Cell-Penetrating Peptides: Correlation between Peptide-Lipid Interaction and Penetration Efficiency

Cell-penetrating peptides are used in the delivery of peptides and biologics, with some cell-penetrating peptides found to be more efficient than others. The exact mechanism of how they interact with the cell membrane and penetrate it, however, remains unclear. This study attempts to investigate the difference in free energy profiles of three cell-penetrating peptides (TAT, CPP1 and CPP9) with a model lipid bilayer (DOPC) using molecular dynamics pulling simulations with umbrella sampling. Potential mean force (PMF) and free energy barrier between the peptides and DOPC are determined using WHAM analysis and MM-PBSA analysis, respectively. CPP9 is found to have the smallest PMF value, followed by CPP1 and TAT, consistent with the experimental data. YDEGE peptide, however, does not give the highest PMF value, although it is a non-cell-permeable peptide. YDEGE is also found to form water pores, alongside with TAT and CPP9, suggesting that it is difficult to distinguish true water pore formation from artefacts arising from pulling simulations. On the contrary, free energy analysis of the peptide-DOPC complex at the lipid-water interface with MM-PBSA provides results consistent with experimental data with CPP9 having the least interaction with DOPC and lowest free energy barrier, followed by CPP1, TAT and YDEGE. These findings suggest that peptide-lipid interaction at the lipid-water interface has a direct correlation with the penetration efficiency of peptides across the lipid bilayer.     

Enhanced hydrophobicity of fluorinated lipid bilayer: a molecular dynamics study

A molecular dynamics simulation of a partially fluorinated phospholipid bilayer has been carried out to understand the effects of fluorination of the hydrophobic chains on the structure and water permeability across the membrane. Fluorocarbon chains typically have an all-trans conformation, showing a highly ordered structure in the membrane core compared to ordinary hydrocarbon chains. The free energy profiles of water across the bilayers were successfully estimated by a revised cavity insertion Widom method. The fluorinated bilayer showed a higher free energy barrier than an ordinary nonfluorinated lipid bilayer by about 1.2 kcal/mol, suggesting a lower water permeability of the fluorinated bilayer membrane. A cavity distribution analysis elucidated the reduced free volume in the fluorinated membrane due to the neatly packed chains, which should account for the higher free energy barrier.     

Convergence of Free Energy Profile of Coumarin in Lipid Bilayer

Atomistic molecular dynamics (MD) simulations of druglike molecules embedded in lipid bilayers are of considerable interest as models for drug penetration and positioning in biological membranes. Here we analyze partitioning of coumarin in dioleoylphosphatidylcholine (DOPC) bilayer, based on both multiple, unbiased 3 μs MD simulations (total length) and free energy profiles along the bilayer normal calculated by biased MD simulations (～7 μs in total). The convergences in time of free energy profiles calculated by both umbrella sampling and z-constraint techniques are thoroughly analyzed. Two sets of starting structures are also considered, one from unbiased MD simulation and the other from "pulling" coumarin along the bilayer normal. The structures obtained by pulling simulation contain water defects on the lipid bilayer surface, while those acquired from unbiased simulation have no membrane defects. The free energy profiles converge more rapidly when starting frames from unbiased simulations are used. In addition, z-constraint simulation leads to more rapid convergence than umbrella sampling, due to quicker relaxation of membrane defects. Furthermore, we show that the choice of RESP, PRODRG, or Mulliken charges considerably affects the resulting free energy profile of our model drug along the bilayer normal. We recommend using z-constraint biased MD simulations based on starting geometries acquired from unbiased MD simulations for efficient calculation of convergent free energy profiles of druglike molecules along bilayer normals. The calculation of free energy profile should start with an unbiased simulation, though the polar molecules might need a slow pulling afterward. Results obtained with the recommended simulation protocol agree well with available experimental data for two coumarin derivatives.     

