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

Abstract

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 anti-cancer 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.

Graphical Abstract

I. Introduction

Targeted delivery of molecular cargo into specific types of cells or cell compartments is a promising approach for the selective transport of drugs and other nonnatural agents to specific cells or even specific organelles within a cell. The ability to transport a therapeutic molecule to a desired location increases its local concentration at the target and reduces nonspecific interactions that could cause deleterious side effects. Therefore, significant research has been conducted to identify molecular agents that support selective delivery of cargo within a biological system.¹ A significant physical obstacle to this goal is the cell’s plasma membrane, composed of amphiphilic phospholipid molecules that self-assemble into a hydrophobic interior and hydrophilic exterior. The hydrophobic interior of the membrane poses a significant free energy barrier to the entry of molecules, which are soluble in aqueous solution, into the cell. This barrier varies between several to tens of kcal mol⁻¹.^2-5

One class of promising molecules for accomplishing the goal of targeted delivery are cell-penetrating peptides (CPPs);^6-12 short sequences of amino acids derived from naturally penetrating proteins that efficiently cross the bilayer energy barrier and can be used to pull cargo molecules into a cell. An interesting observation of this class of biomolecules is that they are often highly positively charged, which seems to conflict with chemical intuition about molecular characteristics that would interact favorably with the bilayer interior. A classic example of this property is a 13-residue sequence from the trans-activator of transcription (TAT) protein from the HIV virus.^{13, 14} Membrane insertion was shown to be facilitated by the TAT^48-60 sequence GRKKRRQRRRPPQ, which carries a +8 charge and is expected to be unstructured. A hypothesis is that the positive charges allow TAT^48-60 to interact with the negatively charged membrane head groups. However, this does not explain how the positively charged amino acids penetrate into the hydrophobic core of the membrane. Molecular dynamics (MD) simulations¹⁵ proposed a mechanism for TAT permeation that is energy independent. Energy independent mechanisms indicates that the translocation is not by endocytosis.⁷ Several arginine residues interact electrostatically with the phospholipid head groups and distort the membrane structure. They create a pore across the membrane that enables transport. Since this discovery, synthetic peptides that are rich with arginine residues have been prepared and shown to act as CPPs in both cellular and model membranes.¹⁶

Another mechanism of CPP function is demonstrated by penetratin, RQIKIWFQNRRMKWKK, which carries a charge of +7.^{17, 18} In this case, hydrophobic residues (F and W) distributed along the sequence presumably assist in its interaction with the hydrophobic interior of the membrane. A model of penetratin permeation assumes a helical structure of the peptide on contact with the membrane, where the interchanging hydrophobic and charged residues of the amphipathic helix interact favorably with the amphiphilic membrane surface.

Of the approximately 1700 CPPs that have been cataloged to date,¹⁹ the majority are amphipathic and highly positively charged in order to exploit the mechanisms demonstrated by TAT^48-60 and penetratin. Exceptions, however, are known, including purely hydrophobic and negatively charged CPPs.¹² CPP-supported endocytosis, pore, and inverted micelle formation have also been reported.²⁰ Given the diverse set of CPP functions and the complex structure of biological membranes, it is not surprising that this class of molecules has evolved multiple permeation mechanisms into cells.¹²

Most CPPs have been derived from proteins that are involved in translocation or permeation functions (e.g. the TAT^{13, 14} and penetratin peptides).¹⁷ In contrast, the CPP isolated from the protein NAF-1/CISD2, which is the subject of this manuscript,^{21, 22} is anchored in the mitochondria (MIT) and endoplasmic reticulum (ER) membranes. The peptide derived from this protein, NAF-1^44-67 (FLGVLALLGYLAVRPFLPKKKQQK), includes an N-terminal transmembrane helix and a water-soluble, presumably unstructured, C-terminal segment. NAF-1^44-67 has significant medical promise. It selectively permeates the plasma membrane of malignant but not normal cells.²³ Once it has penetrated the plasma membrane, it also traffics to specific organelles, targeting the MIT and ER but not the nuclear membrane. This remarkable selectivity is further enhanced by the ability of the peptide to kill cancer cells by itself, without carrying additional therapeutic cargo and without damaging normal cells.²³

Because of the importance of CPPs to medicine, we examine a simplified atomically detailed mechanism as a baseline for investigations of other CPPs. To that end we examined the permeation of NAF-1^44-67 through a membrane composed of dioleoylphosphatidylcholine (DOPC). This lipid is used widely in model calculations and experimental measurements of membrane function, including studies of mechanisms and rates of permeation.²⁴

In this report, we describe measurements of the interactions of NAF-1^44-67 with 100 nm vesicles composed of DOPC by monitoring changes in fluorescence wavelength and intensity of a Dansyl fluorophore attached to the hydrophobic N-terminal end of the peptide. We observed that the helical N-terminal segment of the peptide enters the hydrophobic interior of the membrane with a partition coefficient of about 2, or free energy difference of −0.4 kcal mol⁻¹. MD simulations that exploit the theory and algorithm of Milestoning²⁵ provide a quantitative molecular mechanism for the association, entry, reorganization, and exit of this peptide through the bilayer structure at time scales of hundreds of seconds. Initial attachment of the peptide to the membrane surface is induced by electrostatic attraction of the positively charged peptide residues to the membrane head groups. A significant free energy barrier at the phospholipid heads is predicted due to unfavorable interactions of the membrane surface with the hydrophobic helix. The helix permeates first into the membrane, and eventually reaches a deep and broad free energy minimum in the hydrophobic core that temporarily traps NAF-1^44-67. Only after significant reorganization of lipid molecules, and thus incubation time, is the peptide able to exit from the other side of the membrane. This atomically detailed study of the thermodynamics and kinetics of CPP translocation at time scales of minutes opens the way for further simulations of these important peptides at biologically relevant time scales.

The present investigation focuses on the permeation of NAF-1^44-67 through a homogeneous and symmetric DOPC membrane. Biological membranes are heterogeneous, asymmetric, and include many types of phospholipids. It will be of considerable interest to extend these studies to biological membranes. These projects are in progress in our laboratory.

II. Methods

II.1. Simulations

II.1.1. System preparation:

The CHARMM-GUI Membrane Builder online software was used to generate the DOPC membrane model.^{26, 27} The bilayer consisted of 160 DOPC lipids (80 in each layer) and was solvated with 10743 water molecules. Potassium and chloride ions were added to have a concentration of 150 mM. We also included 5 additional Cl⁻ ions to neutralize the positive charges of the peptide and the overall charge in the simulation box.

