Assessing the extent of the structural and dynamic modulation of membrane lipids due to pore forming toxins: insights from molecular dynamics simulations.

Infections caused by many virulent bacterial strains are triggered by the release of pore forming toxins (PFTs), which form oligomeric transmembrane pore complexes on the target plasma membrane. The spatial extent of the perturbation to the surrounding lipids during pore formation is relatively unexplored. Using all-atom molecular dynamics simulations, we investigate the changes in the structure and dynamics of lipids in a 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) lipid bilayer in the presence of contrasting PFTs. Cytolysin A (ClyA), an α toxin with its inserted wedge shaped bundle of inserted α helices, induces significant asymmetry across the membrane leaflets in comparison with α hemolysin (AHL), a ß toxin. Despite the differences in hydrophobic mismatch and uniquely different topologies of the two oligomers, perturbations to lipid order as reflected in the tilt angle and order parameters and membrane thinning are short ranged, lying within ∼2.5 nm from the periphery of either pore complex, and commensurate with distances typically associated with van der Waals forces. In contrast, the spatial extent of perturbations to the lipid dynamics extends outward to at least 4 nm for both proteins, and the continuous survival probabilities reveal the presence of a tightly bound shell of lipids in this region. Displacement probability distributions show long tails and the distinctly non-Gaussian features reflect the induced dynamic heterogeneity. A detailed profiling of the protein-lipid contacts with tyrosine, tryptophan, lysine and arginine residues shows increased non-polar contacts in the cytoplasmic leaflet for both PFTs, with a higher number of atomic contacts in the case of AHL in the extracellular leaflet due to the mushroom-like topology of the pore complex. The short ranged nature of the perturbations observed in this simple one component membrane suggests inherent plasticity of membrane lipids enabling the recovery of the structure and membrane fluidity even in the presence of these large oligomeric transmembrane protein assemblies. This observation has implications in membrane repair processes such as budding or vesicle fusion events used to mitigate PFT virulence, where the underlying lipid dynamics and fluidity in the vicinity of the pore complex are expected to play an important role.

Influence of surface commensurability on the structure and relaxation dynamics of a confined monatomic fluid.

Molecular dynamics simulations are carried out for a single component, monatomic Lennard-Jones fluid confined between two mica surfaces to investigate the structure and relaxation dynamics of the confined fluid as a function of surface separation. Due to the underlying symmetry of the potassium ions on the mica surface, the contact layers prefer to adopt an incommensurate square or rhombic symmetry. The inner layers adopt a symmetry varying between rhombic, triangular, and square, depending on the density and surface separation. When the surface separation is an integral multiple of the particle diameter, distinct layering is observed, whereas jammed layers are formed at intermediate surface separations. This leads to the formation of both commensurate and incommensurate layering with varying intralayer symmetry. The self-intermediate scattering function exhibits a gamut of rich dynamics ranging from a distinct two-step relaxation indicative of glassy dynamics to slow relaxation processes where the correlations do not relax to zero over a microsecond for specific surface separations. An extended ß relaxation is observed for both commensurate and incommensurate layering. Stretched exponential fits are used to obtain the relaxation times for the late α-relaxation regime of the self-intermediate scattering function. In some cases, we also observed dynamic and structural heterogeneities within individual layers. Although a single-component Lennard-Jones fluid does not exhibit a glass transition in the bulk, this study reveals that such a fluid can display, without supercooling, complex relaxation dynamics with signatures of a fluid approaching a glass transition upon confinement at constant temperature.

Dendrimer Interactions with Lipid Bilayer: Comparison of Force Field and Effect of Implicit vs Explicit Solvation.