Free energy of a trans-membrane pore calculated from atomistic molecular dynamics simulations

Atomistic molecular dynamics simulations of a lipid bilayer were performed to calculate the free energy of a trans-membrane pore as a function of its radius. The free energy was calculated as a function of a reaction coordinate using a potential of mean constraint force. The pore radius was then calculated from the reaction coordinate using Monte Carlo particle insertions. The main characteristics of the free energy that comes out of the simulations are a quadratic shape for a radius less than about 0.3 nm, a linear shape for larger radii than this, and a rather abrupt change without local minima or maxima between the two regions. In the outer region, a line tension can be calculated, which is consistent with the experimentally measured values. Further, this line tension can be rationalized and understood in terms of the energetic cost for deforming a part of the lipid bilayer into a hydrophilic pore. The region with small radii can be described and understood in terms of statistical mechanics of density fluctuations. In the region of crossover between a quadratic and linear free energy there was some hysteresis associated with filling and evacuation of the pore with water. The metastable prepore state hypothesized to interpret the experiments was not observed in this region.     

Modelling the behavior of 5-aminolevulinic acid and its alkyl esters in a lipid bilayer

5-Aminolevulinic acid (5ALA) and ester derivates thereof are used as prodrugs in photodynamic therapy (PDT). The behavior of 5ALA and three esters of 5ALA in a DPPC lipid bilayer is investigated. In particular, the methyl ester displays a very different free energy profile, where the highest barrier is located in the region with highest lipid density, while the others have their peak in the middle of the membrane, and also displays a considerably lower permeability coefficient than neutral 5ALA and the ethyl ester. The zwitterion of 5ALA has the highest permeability constant, but a significant free energy minimum in the polar head-group region renders an accumulation in this region.     

Steered molecular dynamics studies of the potential of mean force of a Na+ or K+ ion in a cyclic peptide nanotube

Potential of mean force (PMF) profiles of a single Na+ or K+ ion passing through a cyclic peptide nanotube, cyclo[-(D-Ala-Glu-D-Ala-Gln)2-], in water are calculated to provide insight into ion transport and to understand the conductance difference between these two ions. The PMF profiles are obtained by performing steered molecular dynamics (SMD) simulations that are based on the Jarzynski equality. The computed PMF profiles for both ions show barriers of around 2.4 kcal/mol at the channel entrances and exits and energy wells in the middle of the tube. The energy barriers, so-called dielectric energy barriers, arise due to the desolvation of water molecules when ions move across the nanotube, and the energy wells appear as a result of attractive interactions between the cations and negatively charged carbonyl oxygens on the backbone of the tube. We find more and deeper energy wells in the PMF profile for Na+ than for K+, which suggests that Na+ ions have a longer residence time inside the nanotube and that permeation of Na+ ions is reduced compared to K+ ions. Calculations of the radial distribution functions (RDF) between the ions and oxygens in the water molecules and in carbonyl groups on the tube and an investigation of the orientations of the carbonyl groups show that, in contrast with the dynamic carbonyl groups observed in the selectivity filter of the KcsA ion channel, the carbonyl groups in the cyclic peptide nanotube are relatively rigid, with only slight reorientation of the carbonyl groups as the cations pass through. The rigidity of the carbonyl groups in the cyclic peptide nanotube can be attributed to their role in hydrogen bonding, which is responsible for the tube structure. Comparison of the PMF profiles with the electrostatic energy profiles calculated from the Poisson-Boltzmann (PB) equation, a dielectric continuum model, reveals that the dielectric continuum model breaks down in the confined region within the tube that governs ion transport.     

Theoretical study of mechanism of cycloaddition reaction between dichloro‐germylene carbene (Cl2GeC:) and aldehyde

The mechanism of the cycloaddition reaction between singlet dichloro‐germylene carbene and aldehyde has been investigated with MP2/6‐31G* method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. The energies of the different conformations are calculated by zero‐point energy and CCSD (T)//MP2/6‐31G* method. From the potential energy profile, it can be predicted that the reaction has two competitive dominant reaction pathways. The channel (A) consists of four steps: (1) the two reactants (R1, R2) first form an intermediate INT2 through a barrier‐free exothermic reaction of 142.4 kJ/mol; (2) INT2 then isomerizes to a four‐membered ring compound P2 via a transition state TS2 with energy barrier of 8.4 kJ/mol; (3) P2 further reacts with aldehyde (R2) to form an intermediate INT3, which is also a barrier‐free exothermic reaction of 9.2 kJ/mol; (4) INT3 isomerizes to a germanic bis‐heterocyclic product P3 via a transition state TS3 with energy barrier of 4.5 kJ/mol. The process of channel (B) is as follows: (1) the two reactants (R1, R2) first form an intermediate INT4 through a barrier‐free exothermic reaction of 251.5 kJ/mol; (2) INT4 further reacts with aldehyde (R2) to form an intermediate INT5, which is also a barrier‐free exothermic reaction of 173.5 kJ/mol; (3) INT5 then isomerizes to a germanic bis‐heterocyclic product P5 via a transition state TS5 with an energy barrier of 69.4 kJ/mol. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Theoretical study of mechanism of forming a silapolycyclic compound between methylenesilylene and acetone

