Bridging microscopic and mesoscopic simulations of lipid bilayers

A lipid bilayer is modeled using a mesoscopic model designed to bridge atomistic bilayer simulations with macro-scale continuum-level simulation. Key material properties obtained from detailed atomistic-level simulations are used to parameterize the meso-scale model. The fundamental length and time scale of the meso-scale simulation are at least an order of magnitude beyond that used at the atomistic level. Dissipative particle dynamics cast in a new membrane formulation provides the simulation methodology. A meso-scale representation of a dimyristoylphosphatidylcholine membrane is examined in the high and low surface tension regimes. At high surface tensions, the calculated modulus is found to be slightly less than the atomistically determined value. This result agrees with the theoretical prediction that high-strain thermal undulations still persist, which have the effect of reducing the value of the atomistically determined modulus. Zero surface tension simulations indicate the presence of strong thermal undulatory modes, whereas the undulation spectrum and the calculated bending modulus are in excellent agreement with theoretical predictions and experiment.     

Surface forces in lungs. I. Alveolar surface tension-lung volume relationships

Alveolar surface tension (gamma)-lung volume relationships were obtained for quasi-static and dynamic lung pressure-volume (PV) histories from measurements of PV curves of liquid- and air-filled excised rabbit lungs. PV relationships were measured at room temperature in lungs filled with test liquids with constant liquid-liquid interfacial tensions with alveolar surface-active materials; and air-filled lungs before and after the normal alveolar surface film was covered with test liquids with constant values of liquid- and air-liquid interfacial tensions. Interfacial tensions of test liquids were measured in a surface balance on monolayers of dipalmitoyl phosphatidylcholine. Values of gamma for the normal air-filled lung were obtained either from points of intersection between PV curves with the normal and test liquid interface or from a general relationship between gamma and the component of recoil pressure due to surface tension derived from the data. In contrast to previous analyses that have used PV measurements, this approach does not depend on assumptions about lung microstructural geometry. Surface tension-volume relationships for the normal air-filled lung show a prominent hysteresis with surface tension ranging from near 0 at low volumes during lung deflation to transiently high values near 40 dyn/cm during inflation; value of equilibrium surface tension (gamma EQ) near 28 dyn/cm; and characteristic transitions in surface film compressibility and associated transitions in film kinetic behavior in nonequilibrium film states where gamma deviates from gamma EQ. These features are consistent with the behavior predicted from current models of alveolar surface film behavior.     

Molecular study of the diffusional process of DMSO in double lipid bilayers

As a way to quantify the diffusion process of molecular compounds through biological membranes, we investigated in this study the dynamics of DMSO through an 1,2-Dipalmitoyl-sn-Glycero-3-Phosphocholine (DPPC) bilayer system. To properly account for the diffusion of DMSO due to a concentration gradient, a double DPPC bilayer was setup for our simulations. In such configuration, the aqueous phases can be explicitly associated with the extra and intracellular domains of the membrane, which is seldom the case in studies of single lipid bilayer due to the periodicity imposed by the simulations. DMSO molecules were initially contained in one of the aqueous phases (extracellular region) at a concentration of 5 wt.%. Molecular dynamics simulation was performed in this system for 95 ns at 350 K and 1 bar. The simulations showed that although many DMSO molecules penetrated the lipid bilayer, only about 10% of them crossed the bilayer to reach the other aqueous phase corresponding to the intracellular region of the membrane. The simulation time considered was insufficient to reach equilibrium of the DMSO concentration between the aqueous phases. However, the simulations provided sufficient information to estimate parameters to apply Fick's Law to model the diffusion process of the system. Using this model, we predicted that for the time considered in our simulation, the concentration of DMSO in the intracellular domain should have been about half of the actual value obtained. The model also predicted that equilibrium of the DMSO concentration in the system would be reached after about 2000 ns, approximately 20 times longer than the performed simulation.     