The understanding of dendrimer interactions with cell membranes has great importance in drug/gene delivery based therapeutics. Although molecular simulations have been used to understand the nature of dendrimer interactions with lipid membranes, its dependency on available force field parameters is poorly understood. In this study, we have carried out fully atomistic molecular dynamics (MD) simulations of a protonated G3 poly(amido amine) (PAMAM) dendrimer-dimyristoylphosphatidylcholine (DMPC) lipid bilayer complex using three different force fields (FFs) namely, CHARMM, GAFF, and GROMOS in the presence of explicit water to understand the structure of the lipid-dendrimer complex and nature of their interaction. CHARMM and GAFF dendrimers initially in contact with the lipid head groups were found to move away from the lipid bilayer during the course of simulation; however, the dendrimer remained strongly bound to the lipid head groups with the GROMOS FF. Potential of the mean force (PMF) computations of the dendrimer along the bilayer normal showed a repulsive barrier (∼20 kcal/mol) between dendrimer and lipid bilayer in the case of CHARMM and GAFF force fields. In contrast, an attractive interaction (∼40 kcal/mol) is obtained with the GROMOS force field, consistent with experimental observations of membrane binding observed with lower generation G3 PAMAM dendrimers. This difference with the GROMOS dendrimer is attributed to the strong dendrimer-lipid interaction and lowered surface hydration of the dendrimer. Assessing the role of solvent, we find that the CHARMM and GAFF dendrimers strongly bind to the lipid bilayer with an implicit solvent (Generalized Born) model, whereas binding is not observed with explicit water (TIP3P). The opposing nature of dendrimer-membrane interactions in the presence of explicit and implicit solvents demonstrates that hydration effects play an important role in modulating the dendrimer-lipid interaction warranting a case for refinement of the existing dendrimer/lipid force fields.

Complex dynamics at the nanoscale in simple biomembranes.

Nature is known to engineer complex compositional and dynamical platforms in biological membranes. Understanding this complex landscape requires techniques to simultaneously detect membrane re-organization and dynamics at the nanoscale. Using super-resolution stimulated emission depletion (STED) microscopy coupled with fluorescence correlation spectroscopy (FCS), we reveal direct experimental evidence of dynamic heterogeneity at the nanoscale in binary phospholipid-cholesterol bilayers. Domain formation on the length scale of ~200-600 nm due to local cholesterol compositional heterogeneity is found to be more prominent at high cholesterol content giving rise to distinct intra-domain lipid dynamics. STED-FCS reveals unique dynamical crossover phenomena at length scales of ~100-150 nm within each of these macroscopic regions. The extent of dynamic heterogeneity due to intra-domain hindered lipid diffusion as reflected from the crossover length scale, is driven by cholesterol packing and organization, uniquely influenced by phospholipid type. These results on simple binary model bilayer systems provide novel insights into pathways leading to the emergence of complex nanodomain substructures with implications for a wide variety of membrane mediated cellular events.

Nanoscale dynamics of phospholipids reveals an optimal assembly mechanism of pore-forming proteins in bilayer membranes.

Cell membranes are believed to be highly complex dynamical systems having compositional heterogeneity involving several types of lipids and proteins as the major constituents. This dynamical and compositional heterogeneity is suggested to be critical to the maintenance of active functionality and response to chemical, mechanical, electrical and thermal stresses. However, delineating the various factors responsible for the spatio-temporal response of actual cell membranes to stresses can be quite challenging. In this work we show how biomimetic phospholipid bilayer membranes with variable lipid fluidity determine the optimal assembly mechanism of the pore-forming protein, listeriolysin O (LLO), belonging to the class of cholesterol dependent cytolysins (CDCs). By combining atomic force microscopy (AFM) and super-resolution stimulated emission depletion (STED) microscopy imaging on model membranes, we show that pores formed by LLO in supported lipid bilayers can have variable conformation and morphology depending on the fluidity of the bilayer. At a fixed cholesterol concentration, pores formed in 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) membranes were larger, flexible and more prone to coalescence when compared with the smaller and more compact pores formed in the lower fluidity 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) membranes. In contrast, 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) membranes did not show any evidence of pore formation. Fluorescence correlation spectroscopy (FCS) in STED mode revealed the appearance of a length scale, ξ, below which lipid dynamics, under the influence of LLO protein binding and assembly, becomes anomalous. Interestingly, the magnitude of ξ is found to correlate with both lipid fluidity and pore dimensions (and flexibility) in DOPC and POPC bilayers. However this length scale dependent crossover, signalling the onset of anomalous diffusion, was not observed in DMPC bilayers. Our study highlights the subtle interplay of lipid membrane mediated protein assembly and lipid fluidity in determining proteo-lipidic complexes formed in biomembranes and the significant insight that STED microscopy provides in unraveling critical aspects of nanoscale membrane biophysics.

