Nonadditive Compositional Curvature Energetics of Lipid Bilayers.

The unique properties of the individual lipids that compose biological membranes together determine the energetics of the surface. The energetics of the surface, in turn, govern the formation of membrane structures and membrane reshaping processes, and thus they will underlie cellular-scale models of viral fusion, vesicle-dependent transport, and lateral organization relevant to signaling. The spontaneous curvature, to the best of our knowledge, is always assumed to be additive. We describe observations from simulations of unexpected nonadditive compositional curvature energetics of two lipids essential to the plasma membrane: sphingomyelin and cholesterol. A model is developed that connects molecular interactions to curvature stress, and which explains the role of local composition. Cholesterol is shown to lower the number of effective Kuhn segments of saturated acyl chains, reducing lateral pressure below the neutral surface of bending and favoring positive curvature. The effect is not observed for unsaturated (flexible) acyl chains. Likewise, hydrogen bonding between sphingomyelin lipids leads to positive curvature, but only at sufficient concentration, below which the lipid prefers negative curvature.

Development of the CHARMM Force Field for Lipids.

The development of the CHARMM additive all-atom lipid force field (FF) is traced from the early 1990's to the most recent version (C36) published in 2010. Though simulations with early versions yielded useful results, they failed to reproduce two important quantities: a zero surface tension at the experimental bilayer surface area, and the signature splitting of the deuterium order parameters in the glycerol and upper chain carbons. Systematic optimization of parameters based on high level quantum mechanical data and free energy simulations have resolved these issues, and bilayers with a wide range of lipids can be simulated in tensionless ensembles using C36. Issues associated with other all-atom lipid FFs, success and limitations in the C36 FF and ongoing developments are also discussed.

Molecular dynamics studies of the conformation of sorbitol.

Molecular dynamics simulations of a 3 molal aqueous solution of D-sorbitol (also called D-glucitol) have been performed at 300 K, as well as at two elevated temperatures to promote conformational transitions. In principle, sorbitol is more flexible than glucose since it does not contain a constraining ring. However, a conformational analysis revealed that the sorbitol chain remains extended in solution, in contrast to the bent conformation found experimentally in the crystalline form. While there are 243 staggered conformations of the backbone possible for this open-chain polyol, only a very limited number were found to be stable in the simulations. Although many conformers were briefly sampled, only eight were significantly populated in the simulation. The carbon backbones of all but two of these eight conformers were completely extended, unlike the bent crystal conformation. These extended conformers were stabilized by a quite persistent intramolecular hydrogen bond between the hydroxyl groups of carbon C-2 and C-4. The conformational populations were found to be in good agreement with the limited available NMR data except for the C-2-C-3 torsion (spanned by the O-2-O-4 hydrogen bond), where the NMR data support a more bent structure.

CHARMM: the biomolecular simulation program.

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

ICAM-1 enhances MHC-peptide activation of CD8(+) T cells without an organized immunological synapse.

In addition to the TCR-ligand interaction, other receptor-ligand pairs, such as LFA-1 and ICAM-1, play a major role in the activation of T cells. Recent studies of T cell activation suggest a coordinated movement of LFA-1 and ICAM-1 in forming a defined zone in the immunological synapse. It is unclear from these studies whether the organized molecular geometry of the immunological synapse is necessary for ICAM-1 enhancement of T cell activation. In this report, we demonstrate that ICAM-1 can enhance the activation of CD8(+) T cells by MHC-peptide in the absence of an organized immunologic synapse. Therefore, although the molecular organization of the immunologic synapse may amplify stimuli, it is not an absolute requirement for either CD8(+) T cell activation or the ICAM-1 enhancement of TCR activation.

The determination of equivalent doses of standardized allergen vaccines.