Molecular study of the diffusional process of DMSO in double lipid bilayers

As a way to quantify the diffusion process of molecular compounds through biological membranes, we investigated in this study the dynamics of DMSO through an 1,2-Dipalmitoyl-sn-Glycero-3-Phosphocholine (DPPC) bilayer system. To properly account for the diffusion of DMSO due to a concentration gradient, a double DPPC bilayer was setup for our simulations. In such configuration, the aqueous phases can be explicitly associated with the extra and intracellular domains of the membrane, which is seldom the case in studies of single lipid bilayer due to the periodicity imposed by the simulations. DMSO molecules were initially contained in one of the aqueous phases (extracellular region) at a concentration of 5 wt.%. Molecular dynamics simulation was performed in this system for 95 ns at 350 K and 1 bar. The simulations showed that although many DMSO molecules penetrated the lipid bilayer, only about 10% of them crossed the bilayer to reach the other aqueous phase corresponding to the intracellular region of the membrane. The simulation time considered was insufficient to reach equilibrium of the DMSO concentration between the aqueous phases. However, the simulations provided sufficient information to estimate parameters to apply Fick's Law to model the diffusion process of the system. Using this model, we predicted that for the time considered in our simulation, the concentration of DMSO in the intracellular domain should have been about half of the actual value obtained. The model also predicted that equilibrium of the DMSO concentration in the system would be reached after about 2000 ns, approximately 20 times longer than the performed simulation.     

Developing initial conditions for simulations of asymmetric membranes: a practical recommendation

It has been proposed that the surface tension difference between leaflets (or differential stress) in asymmetric bilayers is generally nonvanishing. This implies that there is no unique approach to generate initial conditions for simulations of asymmetric bilayers in the absence of experimentally derived constraints. Current generation methods include individual area per lipid (APL) based, leaflet surface area (SA) matching, and zero leaflet tension based (0-DS). This work adds a bilayer-based approach that aims for achieving partial chemical equilibrium by interleaflet switching of selected lipids via P2₁ periodic boundary conditions. Based on a recently proposed theoretical framework, we obtained expressions for tensions in asymmetric bilayers from both the bending and area strains. We also developed a quantitative measure for the energetic penalty from the differential stress. The impacts of APL-, SA-, and 0-DS-based approaches on mechanical properties are assessed for two different asymmetric bilayers. The lateral pressure profile and its moments differ significantly for each method, whereas the area compressibility modulus is relatively insensitive. Application of P2₁ periodic boundary conditions (APL/P2₁, SA/P2₁, and 0-DS/P2₁) results in better agreement in mechanical properties between asymmetric bilayers generated by APL-, SA-, and 0-DS-based approaches, in which changes are the smallest for bilayers from the SA-based method. The estimated differential stress from the theory shows good agreement with that from the simulations. These simulation results and the good agreement between the predicted and observed differential stress further support the theoretical framework in which bilayer mechanical properties are outcomes of the interplay between intrinsic bending and asymmetric lipid packing. Based on the simulation results and theoretical predictions, the SA/P2₁-based, or at least the SA-based (when the differential stress is small), approach is recommended as a practical method for developing initial conditions for asymmetric bilayer simulations.     

An alamethicin channel in a lipid bilayer: molecular dynamics simulations

We present the results of 2-ns molecular dynamics (MD) simulations of a hexameric bundle of Alm helices in a 1-palmitoyl-2-oleoylphosphatidylcholine bilayer. These simulations explore the dynamic properties of a model of a helix bundle channel in a complete phospholipid bilayer in an aqueous environment. We explore the stability and conformational dynamics of the bundle in a phospholipid bilayer. We also investigate the effect on bundle stability of the ionization state of the ring of Glu18 side chains. If all of the Glu18 side chains are ionised, the bundle is unstable; if none of the Glu18 side chains are ionized, the bundle is stable. pKA calculations suggest that either zero or one ionized Glu18 is present at neutral pH, correlating with the stable form of the helix bundle. The structural and dynamic properties of water in this model channel were examined. As in earlier in vacuo simulations (Breed et al., 1996 .Biophys. J. 70:1643-1661), the dipole moments of water molecules within the pore were aligned antiparallel to the helix dipoles. This contributes to the stability of the helix bundle.     

