorb from the interface to aqueous phase, whereas hydrophobic phenylalanine-leucine and amphiphilic serine-leucine tend to accumulate at the interface with a free energy minimum of -3 kcal/mol. All three dipeptides exhibit free energy barriers to permeation across the membrane located at the center of the bilayer. The height of the barrier is strongly sequence dependent and increases with the dipeptide polarity. It is equal to 3.5, 6.4, and 10.0 kcal/mol for phenylalanine-leucine, serine-leucine, and serine-serine, respectively. The corresponding permeability coefficients are equal to 4.6 × 10^-3, 4.5 × 10^-5, and 8.7 × 10^-8 cm/s. The apparent insensitivity of membrane permeability to hydrophobicity of dipeptides, found in some experiments, is attributed to neglecting corrections for unstirred water layers near membrane surface, which are significant for hydrophobic species. Different hydrophobicity of the dipeptides also influences their conformations and orientations, both at the interface and inside the membrane. In particular, penetration of hydrophilic serine-serine dipeptide causes the formation of water-filled defects in the bilayer. These results are relevant to the delivery of peptide-based therapeutic agents.

The Flip-Flop Diffusion Mechanism across Lipids in a Hybrid Bilayer Membrane

In this study, we examine the mechanism of flip-flop diffusion of proton carriers across the lipid layer of a hybrid bilayer membrane (HBM). The HBM consists of a lipid monolayer appended on top of a self-assembled monolayer containing a Cu-based O2 reduction catalyst on a Au electrode. The flip-flop diffusion rates of the proton carriers dictate the kinetics of O2 reduction by the electrocatalyst. By varying both the tail lengths of the proton carriers and the lipids, we find the combinations of lengths that maximize the flip-flop diffusion rate. These experimental results combined with biophysical modeling studies allow us to propose a detailed mechanism for transmembrane flip-flop diffusion in HBM systems, which involves the bending of the alkyl tail of the proton carrier as the rate-determining step. Additional studies with an unbendable proton carrier further validate these mechanistic findings.

How does ytterbium chloride interact with DMPC bilayers? A computational and experimental study

Lanthanide salts have been studied for many years, primarily in Nuclear Magnetic Resonance (NMR) experiments of mixed lipid–protein systems and more recently to study lipid flip-flop in model membrane systems.

Line Tension Assists Membrane Permeation at the Transition Temperature in Mixed-Phase Lipid Bilayers

The umbrella sampling method has been used to evaluate the free energy profile for a large permeant moving through a lipid bilayer, represented using a coarse-grained simulation model, at and below its gel-fluid transition temperature. At the lipid transition temperature, determined to be 302 K for the MARTINI 2.0 model of DPPC, the permeation barrier for passage through an enclosed fluid domain embedded in a patch of gel was significantly lower than that for passage through a fluid stripe domain. In contrast, permeation through a fluid domain in a stripe geometry produced a free energy profile nearly identical to that of a gel-free fluid bilayer. In both cases, insertion of the permeant into a fluid domain coexisting with the gel phase led to a shift in phase composition, as lipids transitioned from fluid to gel to accommodate the area occupied by the permeant. In the case of the enclosed fluid domain, this transition produced a decrease in the length of the fluid-gel interface as the approximately circular fluid domain shrank. The observed decrease in the apparent permeation barrier, combined with an approximation for the change in interfacial length, enabled estimation of the interfacial line tension to be between 10 and 13 pN for this model. The permeation barrier was shown to drop even further in simulations performed at temperatures below the transition temperature. The results suggest a mechanism to explain the experimentally observed anomalous peak in the temperature-dependent permeability of lipid bilayers near their transition temperatures. The contribution of this mechanism toward the permeability of a gel phase containing a thermal distribution of fluid-phase domains is estimated using a simple statistical thermodynamic model.