The mechanism of the cycloaddition reaction of forming a silapolycyclic compound between singlet methylenesilylene and acetone has been investigated with MP2/6‐31G* method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. The energies of the different conformations are calculated by CCSD(T)//MP2/6‐31G* method. From the potential energy profile, we predict that the cycloaddition reaction of forming a silapolycyclic compound between singlet methylenesilylene and acetone has two competitive dominant reaction pathways. First dominant reaction pathway consists of four steps: (I) the two reactants (R1, R2) first form an intermediate (INT1) through a barrier‐free exothermic reaction of 46.2 kJ/mol; (II) intermediate (INT1) then isomerizes to a planar four‐membered ring product (P3) via transition state (TS3) with an energy barrier of 47.1 kJ/mol; (III) planar four‐membered ring product (P3) further reacts with acetone (R2) to form an intermediate (INT4), which is also a barrier‐free exothermic reaction of 40.0 kJ/mol; (IV) intermediate (INT4) isomerizes to a silapolycyclic compound (P4) via transition state (TS4) with an energy barrier of 57.0 kJ/mol. Second dominant reaction pathway consists of three steps: (I) the two reactants (R1, R2) first form a four‐membered ring intermediate (INT2) through a barrier‐free exothermic reaction of 0.5 kJ/mol; (II) INT2 further reacts with acetone (R2) to form an intermediate (INT5), which is also a barrier‐free exothermic reaction of 45.4 kJ/mol; (III) intermediate (INT5) isomerizes to a silapolycyclic compound (P5) via transition state (TS5) with an energy barrier of 49.3 kJ/mol. P4 and P5 are isomeric compounds. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Ab initio Study of Mechanism of Forming Germanic Hetero-Polycyclic Compound between Germylene Carbene (H2Ge=C: ) and Formaldehyde

The mechanism of the cycloaddition reaction of forming germanic hetero‐polycyclic compound between singlet germylene carbene and formaldehyde has been investigated with MP2/6‐31G* method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. The energies of the different conformations are calculated by CCSD (T)//MP2/6‐31G* method. From the potential energy profile, we predict that the cycloaddition reaction of forming germanic hetero‐polycyclic compound between singlet germylene carbene and formaldehyde has two competitive dominant reaction pathways. First dominant reaction pathway consists of four steps: (1) the two reactants (R1, R2) first form an intermediate (INT1) through a barrier‐free exothermic reaction of 117.5 kJ/mol; (2) intermediate (INT1) then isomerizes to a four‐membered ring compound (P2) via a transition state (TS2) with an energy barrier of 25.4 kJ/mol; (3) four‐membered ring compound (P2) further reacts with formaldehyde (R2) to form an intermediate (INT3), which is also a barrier‐free exothermic reaction of 19.6 kJ/mol; (4) intermediate (INT3) isomerizes to a germanic bis‐heterocyclic product (P3) via a transition state (TS3) with an energy barrier of 5.8 kJ/mol. Second dominant reaction pathway is as follows: (1) the two reactants (R1, R2) first form an intermediate (INT4) through a barrier‐free exothermic reaction of 197.3 kJ/mol; (2) intermediate (INT4) further reacts with formaldehyde (R2) to form an intermediate (INT5), which is also a barrier‐free exothermic reaction of 141.3 kJ/mol; (3) intermediate (INT5) then isomerizes to a germanic bis‐heterocyclic product (P5) via a transition state (TS5) with an energy barrier of 36.7 kJ/mol.     