Molecular dynamics generation of nonarbitrary membrane models reveals lipid orientational correlations

This report addresses the following problems associated with the generation of computer models of phospholipid bilayer membranes using molecular dynamics simulations: arbitrary initial structures and short equilibration periods, an Ewald-induced strong coupling of phospholipids, uncertainty regarding which value should be used for surface tension to alleviate the problem of the small size of the membrane, and simultaneous realization of both order parameters and the surface area. We generated a computer model of the liquid-crystalline L-alpha-dimyristoylphosphatidylcholine (DMPC) bilayer, starting from a configuration based on a crystal structure (rather than from an arbitrary structure). To break the crystalline structure, a 20-ps high-temperature pulse of 510 K (but not 450 or 480 K) was effective. The system finally obtained is an all-atom model, with Ewald summation to evaluate Coulombic interactions and a constant surface tension of 35 dynes/cm/water-membrane interface, equilibrated for 12 ns (over 50 ns total calculation time), which reproduces all of the experimentally observed parameters examined in this work. Furthermore, this model shows the presence of significant orientational correlations between neighboring alkyl chains and between shoulder vectors (which show the orientations of the lipids about their long axes) of neighboring DMPCs.     

"Entropic traps" in the kinetics of phase separation in multicomponent membranes stabilize nanodomains

We quantitatively describe the creation and evolution of phase-separated domains in a multicomponent lipid bilayer membrane. The early stages, termed the nucleation stage and the independent growth stage, are extremely rapid (characteristic times are submillisecond and millisecond, respectively) and the system consists of nanodomains of average radius approximately 5-50 nm. Next, mobility of domains becomes consequential; domain merger and fission become the dominant mechanisms of matter exchange, and line tension gamma is the main determinant of the domain size distribution at any point in time. For sufficiently small gamma, the decrease in the entropy term that results from domain merger is larger than the decrease in boundary energy, and only nanodomains are present. For large gamma, the decrease in boundary energy dominates the unfavorable entropy of merger, and merger leads to rapid enlargement of nanodomains to radii of micrometer scale. At intermediate line tensions and within finite times, nanodomains can remain dispersed and coexist with a new global phase. The theoretical critical value of line tension needed to rapidly form large rafts is in accord with the experimental estimate from the curvatures of budding domains in giant unilamellar vesicles.     

Combined monte carlo and molecular dynamics simulation of fully hydrated dioleyl and palmitoyl-oleyl phosphatidylcholine lipid bilayers

We have applied a new equilibration procedure for the atomic level simulation of a hydrated lipid bilayer to hydrated bilayers of dioleyl-phosphatidylcholine (DOPC) and palmitoyl-oleyl phosphatidylcholine (POPC). The procedure consists of alternating molecular dynamics trajectory calculations in a constant surface tension and temperature ensemble with configurational bias Monte Carlo moves to different regions of the configuration space of the bilayer in a constant volume and temperature ensemble. The procedure is applied to bilayers of 128 molecules of POPC with 4628 water molecules, and 128 molecules of DOPC with 4825 water molecules. Progress toward equilibration is almost three times as fast in central processing unit (CPU) time compared with a purely molecular dynamics (MD) simulation. Equilibration is complete, as judged by the lack of energy drift in 200-ps runs of continuous MD. After the equilibrium state was reached, as determined by agreement between the simulation volume per lipid molecule with experiment, continuous MD was run in an ensemble in which the lateral area was restrained to fluctuate about a mean value and a pressure of 1 atm applied normal to the bilayer surface. Three separate continuous MD runs, 200 ps in duration each, separated by 10,000 CBMC steps, were carried out for each system. Properties of the systems were calculated and averaged over the three separate runs. Results of the simulations are presented and compared with experimental data and with other recent simulations of POPC and DOPC. Analysis of the hydration environment in the headgroups supports a mechanism by which unsaturation contributes to reduced transition temperatures. In this view, the relatively horizontal orientation of the unsaturated bond increases the area per lipid, resulting in increased water penetration between the headgroups. As a result the headgroup-headgroup interactions are attenuated and shielded, and this contributes to the lowered transition temperature.     

