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

How Does an Anti-Cancer Peptide Passively Permeate the Plasma Membrane of a Cancer Cell and Not a Normal Cell?

Passive and targeted delivery of peptides to cells and organelles is a fundamental biophysical process controlled by membranes surrounding biological compartments. Embedded proteins, phospholipid composition, and solution conditions contribute to targeted transport. An anticancer peptide, NAF-144-67, permeates to cancer cells but not to normal cells. The mechanism of this selectivity is of significant interest. However, the complexity of biomembranes makes pinpointing passive targeting mechanisms difficult. To dissect contributions to selective transport by membrane components, we constructed simplified phospholipid vesicles as plasma membrane (PM) models of cancer and normal cells and investigated NAF-144-67 permeation computationally and experimentally. We use atomically detailed simulations with enhanced sampling techniques to study kinetics and thermodynamics of the interaction. Experimentally, we study the interaction of the peptide with large and giant unilamellar vesicles. The large vesicles were investigated with fluorescence spectroscopy and the giant vesicles with confocal microscopy. Peptide permeation across a model of cancer PM is more efficient than permeation across a PM model of normal cells. The investigations agree on the mechanism of selectivity, which consists of three steps: (i) early electrostatic attraction of the peptide to the negatively charged membrane, (ii) the penetration of the peptide hydrophobic N-terminal segment into the lipid bilayer, and (iii) exploiting short-range electrostatic forces to create a defect in the membrane and complete the permeation process. The first step is kinetically less efficient in a normal membrane with fewer negatively charged phospholipids. The model of a normal membrane is less receptive to defect creation in the third step.

Statistical Mechanical Theories of Membrane Permeability

A popular theoretical framework to compute the permeability coefficient of a molecule is provided by the classic Smoluchowski-Kramers treatment of the steady-state diffusive flux across a free-energy barrier. Within this framework, commonly termed "inhomogeneous solubility-diffusion" (ISD), the permeability, P, is expressed in closed form in terms of the potential of mean force and position-dependent diffusivity of the molecule of interest along the membrane normal. In principle, both quantities can be calculated from all-atom MD simulations. Although several methods exist for calculating the position-dependent diffusivity, each of these is at best an estimate. In addition, the ISD model does not account for memory effects along the chosen reaction coordinate. For these reasons, it is important to seek alternative theoretical formulations to determine the permeability coefficient that are able to account for the factors ignored by the ISD approximation. Using Green-Kubo linear response theory, we establish the familiar constitutive relation between the flux density across the membrane and the difference in the concentration of a permeant molecule, j = PΔC. On this basis, we derive a time-correlation function expression for the nonequilibrium flux across a membrane that is reminiscent of the transmission coefficient in the reactive flux formalism treatment of transition rates. An analysis based on the transition path theory framework is exploited to derive alternative expressions for the permeability coefficient. The different strategies are illustrated with stochastic simulations based on the generalized Langevin equation in addition to unbiased molecular dynamics simulations of water permeation of a lipid bilayer.

Use of bacterial photosynthetic vesicles to evaluate the effect of ionic liquids on the permeability of biological membranes

Ionic liquids (ILs) are salts composed of a combination of organic or inorganic cations and anions characterized by a low melting point, often below 100 °C. This property, together with an extremely low vapor pressure, low flammability and high thermal stability, makes them suitable for replacing canonical organic solvents, with a reduction of industrial activities impact on the environment. Although in the last decades the eco-compatibility of ILs has been extensively verified through toxicological tests performed on model organisms, a detailed understanding of the interaction of these compounds with biological membranes is far from being exhaustive. In this context, we have chosen to evaluate the effect of some ILs on native membranes by using chromatophores, photosynthetic vesicles that can be isolated from Rhodobacter capsulatus, a member of the purple non‑sulfur bacteria. Here, carotenoids associated with the light-harvesting complex II, act as endogenous spectral probes of the transmembrane electrical potential (ΔΨ). By measuring through time-resolved absorption spectroscopy the evolution of the carotenoid band shift induced by a single excitation of the photosynthetic reaction center, information on the ΔΨ dissipation due to ionic currents across the membrane can be obtained. We found that some ILs cause a rather fast dissipation of the transmembrane ΔΨ even at low concentrations, and that this behavior is dose-dependent. By using two different models to analyze the decay of the carotenoid signals, we attempted to interpret at a mechanistic level the marked increase of ionic permeability caused by specific ILs.

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).