Super-resolution Stimulated Emission Depletion-Fluorescence Correlation Spectroscopy Reveals Nanoscale Membrane Reorganization Induced by Pore-Forming Proteins.

Membrane-protein interactions play a central role in membrane mediated cellular processes ranging from signaling, budding, and fusion, to transport across the cell membrane. Of particular significance is the process of efficient protein olgomerization and transmembrane pore formation on the membrane surface; the primary virulent pathway for the action of antimicrobial peptides and pore forming toxins (PFTs). The suggested nanoscopic length scales and dynamic nature of such membrane lipid-protein interactions makes their detection extremely challenging. Using a combination of super-resolution stimulated emission depletion nanoscopy with fluorescence correlation spectroscopy (STED-FCS) we unravel the emergence of nanoscale lateral heterogeneity in supported bilayer membranes made up of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) and cholesterol upon interaction with the PFT, listeriolysin O (LLO). A distinct length scale-dependent dynamical crossover (<200 nm) from a Brownian diffusive regime is observed at 33 and 50% cholesterol compositions, indicating the partitioning of lipids into domains with variable cholesterol content. At 25% cholesterol content, this dyamical crossover is observed only in bilayers incubated with LLO providing evidence for the existence of sub ∼100 nm dynamical lipid nanodomains bound to LLO pore assemblies. By introducing asymmetry in cholesterol composition across the bilayer leaflets we infer that this domain formation is driven largely due to active cholesterol sequestration and transient trapping of lipids to the membrane bound motifs present in the toxins, en route to LLO oligomerization and subsequent pore formation. Bilayers prepared with labeled lipids present in either the proximal or distal leaflet allow us to track the dynamical perturbation in a leaflet-dependent manner upon LLO incubation. From the differences in the extent and intensity of the dynamical crossover as observed with STED-FCS, these experiments reveal that the affinity for cholesterol in the membrane binding motifs of the LLO subdomains induce cholesterol and lipid reorganization to a greater extent in the distal (upper) leaflet when compared with the proximal (lower) leaflet. The observed length scale-dependent membrane reorganization that occurs due to invasion by LLO could be generalized to other cholesterol-dependent cytolysins and emphasizes the significant advantage of using super-resolution STED nanoscopy to unravel complex lipid-protein interactions in membrane and cellular biophysics.

pH controlled gating of toxic protein pores by dendrimers.

Designing effective nanoscale blockers for membrane inserted pores formed by pore forming toxins, which are expressed by several virulent bacterial strains, on a target cell membrane is a challenging and active area of research. Here we demonstrate that PAMAM dendrimers can act as effective pH controlled gating devices once the pore has been formed. We have used fully atomistic molecular dynamics (MD) simulations to characterize the cytolysin A (ClyA) protein pores modified with fifth generation (G5) PAMAM dendrimers. Our results show that the PAMAM dendrimer, in either its protonated (P) or non-protonated (NP) states can spontaneously enter the protein lumen. Protonated dendrimers interact strongly with the negatively charged protein pore lumen. As a consequence, P dendrimers assume a more expanded configuration efficiently blocking the pore when compared with the more compact configuration adopted by the neutral NP dendrimers creating a greater void space for the passage of water and ions. To quantify the effective blockage of the protein pore, we have calculated the pore conductance as well as the residence times by applying a weak force on the ions/water. Ionic currents are reduced by 91% for the P dendrimers and 31% for the NP dendrimers. The preferential binding of Cl(-) counter ions to the P dendrimer creates a zone of high Cl(-) concentration in the vicinity of the internalized dendrimer and a high concentration of K(+) ions in the transmembrane region of the pore lumen. In addition to steric effects, this induced charge segregation for the P dendrimer effectively blocks ionic transport through the pore. Our investigation shows that the bio-compatible PAMAM dendrimers can potentially be used to develop therapeutic protocols based on the pH sensitive gating of pores formed by pore forming toxins to mitigate bacterial infections.