A three-dimensional finite element model for the mechanics of cell-cell interactions

Technical challenges, including significant ones associated with cell rearrangement, have hampered the development of three-dimensional finite element models for the mechanics of embryonic cells. These challenges have been overcome by a new formulation in which the contents of each cell, assumed to have a viscosity mu, are modeled using a system of orthogonal dashpots. This approach overcomes a stiffening artifact that affects more traditional models, in which space-filling viscous elements are used to model the cytoplasm. Cells are assumed to be polyhedral in geometry, and each n-sided polygonal face is subdivided into n triangles with a common node at the face center so that it needs not remain flat. A constant tension gamma is assumed to act along each cell-cell interface, and cell rearrangements occur through one of two complementary topological transformations. The formulation predicts mechanical interactions between pairs of similar or dissimilar cells that are consistent with experiments, two-dimensional simulations, contact angle theory, and intracellular pressure calculations. Simulations of the partial engulfment of one tissue type by another show that the formulation is able to model aggregates of several hundred cells without difficulty. Simulations carried out using this formulation suggest new experimental approaches for measuring cell surface tensions and interfacial tensions. The formulation holds promise as a tool for gaining insight into the mechanics of isolated or aggregated embryonic cells and for the design and interpretation of experiments that involve them.     

Measurement of low levels of oxygen and their effect on respiration in cell suspensions maintained in an open system

The presence of low levels of oxygen may have profound effects on the cytotoxic activity of radiation, radiosensitizers, and bioreductive alkylating agents. As others have shown, low oxygen tensions may significantly alter rates of cellular and chemical oxygen consumption. When experiments are performed at very low oxygen concentrations, the opposing effects of oxygen leakage into and cellular/chemical oxygen consumption from the system can lead to unpredictable results. Use of a newly designed, highly sensitive Clark-type oxygen sensor has permitted accurate and reproducible measurement of low levels of oxygen. Cellular depletion of oxygen at various cell densities has been monitored for a series of oxygen tensions in solution and the corresponding respiration rates have been calculated. Although oxygen depletion was found to be quite significant at low oxygen tensions, not all oxygen present could be removed by cellular respiration. Respiration rate decreased as oxygen tension decreased and approached zero at low oxygen tensions. This result was independent of cell density. A model is presented to account for the observed effect of oxygen tension on cellular oxygen utilization.     

Surface binding of alamethicin stabilizes its helical structure: molecular dynamics simulations.

Alamethicin is an amphipathic alpha-helical peptide that forms ion channels. An early event in channel formation is believed to be the binding of alamethicin to the surface of a lipid bilayer. Molecular dynamics simulations are used to compare the structural and dynamic properties of alamethicin in water and alamethicin bound to the surface of a phosphatidylcholine bilayer. The bilayer surface simulation corresponded to a loosely bound alamethicin molecule that interacted with lipid headgroups but did not penetrate the hydrophobic core of the bilayer. Both simulations started with the peptide molecule in an alpha-helical conformation and lasted 2 ns. In water, the helix started to unfold after approximately 300 ps and by the end of the simulation only the N-terminal region of the peptide remained alpha-helical and the molecule had collapsed into a more compact form. At the surface of the bilayer, loss of helicity was restricted to the C-terminal third of the molecule and the rod-shaped structure of the peptide was retained. In the surface simulation about 10% of the peptide/water H-bonds were replaced by peptide/lipid H-bonds. These simulations suggest that some degree of stabilization of an amphipathic alpha-helix occurs at a bilayer surface even without interactions between hydrophobic side chains and the acyl chain core of the bilayer.     

Theoretical analysis of hydrophobic matching and membrane-mediated interactions in lipid bilayers containing gramicidin.

