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  • 1. Aman, K.
    et al.
    Lindahl, E.
    Edholm, Olle
    KTH, Superseded Departments, Physics.
    Hakansson, P.
    Westlund, P. O.
    Structure and dynamics of interfacial water in an L-alpha phase lipid bilayer from molecular dynamics simulations2003In: Biophysical Journal, ISSN 0006-3495, E-ISSN 1542-0086, Vol. 84, no 1, p. 102-115Article in journal (Refereed)
    Abstract [en]

    Based on molecular dynamics simulations, an analysis of structure and dynamics is performed on interfacial water at a liquid crystalline dipalmitoylphosphatidycholine/water system. Water properties relevant for understanding NMR relaxation are emphasized. The first and second rank orientational order parameters of the water O-H bonds were calculated, where the second rank order parameter is in agreement with experimental determined quadrupolar splittings. Also, two different interfacial water regions (bound water regions) are revealed with respect to different signs of the second rank order parameter. The water reorientation correlation function reveals a mixture of fast and slow decaying parts. The fast (ps) part of the correlation function is due to local anisotropic water reorientation whereas the much slower part is due to more complicated processes including lateral diffusion along the interface and chemical exchange between free and bound water molecules. The 100-ns-long molecular dynamics simulation at constant pressure (1 atm) and at a temperature of 50degreesC of 64 lipid molecules and 64 x 23 water molecules lack a slow water reorientation correlation component in the ns time scale. The (H2O)-H-2 powder spectrum of the dipalmitoylphosphatidycholine/water system is narrow and consequently, the NMR relaxation time T-2 is too short compared to experimental results.

  • 2.
    Brandt, Erik G.
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Braun, Anthony R.
    Sachs, Jonathan N.
    Nagle, John F.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Interpretation of Fluctuation Spectra in Lipid Bilayer Simulations2011In: Biophysical Journal, ISSN 0006-3495, E-ISSN 1542-0086, Vol. 100, no 9, p. 2104-2111Article in journal (Refereed)
    Abstract [en]

    Atomic resolution and coarse-grained simulations of dimyristoylphosphatidylcholine lipid bilayers were analyzed for fluctuations perpendicular to the bilayer using a completely Fourier-based method. We find that the fluctuation spectrum of motions perpendicular to the bilayer can be decomposed into just two parts: 1), a pure undulation spectrum proportional to q(-4) that dominates in the small-q regime; and 2), a molecular density structure factor contribution that dominates in the large-q regime. There is no need for a term proportional to q(-2) that has been postulated for protrusion fluctuations and that appeared to have been necessary to fit the spectrum for intermediate q. We suggest that earlier reports of such a term were due to the artifact of binning and smoothing in real space before obtaining the Fourier spectrum. The observability of an intermediate protrusion regime from the fluctuation spectrum is discussed based on measured and calculated material constants.

  • 3.
    Brandt, Erik G.
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Dynamic structure factors from lipid membrane molecular dynamics simulations2009In: Biophysical Journal, ISSN 0006-3495, E-ISSN 1542-0086, Vol. 96, no 5, p. 1828-1838Article in journal (Refereed)
    Abstract [en]

    Dynamic structure factors for a lipid bilayer have been calculated from molecular dynamics simulations. From trajectories of a system containing 1024 lipids we obtain wave vectors down to 0.34 nm(-1), which enables us to directly resolve the Rayleigh and Brillouin lines of the spectrum. The results confirm the validity of a model based on generalized hydrodynamics, but also improves the line widths and the position of the Brillouin lines. The improved resolution shows that the Rayleigh line is narrower than in earlier studies, which corresponds to a smaller thermal diffusivity. From a detailed analysis of the power spectrum, we can, in fact, distinguish two dispersive contributions to the elastic scattering. These translate to two exponential relaxation processes in separate time domains. Further, by including a first correction to the wave-vector-dependent position of the Brillouin lines, the results agree favorably to generalized hydrodynamics even up to intermediate wave vectors, and also yields a 20% higher adiabatic sound velocity. The width of the Brillouin lines shows a linear, not quadratic, dependence to low wave vectors.

  • 4.
    Brandt, Erik G.
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Molecular Dynamics Simulations of In-Plane Density Fluctuations in Phospholipid Bilayers2010In: Biophysical Journal, ISSN 0006-3495, E-ISSN 1542-0086, Vol. 98, no 3, p. 664A-664AArticle in journal (Other academic)
  • 5.
    Brandt, Erik G.
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Stretched exponential dynamics in lipid bilayer simulations2010In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 133, no 11, p. 115101-Article in journal (Refereed)
    Abstract [en]

    The decay of fluctuations in fluid biomembranes is strongly stretched and nonexponential on nanometer lengthscales. We report on calculations of structural correlation functions for lipid bilayer membranes from atomistic and coarse-grained molecular dynamics simulations. The time scales extend up to microseconds, whereas the linear size of the largest systems is around 50 nm. Thus, we can cover the equilibrium dynamics of wave vectors over two orders of magnitude (0.2-20 nm(-1)). The time correlations observed in the simulations are best described by stretched exponential functions, with exponents of 0.45 for the atomistic and 0.60 for the coarse-grained model. Area number density fluctuations, thickness fluctuations, and undulations behave dynamically in a similar way and have almost exactly the same dynamics for wavelengths below 3 nm, indicating that in this regime undulations and thickness fluctuations are governed by in-plane density fluctuations. The out-of-plane height fluctuations are apparent only at the longest wavelengths accessible in the simulations (above 6 nm). The effective correlation times of the stretched exponentials vary strongly with the wave vector. The variation fits inverse power-laws that change with wavelength. The exponent is 3 for wavelengths smaller than about 1.25 nm and switches to 1 above this. There are indications for a switch to still another exponent, 2, for wavelengths above 20 nm. Compared to neutron spin-echo (NSE) experiments, the simulation data indicate a faster relaxation in the hydrodynamic limit, although an extrapolation of NSE data, as well as inelastic neutron scattering data, is in agreement with our data at larger wave vectors.