Structure and Dynamics of Octamethylcyclotetrasiloxane Confined between Mica Surfaces.

Using a molecular model for octamethylcyclotetrasiloxane (OMCTS), molecular dynamics simulations are carried out to probe the phase state of OMCTS confined between two mica surfaces in equilibrium with a reservoir. Molecular dynamics simulations are carried out for elevations ranging from 5 to 35 K above the melting point for the OMCTS model used in this study. The Helmholtz free energy is computed for a specific confinement using the two-phase thermodynamic (2PT) method. Analysis of the in-plane pair correlation functions did not reveal signatures of freezing even under an extreme confinement of two layers. OMCTS is found to orient with a wide distribution of orientations with respect to the mica surface, with a distinct preference for the surface parallel configuration in the contact layers. The self-intermediate scattering function is found to decay with increasing relaxation times as the surface separation is decreased, and the two-step relaxation in the scattering function, a signature of glassy dynamics, distinctly evolves as the temperature is lowered. However, even at 5 K above the melting point, we did not observe a freezing transition and the self-intermediate scattering functions relax within 200 ps for the seven-layered confined system. The self-diffusivity and relaxation times obtained from the Kohlrausch-Williams-Watts stretched exponential fits to the late α-relaxation exhibit power law scalings with the packing fraction as predicted by mode coupling theory. A distinct discontinuity in the Helmholtz free energy, potential energy, and a sharp change in the local bond order parameter, Q4, was observed at 230 K for a five-layered system upon cooling, indicative of a first-order transition. A freezing point depression of about 30 K was observed for this five-layered confined system, and at the lower temperatures, contact layers were found to be disordered with long-range order present only in the inner layers. These dynamical signatures indicate that confined OMCTS undergoes a slowdown akin to a fluid approaching a glass transition upon increasing confinement, and freezing under confinement would require substantial subcooling below the bulk melting point of OMCTS.

Estimation of activation energy for electroporation and pore growth rate in liquid crystalline and gel phases of lipid bilayers using molecular dynamics simulations.

Molecular dynamics simulations of electroporation in POPC and DPPC lipid bilayers have been carried out at different temperatures ranging from 230 K to 350 K for varying electric fields. The dynamics of pore formation, including threshold field, pore initiation time, pore growth rate, and pore closure rate after the field is switched off, was studied in both the gel and liquid crystalline (Lα) phases of the bilayers. Using an Arrhenius model of pore initiation kinetics, the activation energy for pore opening was estimated to be 25.6 kJ mol(-1) and 32.6 kJ mol(-1) in the Lα phase of POPC and DPPC lipids respectively at a field strength of 0.32 V nm(-1). The activation energy decreases to 24.2 kJ mol(-1) and 23.7 kJ mol(-1) respectively at a higher field strength of 1.1 V nm(-1). At temperatures below the melting point, the activation energy in the gel phase of POPC and DPPC increases to 28.8 kJ mol(-1) and 34.4 kJ mol(-1) respectively at the same field of 1.1 V nm(-1). The pore closing time was found to be higher in the gel than in the Lα phase. The pore growth rate increases linearly with temperature and quadratically with field, consistent with viscosity limited growth models.

Molecular Dynamics Study of the Structure, Flexibility, and Hydrophilicity of PETIM Dendrimers: A Comparison with PAMAM Dendrimers.