Defect Formation and Peptide Permeation across Phospholipid Membranes

Cell penetrating peptides (CPPs) are natural agents that efficiently permeate biological membranes. They are frequently positively charged, which is surprising since membranes pose hydrophobic barriers. In this Perspective, I discuss computations and experiments of a permeation model that couples permeant displacement with a membrane defect. We call the proposed mechanism Defect Assisted by Charge (DAC) and illustrate that it reduces the free energy barrier for translocation. A metastable state at the center of the membrane may be observed due to the charge interactions with the phospholipid head groups at the two leaflets. The combination of experiments and simulations sheds light on the mechanisms of a charged peptide translocation across phospholipid membranes.

Path sampling with memory reduction and replica exchange to reach long permeation timescales

Assessing kinetics in biological processes with molecular dynamics simulations remains a computational and conceptual challenge, given the large time and length scales involved. For kinetic transport of biochemical compounds or drug molecules, the permeability through the phospholipid membranes is a key kinetic property, but long timescales are hindering the accurate computation. Technological advances in high-performance computing therefore need to be accompanied by theoretical and methodological developments. In this contribution, the replica exchange transition interface sampling (RETIS) methodology is shown to give perspective toward observing longer permeation pathways. It is first reviewed how RETIS, a path-sampling methodology that gives in principle exact kinetics, can be used to compute membrane permeability. Next, recent and current developments in three RETIS aspects are discussed: several new Monte Carlo moves in the path-sampling algorithm, memory reduction by reducing pathlengths, and exploitation of parallel computing with CPU-imbalanced replicas. Finally, the memory reduction presenting a new replica exchange implementation, coined REPPTIS, is showcased with a permeant needing to pass a membrane with two permeation channels, either representing an entropic or energetic barrier. The REPPTIS results showed clearly that inclusion of some memory and enhancing ergodic sampling via replica exchange moves are both necessary to obtain correct permeability estimates. In an additional example, ibuprofen permeation through a dipalmitoylphosphatidylcholine membrane was modeled. REPPTIS succeeded in estimating the permeability of this amphiphilic drug molecule with metastable states along the permeation pathway. In conclusion, the presented methodological advances allow for deeper insight into membrane biophysics even if the pathways are slow, as RETIS and REPPTIS push the permeability calculations to longer timescales.

The Structures of Heterogeneous Membranes and Their Interactions with an Anticancer Peptide: A Molecular Dynamics Study

We conduct molecular dynamics simulations of model heterogeneous membranes and their interactions with a 24-amino acid peptide-NAF-144-67. NAF-144-67 is an anticancer peptide that selectively permeates and kills malignant cells; it does not permeate normal cells. We examine three membranes with different binary mixtures of lipids, DOPC-DOPA, DOPC-DOPS, and DOPC-DOPE, with a single peptide embedded in each as models for the diversity of biological membranes. We illustrate that the peptide organization in the membrane depends on the types of nearby phospholipids and is influenced by the charge and size of the head groups. The present study sheds light on early events of permeation and the mechanisms by which an amphiphilic peptide crosses from an aqueous solution to a hydrophobic membrane. Understanding the translocation mechanism is likely to help the design of new permeants.

Design of Peptides for Membrane Insertion: The Critical Role of Charge Separation

A physical understanding of membrane permeation and translocation by small, positively charged molecules can illuminate cell penetrating peptide mechanisms of entry and inform drug design. We have previously investigated the permeation of the doubly charged peptide WKW and proposed a defect-assisted permeation mechanism where a small molecule with +2 charge can achieve a metastable state spanning the bilayer by forming a membrane defect with charges stabilized by phospholipid phosphate groups. Here, we investigate the membrane permeation of two doubly charged peptides, WWK and WWWK, with charges separated by different lengths. Through complementary experiments and molecular dynamics simulations, we show that membrane permeation was an order of magnitude more favorable when charges were separated by an ∼2-3 Å greater distance on WWWK compared to WWK. These results agree with the previously proposed defect-assisted permeation mechanism, where a greater distance between positive charges would require a less extreme membrane defect to stabilize the membrane-spanning metastable state. We discuss the implications of these results in understanding the membrane permeation of cell-penetrating peptides and other small, positively charged membrane permeants.