The molecular modeling software PEP-FOLD²⁸ was used to create an initial conformation for the peptide. This structure was solvated in a water box and was equilibrated with an MD simulation in the NVT ensemble for 20 ns. The structure of the peptide at the end of the simulation was inserted to the center of the membrane during the membrane assembly with the modeling software Membrane Builder in CHARMM-GUI.²⁶

II.1.2. General setup and exploratory molecular dynamics simulations:

These exploratory calculations were performed with the simulation program GROMACS,²⁹ the CHARMM 36 all-atom force field,³⁰ and the CHARMM TIP3P ³¹ water model. Periodic boundary conditions were applied in all directions. The electrostatic interactions were calculated using the Particle Mesh Ewald (PME) method³² with a real space cut-off of 1.2 nm and a mesh size of 0.12 nm. For the van der Waals interaction a cut-off distance of 1.2 nm was used, with the addition of a force switching term so the force smoothly decayed to zero from 1.0 to 1.2 nm.

We relaxed the system to equilibrium using the standard procedure of the CHARMM-GUI Membrane Builder.²⁶ Initially harmonic restraints with force constant of 1000 kJ mol⁻¹ nm⁻² were applied on the heavy atoms of the phospholipids. The energy was minimized using a conjugate gradient algorithm until the maximum force was smaller than 1000 kJ mol⁻¹ nm⁻¹ (usually more than 1000 steps were needed to reach that tolerance) and followed by 375 ps of MD simulation with a gradual decrease of the restraints on the lipids. A 1 ns simulation in the NPT ensemble without any restraints was the final step of general equilibration.

All the simulations were conducted in the NPT ensemble with a target pressure of 1.0 bar and a semi-isotropic pressure coupling scheme in which the x-y dimensions were coupled together while the z direction was allowed to fluctuate independently. The simulations were run at 323.15 K using a Nose-Hoover thermostat.^{33, 34} A 2 fs time step was used with the SETTLE algorithm³⁵ to constrain the water molecules and the LINCS algorithm³⁶ to constrain the rest of the bonds involving hydrogen atoms. Configurations were saved every 10 ps.

II.1.3. Milestoning:

The simulations of the permeation kinetics and thermodynamics were conducted with Milestoning. A description of the Milestoning calculations is provided in the Supplementary Information (SI) and in comprehensive review articles.^37-39 We briefly summarize essential elements of Milestoning below. Milestoning is based on partition of the reaction space to Voronoi cells.⁴⁰ The centers of the Voronoi cells are conformations in reaction space and are called “anchors.” An anchor α was defined by three distances from F1, R14 and K24, to the membrane center, d_α,F1, d_α,R14, d_α,K24 also called coarse variables. An arbitrary molecular configuration was considered to be in cell α if the RMSD (root mean square distance in the space of the coarse variables) to anchor α was shorter than the RMSD to any other anchors. The boundaries between the Voronoi cells were the milestones.

There are only three coarse variables, but to conduct MD simulations we need the coordinates of all the atoms in the system. Therefore, we provide an atomically detailed configuration at each of the anchors (including the peptide, solvent, and membrane). One should keep in mind that in this work an anchor is defined by only these three variables, but the dynamics is computed in atomic details. Many other values of the atomically detailed coordinates can belong to the same anchor.

In Figure 1 we show a typical permeating conformation and a Milestoning anchor, illustrating the position of the critical residues F1, R14 and K24. These three residues defined the reaction space and their motions unravel the order of events of peptide translocation across the membrane.

Figure 1.

A molecular snapshot of NAF-1^44-67 in a DOPC membrane displaying the locations of the three groups whose distances to the center of the membrane were chosen as coarse variables for the Milestoning calculation. Note that the order of permeation through the membrane is F1, R14 and K24. In this snapshot, F1 is at the center of the membrane, R14 is interacting with the phospholipid heads and K24 is still in the aqueous solution. The position of the charged N atoms of R14 and K24 are shown with red spheres and the location of the C_α of F1 is shown with a silver sphere. The phosphorus atoms of the upper and lower layer of the membrane are shown in yellow and orange spheres, respectively.

The computed observables that are discussed in the Results section are the free energy F

$$F=-k_{B}Tlog(q\cdot t)$$ (1)

and the Mean First Passage Time (MFPT)

$$\langle \tau \rangle =q\cdot t∕q_f$$ (2)

where q is the vector of all the stationary fluxes through the milestones. The flux is the number of trajectories that cross a milestone per unit time, t is a vector of the milestone life times, i.e. the average time difference from trajectory initiation at the milestone until the trajectory crosses another milestone, and q_f is the flux into the product milestone. See SI and recent reviews for more details.^{25, 37, 39}

A widely used definition for a reaction coordinate estimated from trajectory data is the committor function, which is readily computed with Milestoning.^41-44 The committor, C, is a vector of the probabilities that a trajectory initiated at a milestone will reach the product before the reactant state. It is given by the formula⁴²

$$(I-K^{(C)})C=e_f$$ (3)

where I is the identity matrix, K^(c) is the matrix of transition probabilities between the milestones, and e_f is a vector with zero for all entries with the exception of the product milestone, in which the entry is one.

II.2. Experiments

II.2.1. Reagents and Materials:

All materials were used as received. Dansyl-labeled NAF-1^44-67 was purchased from GenScript (Piscataway, NJ, United States). The fluorescent label was located on the N-terminus, and the C-terminus was amidated to neutralize the negative charge. DOPC was purchased in chloroform (25 mg ml⁻¹) from Avanti Polar Lipids, Inc (Alabaster, AL, United States). HEPES buffer, sodium azide salt (NaN₃) and sodium hydroxide salt were all purchased from Fischer Scientific (Waltham, MA, United States).

II.2.2. Sample Preparation:

HEPES buffer was prepared at a concentration of 10 mM, pH = 7.2 and contained 0.01% (w/v) NaN₃. DOPC lipids in chloroform were dried under vacuum and rehydrated in HEPES buffer to a concentration of 30 mM DOPC. These samples were subjected to twelve cycles of freezing in N₂(l) and thawing in a water bath at 40 °C to create unilamellar vesicles as previously described.^{2, 24} Following freeze/thaw cycling, the solutions were extruded through 100 nm Whatman filters, and the size was measured with dynamic light scattering (⟨Z⟨ = 110±10 nm). Dansyl-labeled NAF-1^44-67 was dissolved in HEPES buffer or hexane at a concentration of 10 μM. NAF-1^44-67 in HEPES and DOPC vesicles were mixed in a ratio of 1:3 (v/v) to obtain solutions containing 7.5 mM DOPC and 7.5 μM NAF-1^44-67. These solutions were incubated at 30 °C until the fluorescence spectrum of Dansyl was measured. Spectra denoted as “day 1” data were acquired after 2 hr of incubation unless noted otherwise.