BACKGROUND: Standardized allergen vaccines are tested for potency by manufacturers by using assays proposed in their license applications and approved by the Center for Biologics Evaluation and Research, which reviews and verifies the test results before lot release. The current lot-release limits for mite and grass pollen allergen vaccines impose statistical equivalence to the national reference extract; thus the limits are primarily based on assay variability. OBJECTIVE: We sought to establish a clinical basis for lot-release limits for the relative potency of allergen vaccines and to evaluate alternative specifications. METHODS: We performed literature selection and review, linear and logistic regression analyses of selected studies, and analysis of lots submitted to the Food and Drug Administration for approval since 1995. RESULTS: Therapeutic equivalence is achieved over a 10-fold range of allergen concentration. Safety equivalence is more difficult to assign, but on the basis of injection data, a 4-fold increase in allergen concentration is associated with a 5% to 10% increase in adverse reaction rates. The SD in log relative potency for the submitted allergenic products was determined to be 0.090 for grasses and 0.061 for mites, compared with 0.079 for competition ELISA. CONCLUSIONS: Current lot-release limits are well within literature-based estimates of therapeutic, diagnostic, and safety equivalence ranges for the clinical use of allergen vaccines. In addition, the aggregate consistency of the submitted products is comparable with the precision of the assay that is used to assess the products. These results support expanded release limits for verification of relative potency, provided the submitted lots of material remain at their present level of consistency.

The stability of house dust mite allergens in glycerinated extracts.

BACKGROUND: Mite allergen vaccines are important diagnostic and immunotherapeutic reagents. Previous studies on mite allergen stability under different storage conditions have yielded contradictory results. OBJECTIVE: We sought to compare, over a 12-month period, the stability of mite allergens reconstituted in 50% glycerol and stored at different temperatures and to examine the role of protease inhibitors in enhancing allergen stability. METHODS: Lyophilized allergen extracts were reconstituted in 50% glycerol, with and without protease inhibitors, and stored at -70 degrees C, -20 degrees C, 4 degrees C, or 37 degrees C for 12 months. At 6 and 12 months, the extracts were compared with freshly dissolved extracts by competition ELISA with pooled allergic sera, 2-site ELISA with mite-specific mAbs, and immunoblot analyses. RESULTS: The overall potencies of the stored extracts measured by competition ELISA were stable at -20 degrees C and 4 degrees C. As determined by means of the immunoblot and 2-site ELISA, Der f 1 levels decreased at 4 degrees C. Levels of Der f 2, Der p 1, and Der p 2 decreased in at least one of the allergen-specific assays. Storage at 37 degrees C led to overall loss of potency and allergen content, whereas storage at -70 degrees C was associated with a moderate loss of potency that increased with multiple freeze-thaw cycles. Protease inhibitors had no effect on allergen stability. CONCLUSION: Although overall potency of the extracts, as measured by competition ELISA, was preserved at -20 degrees C and 4 degrees C, allergen-specific assays indicated loss of allergens. These findings suggest that the competition ELISA is insensitive to decreases in the concentrations of individual allergens.

Solution structure and dynamics of linked cell attachment modules of mouse fibronectin containing the RGD and synergy regions: comparison with the human fibronectin crystal structure.