A new class of dendrimers, the poly(propyl ether imine) (PETIM) dendrimer, has been shown to be a novel hyperbranched polymer having potential applications as a drug delivery vehicle. Structure and dynamics of the amine terminated PETIM dendrimer and their changes with respect to the dendrimer generation are poorly understood. Since most drugs are hydrophobic in nature, the extent of hydrophobicity of the dendrimer core is related to its drug encapsulation and retention efficacy. In this study, we carry out fully atomistic molecular dynamics (MD) simulations to characterize the structure of PETIM (G2-G6) dendrimers in salt solution as a function of dendrimer generation at different protonation levels. Structural properties such as radius of gyration (Rg), radial density distribution, aspect ratio, and asphericity are calculated. In order to assess the hydrophilicity of the dendrimer, we compute the number of bound water molecules in the interior of dendrimer as well as the number of dendrimer-water hydrogen bonds. We conclude that PETIM dendrimers have relatively greater hydrophobicity and flexibility when compared with their extensively investigated PAMAM counterparts. Hence PETIM dendrimers are expected to have stronger interactions with lipid membranes as well as improved drug encapsulation and retention properties when compared with PAMAM dendrimers. We compute the root-mean-square fluctuation of dendrimers as well as their entropy to quantify the flexibility of the dendrimer. Finally we note that structural and solvation properties computed using force field parameters derived based on the CHARMM general purpose force field were in good quantitative agreement with those obtained using the generalized Amber force field (GAFF).

Laterally structured ripple and square phases with one and two dimensional thickness modulations in a model bilayer system.

Molecular dynamics simulations of bilayers in a surfactant/co-surfactant/water system with explicit solvent molecules show formation of topologically distinct gel phases depending upon the bilayer composition. At low temperatures, the bilayers transform from the tilted gel phase, Lß', to the one dimensional (1D) rippled, Pß' phase as the surfactant concentration is increased. More interestingly, we observe a two dimensional (2D) square phase at higher surfactant concentration which, upon heating, transforms to the gel Lß' phase. The thickness modulations in the 1D rippled and square phases are asymmetric in two surfactant leaflets and the bilayer thickness varies by a factor of ∼2 between maximum and minimum. The 1D ripple consists of a thinner interdigitated region of smaller extent alternating with a thicker non-interdigitated region. The 2D ripple phase is made up of two superimposed square lattices of maximum and minimum thicknesses with molecules of high tilt forming a square lattice translated from the lattice formed with the thickness minima. Using Voronoi diagrams we analyze the intricate interplay between the area-per-head-group, height modulations and chain tilt for the different ripple symmetries. Our simulations indicate that composition plays an important role in controlling the formation of low temperature gel phase symmetries and rippling accommodates the increased area-per-head-group of the surfactant molecules.

A new microscopic insight into membrane penetration and reorganization by PETIM dendrimers.

Dendrimers are highly branched polymeric nanoparticles whose structure and topology, largely, have determined their efficacy in a wide range of studies performed so far. An area of immense interest is their potential as drug and gene delivery vectors. Realizing this potential, depending on the nature of cell surface-dendrimer interactions, here we report controlled model membrane penetration and reorganization, using a model supported lipid bilayer and poly(ether imine) (PETIM) dendrimers of two generations. By systematically varying the areal density of the lipid bilayers, we provide a microscopic insight, through a combination of high resolution scattering, atomic force microscopy and atomistic molecular dynamics simulations, into the mechanism of PETIM dendrimer membrane penetration, pore formation and membrane re-organization induced by such interactions. Our work represents the first systematic observation of a regular barrel-like membrane spanning pore formation by dendrimers, tunable through lipid bilayer packing, without membrane disruption.

Simulation of influence of bilayer melting on dynamics and thermodynamics of interfacial water.

We investigate the effect of bilayer melting transition on thermodynamics and dynamics of interfacial water using molecular dynamics simulation with the two-phase thermodynamic model. We show that the diffusivity of interface water depicts a dynamic crossover at the chain melting transition following an Arrhenius behavior until the transition temperature. The corresponding change in the diffusion coefficient from the bulk to the interface water is comparable with experimental observations found recently for water near 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) vesicles [Phys. Chem. Chem. Phys. 13, 7732 (2011)]. The entropy and potential energy of interfacial water show distinct changes at the bilayer melting transition, indicating a strong correlation in the thermodynamic state of water and the accompanying first-order phase transition of the bilayer membrane.