Passive Transmembrane Permeation Mechanisms of Monovalent Ions Explored by Molecular Dynamics Simulations

Passive or unassisted ion permeation through lipid bilayers involves a type of rare events by which cells regulate their salt concentrations and pH. It is important to understand its mechanism in order to develop technologies of, for example, delivering or maintaining small drug-like molecules inside cells. In earlier simulations of passive ion permeations, the commonly used sampling methods usually define the positions of ions relative to the membrane as a measure of permeation, i.e., the collective variable, ignoring the active participations of other particles. Newly defined collective variables involving the movements of ions, lipids, and water molecules allow us to identify the transition paths on the free energy landscape using the 2D umbrella sampling techniques. In this work, this technique was used to study the permeation processes of some well-known ions, sodium, potassium, and chloride. It is found permeations of sodium and potassium are assisted by important lipid bilayer deformations and massive water solvation, while chloride may not. Chloride may have two different possible pathways, in which the energetic favorable one is similar to the solubility-diffusion model. The free energy barriers for the permeation of these ions are in semiquantitative agreement with experiments. Further analyses on the distributions of oxygens and interaction energies suggest the electrostatic interactions between ions and polar headgroups of lipids may greatly influence membrane deformation as well as the water wire and furthermore the free energy barriers of waterwire mediated pathways. For chloride, the nonwaterwire pathway may be energetically favorable.

Permeability across lipid membranes

Molecular permeation through lipid membranes is a fundamental biological process that is important for small neutral molecules and drug molecules. Precise characterization of free energy surface and diffusion coefficients along the permeation pathway is required in order to predict molecular permeability and elucidate the molecular mechanisms of permeation. Several recent technical developments, including improved molecular models and efficient sampling schemes, are illustrated in this review. For larger penetrants, explicit consideration of multiple collective variables, including orientational, conformational degrees of freedom, are required to be considered in addition to the distance from the membrane center along the membrane normal. Although computationally demanding, this method can provide significant insights into the molecular mechanisms of permeation for molecules of medical and pharmaceutical importance. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Refining the treatment of membrane proteins by coarse-grained models

Obtaining a quantitative description of the membrane proteins stability is crucial for understanding many biological processes. However the advance in this direction has remained a major challenge for both experimental studies and molecular modeling. One of the possible directions is the use of coarse-grained models but such models must be carefully calibrated and validated. Here we use a recent progress in benchmark studies on the energetics of amino acid residue and peptide membrane insertion and membrane protein stability in refining our previously developed coarse-grained model (Vicatos et al., Proteins 2014;82:1168). Our refined model parameters were fitted and/or tested to reproduce water/membrane partitioning energetics of amino acid side chains and a couple of model peptides. This new model provides a reasonable agreement with experiment for absolute folding free energies of several β-barrel membrane proteins as well as effects of point mutations on a relative stability for one of those proteins, OmpLA. The consideration and ranking of different rotameric states for a mutated residue was found to be essential to achieve satisfactory agreement with the reference data.

Light-Driven Ca(2+) Ion Pump: How Does It Work?

Work done by Bennett et al. [ Nature 2002 , 420 , 398 - 401 ] demonstrated that Ca(2+) ions can be actively transported through a lipid bilayer membrane by an artificial photosynthetic machine. However, details of the pump process, such as the oxidation state of the shuttle molecule and stoichiometry of the shuttle-ion complex, are not fully understood, which hinders the development of ion pumps of this type with higher efficiency. In this study, we combine all atom molecular dynamics simulations and quantum mechanics calculations to estimate the time scale of the shuttle-ion complex diffusion process and charge transfer step. We find that the process of shuttle-ion complex diffusion across the lipid bilayer membrane is the rate-limiting step, with a time scale of seconds to minutes. Other processes such as charge transfer between the redox reaction center and the shuttle molecule have picoseconds time scales. We also show that a shuttle-ion complex with 2:1 stoichiometry ratio has a lower energy barrier across the lipid membrane than other choices of complexes. The calculations show that the Ca(2+) ion is likely to be shuttled by a semiquinone type of shuttle molecule as this has the lowest free energy barrier across the lipid bilayer membrane, the fewest electrons transferred in the redox cycle, and it does not generate (or require) proton flow. Estimates of ion flow rates are consistent with measured values.