We report the three-dimensional solution structure of the mouse fibronectin cell attachment domain consisting of the linked ninth and tenth type III modules, mFnFn3(9,10). Because the tenth module contains the RGD cell attachment sequence while the ninth contains the synergy region, mFnFn3(9,10) has the cell attachment activity of intact fibronectin. Essentially complete signal assignments and approximately 1800 distance and angle restraints were derived from multidimensional heteronuclear NMR spectra. These restraints were used with a hybrid distance geometry/simulated annealing protocol to generate an ensemble of 20 NMR structures having no distance or angle violations greater than 0.3 A or 3 degrees. Although the beta-sheet core domains of the individual modules are well-ordered structures, having backbone atom rmsd values from the mean structure of 0.51(+/-0.12) and 0.40(+/-0.07) A, respectively, the rmsd of the core atom coordinates increases to 3.63(+/-1.41) A when the core domains of both modules are used to align the coordinates. The latter result is a consequence of the fact that the relative orientation of the two modules is not highly constrained by the NMR restraints. Hence, while structures of the beta-sheet core domains of the NMR structures are very similar to the core domains of the crystal structure of hFnFn3(9,10), the ensemble of NMR structures suggests that the two modules form a less extended and more flexible structure than the fully extended rod-like crystal structure. The radius of gyration, Rg, of mFnFn3(9,10) derived from small-angle neutron scattering measurements, 20.5(+/-0.5) A, agrees with the average Rg calculated for the NMR structures, 20.4 A, and is ca 1 A less than the value of Rg calculated for the X-ray structure. The values of the rotational anisotropy, D ||/D perpendicular, derived from an analysis of 15N relaxation data, range from 1.7 to 2.1, and are significantly less than the anisotropy of 2.67 predicted by hydrodynamic modeling of the crystal coordinates. In contrast, hydrodynamic modeling of the NMR coordinates yields anisotropies in the range of 1.9 to 2.7 (average 2.4(+/-0.2)), with NMR structures bent by more than 20 degrees relative the crystal structure having calculated anisotropies in best agreement with experiment. In addition, the relaxation parameters indicate that several loops in mFnFn3(9,10), including the RGD loop, are flexible on the nanosecond to picosecond time-scale. Taken together, our results suggest that, in solution, the limited set of interactions between the mFnFn3(9,10) modules position the RGD and synergy regions to interact specifically with cell surface integrins, and at the same time permit sufficient flexibility that allows mFnFn3(9,10) to adjust for some variation in integrin structure or environment.

Molecular dynamics simulation of unsaturated lipid bilayers at low hydration: parameterization and comparison with diffraction studies.

A potential energy function for unsaturated hydrocarbons is proposed and is shown to agree well with experiment, using molecular dynamics simulations of a water/octene interface and a dioleoyl phosphatidylcholine (DOPC) bilayer. The simulation results verify most of the assumptions used in interpreting the DOPC experiments, but suggest a few that should be reconsidered. Comparisons with recent results of a simulation of a dipalmitoyl phosphatidylcholine (DPPC) lipid bilayer show that disorder is comparable, even though the temperature, hydration level, and surface area/lipid for DOPC are lower. These observations highlight the dramatic effects of unsaturation on bilayer structure.

Length scales of lipid dynamics and molecular dynamics.

Following a brief overview of length scales and system size in computer simulation, it is demonstrated that a simulation sized lipid bilayer (typically a 50 x 50 A2 patch) is in the regime where stretching dominates undulation, while the reverse holds for a flaccid macroscopic membrane. Then it is estimated that current system sizes of membrane simulations must be increased by at least a factor of 10 before thermodynamic limits are approached for quantities such as surface tension.

On simulating lipid bilayers with an applied surface tension: periodic boundary conditions and undulations.

As sketched in Fig. 1, a current molecular dynamics computer simulation of a lipid bilayer fails to capture significant features of the macroscopic system, including long wavelength undulations. Such fluctuations are intrinsically connected to the value of the macroscopic (or thermodynamic) surface tension (cf. Eqs. 1 and 9; for a related treatment, see Brochard et al., 1975, 1976). Consequently, the surface tension that might be evaluated in an MD simulation should not be expected to equal the surface tension obtained from macroscopic measurements. Put another way, the largest of the three simulations presented here contained over 16,000 atoms and required substantial computer time to complete, but modeled a system of only 36 lipids per side. From this perspective it is not surprising that the system is not at the thermodynamic limit. An important practical consequence of this effect is that simulations with fluctuating area should be carried out with a nonzero applied surface tension (gamma 0 of Fig. 2) even when the macroscopic tension is zero, or close to zero. Computer simulations at fixed surface area, which can explicitly determine pressure anisotropy at the molecular level, should ultimately lend insight into the value of gamma 0, including its dependence on lipid composition and other membrane components. As we have noted and will describe further in separate publications (Feller et al., 1996; Feller et al., manuscript in preparation), surface tensions obtained from simulations can be distorted by inadequate initial conditions and convergence, and are sensitive to potential energy functions, force truncation methods, and system size; it is not difficult, in fact, to tune terms in the potential energy function so as to yield surface tensions close to zero. This is why parameters should be tested extensively on simpler systems, for example, monolayers. The estimates of gamma 0 that we have presented here should be regarded as qualitative, and primarily underscore the assertion that the surface tension of a microscopically flat, simulation-sized patch is significantly greater than zero. As the simulation cell length increases, the surface tension that would be evaluated (or should be applied) decreases; in the limit of micrometer-sized simulation cells, gamma would approach zero or its appropriate thermodynamic value. The theories presented here also imply that the estimation of bilayer surface tension from monolayer data should take the degree of flatness into account. These conclusions are independent of the precise values of parameters such as bending constants. In conclusion, from the simulator's perspective, the question "What is the surface tension of a bilayer?" is better phrased as "What is the value of the applied surface tension necessary to simulate a particular experimental system with a given number of lipids?". As we have shown, the answer to the second question varies, but it should not be assumed a priori to equal zero.