Quantifying Energetic and Entropic Pathways in Molecular Systems

When examining dynamics occurring at nonzero temperatures, both energy and entropy must be taken into account to describe activated barrier crossing events. Furthermore, good reaction coordinates need to be constructed to describe different metastable states and the transition mechanisms between them. Here we use a physics-based machine learning method called state predictive information bottleneck (SPIB) to find nonlinear reaction coordinates for three systems of varying complexity. SPIB is able to correctly predict an entropic bottleneck for an analytical flat-energy double-well system and identify the entropy- and energy-dominated pathways for an analytical four-well system. Finally, for a simulation of benzoic acid permeation through a lipid bilayer, SPIB is able to discover the entropic and energetic barriers to the permeation process. Given these results, we thus establish that SPIB is a reasonable and robust method for finding the important entropy, energy, and enthalpy barriers in physical systems, which can then be used to enhance the understanding and sampling of different activated mechanisms.

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-144-67, is a short fragment of a transmembrane protein, consisting of hydrophobic N-terminal and charged C-terminal segments. Experiments using fluorescently labeled NAF-144-67 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.

Markovian Weighted Ensemble Milestoning (M-WEM): Long-Time Kinetics from Short Trajectories

We introduce a rare-event sampling scheme, named Markovian Weighted Ensemble Milestoning (M-WEM), which inlays a weighted ensemble framework within a Markovian milestoning theory to efficiently calculate thermodynamic and kinetic properties of long-time-scale biomolecular processes from short atomistic molecular dynamics simulations. M-WEM is tested on the Müller-Brown potential model, the conformational switching in alanine dipeptide, and the millisecond time-scale protein-ligand unbinding in a trypsin-benzamidine complex. Not only can M-WEM predict the kinetics of these processes with quantitative accuracy but it also allows for a scheme to reconstruct a multidimensional free-energy landscape along additional degrees of freedom, which are not part of the milestoning progress coordinate. For the ligand-receptor system, the experimental residence time, association and dissociation kinetics, and binding free energy could be reproduced using M-WEM within a simulation time of a few hundreds of nanoseconds, which is a fraction of the computational cost of other currently available methods, and close to 4 orders of magnitude less than the experimental residence time. Due to the high accuracy and low computational cost, the M-WEM approach can find potential applications in kinetics and free-energy-based computational drug design.

Structural Mechanism of ω-Currents in a Mutated Kv7.2 Voltage Sensor Domain from Molecular Dynamics Simulations

Activation of voltage-gated ion channels is regulated by conformational changes of the voltage sensor domains (VSDs), four water- and ion-impermeable modules peripheral to the central, permeable pore domain. Anomalous currents, defined as ω-currents, have been recorded in response to mutations of residues on the VSD S4 helix and associated with ion fluxes through the VSDs. In humans, gene defects in the potassium channel Kv7.2 result in a broad range of epileptic disorders, from benign neonatal seizures to severe epileptic encephalopathies. Experimental evidence suggests that the R207Q mutation in S4, associated with peripheral nerve hyperexcitability, induces ω-currents at depolarized potentials, but the fine structural details are still elusive. In this work, we use atom-detailed molecular dynamics simulations and a refined model structure of the Kv7.2 VSD in the active conformation in a membrane/water environment to study the effect of R207Q and four additional mutations of proven clinical importance. Our results demonstrate that the R207Q mutant shows the most pronounced increase of hydration in the internal VSD cavity, a feature favoring the occurrence of ω-currents. Free energy and kinetics calculations of sodium permeation through the native and mutated VSD indicate as more favorable the formation of a cationic current in the latter. Overall, our simulations establish a mechanistic linkage between genetic variations and their physiological outcome, by providing a computational description that includes both thermodynamic and kinetic features of ion permeation associated with ω-currents.

Milestoning: An Efficient Approach for Atomically Detailed Simulations of Kinetics in Biophysics

Recent advances in theory and algorithms for atomically detailed simulations open the way to the study of the kinetics of a wide range of molecular processes in biophysics. The theories propose a shift from the traditionally very long molecular dynamic trajectories, which are exact but may not be efficient in the study of kinetics, to the use of a large number of short trajectories. The short trajectories exploit a mapping to a mesh in coarse space and allow for efficient calculations of kinetics and thermodynamics. In this review, I focus on one theory: Milestoning is a theory and an algorithm that offers a hierarchical calculation of properties of interest, such as the free energy profile and the mean first passage time. Approximations to the true long-time dynamics can be computed efficiently and assessed at different steps of the investigation. The theory is discussed and illustrated using two biophysical examples: ion permeation through a phospholipid membrane and protein translocation through a channel.