Membrane-mediated amyloid formation of PrP 106-126: A kinetic study

PrP 106-126 conserves the pathogenic and physicochemical properties of the Scrapie isoform of the prion protein. PrP 106-126 and other amyloidal proteins are capable of inducing ion permeability through cell membranes, and this property may represent the common primary mechanism of pathogenesis in the amyloid-related degenerative diseases. However, for many amyloidal proteins, despite numerous phenomenological observations of their interactions with membranes, it has been difficult to determine the molecular mechanisms by which the proteins cause ion permeability. One approach that has not been undertaken is the kinetic study of protein-membrane interactions. We found that the reaction time constant of the interaction between PrP 106-126 and membranes is suitable for such studies. The kinetic experiment with giant lipid vesicles showed that the membrane area first increased by peptide binding but then decreased. The membrane area decrease was coincidental with appearance of extramembranous aggregates including lipid molecules. Sometimes, the membrane area would increase again followed by another decrease. The kinetic experiment with small vesicles was monitored by circular dichroism for peptide conformation changes. The results are consistent with a molecular simulation following a simple set of well-defined rules. We deduced that at the molecular level the formation of peptide amyloids incorporated lipid molecules as part of the aggregates. Most importantly the amyloid aggregates desorbed from the lipid bilayer, consistent with the macroscopic phenomena observed with giant vesicles. Thus we conclude that the main effect of membrane-mediated amyloid formation is extraction of lipid molecules from the membrane. We discuss the likelihood of this effect on membrane ion permeability.

A Permeability Study of O2 and the Trace Amine p-Tyramine through Model Phosphatidylcholine Bilayers

We study here the permeability of the hydrophobic O2 molecule through a model DPPC bilayer at 323K and 350K, and of the trace amine p-tyramine through PC bilayers at 310K. The tyramine results are compared to previous experimental work at 298K. Nonequilibrium work methods were used in conjunction to simultaneously obtain both the potential of mean force (PMF) and the position dependent transmembrane diffusion coefficient, D(z), from the simulations. These in turn were used to calculate the permeability coefficient, P, through the inhomogeneous solubility-diffusion model. The results for O2 are consistent with previous simulations, and agree with experimentally measured P values for PC bilayers. A temperature dependence in the permeability of O2 through DPPC was obtained, with P decreasing at higher temperatures. Two relevant species of p-tyramine were simulated, from which the PMF and D(z) were calculated. The charged species had a large energetic barrier to crossing the bilayer of ~ 21 kcal/mol, while the uncharged, deprotonated species had a much lower barrier of ~ 7 kcal/mol. The effective in silico permeability for p-tyramine was calculated by applying three approximations, all of which gave nearly identical results (presented here as a function of the pKa). As the permeability value calculated from simulation was highly dependent on the pKa of the amine group, a further pKa study was performed that also varied the fraction of the uncharged and zwitterionic p-tyramine species. Using the experimental P value together with the simulated results, we were able to label the phenolic group as responsible for the pKa1 and the amine for the pKa2, that together represent all of the experimentally measured pKa values for p-tyramine. This agrees with older experimental results, in contrast to more recent work that has suggested there is a strong ambiguity in the pKa values.

All-atom molecular dynamics simulations of an artificial sodium channel in a lipid bilayer: the effect of water solvation/desolvation of the sodium ion

All-atom molecular dynamics is used to investigate the transport of Na(+) across a 1,2-dioleoyl-sn-glycero-3-phosphocholine lipid bilayer facilitated by a diazacrown hydraphile. Specifically, the free energy of Na(+) passing through the bilayer is calculated using the adaptive biasing force method to study the free energy associated with the increase in Na(+) transport in the presence of the hydraphile molecule. The results show that water interaction greatly influences Na(+) transport through the lipid bilayer as water is pulled through the bilayer with Na(+) forming a water channel. The hydraphile causes a reduction in the free energy barrier for the transport of Na(+) through the head group part of the lipid bilayer since it complexes the Na(+) reducing the necessity for water to be complexed and, therefore, dragged through with Na(+), an energetically unfavorable process. The free energy associated with Na(+) being desolvated within the bilayer is significantly decreased in the presence of the hydraphile molecule; the hydraphile increases the number of solvation states of Na(+) that can be adopted, and this increase in the number of available configurations provides an entropic explanation for the success of the hydraphile.

Membrane permeation of a peptide: it is better to be positive

A joint experimental and computational study investigates the translocation of a tryptophan molecule through a phospholipid membrane. Time dependent spectroscopy of the tryptophan side chain determines the rate of permeation into 150 nm phospholipid vesicles. Atomically detailed simulations are conducted to calculate the free energy profiles and the permeation coefficient. Different charging conditions of the peptide (positive, negative, or zwitterion) are considered. Both experiment and simulation reproduce the qualitative trend and suggest that the fastest permeation is when the tryptophan is positively charged. The permeation mechanism, which is revealed by molecular dynamics simulations, is of a translocation assisted by a local defect. The influence of long-range electrostatic interactions, such as the membrane dipole potential on the permeation process, is not significant.