A method for characterizing transition concertedness from polymer dynamics computer simulations.

A statistical method based on classifying the transitions among a set of dihedral angles within an "energy transfer window" is developed, and used to analyze Brownian (BD) and molecular dynamics (MD) simulations of the acyl chains in a lipid bilayer, and MD of neat hexadecane. It is shown for the BD simulation that when a transition of the dihedral angle in the center of the chain occurs, a transition of a particular next nearest neighbor (or angle 2-apart) will follow concertedly with a probability of approximately 0.10 within a time window of approximately 3 ps. The MD bilayer simulations, which are based on a more flexible model of the hydrocarbon chains, yield corresponding concerted transition probabilities of approximately 0.083 and window sizes of 1-2 ps. An analysis of angles 4-apart yields concerted transition probabilities of 0.03 and 0.04 for the BD and MD bilayer simulations, respectively, and window sizes close to those of the corresponding 2-apart cases. Statistical hypothesis testing very strongly rejects the assertion that these follower transitions are occurring at random. Similar analysis reveals marginal or no evidence of concertedness between 1-apart (nearest neighbor) and between 3-apart dihedral angle transitions. The pattern of concertedness for hexadecane is qualitatively similar to that of the lipid chains, although concertedness is somewhat stronger for the 3-apart transitions and somewhat weaker for those 4-apart. Finally, it is suggested that the diffusion of small solute molecules in membranes is better facilitated by nonconcerted transitions, which are associated with relatively large displacements of the chains, than by concerted transitions, which do little to change the chain shape.

Molecular dynamics simulations of a lipid bilayer and of hexadecane: an investigation of membrane fluidity.

Molecular dynamics simulations of a fluid-phase dipalmitoyl phosphatidylcholine lipid bilayer in water and of neat hexadecane are reported and compared with nuclear magnetic resonance spin-lattice relaxation and quasi-elastic neutron scattering data. On the 100-picosecond time scale of the present simulations, there is effectively no difference in the reorientational dynamics of the carbons in the membrane interior and in pure hexadecane. Given that the calculated fast reorientational correlation times and the "microscopic" lateral diffusion of the lipids show excellent agreement with the experimental results, it is concluded that the apparently high viscosity of the membrane is more closely related to molecular interactions on the surface rather than in the interior.

Conformational states of a TT mismatch from molecular dynamics simulation of duplex d (CGCGATTCGCG).

The TT mismatch region in duplex d (CGCGATTCGCG) was studied using a 500-ps molecular dynamics (MD) simulation in water, and a series of 1-ps MD simulations and energy minimizations in vacuum. The DNA maintained its duplex structure, although the mismatch region showed significantly higher flexibility than the GC regions. The predominant conformation in the 500-ps MD simulation involved an average -42 degrees propeller twist between T6 and T'6, and a -22 degree buckle between A5 and T'7. One hydrogen bond was formed between T6 and T'6, and another between T6 and the O2 of T'7, with both Watson-Crick hydrogen bonds between A5 and T'7 remaining intact. The minimizations resulted in conformations with the equivalent hydrogen-bonding pattern, as well as ones with "wobble pair" hydrogen bonds between T6 and T'6. However, the wobble pair conformation was found to be unstable in the water simulation.

Backbone dynamics of calmodulin studied by 15N relaxation using inverse detected two-dimensional NMR spectroscopy: the central helix is flexible.