II.2.3. Fluorescence Spectra:

Fluorescence spectra were acquired using a Fluorolog3 Fluorimeter (HORIBA Ltd., Kyoto, Japan). Dansyl was excited at 337 nm, and the spectrum was collected from 390–650 nm with a resolution of 0.5 nm. The excitation monochromator had a standard correction applied, and excitation and detection slit widths were set to 5 nm. All spectra were normalized to the peak intensity to show relative changes in peak position and spectral line shape.

III. Results

CPPs participate in numerous biological events, such as intra-compartment translocation of matter and signaling molecules.⁷ They offer biological defense and offense mechanisms, and have significant potential as drugs and drug delivery agents to target specific cells. However, investigating CPP structure and mechanism at the atomic level is challenging. Studies of CPP permeation through phospholipid membranes are complex for several reasons. First, the process covers a vast range of time scales spanning from nanoseconds in which the peptide touches the membrane surface to hours and even days for the entire permeation event. These extended timescales make it necessary to use diverse experimental and simulation techniques to probe multiple temporal events. Second, the diversity of chemical compositions as a function of membrane depth leads to a spatially heterogeneous system with varied dielectric medium, fluidity, and viscosity adding significantly to modeling and experimental complexity. Third, CPPs may adopt multiple conformations or may be unstructured, making it more difficult to probe their position and their mode of interaction with the membrane and solution, as well as to efficiently sample their conformations.

We present first results of Milestoning simulations of permeation events accompanied by experiments on the same system: NAF-1^44-67 interacting with a DOPC lipid bilayer membrane. In the experiments, a Dansyl label was added to the N terminus to observe the interaction with the membrane spectroscopically. The simulations offer a detailed microscopic picture of the kinetics at timescales of minutes. We highlight mechanistic features that were both detected by experiments and probed by simulations of this complex dynamic system.

III.1. Simulations

The details of the Milestoning calculations are discussed in Methods and in the SI. Here we discuss thermodynamic and kinetic observables.

III.1.1. Free energies calculations:

In Figure 2 we show free energy profile calculated from Milestoning (Eq. (1)) of NAF-1^44-67 for the three coarse variables: the distances from the center of the membrane of the residues F1, R14 and K24. Significant free energy barriers (~18 kcal mol⁻¹, red shading in Figure 2) were found near the phospholipid head groups at the membrane exterior, but were quite narrow in depth. The lowest calculated free energy positions (blue shading in Figure 2), covered a broad region around the geometric center of the membrane (0 Å in Figure 2). This indicates that once the energy barrier created by the phosphocholine headgroup is surpassed, there is a relatively flat energy landscape at the center of the membrane where the peptide is stable within the bilayer.

Figure 2.

A schematic plot of the free energy profile as a function of the three coarse variables: The distances between residues K24, R14, and F1 from the center of the membrane. The free energy is color coded with the red the highest energy value (~18 kcal mol⁻¹) and blue the lowest energy (~2 kcal mol⁻¹) at the center of the membrane. In this Figure and Figure 3 the free energy represents the symmetrized average of the free energies computed for both layers. In the SI a movie is presented where this plot is continuously rotated to display better the spatial shape of the free energy profile.

Because the DOPC membrane is symmetric, we can compare the results from the two layers to estimate the error in the calculated free energy. This analysis is provided in the SI. The errors, δ, (Fig 3S of the SI) varied between 0 to 3 kcal mol⁻¹ and depended on the values of the coarse variables. These errors are small (~0-1 kcal mol⁻¹) at the metastable state in which the peptide is at the center of the membrane, and they are at a maximum (~3 kcal mol⁻¹) at the interface between the membrane and the aqueous solution where the barrier, ΔE, is located and estimated to be ~16 kcal mol⁻¹. A discussion about the impact of these errors on the rate is provided in section III.1.4 in which we consider the calculations of the Mean First Passage Time.

Perhaps the most striking feature of the free energy contours is the broad free energy minimum at the center of the membrane seen in Figures 2 and 3. Typically, we think of the hydrophobic center of the membrane as posing a significant barrier for molecules that are solvated in aqueous solution. Because NAF-1^44-67 is positively charged, it is likely to be well solvated in aqueous solution and less so in the hydrophobic core of the membrane. Interestingly, NAF-1^44-67 had a significant and narrow barrier to enter the membrane (seen by the relatively narrow regime of the high energy (red) areas of the membrane in Figures 2 and 3; see also section II.1.6). After the insertion of the peptide into the membrane overcame the initial barrier, NAF-1^44-67 entered a metastable free energy minimum that spanned nearly the entire hydrophobic interior, ~40 Å. The design of NAF-1^44-67 from a fragment of a stable transmembrane protein that includes both membrane- and water-soluble parts, may explain this observation. The barrier consisted of the relatively thin domain (of about 1 nm) of the phospholipid head groups, leading to a narrow barrier. The hydrophobic core, however, was homogenous over depths of more than ~40 Å combining the two layers. It contained no directional interactions such as hydrogen bonds and allowed significant orientational freedom through random thermal motions within the aliphatic lipid tails. This free energy landscape therefore supports a multitude of peptide conformations, and thus a broad metastable state of the membrane-solubilized peptide.

Figure 3.

Free energy contour plots as a function of all pairs of the three coarse variables: the distances of F1, R14 and K24 from the center of the membrane. Panel (A) probes the pair R14 and K24, Panel (B) F1 and K24, and panel (C) F1 and R14. The free energy is color coded where red is the highest energy (~18 kcal mol⁻¹) and blue are the deepest minima (~2 kcal mol⁻¹). The distances vary from about −40 to +40 Å, which are the lower and upper locations of the aqueous solution-membrane interface in the simulation box. The MaxFlux path, the path that carries the largest number of trajectories and provides a one-dimensional reaction coordinate, is also illustrated (orange line). The numbers indicated on the MaxFlux path refer to snapshot images shown in Figure 4.

III.1.2. Reaction mechanism:

To obtain an atomically detailed picture of the mechanism we considered the MaxFlux pathway in the reaction space. The MaxFlux pathway is a curvilinear coordinate that carries most of the trajectory flux^45-47 and was originally derived from the diffusion equation.⁴⁶ It can be used to define the reaction coordinate from path optimization in continuous space.⁴⁷ Here, we have used it to determine optimal pathways in a discrete space (a network of Voronoi cells or of milestones).⁴⁸ It has the advantage of simplicity, ease of calculation, and ability to predict the sequence of reaction events. It has the disadvantage of inadequate weighting of path entropy and lack of a connection to observables such as rate. If many distinct pathways similar in their overall weights are contributing to the reactive flux, then the selection of a single pathway may be misleading. Nevertheless, this path is useful for identifying significant bottlenecks and provides a qualitative one-dimensional mechanism.