Interaction of daptomycin with lipid bilayers: a lipid extracting effect

Daptomycin is the first approved member of a new structural class of antibiotics, the cyclic lipopeptides. The peptide interacts with the lipid matrix of cell membranes, inducing permeability of the membrane to ions, but its molecular mechanism has been a puzzle. Unlike the ubiquitous membrane-acting host-defense antimicrobial peptides, daptomycin does not induce pores in the cell membranes. Thus, how it affects the permeability of a membrane to ions is not clear. We studied its interaction with giant unilamellar vesicles (GUVs) and discovered a lipid-extracting phenomenon that correlates with the direct action of daptomycin on bacterial membranes observed in a recent fluorescence microscopy study. Lipid extraction occurred only when the GUV lipid composition included phosphatidylglycerol and in the presence of Ca(2+) ions, the same condition found to be necessary for daptomycin to be effective against bacteria. Furthermore, it occurred only when the peptide/lipid ratio exceeded a threshold value, which could be the basis of the minimal inhibitory concentration of daptomycin. In this first publication on the lipid extracting effect, we characterize its dependence on ions and lipid compositions. We also discuss possibilities for connecting the lipid extracting effect to the antibacterial activity of daptomycin.

Continuum approaches to understanding ion and peptide interactions with the membrane

Experimental and computational studies have shown that cellular membranes deform to stabilize the inclusion of transmembrane (TM) proteins harboring charge. Recent analysis suggests that membrane bending helps to expose charged and polar residues to the aqueous environment and polar head groups. We previously used elasticity theory to identify membrane distortions that minimize the insertion of charged TM peptides into the membrane. Here, we extend our work by showing that it also provides a novel, computationally efficient method for exploring the energetics of ion and small peptide penetration into membranes. First, we show that the continuum method accurately reproduces energy profiles and membrane shapes generated from molecular simulations of bare ion permeation at a fraction of the computational cost. Next, we demonstrate that the dependence of the ion insertion energy on the membrane thickness arises primarily from the elastic properties of the membrane. Moreover, the continuum model readily provides a free energy decomposition into components not easily determined from molecular dynamics. Finally, we show that the energetics of membrane deformation strongly depend on membrane patch size both for ions and peptides. This dependence is particularly strong for peptides based on simulations of a known amphipathic, membrane binding peptide from the human pathogen Toxoplasma gondii. In total, we address shortcomings and advantages that arise from using a variety of computational methods in distinct biological contexts.

Ion-induced defect permeation of lipid membranes

We have explored the mechanisms of uncatalyzed membrane ion permeation using atomistic simulations and electrophysiological recordings. The solubility-diffusion mechanism of membrane charge transport has prevailed since the 1960s, despite inconsistencies in experimental observations and its lack of consideration for the flexible response of lipid bilayers. We show that direct lipid bilayer translocation of alkali metal cations, Cl(-), and a charged arginine side chain analog occurs via an ion-induced defect mechanism. Contrary to some previous suggestions, the arginine analog experiences a large free-energy barrier, very similar to those for Na(+), K(+), and Cl(-). Our simulations reveal that membrane perturbations, due to the movement of an ion, are central for explaining the permeation process, leading to both free-energy and diffusion-coefficient profiles that show little dependence on ion chemistry and charge, despite wide-ranging hydration energies and the membrane's dipole potential. The results yield membrane permeabilities that are in semiquantitative agreement with experiments in terms of both magnitude and selectivity. We conclude that ion-induced defect-mediated permeation may compete with transient pores as the dominant mechanism of uncatalyzed ion permeation, providing new understanding for the actions of a range of membrane-active peptides and proteins.

Nontrivial behavior of water in the vicinity and inside lipid bilayers as probed by molecular dynamics simulations