  • 6.
    Brandt, Erik G.
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Hellgren, Mikko
    Brinck, Tore
    KTH, School of Chemical Science and Engineering (CHE), Chemistry, Physical Chemistry.
    Bergman, Tomas
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Molecular dynamics study of zinc binding to cysteines in a peptide mimic of the alcohol dehydrogenase structural zinc site2009In: Physical Chemistry, Chemical Physics - PCCP, ISSN 1463-9076, E-ISSN 1463-9084, Vol. 11, no 6, p. 975-983Article in journal (Refereed)
    Abstract [en]

    The binding of zinc (Zn) ions to proteins is important for many cellular events. The theoretical and computational description of this binding (as well as that of other transition metals) is a challenging task. In this paper the binding of the Zn ion to four cysteine residues in the structural site of horse liver alcohol dehydrogenase (HLADH) is studied using a synthetic peptide mimic of this site. The study includes experimental measurements of binding constants, classical free energy calculations from molecular dynamics (MD) simulations and quantum mechanical (QM) electron structure calculations. The classical MD results account for interactions at the molecular level and reproduce the absolute binding energy and the hydration free energy of the Zn ion with an accuracy of about 10%. This is insufficient to obtain correct free energy differences. QM correction terms were calculated from density functional theory (DFT) on small clusters of atoms to include electronic polarisation of the closest waters and covalent contributions to the Zn-S coordination bond. This results in reasonably good agreement with the experimentally measured binding constants and Zn ion hydration free energies in agreement with published experimental values. The study also includes the replacement of one cysteine residue to an alanine. Simulations as well as experiments showed only a small effect of this upon the binding free energy. A detailed analysis indicate that the sulfur is replaced by three water molecules, thereby changing the coordination number of Zn from four (as in the original peptide) to six (as in water).

  • 7. Braun, A R
    et al.
    Brandt, Erik
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Edholm, Olof
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Nagle, J F
    Sachs, J N
    Determination of electron density pro les and area-per-lipid from molecular dynamics simulations of large undulating lipid bilayers2011In: Abstract of Papers of the American Chemical Society, ISSN 0065-7727, Vol. 241Article in journal (Other academic)
  • 8. Braun, Anthony R.
    et al.
    Brandt, Erik G.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Nagle, John F.
    Sachs, Jonathan N.
    Determination of Electron Density Profiles and Area from Simulations of Undulating Membranes2011In: Biophysical Journal, ISSN 0006-3495, E-ISSN 1542-0086, Vol. 100, no 9, p. 2112-2120Article in journal (Refereed)
    Abstract [en]

    The traditional method for extracting electron density and other transmembrane profiles from molecular dynamics simulations of lipid bilayers fails for large bilayer systems, because it assumes a flat reference surface that does not take into account long wavelength undulations. We have developed what we believe to be a novel set of methods to characterize these undulations and extract the underlying profiles in the large systems. Our approach first obtains an undulation reference surface for each frame in the simulation and subsequently isolates the long-wavelength undulations by filtering out the intrinsic short wavelength modes. We then describe two methods to obtain the appropriate profiles from the undulating reference surface. Most combinations of methods give similar results for the electron density profiles of our simulations of 1024 DMPC lipids. From simulations of smaller systems, we also characterize the finite size effect related to the boundary conditions of the simulation box. In addition, we have developed a set of methods that use the undulation reference surface to determine the true area per lipid which, due to undulations, is larger than the projected area commonly reported from simulations.

  • 9. Cordomi, Arnau
    et al.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Perez, Juan J.
    Effect of different treatments of long-range interactions and sampling conditions in molecular dynamic simulations of rhodopsin embedded in a dipalmitoyl phosphatidylcholine bilayer2007In: Journal of Computational Chemistry, ISSN 0192-8651, E-ISSN 1096-987X, Vol. 28, no 6, p. 1017-1030Article, review/survey (Refereed)
    Abstract [en]

    The present study analyzes the effect of the simulation conditions on the results of molecular dynamics simulations of G-protein coupled receptors (GPCRs) performed with an explicit lipid bilayer. Accordingly, the present work reports the analysis of different simulations of bovine rhodopsin embedded in a dipalmitoyl phosphatidylcholine (DPPC) lipid bilayer using two different sampling conditions and two different approaches for the treatment of long-range electrostatic interactions. Specifically, sampling was carried out either by using the statistical ensembles NVT or NPT (constant number of atoms, a pressure of 1 arm in all directions and fixed temperature), and the electrostatic interactions were treated either by using a twin-cutoff, or the particle mesh Ewald summation method (PME). The results of the present study suggest that the use of the NPT ensemble in combination with the PME method provide more realistic simulations. The use of NPT during the equilibration avoids the need of an a priori estimation of the box dimensions, giving the correct area per lipid. However, once the system is equilibrated, the simulations are irrespective of the sampling conditions used. The use of an electrostatic cutoff induces artifacts on both lipid thickness and the ion distribution, but has no direct effect on the protein and water molecules.

  • 10. Cordomi, Arnau
    et al.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Perez, Juan J.
    Effect of Force Field Parameters on Sodium and Potassium Ion Binding to Dipalmitoyl Phosphatidylcholine Bilayers2009In: Journal of Chemical Theory and Computation, ISSN 1549-9618, E-ISSN 1549-9626, Vol. 5, no 8, p. 2125-2134Article in journal (Refereed)
    Abstract [en]

    The behavior of electrolytes in molecular dynamics simulations of zwitterionic phospholipid bilayers; is very sensitive to the force field parameters used. Here, several 200 ns molecular dynamics of simulations of dipalmitoyl phosphotidylcholine (PC) bilayers in 0.2 M sodium or potassium chloride using various common force field parameters for the cations are presented. All employed parameter sets give a larger number of Na+ ions than K+ ions that bind to the lipid heads, but depending on the parameter choice quite different results are seen. A wide range of coordination numbers for the Na+ and K+ ions is also observed. These findings have been analyzed and compared to published experimental data. Some simulations produce aggregates of potassium chloride, indicating (in accordance with published simulations) that these force fields do not reproduce the delicate balance between salt and solvated ions. The differences between the force fields can be characterized by one single parameter, the electrostatic radius of the ion, which is correlated to sigma(MO) (M represents Na+/K+), the Lennard-Jones radius. When this parameter exceeds a certain threshold, binding to the lipid heads is no longer observed. One would, however, need more accurate experimental data to judge or rank the different force fields precisely. Still, reasons for the poor performance of some of the parameter sets are clearly demonstrated, and a quality control. procedure is provided.