Glassy dynamics in a confined monatomic fluid.

Molecular dynamic simulations of a strongly inhomogeneous system reveals that a single-component soft-sphere fluid can behave as a fragile glass former due to confinement. The self-intermediate scattering function, F(s)(k,t), of a Lennard-Jones fluid confined in slit-shaped pores, which can accommodate two to four fluid layers, exhibits a two-step relaxation at moderate temperatures. The mean-squared displacement data are found to follow time-temperature superposition and both the self-diffusivity and late α relaxation times exhibit power-law divergences as the fluid is cooled. The system possesses a crossover temperature and follows the scalings of mode coupling theory for the glass transition. The temperature dependence of the self-diffusivity can be expressed using the Vogel-Fulcher-Tammann equation, and estimates of the fragility index of the system indicates a fragile glass former. At lower temperatures, signatures of additional relaxation processes are observed in the various dynamical quantities with a three-step relaxation observed in the F(s)(k,t).

Methane and carbon dioxide adsorption on edge-functionalized graphene: a comparative DFT study.

With a view towards optimizing gas storage and separation in crystalline and disordered nanoporous carbon-based materials, we use ab initio density functional theory calculations to explore the effect of chemical functionalization on gas binding to exposed edges within model carbon nanostructures. We test the geometry, energetics, and charge distribution of in-plane and out-of-plane binding of CO(2) and CH(4) to model zigzag graphene nanoribbons edge-functionalized with COOH, OH, NH(2), H(2)PO(3), NO(2), and CH(3). Although different choices for the exchange-correlation functional lead to a spread of values for the binding energy, trends across the functional groups are largely preserved for each choice, as are the final orientations of the adsorbed gas molecules. We find binding of CO(2) to exceed that of CH(4) by roughly a factor of two. However, the two gases follow very similar trends with changes in the attached functional group, despite different molecular symmetries. Our results indicate that the presence of NH(2), H(2)PO(3), NO(2), and COOH functional groups can significantly enhance gas binding, making the edges potentially viable binding sites in materials with high concentrations of edge carbons. To first order, in-plane binding strength correlates with the larger permanent and induced dipole moments on these groups. Implications for tailoring carbon structures for increased gas uptake and improved CO(2)/CH(4) selectivity are discussed.

Non-monotonic, distance-dependent relaxation of water in reverse micelles: propagation of surface induced frustration along hydrogen bond networks.

Layer-wise, distance-dependent orientational relaxation of water confined in reverse micelles (RM) is studied using theoretical and computational tools. We use both a newly constructed "spins on a ring" (SOR) Ising-type model (with Shore-Zwanzig rotational dynamics) and atomistic simulations with explicit water. Our study explores the effect of reverse micelle size and role of intermolecular correlations, compromised by the presence of a highly polar surface, on the distance (from the interface) dependence of water relaxation. The "spins on a ring" model can capture some aspects of distance dependence of relaxation, such as acceleration of orientational relaxation at intermediate layers. In atomistic simulations, layer-wise decomposition of hydrogen bond formation pattern clearly reveals that hydrogen bond arrangement of water at a certain distance away from the surface can remain frustrated due to the interaction with the polar surface head groups. This layer-wise analysis also reveals the presence of a non-monotonic slow relaxation component which can be attributed to this frustration effect and which is accentuated in small to intermediate size RMs. For large size RMs, the long time component decreases monotonically from the interface to the interior of the RMs with slowest relaxation observed at the interface.

Relaxation and jump dynamics of water at the mica interface.