Stretching effects on the permeability of water molecules across a lipid bilayer

Using a coarse grained molecular dynamics model of a solvent-surfactant system, we study the effects of stretching on the permeability of water across a lipid bilayer. The density profile, free energy profile, diffusion profile, and tail ordering parameter were computed for a set of stretched membranes maintained at constant area. We computed the water permeability across each membrane using the inhomogeneous solubility-diffusion model first proposed by Marrink and Berendsen [J. Phys. Chem. 98, 4155 (1994)]. We find that even though the resistance to permeation profile shows a great deal of qualitative change as the membranes are stretched, the overall permeability remains nearly constant within the relevant range of stretching. This is explained by the fact that the main barrier to permeation, located in the densest section of the tails, is insensitive to increased area per lipid, as a result of competing effects. Expansion leads to thinning and a higher density in the tail region, the latter leading to an increase in the free energy barrier. However, this is compensated by the reduction in the transverse distance to cross and a larger diffusion coefficient due to increased disordering in the chains.     

Mechanism of unassisted ion transport across membrane bilayers

To establish how charged species move from water to the nonpolar membrane interior and to determine the energetic and structural effects accompanying this process, we performed molecular dynamics simulations of the transport of Na+ and Cl- across a lipid bilayer located between two water lamellae. The total length of molecular dynamics trajectories generated for each ion was 10 ns. Our simulations demonstrate that permeation of ions into the membrane is accompanied by the formation of deep, asymmetric thinning defects in the bilayer, whereby polar lipid head groups and water penetrate the nonpolar membrane interior. Once the ion crosses the midplane of the bilayer the deformation "switches sides"; the initial defect slowly relaxes, and a defect forms in the outgoing side of the bilayer. As a result, the ion remains well solvated during the process; the total number of oxygen atoms from water and lipid head groups in the first solvation shell remains constant. A similar membrane deformation is formed when the ion is instantaneously inserted into the interior of the bilayer. The formation of defects considerably lowers the free energy barrier to transfer of the ion across the bilayer and, consequently, increases the permeabilities of the membrane to ions, compared to the rigid, planar structure, by approximately 14 orders of magnitude. Our results have implications for drug delivery using liposomes and peptide insertion into membranes.     

Entropy and dynamics of water in hydration layers of a bilayer

We compute the entropy and transport properties of water in the hydration layer of dipalmitoylphosphatidylcholine bilayer by using a recently developed theoretical scheme [two-phase thermodynamic model, termed as 2PT method; S.-T. Lin et al., J. Chem. Phys. 119, 11792 (2003)] based on the translational and rotational velocity autocorrelation functions and their power spectra. The weights of translational and rotational power spectra shift from higher to lower frequency as one goes from the bilayer interface to the bulk. Water molecules near the bilayer head groups have substantially lower entropy (48.36 J/mol/K) than water molecules in the intermediate region (51.36 J/mol/K), which have again lower entropy than the molecules (60.52 J/mol/K) in bulk. Thus, the entropic contribution to the free energy change (TΔS) of transferring an interface water molecule to the bulk is 3.65 kJ/mol and of transferring intermediate water to the bulk is 2.75 kJ/mol at 300 K, which is to be compared with 6.03 kJ/mol for melting of ice at 273 K. The translational diffusion of water in the vicinity of the head groups is found to be in a subdiffusive regime and the rotational diffusion constant increases going away from the interface. This behavior is supported by the slower reorientational relaxation of the dipole vector and OH bond vector of interfacial water. The ratio of reorientational relaxation time for Legendre polynomials of order 1 and 2 is approximately 2 for interface, intermediate, and bulk water, indicating the presence of jump dynamics in these water molecules.     

Calculation of the water-cyclohexane transfer free energies of neutral amino acid side-chain analogs using the OPLS all-atom force field

We calculated the free energy of solvation of the neutral analogs of 18 amino acid side-chains (not including glycine and proline) using the OPLS all-atom force field in TIP4P water, SPC water, and cyclohexane by molecular dynamics simulation and thermodynamic integration. The average unsigned errors in the free energies of solvation in TIP4P, SPC, and cyclohexane are 4.4, 4.9, and 2.1 kJ/mol respectively. Most of the calculated hydration free energies are not favorable enough compared to experiment. The largest errors are found for tryptophan, histidine, glutamic acid, and glutamine. The average unsigned errors in the free energy of transfer from TIP4P to cyclohexane and from SPC to cyclohexane are 4.0 and 4.1 kJ/mol, respectively. The largest errors, of more than 7.5 kJ/mol, are found for histidine, glutamine, and glutamatic acid.     

