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  • 1.
    Brandt, Erik G.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Interactions and dynamics in biophysical model systems2009Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    Computer simulations of simplified model systems provide understanding of how complex biological systems behave. The simulations give detailed information about the systems, with atomistic resolution, that can be used in combination with experimental knowledge to shed light on underlying physical principles. The thesis presents background information about the studies of two important model systems in biological physics.

    First, metal ion-binding to proteins is investigated in a computational study on a zinc-binding synthetic peptide, to elucidate the binding details. The major scientific contributions from the study are the identification and mapping of the detailed contributions to the binding. A novel correction scheme is worked out, where classic free energy calculations are combined with density functional theory to adjust for quantum mechanical effects.  The sensitivity of the zinc-binding to a specific amino acid segment can be explained in terms of the zinc coordination.

    Second, equilibrium density fluctuations in biological membranes are studied using computer simulations of the lipid bilayer. The fluctuations are linked to several processes; pore formation, membrane permeability and transport of small molecules across themembrane. Because the lipid bilayer behaves similar to a 2D fluid the density fluctuations can be described in the framework of generalized hydrodynamics. The major scientific contributions from the study are the direct calculation of the density-density autocorrelation function from raw data and the observation that the diffusive contribution to the power spectrum (the Rayleigh line) is not single-exponential. In addition, the accuracy of the approximate hydrodynamic solutions is questionable for the propagation of sound waves in the membrane.

  • 2.
    Brandt, Erik G.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Molecular Dynamics Simulations of Fluid Lipid Membranes2011Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Lipid molecules form thin biological membranes that envelop all living cells, and behave as two-dimensional liquid sheets immersed in bulk water. The interactions of such biomembranes with their environment lay the foundation of a plethora of biological processes rooted in the mesoscopic domain - length scales of 1-1000 nm and time scales of 1-1000 ns. Research in this intermediate regime has for a long time been out of reach for conventional experiments, but breakthroughs in computer simulation methods and scattering experimental techniques have made it possible to directly probe static and dynamic properties of biomembranes on these scales.

    Biomembranes are soft, with a relatively low energy cost of bending, and are thereby influenced by random, thermal fluctuations of individual molecules. Molecular dynamics simulations show how in-plane (density fluctuations) and out-of-plane (undulations) motions are intertwined in the bilayer in the mesoscopic domain. By novel methods, the fluctuation spectra of lipid bilayers can be calculated withdirect Fourier analysis. The interpretation of the fluctuation spectra reveals a picture where density fluctuations and undulations are most pronounced on different length scales, but coalesce in the mesoscopic regime. This analysis has significant consequences for comparison of simulation data to experiments. These new methods merge the molecular fluctuations on small wavelengths, with continuum fluctuations of the elastic membrane sheet on large wavelengths, allowing electron density profiles (EDP) and area per lipid to be extracted from simulations with high accuracy.

    Molecular dynamics simulations also provide insight on the small-wavelength dynamics of lipid membranes. Rapidly decaying density fluctuations can be described as propagating sound waves in the framework of linearized hydrodynamics, but there is a slow, dispersive, contribution that needs to be described by a stretched exponential over a broad range of length- and time scales - recent experiments suggest that this behavior can prevail even on micrometer length scales. The origin of this behavior is discussed in the context of fluctuations of the bilayer interface and the molecular structure of the bilayer itself. Connections to recent neutron scattering experiments are highlighted.

  • 3.
    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.

  • 4.
    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.

  • 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.
    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)
  • 6.
    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.

  • 7.
    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).

  • 8. 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)
  • 9. 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.

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