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

Comparison of Accuracy and Efficiency of Milestoning Variants: Introducing Buffer Milestoning

The Milestoning algorithm is a method for long-time molecular dynamics simulations. It enables the sampling of rare events. The precise calculations of observables depend on accurately determining the first hitting point distribution (FHPD) for each milestone. There is no analytical expression for FHPD, which is estimated numerically. Several variants of Milestoning offer approximations to the FHPD. Here, we examine in detail the FHPD of an exact calculation and Milestoning variants. We also introduce a new version of the Milestoning algorithm, buffer Milestoning, with a comparable cost to conventional Milestoning but higher accuracy. We use the mean first passage time and the free energy to assess the simulation quality, and we compare the accuracy and efficiency of buffer Milestoning to exact calculations, conventional Milestoning, local-passage-time-weighted Milestoning, Markovian Milestoning with Voronoi tessellation, and exact Milestoning. Conventional Milestoning requires milestone decorrelation. If this condition is not satisfied, it is the least accurate approach of all the techniques we examined. We conclude that for a small increase in cost compared to conventional Milestoning, buffer Milestoning provides accurate results for a range of problems, including more correlated milestones and is, therefore, versatile compared to other variants. Local-passage-time-weighted Milestoning provides accuracy similar to that of buffer Milestoning but at an increased simulation cost. Markovian Milestoning with Voronoi tessellation is the most accurate compared with other approximations, but it is less stable for high barriers and more expensive.

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.

Leaflet-Dependent Effect of Anionic Lipids on Membrane Insertion by Cationic Cell-Penetrating Peptides

Cationic membrane-permeating peptides can cross membranes unassisted by transmembrane protein machinery, and there is consensus that anionic lipids facilitate this process. Although membranes are asymmetric in lipid composition, investigations of the impact of anionic lipids on peptide-membrane insertion in model vesicles primarily use symmetric anionic lipid distributions between bilayer leaflets. Here, we investigate the leaflet-specific influence of three anionic lipid headgroups [phosphatidic acid (PA), phosphatidylserine (PS), and phosphatidylglycerol (PG)] on insertion into model membranes by three cationic membrane-permeating peptides (NAF-144-67, R6W3, and WWWK). We report that outer leaflet anionic lipids enhanced peptide-membrane insertion for all peptides while inner leaflet anionic lipids did not have a significant effect except in the case of NAF-144-67 incubated with PA-containing vesicles. The insertion enhancement was headgroup-dependent for arginine-containing peptides but not WWWK. These results provide significant new insight into the potential role of membrane asymmetry in insertion of peptides into model membranes.

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.

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.

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

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

Long-time methods for molecular dynamics simulations: Markov State Models and Milestoning

Molecular dynamics (MD) studies of biomolecules require the ability to simulate complex biochemical systems with an increasingly larger number of particles and for longer time scales, a problem that cannot be overcome by computational hardware advances alone. A main problem springs from the intrinsically high-dimensional and complex nature of the underlying free energy landscape of most systems, and from the necessity to sample accurately such landscapes for identifying kinetic and thermodynamic states in the configurations space, and for accurate calculations of both free energy differences and of the corresponding transition rates between states. Here, we review and present applications of two increasingly popular methods that allow long-time MD simulations of biomolecular systems that can open a broad spectrum of new studies. A first approach, Markov State Models (MSMs), relies on identifying a set of configuration states in which the system resides sufficiently long to relax and loose the memory of previous transitions, and on using simulations for mapping the underlying complex energy landscape and for extracting accurate thermodynamic and kinetic information. The Markovian independence of the underlying transition probabilities creates the opportunity to increase the sampling efficiency by using sets of appropriately initialized short simulations rather than typically long MD trajectories, which also enhances sampling. This allows MSM-based studies to unveil bio-molecular mechanisms and to estimate free energy barriers with high accuracy, in a manner that is both systematic and relatively automatic, which accounts for their increasing popularity. The second approach presented, Milestoning, targets accurate studies of the ensemble of pathways connecting specific end-states (e.g., reactants and products) in a similarly systematic, accurate and highly automatic manner. Applications presented range from studies of conformational dynamics and binding of amyloid-forming peptides, cell-penetrating peptides and the DFG-flip dynamics in Abl kinase. As highlighted by the increasing number of studies using both methods, we anticipate that they will open new avenues for the investigation of systematic sampling of reactions pathways and mechanisms occurring on longer time scales than currently accessible by purely computational hardware developments.