The orange line on Figure 3 shows the MaxFlux pathway of the peptide crossing the membrane. This is determined by a discrete network analysis of the anchors as nodes and milestones fluxes as weights of the edges in the space of the three coarse variables.^{46, 47} The pathway provides the sequence of events leading to peptide entry and permeation through the membrane. Atomically detailed snapshots from the numbered points along the MaxFlux pathway are shown in Figure 4.

Figure 4.

Atomically detailed images along the MaxFlux pathway. The MaxFlux pathway as a function of the three coarse variables is shown in Figure 3 and the numbered locations along the pathway correspond to the snapshot indices. Images were picked visually from the MaxFlux pathway of about 100 structures to illustrate important steps during the permeation events. For some snapshots (for example images 2 and 3) the simulation cell was rotated around the normal to the membrane plane to ease visualization of the peptide. The images use the same color code described in the legend of Figure 1.

The snapshots in Fig. 4 are indexed according to their positions along the path. In Figure 4 panel 1, we observed the initial binding of NAF-1^44-67 to the membrane surface through the interaction between the positively charged residue R14 and the phosphate groups of DOPC. This interaction distorted the membrane surface slightly, bringing some phosphates groups above the average position of the membrane surface plane. Membrane fluctuations are discussed in Section III.1.5. The hydrophobic F1 residue lay flat on the membrane surface before its initial penetration into the membrane in the next step. Because R14 is at the end of the hydrophobic helix, its interaction with head groups keeps the peptide at the membrane surface while allowing the hydrophobic segment to enter the bilayer structure (Figure 4, panel 2).

In Figure 4, panel 3, R14 maintained its position on the surface while the nonpolar helix of the N-terminus was perpendicular to the plane of the membrane and was able to reach deep into the bilayer. Figure 4, panel 3 shows that to accommodate the peptide, the membrane deformed slightly.

In Figure 4, panel 4, R14 had inserted completely and is at the membrane center while K24, the other charged residue we are using for a coarse variable, finally began interacting with the upper surface of the lipid-water interface. The presence of R14 at the membrane center further enhanced the distortion of the membrane, and both the negatively charged phosphate functional groups and water molecules permeated significantly into the hydrophobic core of the membrane structure. Membrane distortions accompanied the full penetration of K24 to the membrane (Figure 4, panels 5 and 6, see also Section III.I.5).

Figure 4, panels 7 and 8 show the entire peptide near the membrane center, where it executed a rotation motion (a flip flop) to invert the direction of the helix and charged groups (Figure 4 panels 6 to 9). This motion is in preparation to exit the inner leaflet of the membrane in a symmetric fashion to the entrance event. Finally, in Figure 4, panels 9 to 12, the mechanism of entry was mirrored as the peptide exited from the inner leaflet of the membrane to complete the translocation of the entire peptide through the DOPC bilayer.

III.1.3. The Committor Function and the Transition Domain:

Figures 3 and 4 show a complete pathway of a peptide translocating across the lipid bilayer membrane, which was discussed in the forward direction. However, the permeation is diffusive and at any point the reverse process can occur and the peptide can exit the membrane from the same leaflet it entered. Moreover, the picture offered in III.1.2 is inherently one-dimensional, while the peptide may diffuse through a large number of alternative pathways. Many pathways are likely on the broad and flat free energy surface of the membrane interior shown in Figures 2 and 3. Therefore, we computed the committor function, C_i (Eq. (3)) as a function of the milestone index i and for the entire reaction space. The committor is the probability that a trajectory initiated from milestone i will reach the product state before the state of the reactant. The committor function returns a value between zero and one, with the set of points with a committor value of 0.5 defining a transition domain.

In typical chemical reactions the transition state is associated with a significant free energy barrier and it spans only a small fraction of the reaction space.⁴⁹ Here, the transition domain (committor value of about 0.5, represented in teal in Figure 5) is exceptionally broad and covers more than a half of the relevant reaction space equivalent to the hydrophobic membrane interior. This is consistent with the mechanistic picture shown in Figure 4. Once the hydrophobic helix successfully overcame the barrier associated with the polar phospholipid heads, the free energy landscape was flat. Therefore, passage of the first barrier created a quasi-equilibrium for the peptide in the membrane, with equal exit probabilities to the upper or lower leaflets.

Figure 5.

Two dimensional cross sections of the committor as a function of the three coarse variables: the distances from the center of the membrane of F1, R14 and K24. The committor function is one at the product state (the lower leaflet of the membrane) and is zero at the reactant. Note the exceptionally broad transition domain in which the committor function is equal 0.5. This is another confirmation of the existence of a metastable state at the membrane center.

III.1.4. The Mean First Passage Time:

In Figure 6 we show a plot of the mean first passage time (MFPT) along the MaxFlux pathway. This is the average time it takes a trajectory to reach a given position along the pathway indexed by the milestone number, given that it started at the reactant state. Note the relatively weak dependence of the MFPT (less than two orders of magnitude) on the milestones’ indices 10-80. The entry of the entire hydrophobic helix of the peptide into the membrane occurs near milestone 10 and the exit of the hydrophilic C-terminal segment from the lower leaflet of the membrane to the aqueous solution occurs near milestone 80. Between milestones 10-80 the peptide is at the lipidic environment of the membrane. Therefore, the transition time of the peptide from the reactant to hydrophobic part of the membrane is relatively short. This weak time dependence contrasts with the steep changes in the MFPT near the membrane boundaries and especially near the product state. The exit of the peptide from the hydrophobic core to the aqueous solution occurs between milestone 80 to 100 and is about a factor of a million longer than the residence time at the membrane core. This picture is consistent with our observation of a steep free energy barrier at the membrane boundary, and a flat energy landscape at the membrane center (Figures 2 and 3).

Figure 6.

Mean First Passage Time (MFPT) for the translocation of NAF-1^44-67 from one side of the DOPC membrane to the opposite side estimated by Milestoning along the MaxFlux pathway. The MaxFlux pathway described in Figure 3 and 4 is a complex function of the three coarse variables and is not monotonic in any of them. Therefore, the proper description of the progress along the pathway is using the sequential indices of the milestones. The membrane composition is symmetric. Therefore, we compute the MFPT from the upper (and lower) membrane boundaries to the membrane center and from the membrane center to the upper (amnd lower boundaries. We use the results for each of the layers that were constructed independently to estimate the errors; the black line shows the average. Errors are the deviations of the MFPT through each layer from the average. The blue numerical labels are the indices of the configurations represented in Figure 4.