The orientational relaxation dynamics of water confined between mica surfaces is investigated using molecular dynamics simulations. The study illustrates the wide heterogeneity that exists in the dynamics of water adjacent to a strongly hydrophilic surface such as mica. Analysis of the survival probabilities in different layers is carried out by normalizing the corresponding relaxation times with bulk water layers of similar thickness. A 10-fold increase in the survival times is observed for water directly in contact with the mica surface and a non-monotonic variation in the survival times is observed moving away from the mica surface to the bulk-like interior. The orientational relaxation time is highest for water in the contact layer, decreasing monotonically away from the surface. In all cases the ratio of the relaxation times of the 1st and 2nd rank Legendre polynomials of the HH bond vector is found to lie between 1.5 and 1.9 indicating that the reorientational relaxation in the different water layers is governed by jump dynamics. The orientational dynamics of water in the contact layer is particularly novel and is found to undergo distinct two-dimensional hydrogen bond jump reorientational dynamics with an average waiting time of 4.97 ps. The waiting time distribution is found to possess a long tail extending beyond 15 ps. Unlike previously observed jump dynamics in bulk water and other surfaces, jump events in the mica contact layer occur between hydrogen bonds formed by the water molecule and acceptor oxygens on the mica surface. Despite slowing down of the water orientational relaxation near the surface, life-times of water in the hydration shell of the K(+) ion are comparable to that observed in bulk salt solutions.

Melting and mechanical properties of polymer grafted lipid bilayer membranes.

The influence of polymer grafting on the phase behavior and elastic properties of two tail lipid bilayers have been investigated using dissipative particle dynamics simulations. For the range of polymer lengths studied, the L(c) to L(α) transition temperature is not significantly affected for grafting fractions, G(f) between 0.16 and 0.25. A decrease in the transition temperature is observed at a relatively high grafting fraction, G(f) = 0.36. At low temperatures, a small increase in the area per head group, a(h), at high G(f) leads to an increase in the chain tilt, inducing order in the bilayer and the solvent. The onset of the phase transition occurs with the nucleation of small patches of thinned membrane which grow and form continuous domains as the temperature increases. This region is the co-existence region between the L(ß)(thick) and the L(α)(thin) phases. The simulation results for the membrane area expansion as a function of the grafting density conform extremely well to the scalings predicted by self-consistent mean field theories. We find that the bending modulus shows a small decrease for short polymers (number of beads, N(p) = 10) and low G(f), where the influence of polymer is reduced when compared to the effect of the increased a(h). For longer polymers (N(p) > 15), the bending modulus increases monotonically with increase in grafted polymer. Using the results from mean field theory, we partition the contributions to the bending modulus from the membrane and the polymer and show that the dominant contribution to the increased bending modulus arises from the grafted polymer.

Investigations on the melting and bending modulus of polymer grafted bilayers using dissipative particle dynamics.

Understanding the influence of polymer grafted bilayers on the physicomechanical properties of lipid membranes is important while developing liposomal based drug delivery systems. The melting characteristics and bending moduli of polymer grafted bilayers are investigated using dissipative particle dynamics simulations as a function of the amount of grafted polymer and lipid tail length. Simulations are carried out using a modified Andersen barostat, whereby the membrane is maintained in a tensionless state. For lipids made up of four to six tail beads, the transition from the low temperature L(ß) phase to the L(α) phase is lowered only above a grafting fraction of G(f)=0.12 for polymers made up of 20 beads. Below G(f)=0.12 small changes are observed only for the HT(4) bilayer. The bending modulus of the bilayers is obtained as a function of G(f) from a Fourier analysis of the height fluctuations. Using the theory developed by Marsh et al. [Biochim. Biophys. Acta 1615, 33 (2003)] for polymer grafted membranes, the contributions to the bending modulus due to changes arising from the grafted polymer and bilayer thinning are partitioned. The contributions to the changes in κ from bilayer thinning were found to lie within 11% for the lipids with four to six tail beads, increasing to 15% for the lipids containing nine tail beads. The changes in the area stretch modulus were also assessed and were found to have a small influence on the overall contribution from membrane thinning. The increase in the area per head group of the lipids was found to be consistent with the scalings predicted by self-consistent mean field results.

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.