Sequential Water and Headgroup Merger: Membrane Poration Paths and Energetics from MD Simulations

Membrane topology changes such as poration, stalk formation, and hemifusion rupture are essential to cellular function, but their molecular details, energetics, and kinetics are still not fully understood. Here, we present a unified energetic and mechanistic picture of metastable pore defects in tensionless lipid membranes. We used an exhaustive committor analysis to test and select optimal reaction coordinates and also to determine the nucleation mechanism. These reaction coordinates were used to calculate free-energy landscapes that capture the full process and end states. The identified barriers agree with the committor analysis. To enable sufficient sampling of the complete transition path for our molecular dynamics simulations, we developed a “gizmo” potential biasing scheme. The simulations suggest that the essential step in the nucleation is the initial merger of lipid headgroups at the nascent pore center. To facilitate this event, an indentation pathway is energetically preferred to a hydrophobic defect. Continuous water columns that span the indentation were determined to be on-path transients that precede the nucleation barrier. This study gives a quantitative description of the nucleation mechanism and energetics of small metastable pores and illustrates a systematic approach to uncover the mechanisms of diverse cellular membrane remodeling processes.

Membrane permeability of small molecules from unbiased molecular dynamics simulations

Permeation of many small molecules through lipid bilayers can be directly observed in molecular dynamics simulations on the nano- and microsecond timescale. While unbiased simulations provide an unobstructed view of the permeation process, their feasibility for computing permeability coefficients depends on various factors that differ for each permeant. The present work studies three small molecules for which unbiased simulations of permeation are feasible within less than a microsecond, one hydrophobic (oxygen), one hydrophilic (water), and one amphiphilic (ethanol). Permeabilities are computed using two approaches: counting methods and a maximum-likelihood estimation for the inhomogeneous solubility diffusion (ISD) model. Counting methods yield nearly model-free estimates of the permeability for all three permeants. While the ISD-based approach is reasonable for oxygen, it lacks precision for water due to insufficient sampling and results in misleading estimates for ethanol due to invalid model assumptions. It is also demonstrated that simulations using a Langevin thermostat with collision frequencies of 1/ps and 5/ps yield oxygen permeabilities and diffusion constants that are lower than those using Nosé-Hoover by statistically significant margins. In contrast, permeabilities from trajectories generated with Nosé-Hoover and the microcanonical ensemble do not show statistically significant differences. As molecular simulations become more affordable and accurate, calculation of permeability for an expanding range of molecules will be feasible using unbiased simulations. The present work summarizes theoretical underpinnings, identifies pitfalls, and develops best practices for such simulations.

Exploring the Reaction Mechanism of HIV Reverse Transcriptase with a Nucleotide Substrate

Enzymatic reactions consist of several steps: (i) a weak binding event of the substrate to the enzyme, (ii) an induced fit or a protein conformational transition upon ligand binding, (iii) the chemical reaction, and (iv) the release of the product. Here we focus on step iii of the reaction of a DNA polymerase, HIV RT, with a nucleotide. We determine the rate and the free energy profile for the addition of a nucleotide to a DNA strand using a combination of a QM/MM model, the string method, and exact Milestoning. The barrier height and the time scale of the reaction are consistent with experiment. We show that the observables (free energies and mean first passage time) converge rapidly, as a function of the Milestoning iteration number. We also consider the substitution of an oxygen of the incoming nucleotide by a nonbridging sulfur atom and its impact on the enzymatic reaction. This substitution has been suggested in the past as a tool to examine the influence of the chemical step on the overall rate. Our joint computational and experimental study suggests that the impact of the substitution is small. Computationally, the differences between the two are within the estimated error bars. Experiments suggest a small difference. Finally, we examine step i, the weak binding of the nucleotide to the protein surface. We suggest that this step has only a small contribution to the selectivity of the enzyme. Comments are made on the impact of these steps on the overall mechanism.

ScMile: A Script to Investigate Kinetics with Short Time Molecular Dynamics Trajectories and the Milestoning Theory

Studies of complex and rare events in condensed phase systems continue to attract considerable attention. Milestoning is a useful theory and algorithm to investigate the long-time dynamics of activated molecular events. It is based on launching a large number of short trajectories and statistical analysis of the outcome. The implementation of the theory in a computer script is described that enables more efficient Milestoning calculation, reducing user time and errors, and automating a significant fraction of the algorithm. The script exploits a molecular dynamics engine, which at present is NAMD, to run the short trajectories. However, since the script is external to the engine, the script can be easily adapted to different molecular dynamics codes. The outcomes of the short trajectories are analyzed to obtain a kinetic and thermodynamic description of the entire process. While many examples of Milestoning were published in the past, we provide two simple examples (a conformational transition of alanine dipeptide in a vacuum and aqueous solution) to illustrate the use of the script.

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.