It is interesting to compare the error results of the MFPT calculations to a rough estimate from a rate theory. We assume a transition state theory (TST) expression with a rate coefficient given by k_± = ω · exp(−β(ΔE ± δ)) where β is the Boltzmann factor. The barrier height, ΔE = 16 kcal mol⁻¹ and the error, δ = 3 kcal mol⁻¹ were discussed and given in section III.1.1. We further assume that the changes in the collision frequency ω are small. The ratio of the rate coefficients of the two extreme values is $\frac{k_{+}}{k_{-}}=exp(2\beta \delta )$. Substituting $2\beta \delta =2\cdot \frac{3}{0.002\cdot 323.15}=9.28$ we have $\frac{k_{+}}{k_{-}}=exp(9.28)\cong {10}^4$. Hence, the error bars of kinetic predictions from the simplified version of TST using the free energy calculations are substantial. Statistical errors of the time scale which can be computed within the Milestoning theory,⁵⁰ are smaller. In Fig. 6 we plot the Mean First Passage Time (MFPT) with statistical error bars. The inverse of the MFPT is an estimate of the rate coefficient. The errors in Fig 6 for the longest MFPT are about two orders of magnitude, significantly less than the TST estimate that is based on the free energy barrier.

III.1.5. Membrane fluctuations and their coupling to permeation events:

Membranes form dynamic barriers that are constantly shifting. They are elastic. They can bend without changing significantly their internal structure. They can also deform locally, displacing phospholipid molecules from the membrane surface and allowing water molecules to penetrate into the hydrophobic core. These deformations occur spontaneously as a result of thermal noise or as a response to systematic forces. Some external interactions leading to deformations are with molecules attaching themselves to the membrane surface or attempt permeation. It is expected that at least the local deformations are coupled to permeation events. The inclusion of membrane distortions as coarse variables therefore comes to mind. However, a reason to ignore membrane dynamics as part of the reaction space can be time scale separation. For example, if the local deformations adapt quickly to adjustments in the permeation state of the peptide, then the membrane state is in local equilibrium with the translocation coordinates of NAF-1^44-67 and need not be included in the reaction space.

We assume in the above Milestoning calculations that the three coarse variables are sufficient to quantitatively describe the mechanism of the reaction. The distances from peptide groups to the center of the membrane fixed the overall position and orientation of the peptide with respect to the membrane core. In an earlier study of peptide permeation, we propose the use of membrane distortion as another coarse variable.⁵¹ In the present investigation we determined that at a fixed position of the peptide with respect to the membrane center, the phospholipids rapidly adjusted to equilibrium over a period shorter than ~100 ns. Therefore, variables describing explicitly membrane distortions were not included in the coarse space to investigate the overall kinetics. Membrane fluctuations are in local equilibrium with respect to the permeation coordinates. It is, however, of interest to quantify what membrane deformations are formed in response to the peptide insertion.

We examined membrane defects using the positions of phospholipid head groups and the number of water molecules. The distortions are probed as a function of the coarse variables and the membrane depth. We present the membrane depth using two slabs. The first slab is from −1 to 1 nm from the center of membrane (interior or inner slab) and the second slab is from 1 to 2 nm (outer slab). The slabs are illustrated in an inset in Figure 7D. The outer slab ends at the interface of the membrane and the aqueous solution. Therefore, it is expected to absorb a significantly larger number of water molecules than the inner slab.

Figure 7.

Water permeation to the membrane as a function of peptide translocation (color coded inset in panel A) and membrane slabs. The outer membrane slab is between the orange and mauve lines in the embedded snapshot in panel D. The inner slab is between the two orange lines. Panels A to C examine the water permeation to membrane layer between 1 and 2 nm from the membrane center. This layer touches the interface of the aqueous solution and the phospholipids. We examined the number of water molecules as a function of the permeation depths of different coarse variables which are coded by colors. Panels D to F report similar observations, this time for the outer membrane slab close to the hydrophobic center between −1 and 1 nm. See text for more details.

Figure 7A-C shows the distributions of water molecules for the outer slab and Figure 7D-F shows the distributions for the inner slab. Every panel shows the probability density of the number of water molecules as determined from MD simulations with restrained values of the coarse variables (see SI). In each panel we show multiple distributions for different values of the coarse variable. The values of the coarse-grained variables are color coded for each water distribution (inset in panel 7A). For example, the black curves represent the water distribution when the coarse variables are at the center of the membrane and the orange lines when the coarse variables are outside the membrane in the aqueous solution.

The outer slab of the membrane accommodated hundreds to more than a thousand water molecules. The distributions are roughly bell-shaped with a slightly longer tail at the high end. Peptide permeation has an impact on locations of the centers of these distributions but less on their widths. Interestingly, the distribution of permeating water molecules at the outer slabs was not affected by the permeation of F1 (Figure 7A). All the distributions with F1 at the different membrane depths overlapped within the error bars. We rationalize this observation by noting that F1 is at the beginning of the hydrophobic helix, which is well solvated at the lipid phase and does not encourage water permeation.

In contrast, the distribution of the number of water molecules changed significantly as a function of the other two coarse variables. R14 (panel 7B) follows F1 in sequence and in the order of membrane permeation. It was the leading charged group entering the membrane, and it dragged a considerable number of water molecules with it. When R14 was at the membrane center (black curve) the number of water molecules in the outer slab had a maximum near 1100, which then decreased monotonically as R14 left the center. The peak of a distribution with the smallest number of water molecules (orange line, near the membrane-water interface) was near 950. It is even less than the peaks for F1 (~1,000). Based on this observation, R14 is not only associate with an enhancement in water permeation to the outer membrane layer, but also a depletion. The depletion is probably induced by excluded volume effects in which the presence of the peptide reduces the nearby free volume for the water molecules. See for instance panels 1 and 2 of Figure 4.

The distributions of water molecules are more complex for K24 (panel 7C). The permeation of K24 followed R14 and therefore was coupled to the permeation of the latter. The largest number of water molecules at the outer slab was observed when K24 was at 0.5 nm from the membrane center (and R14 was also close to the center, see Figure 4, panels 5-8). The water distribution as a function of K24 permeation depth is doubly peaked. One cluster of distributions includes depths from 2.0 to 3.5 nm and a peak of less than 1000 water molecules. The second cluster of water distributions with depths of 0-1.5 nm (closer to the membrane center) is peaked at ~1100 water molecules. This difference can be rationalized by Figure 4, panels 5-8 in which both residues, R14 and K24 are embedded in the hydrophobic core of the membrane. Therefore, a higher number of water molecules is required to screen the excessive charges. When K24 is far from the center the screening by water molecules is less essential. An interesting observation is that the clusters are well separated and the transition as a function of K24 depth is between two states and not continuous.