We present a quantitative analysis of the effects of hydrophobic matching and membrane-mediated protein-protein interactions exhibited by gramicidin embedded in dimyristoylphosphatidylcholine (DMPC) and dilauroylphosphatidylcholine (DLPC) bilayers (Harroun et al., 1999. Biophys. J. 76:937-945). Incorporating gramicidin, at 1:10 peptide/lipid molar ratio, decreases the phosphate-to-phosphate (PtP) peak separation in the DMPC bilayer from 35.3 A without gramicidin to 32.7 A. In contrast, the same molar ratio of gramicidin in DLPC increases the PtP from 30.8 A to 32.1 A. Concurrently, x-ray in-plane scattering showed that the most probable nearest-neighbor separation between gramicidin channels was 26.8 A in DLPC, but reduced to 23.3 A in DMPC. In this paper we review the idea of hydrophobic matching in which the lipid bilayer deforms to match the hydrophobic surface of the embedded proteins. We use a simple elasticity theory, including thickness compression, tension, and splay terms to describe the membrane deformation. The energy of membrane deformation is compared with the energy cost of hydrophobic mismatch. We discuss the boundary conditions between a gramicidin channel and the lipid bilayer. We used a numerical method to solve the problem of membrane deformation profile in the presence of a high density of gramicidin channels and ran computer simulations of 81 gramicidin channels to find the equilibrium distributions of the channels in the plane of the bilayer. The simulations contain four parameters: bilayer thickness compressibility 1/B, bilayer bending rigidity Kc, the channel-bilayer mismatch Do, and the slope of the interface at the lipid-protein boundary s. B, Kc, and Do were experimentally measured; the only free parameter is s. The value of s is determined by the requirement that the theory produces the experimental values of bilayer thinning by gramicidin and the shift in the peak position of the in-plane scattering due to membrane-mediated channel-channel interactions. We show that both hydrophobic matching and membrane-mediated interactions can be understood by the simple elasticity theory.     

How shortening a channel may lower its conductance. The case of des-Val7-DVal8-gramicidin A

A shortened analog of gramicidin A has been shown by Urry et al. (Biochim. Biophys. Acta 775, 115-119) to have lower conductance than native gramicidin A. They argue this suggests that the major current carrier is the doubly occupied channel. A different perspective is presented here. Channel formation does not alter bilayer width. In a shortened channel an ion approaching the binding site moves further toward the center of the lipid-pore system. The electrostatic contribution to the energy barrier near the constriction mouth is greater for the shorter channel. As long as entry to the channel is rate limiting singly occupied short channels should exhibit lower conductance. The data are not inconsistent with singly occupied channels being the major current carriers. Experiments on other gramicidin analogs are suggested to more clearly distinguish between singly and doubly occupied channels as the dominant conducting species.     

Undulation Contributions to the Area Compressibility in Lipid Bilayer Simulations

It is here shown that there is a considerable system size-dependence in the area compressibility calculated from area fluctuations in lipid bilayers. This is caused by the contributions to the area fluctuations from undulations. This is also the case in experiments. At present, such a contribution, in most cases, is subtracted from the experimental values to obtain a true area compressibility. This should also be done with the simulation values. Here, this is done by extrapolating area compressibility versus system size, down to very small (zero) system size, where undulations no longer exist. The area compressibility moduli obtained from such simulations do not agree with experimental true area compressibility moduli as well as the uncorrected ones from contemporary or earlier simulations, but tend, instead, to be ∼50% too large. As a byproduct, the bending modulus can be calculated from the slope of the compressibility modulus versus system-size. The values obtained in this way for the bending modulus are then in good agreement with experiment.     

Floating lipid bilayers: models for physics and biology

Progress in the determination of structure and fluctuation spectrum of a floating bilayer system, as well as potential applications for biological studies, is reviewed. The system described here was first introduced by Charitat et al. (Eur Phys J B 8:583–593, 1999) and consists of a planar bilayer floating at 2–3?nm away from an adsorbed one on a solid surface in contact with bulk water. This model has been widely used for surface scattering studies using both neutrons and synchrotron radiation and its use in studies of relevance for physics and biology research areas will be described, together with the progress towards the production of complex biomimetic samples for use with scattering techniques.     