  • 11. Cordomi, Arnau
    et al.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Perez, Juan J.
    Effect of ions on a dipalmitoyl phosphatidylcholine bilayer. A molecular dynamics simulation study2008In: Journal of Physical Chemistry B, ISSN 1520-6106, E-ISSN 1520-5207, Vol. 112, no 5, p. 1397-1408Article in journal (Refereed)
    Abstract [en]

    The effect of physiological concentrations of different chlorides on the structure of a dipalmitoyl phosphatidylcholine (DPPC) bilayer has been investigated through atomistic molecular dynamics simulations. These calculations provide support to the concept that Li+, Na+, Ca2+, Mg2+, Sr2+, Ba2+, and Ac3+, but not K+, bind to the lipid-head oxygens. Ion binding exhibits an influence on lipid order, area per lipid, orientation of the lipid head dipole, the charge distribution in the system, and therefore the electrostatic potential across the head-group region of the bilayer. These structural effects are sensitive to the specific characteristics of each cation, i.e., radius, charge, and coordination properties. These results provide evidence aimed at shedding some light into the apparent contradictions among different studies reported recently regarding the ordering effect of ions on zwitterionic phosphatidylcholine lipid bilayers.

  • 12.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Time and length scales in lipid bilayer simulations2008In: Computational Modeling Of Membrane Bilayers / [ed] Feller, SE, 2008, Vol. 60, p. 91-110Chapter in book (Refereed)
    Abstract [en]

    Time and length scales for different kinds of local and collective motions in lipid bilayers that may be probed in molecular dynamics simulations are discussed. The possibility to determine parameters in continuum models using simulation techniques is discussed. Agreements and discrepancies between simulations and experimental data are presented and discussed. The chapter covers large scale undulations and peristaltic thickness fluctuations, hydrocarbon chain reorientation motion, lipid lateral diffusion and motion of the entire monolayers with respect to each other and with respect to the water.

  • 13.
    Edholm, Olle
    et al.
    KTH, Superseded Departments, Physics.
    Blomberg, C.
    Stretched exponentials and barrier distributions2000In: Chemical Physics, ISSN 0301-0104, E-ISSN 1873-4421, Vol. 252, no 02-jan, p. 221-225Article in journal (Refereed)
    Abstract [en]

    Non exponential relaxation in complex macromolecular systems may be the consequence of dispersedness giving rise to different free energy barriers for different molecules. An approximate analytic formula that relates the time derivative of the decaying function to a probability distribution for the barrier is derived. From this, so called stretched exponentials, e(-t beta),are obtained from barrier distributions with width k(B)T/beta in energy and some asymmetry towards low energies. They may be represented as double exponential functions. An exact general formula that relates the Fourier transforms of the barrier height distribution and the time decaying function is also derived. This is gives a much more stable method for the numerical determination of the barrier height distribution than direct inversion of the Laplace transform.

  • 14.
    Edholm, Olle
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Nagle, J. F.
    Areas of molecules in membranes consisting of mixtures2005In: Biophysical Journal, ISSN 0006-3495, E-ISSN 1542-0086, Vol. 89, no 3, p. 1827-1832Article in journal (Refereed)
    Abstract [en]

    The question has arisen in recent literature: how to partition the total area in simulations of membranes consisting of more than one kind of molecule into average areas for each kind of molecule. Several definitions have been proposed, each of which has arbitrary features. When applied to mixtures of cholesterol and DPPC, these definitions give different results. This note recalls that physical chemistry provides a canonical way to de. ne molecular area, in analogy to the definition of partial-specific volume. Results for partial-specific area are obtained from simulations of DPPC/cholesterol bilayers and compared to the results from the other recent definitions. The partial-specific-area formalism dramatically demonstrates the condensing effect of cholesterol and this leads to the introduction of a specific model that accounts for the area of mixtures of cholesterol and lipid over the entire range of cholesterol concentrations.

  • 15.
    Edholm, Olle
    et al.
    KTH, Superseded Departments, Physics.
    Nordlander, P.
    Chen, W.
    Ohlsson, P. I.
    Smith, M. L.
    Paul, J.
    The effect of water on the Fe3+/Fe2+ reduction potential of heme2000In: Biochemical and Biophysical Research Communications - BBRC, ISSN 0006-291X, E-ISSN 1090-2104, Vol. 268, no 3, p. 683-687Article in journal (Refereed)
    Abstract [en]

    Hemeproteins can act as catalysts, oxygen carriers or electron conductors. The ferric/ferrous reduction potential E-m7 of iron in the center of the prosthetic group ranges from negative values for peroxidases to an extreme positive value for cytochrome a, with Hb and Mb in the middle [1]. Proteins exercise their influence on E-m7 in several ways: via substituents at the periphery of the chelate structure, via the proximal ligand, and via interaction with the surrounding medium, amino acid side chains, or polar solvents. Work on recombined proteins and ap-substituted free hemes documented that the first two effects are additive [2]. For the third effect, models of the dielectric media on a molecular level have been successfully applied [3-5]. E-m7 has also been empirically correlated to the degree of heme exposure to water [6-8]. The apoprotein/porphyrin and water/porphyrin interfaces are complementary since water molecules fill any empty space in the crevice and surround any pertinent part of heme outside the protein boundary. The present work links to this idea by a combination of statistical mechanics simulations and quantum mechanical calculations comparing heme in water with heme in an apolar environment. Our results show that polarization of the porphyrin pi-electron cloud by the held from water dipoles influences E-m7 The dominant effect of this and other determinates of iron electron availability is perturbations of delocalized electron density in the porphyrin chelate, reproduced by a model where the prosthetic group is treated as a disc of uniform electron density. The present work is also of interest since the interfacial energy constitutes the main barrier for heme-protein Separation [9-11].