We consider next the interior membrane slab in panels 7D-F. The water distributions were coupled to more than one coarse variable. For example, F1 showed the largest number of permeating water molecules at 0.5 nm, unexpected for a hydrophobic residue on its own, but acceptable when coupled to nearby charged residues. Like in the outer layer, R14 showed a monotonic increase in the number of water molecules as the residue moved from the water-membrane interface to the center of the membrane. When R14 was at the center of the interior slab the water distribution is exceptionally broad and has more than one peak. The double peak correlates with the dual distributions of K24 in the outer layer. The peak with a larger number of water molecules corresponds to peptide conformations with more than one charge in the hydrophobic core. Again, a surprising discrete behavior for the water distributions as a function of the peptide depth, and a supporting evidence for the sequential mechanism we proposed in Figure 4.

We had considered the permeation of a potassium ion through a DOPC membrane and had shown two distinct permeation pathways, each with a different number of water molecules.⁵² Discrete sizes of clusters of water molecules, coupled to the permeant, were therefore observed for more systems than the peptide under considerations. The broad distributions with R14 at the center of the membrane also suggested that the peptide had more than a single configuration, pointing again to the flat energy landscape the peptide “sees” after passing the phospholipid heads. Finally, K24 showed simpler behavior with a water distribution with a single peak. The number of water molecules decreases monotonically as K24 is further away from the membrane center.

We also examined the distribution of phosphate head groups as a function of the coarse variables at different membrane depths, summarized in Figure 8. The results supported a two-state model for the permeation of the head groups. There was sharp transition between the peaks of the distributions as the peptide permeated more deeply into the membrane. For example, when R14 was at the center of the membrane there was a significant depletion of about 10 phosphate groups in the outer slab. Moving R14 away from the center immediately restored the number of phosphate groups in the outer layer. The missing phosphate groups migrate partially to the inner layer (~5) to support the charged residue at the hydrophobic core. The other five groups were displaced from the outer slab by excluded volume as the peptide enters the membrane core.

Figure 8.

The distribution of phospholipid head groups as a function of the membrane slab and the peptide permeation depth. Panels A to C show the distributions in the outer membrane slab. Panels D to F provide the distributions of phospholipid heads near the membrane center (see Figure 7 for the location of both slabs in the membrane system). For panels D to F several of the distributions overlap with the distribution at 3.5 nm (orange color).

We also note the two-state description of the inner slab for R14. One state had essentially no phosphate groups at the membrane core and another state had a broad singly peak distribution with a peak near four. With the exception of K24, the change in the number of phosphates as a function of residue depth was steeper than the change in the number of water molecules. When any of the coarse variables were at the center of the membrane, or near it (black curves, panels 8A-C) a significant number of phosphate groups was depleted from the outer slab. F1 is the first residue to enter, but it is uncharged. Nevertheless, depletion was observed for F1 at 0 and 0.5 nm from the membrane center. K24 is the last residue to permeate and the depletion process is stretched over depths of 0-1.5 nm. The same range of the K24 coarse variable was observed for the large water cluster (Figure 7C).

In summary, the water molecules followed the peptide and permeated to the membrane continuously, providing polar cloud to the translocating charges. The size of the water cloud changed discretely. In contrast, defects in phospholipid positions are sharp and they show a binary, all-or-none behavior. Only if the coarse variable is close to the membrane core significant deviation in phospholipid positions can be detected.

III.1.6. The initial barrier from the aqueous solution to the membrane surface

The free energy profile presented so far focuses on membrane translocation given an initial starting position of the peptide in aqueous solution but near the membrane interface (Figure 9a, milestone 95, the indices of the milestones follow Figure 6). To better investigate the transition of the peptide from aqueous solution to the membrane surface we extended our simulations farther from the membrane. We increased the size of the simulation box along the direction normal to the membrane plane by 4 nm (to 13 nm). We placed the NAF-1 peptide at the upper part of the box in which it is better solvated (Figure 9b, milestone 114).

Figure 9.

The first and the last milestones describing the progress of the peptide from the aqueous solution to or from the membrane surface. (a) Milestone 95 with the peptide “touching” the membrane surface. (b) Milestone 114 of a well solvated peptide with a distance of 6.2 nm from the membrane center. We use the same color code described in the legend of Figure 1 to display the phosphates and atoms used in computing the coarse variables. The nitrogen atoms of the choline groups are shown as blue van der Waals spheres.

We equilibrated the enlarged system using the same steps as in section II.1.1 and II.1.2. To prevent peptide diffusion further into the solution we placed a repulsive wall in the aqueous solution at 6.2 nm from the membrane center. Then we run 200 ns of unbiased simulation to identify anchors. We generated 469 new anchors. Once these anchors were at hand, we conducted Milestoning calculations to extend our free energy landscape to regions further away from the membrane surface. A one-dimensional profile along the MaxFlux pathway is shown in Figure 10 illustrating a barrier of about 2-3 kcal/mol for the peptide entry, starting from milestone 114.

Figure 10.

The free energy profile along the MaxFlux pathway from the center of the membrane (milestone 48) to the aqueous solution (milestone 114). The curve is an average of the free energy profiles of both layers with the deviations shown as error bars. The results from milestone 48 to 94 are from the simulation with the smaller box (section III.1.1). The free energy profile from milestone 95 to 114 is extracted from simulations with the larger box.

III.1.7. The secondary structure of the permeating peptide.

The NAF-1^44-67 peptide is moving between aqueous solution and membrane. Changing the environment can have strong influence on the preferred peptide conformations and secondary structure. Different conformations may permeate at alternate rate. Therefore, examining the secondary structure is of interest. A visual examination of the Milestoning trajectories suggested that the hydrophobic helix is preserved. To quantify this observation, we run additional molecular dynamics simulations at each point of the MaxFlux pathway, from the membrane center (milestone 48) to the interface of the aqueous solution with the membrane (milestone 94). Specifically, we computed 50-ns molecular dynamics trajectories for each point while restraining the coarse variables to their corresponding values on the path. We determined the transient helical content every 10 ps with the GROMACS tool do_dssp that uses the secondary assignment method of Kabsch and Sander^53,54. The average helical content and its fluctuations are reported in Figure 11. The figure shows that the N-terminal helix is stable when the peptide is inside the membrane. There is a slight loss of the stability when the peptide reaches the aqueous solution and the helix is most stable close to the phospholipid heads (Figure 4, panel 3 and 11).