The atomic-scale diffusion of water in the presence of several lipid bilayers mimicking biomembranes is characterized via unconstrained molecular dynamics (MD) simulations. Although the overall water dynamics corresponds well to literature data, namely, the efficient braking near polar head groups of lipids, a number of interesting and biologically relevant details observed in this work have not been sufficiently discussed so far; for instance, the fact that waters "sense" the membrane unexpectedly early, before water density begins to decrease. In this "transitional zone" the velocity distributions of water and their H-bonding patterns deviate from those in the bulk solution. The boundaries of this zone are well preserved even despite the local (<1 nm size) perturbation of the lipid bilayer, thus indicating a decoupling of the surface and bulk dynamics of water. This is in excellent agreement with recent experimental data. Near the membrane surface, water movement becomes anisotropic, that is, solvent molecules preferentially move outward the bilayer. Deep in the membrane interior, the velocities can even exceed those in the bulk solvent and undergo large-scale fluctuations. The analysis of MD trajectories of individual waters in the middle part of the acyl chain region of lipids reveals a number of interesting rare phenomena, such as the fast (ca. 50 ps) breakthrough across the membrane or long-time (up to 750 ps) "roaming" between lipid leaflets. The analysis of these events was accomplished to delineate the mechanisms of spontaneous water permeation inside the hydrophobic membrane core. It was shown that such nontrivial dynamics of water in an "alien" environment is driven by the dynamic heterogeneities of the local bilayer structure and the formation of transient atomic-scale "defects" in it. The picture observed in lipid bilayers is drastically different from that in a primitive membrane mimic, a hydrated cyclohexane slab. The possible biological impact of such phenomena in equilibrated lipid bilayers is discussed.

Nanoparticle permeation induces water penetration, ion transport, and lipid flip-flop

Nanoparticles are generally considered excellent candidates for targeted drug delivery. However, ion leakage and cytotoxicity induced by nanoparticle permeation is a potential problem in such drug delivery schemes because of the toxic effect of many ions. In this study, we have carried out a series of coarse-grained molecular dynamics simulations to investigate the water penetration, ion transport, and lipid molecule flip-flop in a protein-free phospholipid bilayer membrane during nanoparticle permeation. The effect of ion concentration gradient, pressure differential across the membrane, nanoparticle size, and permeation velocity have been examined in this work. Some conclusions from our studies include (1) The number of water molecules in the interior of the membrane during the nanoparticle permeation increases with the nanoparticle size and the pressure differential across the membrane but is unaffected by the nanoparticle permeation velocity or the ion concentration gradient. (2) Ion transport is sensitive to the size of nanoparticle as well as the ion concentration gradient between two sides of the membrane; no anion/cation selectivity is observed for small nanoparticle permeation, while anions are preferentially translocated through the membrane when the size of nanoparticle is large enough. (3) Incidences of lipid molecule flip-flop increases with the size of nanoparticle and ion concentration gradient and decreases with the pressure differential and the nanoparticle permeation velocity.

Transfer of the K+ cation across a water/dichloromethane interface: a steered molecular dynamics study with implications in cation extraction

In this paper we report the characterization of the dichloromethane (DCM)/water interface in terms of density profile, width, and surface structure. The use of steered molecular dynamics (SMD) to study the transfer of the K(+) cation from the organic layer to the water layer is also described. The corresponding free energy is in semiquantitative agreement with published experimental and theoretical results. The transference of the K(+) cation from the water layer toward the DCM layer occurs with concomitant water transport as a water microdroplet that detaches itself from the water layer after ca. 16 Å of penetration into the organic layer by breaking the thin water thread that unites both. Complexation of the water microdroplet by a polyethylene-glycol type podand induces the loss of water molecules from the water microdroplet to bulk DCM and, eventually, to the water layer.

Burst firing transitions in two-compartment pyramidal neuron induced by the perturbation of membrane capacitance

Neuronal membrane capacitance C (m) is one of the prominent factors in action potential initiation and propagation and then influences the firing patterns of neurons. Exploring the roles that C (m) plays in different firing patterns can facilitate the understanding of how different factors might influence neuronal firing behaviors. However, the impacts of variations in C (m) on neuronal firing patterns have been only partly explored until now. In this study, the influence of C (m) on burst firing behaviors of a two-compartment pyramidal neuron (including somatic compartment and dendritic compartment) was investigated by means of computer simulation, the value of C (m) in each compartment was denoted as C (m,s) and C (m,d), respectively. Two cases were considered, in the first case, we let C (m,s) =C (m,d), and then changed them simultaneously. While in the second case, we assumed C (m,s) ≠C (m,d), and then changed them, respectively. From the simulation results obtained from these two cases, it was found that the variation of C (m) in the somatic compartment and the dendritic compartment show much difference, simulated results obtained from the variation of C (m,d) have much more similarities than that of C (m,s) when comparing with the results obtained in the first case under which C (m,s) =C (m,d). These different effects of C (m,s) and C (m,d) on neuronal firing behaviors may result from the different topology and functional roles of soma and dendrites. Numerical results demonstrated in this paper may give us some inspiration in understanding the possible roles of C (m) in burst firing patterns, especially their transitions in compartmental neurons.