  • 16.
    Edholm, Olle
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Tjörnhammar, Richard
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Waheed, Qaiser
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Cholesterol/Phospholipid Bilayer Phase Diagrams from Coarse Grained Simulations2013In: Biophysical Journal, ISSN 0006-3495, E-ISSN 1542-0086, Vol. 104, no 2, p. 590A-590AArticle in journal (Other academic)
  • 17. Hakansson, P.
    et al.
    Westlund, P. O.
    Lindahl, E.
    Edholm, Olle
    KTH, Superseded Departments, Physics.
    A direct simulation of EPR slow-motion spectra of spin labelled phospholipids in liquid crystalline bilayers based on a molecular dynamics simulation of the lipid dynamics2001In: Physical Chemistry, Chemical Physics - PCCP, ISSN 1463-9076, E-ISSN 1463-9084, Vol. 3, no 23, p. 5311-5319Article in journal (Refereed)
    Abstract [en]

    EPR line shapes can be calculated from the stochastic Liouville equation assuming a stochastic model for the reorientation of the spin probe. Here we use instead and for the first time a detailed molecular dynamics (MD) simulation to generate the stochastic input to the Langevin form of the Liouville equation. A 0.1 mus MD simulation at T = 50 degreesC of a small lipid bilayer formed by 64 dipalmitoylphosphatidylcholine (DPPC) molecules at the water content of 23 water molecules per lipid was used. In addition, a 10 ns simulation of a 16 times larger system consisting of 32 DPPC molecules with a nitroxide spin moiety attached at the sixth position of the sn2 chain and 992 ordinary DPPC molecules, was used to investigate the extent of the perturbation caused by the spin probe. Order parameters, reorientational dynamics and the EPR FID curve were calculated for spin probe molecules and ordinary DPPC molecules. The timescale of the electron spin relaxation for a spin-moiety attached at the sixth carbon position of a DPPC lipid molecule is 11.9 x 10(7) rad s(-1) and for an unperturbed DPPC molecule it is 3.5 x 10(7) rad s(-1).

  • 18. Hellgren, M.
    et al.
    Sandberg, L.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    A comparison between two prokaryotic potassium channels (KirBac1.1 and KcsA) in a molecular dynamics (MD) simulation study2006In: Biophysical Chemistry, ISSN 0301-4622, E-ISSN 1873-4200, Vol. 120, no 1, p. 1-9Article in journal (Refereed)
    Abstract [en]

    The two potassium ion channels KirBac1.1 and KcsA are compared in a Molecular Dynamics (MD) simulation study. The location and motion of the potassium ions observed in the simulations are compared to those in the X-ray structures and previous simulations. In our simulations several of the crystallography resolved ion sites in KirBac1.1 are occupied by ions. In addition to this, two in KirBac1.1 unresolved sites where occupied by ions at sites that are in close correspondence to sites found in KcsA. There is every reason to believe that the conserved alignment of the selectivity filter in the potassium ion channel family corresponds to a very similar mechanism for ion transport across the filter. The gate residues, Phe146 in KirBac1.1 and Ala111 in KcsA acted in the simulations as effective barriers which never were passed by ions nor water molecules.

  • 19. Hofsass, C.
    et al.
    Lindahl, E.
    Edholm, Olle
    KTH, Superseded Departments, Physics.
    Molecular dynamics simulations of phospholipid bilayers with cholesterol2003In: Biophysical Journal, ISSN 0006-3495, E-ISSN 1542-0086, Vol. 84, no 4, p. 2192-2206Article in journal (Refereed)
    Abstract [en]

    To investigate the microscopic interactions between cholesterol and lipids in biological membranes, we have performed a series of molecular dynamics simulations of large membranes with different levels of cholesterol content. The simulations extend to 10 ns, and were performed with hydrated dipalmitoylphosphatidylcholine (DPPC) bilayers. The bilayers contain 1024 lipids of which 0-40% were cholesterol and the rest DPPC. The effects of cholesterol on the structure and mesoscopic dynamics of the bilayer were monitored as a function of cholesterol concentration. The main effects observed are a significant ordering of the DPPC chains (as monitored by NMR type order parameters), a reduced fraction of gauche bonds, a reduced surface area per lipid, less undulations-corresponding to an increased bending modulus for the membrane, smaller area fluctuations, and a reduced lateral diffusion of DPPC-lipids as well as cholesterols.

  • 20. Lindahl, E.
    et al.
    Edholm, Olle
    KTH, Superseded Departments, Physics.
    Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations2000In: Biophysical Journal, ISSN 0006-3495, E-ISSN 1542-0086, Vol. 79, no 1, p. 426-433Article in journal (Refereed)
    Abstract [en]

    Molecular dynamics simulations of fully hydrated Dipalmitoylphosphatidylcholine bilayers, extending temporal and spatial scales by almost one order of magnitude, are presented. The present work reaches system sizes of 1024 lipids and times 10-60 ns. The simulations uncover significant dynamics and fluctuations on scales of several nanoseconds, and enable direct observation and spectral decomposition of both undulatory and thickness fluctuation modes. Although the former modes are strongly damped, the latter exhibit signs of oscillatory behavior. From this, it has been possible to calculate mesoscopic continuum properties in good agreement with experimental values. A bending modulus of 4 x 10(-20) J, bilayer area compressibility of 250-300 mN/m, and mode relaxation times in the nanosecond range are obtained. The theory of undulatory motions is revised and further extended to cover thickness fluctuations. Finally, it is proposed that thickness fluctuations is the explanation to the observed system-size dependence of equilibrium-projected area per lipid.