The Fusion of Membranes and Vesicles: Pathway and Energy Barriers from Dissipative Particle Dynamics

The fusion of lipid bilayers is studied with dissipative particle dynamics simulations. First, to achieve control over membrane properties, the effects of individual simulation parameters are studied and optimized. Then, a large number of fusion events for a vesicle and a planar bilayer are simulated using the optimized parameter set. In the observed fusion pathway, configurations of individual lipids play an important role. Fusion starts with individual lipids assuming a splayed tail configuration with one tail inserted in each membrane. To determine the corresponding energy barrier, we measure the average work for interbilayer flips of a lipid tail, i.e., the average work to displace one lipid tail from one bilayer to the other. This energy barrier is found to depend strongly on a certain dissipative particle dynamics parameter, and, thus, can be adjusted in the simulations. Overall, three subprocesses have been identified in the fusion pathway. Their energy barriers are estimated to lie in the range 8-15 k_BT. The fusion probability is found to possess a maximum at intermediate tension values. As one decreases the tension, the fusion probability seems to vanish before the tensionless membrane state is attained. This would imply that the tension has to exceed a certain threshold value to induce fusion.     

Thermally induced proliferation of pores in a model fluid membrane.

The growth of thermally induced pores in a two-dimensional model fluid membrane is investigated by Monte Carlo simulation. Holes appear in the membrane via an activated process, and their subsequent growth is controlled by an edge energy per unit length or line tension. The barrier height and line tension, together with a lateral tension, are the independent parameters of the model. In the resulting phase diagram, a rupture transition separates an intact membrane from a disintegrated state. The approach to the ruptured state shows distinct regimes. Reducing the barrier height at large line tension produces multiple, quasi-independent, small holes whose behavior is dominated by their edge energy, whereas at lower line tensions shape fluctuations of the holes facilitate their coalescence into a single large hole. At a small value of line tension and large barrier height, a single hole spontaneously permeabilizes the membrane in an entropically driven phase transition. Entropy dominates pore growth for line tensions not far below those measured for artificial vesicles. Permeabilization of lipid bilayers by certain peptides involves perturbing lipid-lipid cohesive energies, and our simulations show that at small line tensions the entropy of hole shape fluctuations destroys the model membrane's stability.     

Incorporation of surface tension into molecular dynamics simulation of an interface: a fluid phase lipid bilayer membrane.

In this paper we report on the molecular dynamics simulation of a fluid phase hydrated dimyristoylphosphatidylcholine bilayer. The initial configuration of the lipid was the x-ray crystal structure. A distinctive feature of this simulation is that, upon heating the system, the fluid phase emerged from parameters, initial conditions, and boundary conditions determined independently of the collective properties of the fluid phase. The initial conditions did not include chain disorder characteristic of the fluid phase. The partial charges on the lipids were determined by ab initio self-consistent field calculations and required no adjustment to produce a fluid phase. The boundary conditions were constant pressure and temperature. Thus the membrane was not explicitly required to assume an area/phospholipid molecule thought to be characteristic of the fluid phase, as is the case in constant volume simulations. Normal to the membrane plane, the pressure was 1 atmosphere, corresponding to the normal laboratory situation. Parallel to the membrane plane a negative pressure of -100 atmospheres was applied, derived from the measured surface tension of a monolayer at an air-water interface. The measured features of the computed membrane are generally in close agreement with experiment. Our results confirm the concept that, for appropriately matched temperature and surface pressure, a monolayer is a close approximation to one-half of a bilayer. Our results suggest that the surface area per phospholipid molecule for fluid phosphatidylcholine bilayer membranes is smaller than has generally been assumed in computational studies at constant volume. Our results confirm that the basis of the measured dipole potential is primarily water orientations and also suggest the presence of potential barriers for the movement of positive charges across the water-headgroup interfacial region of the phospholipid.     

Keeping lung surfactant where it belongs: protein regulation of two-dimensional viscosity

Lung surfactant causes the surface tension, gamma, in the alveoli to drop to nearly zero on exhalation; in the upper airways gamma is approximately 30 mN/m and constant. Hence, a surface tension gradient exists between alveoli and airways that should lead to surfactant flow out of the alveoli and elimination of the surface tension gradient. However, the lung surfactant specific protein SP-C enhances the resistance to surfactant flow by regulating the ratio of solid to fluid phase in the monolayer, leading to a jamming transition at which the monolayer transforms from fluidlike to solidlike. The accompanying three orders of magnitude increase in surface viscosity helps minimize surfactant flow to the airways and likely stabilizes the alveoli against collapse.