Figure 11.

The fraction of helical content for the N-terminal segment (residues 1 to 13) of NAF-1^44-67 along the MaxFlux path. At milestone 48 the peptide is at the membrane center. It is outside the membrane at milestone 94. Milestones at the left of the blue dashed line correspond to conformations with the N-terminal segment inside the membrane. The milestone indices are the same as shown in Figure 6. The error bars are the standard deviation of the helical content averaged in each trajectory.

III.2. Experiments

III.2.1. NAF-1^44-67 Partitions into DOPC Membranes:

To calibrate the spectra for peptide transitions from aqueous solution to the membrane hydrophobic environment, Dansyl-labeled NAF-1^44-67 was added to either hexane solvent or aqueous HEPES buffer (Figure 12A). The solution of hexane models a hydrophobic environment similar to the bilayer interior, while the HEPES buffer is the aqueous solution for the permeation experiments. In separate experiments the peptide was added to solutions containing DOPC vesicles (Figure 12B). If the spectrum of the peptide in the presence of the DOPC vesicles is shifted towards the wavelength found in hexane and away from that in aqueous buffer, we expect the spectroscopic probe to be at the hydrophobic core of the membrane.

Figure 12.

(A) Fluorescence emission spectra of Dansyl-labeled NAF-1^44-67 dissolved in hexane (blue) or aqueous HEPES buffer (orange). (B) Emission spectra of the labeled peptide in solutions containing DOPC vesicles collected after incubating lipids and NAF-1^44-67 for 2 hr. (red) or four days (blue). The spectrum in buffer without vesicles is again provided (orange) and a small red shift upon the addition DOPC is indicated with a black arrow. The sequence of labeled NAF-1^44-67 in provided at the top of the figure. The concentration of NAF-1^44-67 was 7.5 μM in all cases. The concentration of DOPC lipids in (B) was 7.5 mM. Dansyl was excited with 337 nm light in all cases.

In hexane, the emission peak was located at ~470 nm and shifted to ~540 nm in aqueous buffer (Figure 12A). This solvatochromic shift is consistent with an increase in solvent polarity of the buffer compared to hexanes. When the peptide was added to solutions containing DOPC vesicles, the emission peak was found at ~550 nm (Figure 12B; red curve), indicating a more polar environment than the buffer solution. This shift in the presence of vesicles likely results from the electric field created by dipoles on the phosphocholine lipid headgroups as the peptide interacts with the membrane surface, as seen in panel 1 of Figure 4.

A new peak appeared at ~425 nm after incubating NAF-1^44-67 with vesicles after 4 days, presumably as the system approaches equilibrium. The signal concurrently disappeared from the long wavelength side of the peak (Figure 12B; blue curve). Based on the sensitivity of Dansyl to local polarity (Figure 12A), the appearance of this new peak in 4 days reveals a population of NAF-1^44-67 molecules that have partitioned into the hydrophobic interior region of the bilayer as the dye-labeled N-terminus of the peptide entered the lipid tail region of the membrane. The transition from panel 1 to 2 in Figure 4 is consistent with these observations. Experiments (SI) demonstrated that monomeric Dansyl entered the membrane interior within 10 min. We therefore assume that the slow permeation rate of the Dansyl-peptide system is not due to the dye. These experiments demonstrate that the NAF-1^44-67 molecules that eventually enter the membrane under equilibrium conditions were those that were located immediately adjacent to the headgroup dipoles at the beginning, as intensity disappears from the long wavelength side of the spectrum over the course of 4 days and reappears in the new peak found at 425 nm.

The shifts observed in the fluorescence spectrum can be used to estimate a partition coefficient and a corresponding free energy change for the partitioning process. First, the areas under the curve of the spectra in hexane and aqueous HEPES buffer (Figure 12A) were used to determine the relative change in the emission cross section of Dansyl in hydrophobic and polar environments, respectively. Specifically, the area under the raw (unnormalized) hexane spectrum, A_hex, and the unnormalized spectrum in HEPES buffer, A_HEPES, were determined with numerical integration. Next, the area of the shoulder at 425 nm, A₄₂₅, and the remaining area under the peak, A₅₅₀, were determined from the raw fluorescence spectrum collected on day 4 (blue spectrum in Figure 12B). The resulting partition coefficient, K, and corresponding free energy change for partitioning, ΔG_par, can be determined from Eq. (4)

$$K=\frac{[tailregion]}{[headgroupregion]}=\frac{A_{425}}{A_{550}}\ast \frac{A_{HEPES}}{A_{hex}}$$ (4)

$$\Delta G_{par}=-RTln(K)$$

The partition coefficient is defined as the ratio of the concentration found in the tail region to the concentration found in the headgroup region. Since the main peak shifted to wavelengths longer than that observed in buffer when DOPC vesicles were first added and the shoulder at 425 nm was shifted to shorter wavelength compared to buffer, the area ratio of these two peaks provides this ratio of concentrations. However, the emission cross section of dyes like Dansyl can be much smaller in nonpolar environments than in aqueous ones. Because of these observations, the ratio of A₄₂₅/A₅₅₀ needs to be weighted by the areas found in Figure 12A to correct for position dependent changes to the emission cross section when the N-terminal helix enters the bilayer. Our analysis reveals that K = 2 and ΔG_par = −0.4 kcal/mol at 298 K. We compared this to the free energy change between points 1 and 2 along the MaxFlux Path from our simulations, which also revealed a free energy change of −0.4 kcal mol⁻¹ when the N-terminus initially moves from the headgroup region to the tail region. This agreement reveals that observations in our experiments capture only the first step of permeation. Only the transition from membrane-associated to membrane-inserted (transition from panels 1 to 2 in Figure 4) is being measured by our experiments and results in an observation of ΔG_par = −0.4 kcal mol⁻¹. In fact, the total change in free energy when the peptide moves from the bulk aqueous solution to the center of the tail region from the computational data was −8 kcal mol⁻¹. Clearly this overall favorable trajectory into the bilayer is initiated by a small but thermodynamically favorable (ΔG_par = −0.4 kcal mol⁻¹ < 0) set of interfacial interactions that allows the peptide to transition from a polar to a hydrophobic environment.