Comparative molecular dynamics study of ether- and ester-linked phospholipid bilayers

The lipid membranes found in archaea have high bilayer stability and low permeability. The molecular structure of their constituent lipids is characterized by ether-linked, branched hydrophobic chains, whereas the conventional lipids obtained from eukaryotic or eubacterial sources have ester linked straight chains. In order to elucidate the influence of the ether linkage, instead of an ester one, on the physical properties of the lipid bilayers, we have carried out comparative 10 ns molecular dynamics simulations of diphytanyl phosphatidylcholine (ether-DPhPC) and diphytanoyl phosphatidylcholine (ester-DPhPC) bilayers in water, respectively. We analyze bilayer structures, hydration of the lipids, membrane dipole potentials, and free energy profiles of water and oxygen across the bilayers. We observe that the membrane dipole potential for the ether-DPhPC bilayer, which arises mainly from the ether linkage, is about half of that of the ester-DPhPC. The calculated free energy barrier for a water molecule in the ether-DPhPC bilayer system is slightly higher than that in the ester-DPhPC counterpart, which is in accord with experimental data.     

Thermodynamic study of benzocaine insertion into different lipid bilayers

Despite the general consensus concerning the role played by sodium channels in the molecular mechanism of local anesthetics, the potency of anaesthetic drugs also seems to be related with their solubility in lipid bilayers. In this respect, this work represents a thermodynamic study of benzocaine insertion into lipid bilayers of different compositions by means of molecular dynamics simulation. Thus, the free energy profiles associated with benzocaine insertion into symmetric lipid bilayers composed of different proportions of dipalmitoylphosphatidylcholine and dipalmitoylphosphatidylserine were studied. From the simulation results, a maximum in the free energy (ΔG) profile was measured in the region of the lipid/solution interface. This free energy barrier appears to be very much dependent on the lipid composition of the membrane. On the other hand, the minimum free energy (ΔG) within the bilayer remained almost independent of the lipid composition of the bilayer. By repeating the study at different temperatures, it was seen how the spontaneity of benzocaine insertion into the lipid bilayer is due to an increase in the entropy associated with the process.     

Structure and energetics of water-silanol binding on the surface of silicalite-1: quantum chemical calculations

Quantum mechanical calculations have been carried out to investigate the structural properties and the interaction between water molecules and silanol groups on the surface of silicalite-1. The (010) surface, which is perpendicular to the straight channel, has been selected and represented by three fragments taken from different parts of the surface. Calculations have been performed using different levels of accuracy: HF/6-31G(d,p), B3LYP/6-31G(d,p), HF/6-31++G(d,p), and B3LYP/6-31++G(d,p). The basis set superposition error has been taken into account. The geometry of the silanol groups and that of the water molecules have been fully optimized. The results show that the most stable conformation takes place when a water molecule forms two hydrogen bonds with two silanols, with only one silanol lying on the opening of the pore of the straight channel. The corresponding binding energy is -48.82 kJ/mol. These areas are supposed to be the first binding sites which have to be covered when the water molecule approaches the surface. When the water loading increases, the next favorable silanols are those of the opening of the pore in which the four possible complex conformations yield a binding energy between -25.62 and -37.41 kJ/mol. It was also found that the calculated O-H bond length of the silanol in the free form was slightly shorter than that in the complex. In terms of the stretching frequency, the complexation leads to a red shift of the O-H stretching of the silanol group.     