  • 21. Lindahl, E.
    et al.
    Edholm, Olle
    KTH, Superseded Departments, Physics.
    Molecular dynamics simulation of NMR relaxation rates and slow dynamics in lipid bilayers2001In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 115, no 10, p. 4938-4950Article in journal (Refereed)
    Abstract [en]

    By performing a 100 ns molecular dynamics simulation of a dipalmitoylphosphatidylcholine lipid bilayer we are able to calculate the full rotational correlation functions of the hydrocarbon chain C-H vectors and determine rotational diffusion of entire lipid molecules with high accuracy. The simulated relaxation is strongly nonexponential already on time scales from 0.1 ps. Fourier transformation of the correlation functions yields data that in the relatively narrow frequency range accessible to H-2 and C-13 NMR experiments are consistent with the reported 1/root omega dependence of spin-lattice relaxation rates. The simulated relaxation dynamics is found to be slightly faster than experimental, which we suggest is explained by the limited accuracy in dihedral potentials of present force fields. By introducing a local frame of reference, the chain motion is separated into local dihedral transitions and overall lipid reorientation. The internal chain isomerization dominates the relaxation and is well-described by power laws. The small molecular reorientation contribution to the decay is exponential with separate time scales for motions of the lipid long axis (D-perpendicular to = 2.9 x 10(7) s(-1)) and spinning rotation around it (D-parallel to = 3.8 x 10(8) s(-1)). The mean square lateral displacement over 100 ns, corrected for the relative motions of the layers, corresponds to a long-time translational diffusion coefficient of D-lat = 1.2 x 10(-7) cm(2) s(-1) at 323 K.

  • 22. Lindahl, E.
    et al.
    Edholm, Olle
    KTH, Superseded Departments, Physics.
    Spatial and energetic-entropic decomposition of surface tension in lipid bilayers from molecular dynamics simulations2000In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 113, no 9, p. 3882-3893Article in journal (Refereed)
    Abstract [en]

    The spatial and groupwise distribution of surface tension in a fully hydrated 256 lipid dipalmitoylphosphatidylcholine (DPPC) bilayer is determined from a 5 ns molecular dynamics simulation by resolving the normal and lateral pressures in space through the introduction of a local virial. The resulting surface tension is separated into contributions from different types of interactions and pairwise terms between lipid headgroups, chains and water. By additionally performing a series of five simulations at constant areas ranging from 0.605 to 0.665 nm(2) (each of 6 ns length), it is possible to independently resolve the energetic contributions to surface tension from the area dependence of the interaction energies. This also enables us to calculate the remaining entropic part of the tension and the thermal expansivity. Together with the total lateral pressures this yields a full decomposition of surface tension into energetic and entropic contributions from electrostatics, Lennard-Jones and bonded interactions between lipid chains, headgroups and water molecules. The resulting total surface tension in the bilayer is found to be a sum of very large terms of opposing signs, explaining the sensitivity of simulation surface tension to details in force fields. Headgroup and headgroup-water interactions are identified as attractive on average while the chain region wants to expand the bilayer. Both effects are dominated by entropic contributions but there are also substantial energetic terms in the hydrophobic core. The net lateral pressure is small and relatively smooth compared to the individual components, in agreement with experimental observations of DPPC lipids forming stable bilayers.

  • 23.
    Lindahl, Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical & Computational Biophysics.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Solvent diffusion outside macromolecular surfaces1998In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 57, p. 791-796Article in journal (Refereed)
    Abstract [en]

    The effect of the inhomogeneous environment upon solvent molecules close to a macromolecular surface is evaluated from a molecular-dynamics simulation of a protein, myoglobin, in water solution. The simulation is analyzed in terms of a mean-field potential from the protein upon the water molecules and spatially varying translational diffusion coefficients for solvent molecules in directions parallel and perpendicular to the protein surface. The diffusion coefficients can be obtained from the slope of the average-square displacements vs time, as well as from the integral of the velocity autocorrelation functions. It is shown that the former procedure gives a lot of ambiguities due to the variation of the slope of the curve with time. The latter, however, after analytic correction for the contribution from algebraic long-time tails, furnish a much more reliable alternative.

  • 24.
    Lundberg, Linnea
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Dispersion Corrections to the Surface Tension at Planar Surfaces2016In: Journal of Chemical Theory and Computation, ISSN 1549-9618, E-ISSN 1549-9626, Vol. 12, no 8, p. 4025-4032Article in journal (Refereed)
    Abstract [en]

    Molecular dynamics simulations are usually performed using cutoffs (r(c)) for the short-ranged dispersion interactions (r(-6)). For isotropic systems, long-range interactions are often added in a continuum approximation. This usually leads to excellent results that are independent of the cutoff length down to about 1 nm. For systems with interfaces or other anisotropic systems the situation is more complicated. We study here planar interfaces, focusing on the surface tension, which is sensitive to cutoffs. Previous analytic results giving the long-range correction to the surface tension of a liquid-vapor interface as a two- or three-dimensional integral are revisited. They are generalized by introducing a dispersion density profile which makes it possible to handle multicomponent systems. For the simple but common hyperbolic tangent profile the integral may be Taylor-expanded in the dimensionless parameter obtained by dividing the profile width with the cutoff length. This parameter is usually small, and excellent agreement with numerical calculations of the integral is obtained by keeping two terms in the expansion. The results are compared to simulations with different lengths of the cutoff for some simple systems. The surface tension in the simulations varies linearly in r(c)(-2), although a small r(c)(-4)-term may be added to improve the agreement. The slope of the r(c)(-2)-line could in several cases be predicted from the change in dispersion density at the interface. The disagreements observed in some cases when comparing to theory occur when the finite cutoff used in the simulations causes structural differences compared to long-range cutoffs or Ewald summation for the r(-6)-interactions.