IV. Discussions

We summarize the permeation mechanism suggested by computations and spectroscopic measurements in cartoon form in Figure 13, which has six elementary steps. (i) A positively charged residue at the boundary between the hydrophobic and hydrophilic portions of the peptide (R14 in this case) interacts with negatively charged phosphates at the membrane surface, anchoring the peptide at the membrane/water interface and increasing the likelihood that the hydrophobic, helical portion of the peptide (shown as a blue cylinder in Figure 13) will sample configurations within the nonpolar membrane interior, lowering free energy. (ii) The hydrophobic helix of the N-terminus permeates first to the membrane, overcoming the significant energy barrier seen in positions 1 and 2 along the MaxFlux pathway on Figures 3 and 4. We suggest that this transition is observed experimentally. Positively charged residues immediately outside of this helix remain in close contact with the negatively charged phosphate groups, thus anchoring the peptide. (iii) The anchoring positively charged residue joins the helix at the membrane core, resulting in significant distortion of both the inner and outer leaflets of the bilayer. However, the positively charged residue further away from the hydrophobic helix (K24 in this case) is closer to interact with the membrane surface to serve as the new hook (seen in Figure 4, panel 4, as well as labeled as position 4 along the MaxFlux pathway of Figure 3). (iv) The remaining positively charged portion of the peptide fully enters the membrane interior. (v) The helix reverses its orientation to allow these positive charges to interact with the head group region of the opposite leaflet. (vi) The peptide exits the membrane by mirroring the entry mechanism.

Figure 13.

A sketch of the permeation mechanism of the peptide fragment of NAF-1^44-67. Panel (i) describes the initial attachment to the membrane surface. Panel (ii) shows the permeation of the hydrophobic helix into the membrane interior. In panel (iii) the entire peptide enters the hydrophobic core and the membrane is distorted significantly. In panel (iv) the peptide reorients itself at the hydrophobic part of the membrane in preparation to the membrane exit. In panel (v) the C terminal segment of the peptide exits to the aqueous solution. In step (vi) the entire peptide leaves the membrane. Steps (ii) to (v) correspond to a metastable state.

A surprising result of the above mechanism and the free energy landscape is the ease in which the C terminal part of the peptide crosses the membrane. The process in steps (iii) to (v) of the mechanism has no barrier. It is surprising since the C terminal segment contains four positively charged lysine residues passing through a hydrophobic membrane. We gained insight into this process from images of the translocation of the C terminal segment (Figure 14). We observed that the prior entry of the N terminal segment significantly distorts the structure of the bilayer. The distortions bring phosphate head groups and water molecules closer to the center of the membrane and assists the permeation of the C terminal segment. The “rule-of-the thumb” suggested is that the first to be inserted is the easy segment (the hydrophobic helix) with a small barrier. The inserted segment distorts the membrane in preparation for a more challenging transport event (the translocation of the charged C terminal segment).

Figure 14.

A trajectory snapshot illustrating the membrane perturbation caused by the initial insertion of the N-terminal helix of NAF-1^46-67. The yellow and orange lines trace the location of the phosphate groups in the upper and lower layers of the membrane, respectively. The figure shows large displacement of several phosphates and water molecules from their normal location that assist the permeation of the C terminal segment of the peptide.

Cell penetrating peptides were investigated extensively in the past because of their therapeutic potential.⁵⁵ A recent review discusses permeation mechanisms to cells.⁷ In biological cells the permeation mechanisms are divided into two classes, energy dependent (endocytosis) and energy independent (direct permeation). The mechanism we investigated here is of direct permeation. The review discussed three energy-independent mechanisms: (i) inverted micelle (ii) pore formation, and (iii) a carpet model. The proposed mechanism for NAF-1^46-67 is different from all three since it is focused on an isolated peptide. Below we compare our mechanism to that of TAT in more details.

Another CPP was investigated by atomically detailed simulations, the TAT peptide, which was the first to be discovered experimentally.¹⁸ A comparison between the present and previous study is therefore desired. A detailed molecular dynamics study suggested a mechanism for the permeation of this highly charged peptide.⁵⁶ The first step involved the binding of the peptide to the surface of the membrane, which is similar to the first step of permeation observed here (panel 1 in Figure 4). In the second step the arginine residues of TAT form a pore in the membrane that enables translocation.

In contrast to TAT, the peptide of the present manuscript is derived from a transmembrane protein. It includes a hydrophobic segment in addition to the charged C terminal end. As a result, it permeates with a different mechanism. In the second step the hydrophobic component of the peptide NAF-1^44-67 (a component which is missing in TAT) permeates to the hydrophobic core of the membrane and establishes an anchor for the rest of the peptide. The hydrophobic permeation is conducted with a relatively small interruption to the membrane structure. This gentle permeation relates to the source of the peptide, as the hydrophobic helix is a fragment of the transmembrane protein NAF-1 and may hint to the mechanism of incorporation of transmembrane proteins.

Our model describes a permeation of a single peptide. The concentration of the peptide is low (10 μM in the experiments described in this paper), and in the computational model we observed permeation with one peptide. Therefore, we do not expect mechanisms that require a large number of peptides, such as “carpeting”.⁷ In the last mechanism the surface of the vesicle is essentially covered by multiple peptides.

Other CPPs damage and even destroy plasma membranes, however, NAF-1^46-67 can cross a plasma membrane with a minimal perturbation, and then target specific compartments within a cell.²³ This novel design opens the way for the creation of new CPPs based on fragmentation of transmembrane proteins. A first step in quantifying the operation of a member of this class is taken in the present manuscript. There are still many questions open. For example, (i) What is the impact of the environmental conditions, such as pH and ionic strength? (ii) Does the peptide permeate using only a single unique mechanism, or are other mechanisms possible (e.g., does endocytosis play a role)? (iii) Can NAF-1^46-67 permeate collectively using several peptides instead of the only one peptide we considered here? We hope that a combination of atomically detailed simulation and chemical physics experiments on this system will continue to shed light on these important molecules.

V. Conclusions

Our findings demonstrate that NAF-1^44-67 passively crosses lipid bilayers by a combination of electrostatic and hydrophobic interfacial interactions that create a free energy barrier in the headgroup region. Specifically, early charge-charge interactions are followed by a hydrophobic insertion step that occur due to the amphiphilic nature of NAF-1^44-67. These findings point to a general mechanism by which amphiphilic CPPs that consist of two separate segments (hydrophobic and charged) pass through membranes while being trapped for considerable time at the hydrophobic core. Considering the diversity of phospholipid molecules in biology, (different charges, sizes of head groups, etc.) flexible design of targeting molecules is needed. NAF-1^44-67 with hydrophobic and charged segments has the potential to respond differently to alternate membrane targets.

We note that the use of Milestoning, a technology for enhanced sampling of kinetics, opened the way to quantitative atomistic simulations of these long-time permeation events that are important in biology and medicine.