A molecular dynamics study of the lateral free energy profile of a pair of cholesterol molecules as a function of their distance in phospholipid bilayers

Free energy profile of a pair of cholesterol molecules in a leaflet of 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPC) bilayers in the liquid-crystalline phase has been calculated as a function of their lateral distance using a combination of NPT-constant atomistic molecular dynamics calculations (P = 1 atm and T = 310.15 K) and the thermodynamic integration method. The calculated free energy clearly shows that the two cholesterol molecules form a dimer separated by a distance of 1.0-1.5 nm in POPC bilayers. Well depth of the free energy profile is about 3.5 kJ/mol, which is comparable to the thermal energy k(B)T at 310.15 K. This indicates that the aggregation of cholesterol molecules in the bilayers depends on the temperature as well as the concentration of the system. The free energy function obtained here may be used as a reference when coarse grained potential model is investigated for this two-component system. Local structure of POPC molecules around two cholesterol molecules has also been investigated.     

Metastability of MCM-41 and Al-MCM-41

The apparent stability of MCM-41 and Al-MCM-41 in water was appraised in a series of solubility experiments. MCM-41 is a siliceous, mesoporous material of hexagonal symmetry and exceptionally high surface area first synthesized in 1992. The dissolution experiments were carried out at several solid/water ratios: 1/200, 1/100, and 1/75. Results indicated that MCM-41 and Al-MCM-41 are more soluble than amorphous silica at ambient temperatures. Using standard thermodynamic data, a minimum Gibbs free energy of formation of -847.9 kJ/mol for MCM-41 was calculated compared to -848.85 kJ/mol for amorphous silica and -856.3 kJ/mol for quartz. X-ray diffraction (XRD) analyses of recovered solids indicated a progressive loss of crystallinity in MCM-41 and Al-MCM-41 over the 79 day dissolution experiment. BET nitrogen surface area analyses of recovered solids revealed no appreciable change in the surface area of either material after 79 days of reaction in water. Field emission scanning electron microscope (SEM) images taken of the 79 day MCM-41 sample showed some degradation of the initial structure-fine, worm-like particles.     

Efficient free energy calculation of water across lipid membranes

An efficient free energy (FE) calculation of a water molecule to go across lipid membranes is presented. Both overlapping distribution and cavity insertion Widom methods are complementarily used. The former is useful for a dense region where water molecules are found, i.e., from the interfacial to bulk water region, while the latter works well in the low density region, i.e., the hydrocarbon region. Since both methods evaluate the excess chemical potential of water, the obtained FE profile is free from the fitting problem usually arisen when a FE difference method is used. A diphytanyl phosphatidylcholine bilayer is used for our test calculations. An excellent and fast convergence of the chemical potential is obtained when each method is applied for the appropriate region. The estimated FE barrier using the Ewald method for the electrostatic interaction is approximately 7.2 kcal/mol, which is higher than that using the interaction cutoff of 20 A by about 0.9 kcal/mol.     

Multinuclear NMR studies of single lipid bilayers supported in cylindrical aluminum oxide nanopores

Lipid bilayers were deposited inside the 0.2 microm pores of anodic aluminum oxide (AAO) filters by extrusion of multilamellar liposomes and their properties studied by 2H, 31P, and 1H solid-state NMR. Only the first bilayer adhered strongly to the inner surface of the pores. Additional layers were washed out easily by a flow of water as demonstrated by 1H magic angle spinning NMR experiments with addition of Pr3+ ions to shift accessible lipid headgroup resonances. A 13 mm diameter Anopore filter of 60 microm thickness oriented approximately 2.5 x 10(-7) mol of lipid as a single bilayer, corresponding to a total membrane area of about 500 cm2. The 2H NMR spectra of chain deuterated POPC are consistent with adsorption of wavy, tubular bilayers to the inner pore surface. By NMR diffusion experiments, we determined the average length of those lipid tubules to be approximately 0.4 microm. There is evidence for a thick water layer between lipid tubules and the pore surface. The ends of tubules are well sealed against the pore such that Pr3+ ions cannot penetrate into the water underneath the bilayers. We successfully trapped poly(ethylene glycol) (PEG) with a molecular weight of 8000 in this water layer. From the quantity of trapped PEG, we calculated an average water layer thickness of 3 nm. Lipid order parameters and motional properties are unperturbed by the solid support, in agreement with existence of a water layer. Such unperturbed, solid supported membranes are ideal for incorporation of membrane-spanning proteins with large intra- and extracellular domains. The experiments suggest the promise of such porous filters as membrane support in biosensors.