  • 25. Marrink, S. J.
    et al.
    Lindahl, E.
    Edholm, Olle
    KTH, Superseded Departments, Physics.
    Mark, A. E.
    Simulation of the spontaneous aggregation of phospholipids into bilayers2001In: Journal of the American Chemical Society, ISSN 0002-7863, E-ISSN 1520-5126, Vol. 123, no 35, p. 8638-8639Article in journal (Refereed)
  • 26.
    Pousaneh, Faezeh
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Maciolek, Anna
    Molecular dynamics simulation of a binary mixture near the lower critical point2016In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 145, no 1, article id 014501Article in journal (Refereed)
    Abstract [en]

    2,6-lutidine molecules mix with water at high and low temperatures but in a wide intermediate temperature range a 2,6-lutidine/water mixture exhibits a miscibility gap. We constructed and validated an atomistic model for 2,6-lutidine and performed molecular dynamics simulations of 2,6-lutidine/water mixture at different temperatures. We determined the part of demixing curve with the lower critical point. The lower critical point extracted from our data is located close to the experimental one. The estimates for critical exponents obtained from our simulations are in a good agreement with the values corresponding to the 3D Ising universality class.

  • 27. Sandberg, L.
    et al.
    Casemyr, R.
    Edholm, Olle
    KTH, Superseded Departments, Physics.
    Calculated hydration free energies of small organic molecules using a nonlinear dielectric continuum model2002In: Journal of Physical Chemistry B, ISSN 1520-6106, E-ISSN 1520-5207, Vol. 106, no 32, p. 7889-7897Article in journal (Refereed)
    Abstract [en]

    Prediction of solvation free energies is an important subject in fundamental natural science but also important to the pharmaceutical and food industry. A popular modeling approach is to treat the solution by an implicit solvent model. The solute molecule is rigid with a fixed effective charge distribution localized at the atomic nuclei positions. The hydration free energy is described by the van der Waals energy, the solute cavity formation energy in the water phase, and the-change in electrostatic solute-solvent interaction energy. The dielectric continuum is generally assumed to be a simple medium, that is, linear, homogeneous, and isotropic. However, this approximation is quite severe and will give too hydrophilic solvation free energies. We show here that the simple medium approximation must be relaxed and nonlinearity must be taken into consideration. In strong electric fields, the solvent polarization becomes saturated and the dielectric no longer responds linearly in the applied field. This effect is well-described by the modified Langevin-Debye model. This nonlinear solvation model is used to study the hydration of 181 small organic molecules. Atomic charges and radii of the solute molecule are described by a standard classical force field. We apply the optimized potentials for liquid simulation all atom (OPLS-AA) force field, which is parametrized to reproduce both structural and thermodynamical data. This leads to a mean unsigned error of 0.6 kcal/mol, which is a 25% improvement compared to a simple medium approach. The nonlinear solvation model is further improved by introducing a few charge-scaling parameters for some functional groups that show a systematic deviation from their experimental data. This yields a mean unsigned error of 0.4 kcal/mol, which is only twice the experimental uncertainty. Hence, we conclude that nonlinear dielectric effects are indeed important to incorporate in implicit solvent models, even for neutral polar molecules.

  • 28. Sandberg, L.
    et al.
    Edholm, Olle
    KTH, Superseded Departments, Physics.
    Calculated solvation free energies of amino acids in a dipolar approximation2001In: Journal of Physical Chemistry B, ISSN 1089-5647, Vol. 105, no 1, p. 273-281Article in journal (Refereed)
    Abstract [en]

    The solvation foe energies of amino acids (hydrophobicities) are rationalized here by using a simple electrostatic ab initio model. The parameters of the model are the surface energy density (gamma = 9.55 kJ/mol/nm(2), the same for all atoms), the fractional charges, and the radii of the atoms of the amino acids. From the fractional charges, dipoles are constructed, and the polarization energies (self-energies) of the dipoles are calculated. The saturation effect of the solvent is included in the model. The dipole electrostatic contribution is in general not very sensitive to the choice of parameters. In contrast, the self-energies of single net charges are extremely sensitive to the choice of the Born radius. However, for amino acids that may carry a net charge, this energy will be prohibitively large in a low-dielectric medium. Therefore, they will in general change their protonation state to become neutral. The energetic cost of this is calculated from the difference between the amino acid side chain pK(a)'s and the pH of the solvent. This results in a hydrophobicity scale for amino acid side chains based on fundamental physics that agrees well with experimental hydrophobicity scales. The solvation energy for the amino acid backbone (the peptide bond) can also be calculated in this way. This gives good agreement with available experimental data.

  • 29. Sandberg, L.
    et al.
    Edholm, Olle
    KTH, Superseded Departments, Physics.
    Nonlinear response effects in continuum models of the hydration of ions2002In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 116, no 7, p. 2936-2944Article in journal (Refereed)
    Abstract [en]

    The evaluation of the free energy of hydration depends essentially upon a calculation of the difference in polarization energy in a vacuum and in water. This is feasible by electrostatic continuum theory which is lucid and computationally effortless. It is, however, insufficient to apply the frequently used linear response approximation and nonlinear response effects must be integrated with the continuum model. We start from the time-honored Langevin-Debye theory and modify it to even describe polar liquids such as aqueous solvents. The modified Langevin-Debye model is then applied to study the hydration of cations. It is to be noted that reaction-field models are unapplicable to a nonlinear dielectric in an inhomogeneous field. The nonlinear effects are less than 10 kJ/mol or 2% for monovalent ions. However, for multiply charged ions the effect can be as large as 1000 kJ/mol or 15% and the nonlinear response model reduces the mean error of the calculated hydration free energy by at least 60%, which results in a mean error of only 4% for such ions. The mean error is of the same magnitude as the electrostatic free energy uncertainty.