The backbone dynamics of Ca(2+)-saturated recombinant Drosophila calmodulin has been studied by 15N longitudinal and transverse relaxation experiments, combined with 15N(1H) NOE measurements. Results indicate a high degree of mobility near the middle of the central helix of calmodulin, from residue K77 through S81, with order parameters (S2) in the 0.5-0.6 range. The anisotropy observed in the motion of the two globular calmodulin domains is much smaller than expected on the basis of hydrodynamic calculations for a rigid dumbbell type structure. This indicates that, for the purposes of 15N relaxation, the tumbling of the N-terminal (L4-K77) and C-terminal (E82-S147) lobes of calmodulin is effectively independent. A slightly shorter motional correlation time (tau c approximately 6.3 ns) is obtained for the C-terminal domain compared to the N-terminal domain (tau c approximately 7.1 ns), in agreement with the smaller size of the C-terminal domain. A high degree of mobility, with order parameters of approximately 0.5, is also observed in the loop that connects the first with the second EF-hand type calcium binding domain and in the loop connecting the third and fourth calcium binding domain.

Langevin dynamics of peptides: the frictional dependence of isomerization rates of N-acetylalanyl-N'-methylamide.

The rate constant for the transition between the equatorial and axial conformations of N-acetylalanyl-N'-methylamide has been determined from Langevin dynamics (LD) simulations with no explicit solvent. The isomerization rate is maximum at collision frequency gamma = 2 ps-1, shows diffusive character for gamma greater than or equal to 10 ps-1, but does not approach zero even at gamma = 0.01 ps-1. This behavior differs from that found for a one-dimensional bistable potential and indicates that both collisional energy transfer with solvent and vibrational energy transfer between internal modes are important in the dynamics of barrier crossing for this system. It is suggested that conformational searches of peptides be carried out using LD with a collision frequency that maximizes the isomerization rate (i.e., gamma approximately 2 ps-1). This method is expected to be more efficient than either molecular dynamics in vacuo (which corresponds to LD with gamma = 0) or molecular dynamics in solvent (where dynamics is largely diffusive).

Model for the structure of the lipid bilayer.

A detailed model for the structure and dynamics of the interior of the lipid bilayer in the liquid crystal phase is presented. The model includes two classes of motion: (i) the internal dynamics of the chains, determined from Brownian dynamics simulations with a continuous version of the Marcelja mean-field potential, and (ii) noncollective reorientation (axial rotation and wobble) of the entire molecule, introduced by a cone model. The basic unit of the model is a single lipid chain with field parameters adjusted to fit the 2H order parameters and the frequency-dependent 13C NMR T1 relaxation times of dipalmitoyl phosphatidylcholine bilayers. The chain configurations obtained from the trajectory are used to construct a representation of the bilayer. The resulting lipid assembly is consistent with NMR, neutron diffraction, surface area, and density data. It indicates that a high degree of chain disorder and entanglement exists in biological membranes.

Mean field stochastic boundary molecular dynamics simulation of a phospholipid in a membrane.

Computer simulations of phospholipid membranes have been carried out by using a combined approach of molecular and stochastic dynamics and a mean field based on the Marcelja model. First, the single-chain mean field simulations of Pastor et al. [(1988) J. Chem. Phys. 89, 1112-1127] were extended to a complete dipalmitoylphosphatidylcholine molecule; a 102-ns Langevin dynamics simulation is presented and compared with experiment. Subsequently, a hexagonally packed seven-lipid array was simulated with Langevin dynamics and a mean field at the boundary and with molecular dynamics (and no mean field) in the center. This hybrid method, mean field stochastic boundary molecular dynamics, reduces bias introduced by the mean field and eliminates the need for periodic boundary conditions. As a result, simulations extending to tens of nanoseconds may be carried out by using a relatively small number of molecules to model the membrane environment. Preliminary results of a 20-ns simulation are reported here. A wide range of motions, including overall reorientation with a nanosecond decay time, is observed in both simulations, and good agreement with NMR, IR, and neutron diffraction data is found.