  • 30. Sandberg, L.
    et al.
    Edholm, Olle
    KTH, Superseded Departments (pre-2005), Physics.
    Response to A fast and simple method to calculate protonation states in proteins2000In: Proteins: Structure, Function, and Bioinformatics, ISSN 0887-3585, E-ISSN 1097-0134, Vol. 40, no 1, p. 4-5Article in journal (Refereed)
  • 31.
    Tjörnhammar, Richard
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Molecular dynamics simulations of Zn2+ coordination in protein binding sites2010In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 132, no 20, p. 205101-Article in journal (Refereed)
    Abstract [en]

    A systematic molecular dynamics (MD) study of zinc binding to a peptide that mimics the structural binding site of horse liver alcohol dehydrogenase (HLADH) has been conducted. The four zinc binding cysteines were successively mutated into alanines to study the stability, zinc coordination, and free energy of binding. The zinc ion is coordinated to four sulfurs in the native peptide as in x-ray structures of HLADH. When the cysteines are replaced by alanines, the zinc coordinating sulfurs are replaced by waters and/or polypeptide backbone carbonyl oxygens. With two or fewer cysteines, the coordination number increases from four to six, while the coordination number varies between four and six with three cysteines depending on which of the cysteines that is replaced by an alanine. The binding free energies of zinc to the proteins were calculated from MD free energy integration runs to which corrections from quantum mechanical cluster calculations were added. There is a reasonable correlation with experimental binding free energies [T. Bergman , Cell. Mol. Life Sci. 65, 4019 (2008)]. For the chains with the lowest structural fluctuations and highest free energies lower coordination numbers for zinc are obtained. Finally, x-ray absorption fine structure spectra were calculated from the MD structures.

  • 32.
    Tjörnhammar, Richard
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Reparameterized united atom model for molecular dynamics simulations of gel and fluid phosphatidylcholine bilayers2014In: Journal of Chemical Theory and Computation, ISSN 1549-9618, E-ISSN 1549-9626, Vol. 10, no 12, p. 5706-5715Article in journal (Refereed)
    Abstract [en]

    A new united atom parametrization of diacyl lipids like dipalmitoylphosphatidylcholine (DPPC) and the dimyristoylphosphatidylcholine (DMPC) has been constructed based on ab initio calculations to obtain fractional charges and the dihedral potential of the hydrocarbon chains, while the Lennard-Jones parameters of the acyl chains were fitted to reproduce the properties of liquid hydrocarbons. The results have been validated against published experimental X-ray and neutron scattering data for fluid and gel phase DPPC. The derived charges of the lipid phosphatidylcholine (PC) headgroup are shown to yield dipole components in the range suggested by experiments. The aim has been to construct a new force field that retains and improves the good agreement for the fluid phase and at the same time produces a gel phase at low temperatures, with properties coherent with experimental findings. The gel phase of diacyl-PC lipids forms a regular triangular lattice in the hydrocarbon region. The global bilayer tilt obtains an azimuthal value of 31 degrees and is aligned between lattice vectors in the bilayer plane. We also show that the model yields a correct heat of melting as well as decent heat capacities in the fluid and gel phase of DPPC.

  • 33.
    Tjörnhammar, Richard
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    The shape and free energy of a lipid bilayer surrounding a membrane inclusion2013In: Chemistry and Physics of Lipids, ISSN 0009-3084, E-ISSN 1873-2941, Vol. 169, p. 2-8Article in journal (Refereed)
    Abstract [en]

    Membrane inclusion interactions are studied within the scope of continuum theory. We show that the free energy functional for the membrane thickness can be rewritten as a constant times a dimensionless integral. For cylindrical inclusions, the resulting differential equation gives a thickness profile that depends on the radius of the cylinder and one single lipid property, a correlation length that is determined by the ratio of the thickness compressibility and bending moduli. The solutions decay in a non-monotonic fashion with one single observable minimum. A solution for planar geometry may either be explicitly constructed or obtained by letting the radius of the cylinder go to infinity. In dimensionless units the initial derivative of the thickness profile is universal and equal to -1/root 2 In physical units, the derivative depends on the size of the hydrophobic mismatch as well as the membrane correlation length and will usually be fairly small but clearly non-zero. The line tension between the protein inclusion and a fluid phase membrane will depend on the hydrophobic mismatch and be of the order of 10 pN (larger for the gel phase). This results in free energy costs for the inclusion that will be up to tens of kJ/mol (in the fluid phase).

  • 34.
    Tjörnhammar, Richard
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Edholm, Olof
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical & Computational Biophysics.
    Atomistic Simulations of Gel and Liquid Crystalline Lipid Bilayers2014In: Biophysical Journal, ISSN 0006-3495, E-ISSN 1542-0086, Vol. 106, no 2, p. 403A-403AArticle in journal (Other academic)
  • 35.
    Waheed, Qaiser
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Free energy for cholesterol insertion into lipid bilayers studied by molecular dynamic simulationsArticle in journal (Other academic)
    Abstract [en]

    Lipid bilayers consisting of binary mixtures of phospholipids and cholesterol are studied above and below the main phase transition temperature using coarse grained (CG) and united atom (UA) models by molecular dynamics simulations. The purpose is to explore whether phase segregation into cholesterol-rich and cholesterol-poor domains is favorable from a free energy point of view and what the required size of these domains would be. We observe directly in simulations that phase separated fluid phase systems mix in less than 200 ns. Since, the dynamics is about 2 orders of magnitude slower in the gel phase mixing was not observed in such system. The chemical potential for cholesterol insertion was calculated from simulations. This resulted in a small bulk free energy of about 0.3kBT per lipid that favors phase separation while a small line tension (a couple of pN) between cholesterol-rich and -poor regions favors mixing. Although a simple continuum theory would indicate stabilization of domains as small as 1-2 nm in size, this was not observed in direct simulations.

  • 36.
    Waheed, Qaiser
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Quantum Corrections to Classical Molecular Dynamics Simulations of Water and Ice2011In: Journal of Chemical Theory and Computation, ISSN 1549-9618, E-ISSN 1549-9626, Vol. 7, no 9, p. 2903-2909Article in journal (Refereed)
    Abstract [en]

    Classical simulations of simple water models reproduce many properties of the liquid and ice but overestimate the heat capacity by about 65% at ordinary temperatures and much more for low temperature ice. This is due to the fact that the atomic vibrations are quantum mechanical. The application of harmonic quantum corrections to the molecular motion results in good heat capacities for the liquid and for ice at low temperatures but a successively growing positive deviation from experimental results for ice above 200 K that reaches 15% just below melting. We suggest that this deviation is due to the lack of quantum corrections to the anharmonic motions. For the liquid, the anharmonicities are even larger but also softer and thus in less need of quantum correction. Therefore, harmonic quantum corrections to the classically calculated liquid heat capacities result in agreement with the experimental values. The classical model underestimates the heat of melting by 15%, while the application of quantum corrections produces fair agreement. On the other hand, the heat of vaporization is overestimated by 10% in the harmonically corrected classical model.

  • 37.
    Waheed, Qaiser
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Undulation Contributions to the Area Compressibility in Lipid Bilayer Simulations2009In: Biophysical Journal, ISSN 0006-3495, E-ISSN 1542-0086, Vol. 97, no 10, p. 2754-2760Article in journal (Refereed)
    Abstract [en]

    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 similar to 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.

  • 38.
    Waheed, Qaiser
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Edholm, Olof
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Material Properties of Lipid Membranes from Molecular Dynamics Simulations2010In: Biophysical Journal, ISSN 0006-3495, E-ISSN 1542-0086, Vol. 98, no 3, p. 490A-490AArticle in journal (Other academic)
  • 39.
    Waheed, Qaiser
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Tjörnhammar, Richard
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Phase Transitions in Coarse-Grained Lipid Bilayers Containing Cholesterol by Molecular Dynamics Simulations2012In: Biophysical Journal, ISSN 0006-3495, E-ISSN 1542-0086, Vol. 103, no 10, p. 2125-2133Article in journal (Refereed)
    Abstract [en]

    Coarse-grained simulations of model membranes containing mixtures of phospholipid and cholesterol molecules at different concentrations and temperatures have been performed. A random mixing without tendencies for segregation or formation of domains was observed on spatial scales corresponding to a few thousand lipids and timescales up to several micro-seconds. The gel-to-liquid crystalline phase transition is successively weakened with increasing amounts of cholesterol without disappearing completely even at a concentration of cholesterol as high as 60%. The phase transition temperature increases slightly depending on the cholesterol concentration. The gel phase system undergoes a transition with increasing amounts of cholesterol from a solid-ordered phase into a liquid-ordered one. In the solid phase, the amplitude of the oscillations in the radial distribution function decays algebraically with a prefactor that goes to zero at the solid-liquid transition.

  • 40.
    Wohlert, Jakob
    et al.
    KTH, School of Engineering Sciences (SCI), Physics.
    den Otter, W. K.
    Edholm, Olof
    KTH, School of Engineering Sciences (SCI), Physics.
    Briels, W.J.
    Free energy of a trans-membrane pore calculated from atomistic molecular dynamics simulations2006In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 124, p. 154905-Article in journal (Refereed)
    Abstract [en]

    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.

  • 41.
    Wohlert, Jakob
    et al.
    KTH, Superseded Departments, Physics.
    Edholm, Olle
    KTH, Superseded Departments, Physics.
    The Range and Shielding of Dipole-Dipole Interactions in Phospholipid Bilay2004In: Biophysical Journal, ISSN 0006-3495, E-ISSN 1542-0086, Vol. 87, p. 2433-Article in journal (Refereed)
  • 42.
    Wohlert, Jakob
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Edholm, Olle
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    The range and shielding of dipole-dipole interactions in phospholipid bilayers2004In: Biophysical Journal, ISSN 0006-3495, E-ISSN 1542-0086, Vol. 87, no 4, p. 2433-2445Article in journal (Refereed)
    Abstract [en]

    In molecular dynamics simulations of lipid bilayers, the structure is sensitive to the precise treatment of electrostatics. The dipole-dipole interactions between headgroup dipoles are not long-ranged, but the area per lipid and, through it, other properties of the bilayer are very sensitive to the detailed balance between the perpendicular and in-plane components of the headgroup dipoles. This is affected by the detailed properties of the cutoff scheme or if long-range interactions are included by Ewald or particle-mesh Ewald techniques. Interaction between the in-plane components of the headgroup dipoles is attractive and decays as the inverse sixth power of distance. The interaction is screened by the square of a dielectric permittivity close to the value for water. Interaction between the components perpendicular to the membrane plane is repulsive and decays as the inverse third power of distance. These interactions are screened by a dielectric permittivity of the order 10. Thus, despite the perpendicular components being much smaller in magnitude than the in-plane components, they will dominate the interaction energies at large distances.

  • 43.
    Wohlert, Jakob
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Edholm, Olof
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Dynamics in atomistic simulations of phospholipid membranes: Nuclear magnetic resonance relaxation rates and lateral diffusion2006In: Journal of chemical physics, ISSN 0021-9606, Vol. 125, p. 204703-Article in journal (Refereed)
    Abstract [en]

    It is shown that a long, near microsecond, atomistic simulation can shed some light upon the dynamical processes occurring in a lipid bilayer. The analysis focuses on reorientational dynamics of the chains and lateral diffusion of lipids. It is shown that the reorientational correlation functions exhibits an algebraic decay (rather than exponential) for several orders of magnitude in time. The calculated nuclear magnetic resonance relaxation rates agree with experiments for carbons at the C7 position while there are some differences for C3. Lateral diffusion can be divided into two stages. In a first stage occurring at short times, t < 5 ns, the center of mass of the lipid moves due to conformational changes of the chains while the headgroup position remains relatively fixed. In this stage, the center of mass can move up to similar to 0.8 nm. The fitted short-time diffusion coefficient is D-1=13x10(-7) cm(2) s(-1) On a longer time scale, the diffusion coefficient becomes D-2=0.79x10(-7) cm(2) s(-1).

1 - 43 of 43
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