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  • 1.
    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)
  • 2.
    Waheed, Qaiser
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Theoretical Biological Physics.
    Molecular Dynamic Simulations of Biological Membranes2012Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Biological membranes mainly constituent lipid molecules along with some proteins and steroles. The properties of the pure lipid bilayers as well as in the presence of other constituents (in case of two or three component systems) are very important to be studied carefully to model these systems and compare them with the realistic systems. Molecular dynamic simulations provide a good opportunity to model such systems and to study them at microscopic level where experiments fail to do. In this thesis we study the structural and dynamic properties of the pure phospholipid bilayers and the phase behavior of phospholipid bilayers when other constituents are present in them. Material and structural properties like area per lipid and area compressibility of the phospholipids show a big scatter in experiments. These properties are studied for different system sizes and it was found that the increasing undulations in large systems effect these properties. A correction was applied to area per lipid and area compressibility using the Helfrich theory in Fourier space. Other structural properties like order of the lipid chains, electron density and radial distribution functions are calculated which give the structure of the lipid bilayer along the normal and in the lateral direction. These properties are compared to the X-ray and neutron scattering experiments after Fourier transform. Thermodynamic properties like heat capacity and heat of melting are also calculated from derivatives of energies available in molecular dynamics. Heat capacity on the other hand include quantum effect and are corrected for that by applying quantum correction using normal mode analysis for a simple as well as ambiguous system like water. Here it is done for SPC/E water model. The purpose of this study is to further apply the quantum corrections on macromolecules like lipids by using this technique. Furthermore the phase behavior of two component systems (phospholipids/cholesterol) is also studied. Phase transition in these systems is observed at different cholesterol concentrations as a function of temperature by looking at different quantities (as an order parameter) like the order of chains, area per molecule and partial specific area. Radial distribution functions are used to look at the in plane structure for different phases having a different lateral or positional order. Adding more cholesterol orders the lipid chains changing a liquid disordered system into a liquid ordered one and turning a solid ordered system into a liquid ordered one. Further more the free energy of domain formation is calculated to investigate the two phasecoexistence in binary systems. Free energy contains two terms. One is bulk freeenergy which was calculated by the chemical potential of cholesterol moleculein a homogeneous system which is favorable for segregation. Second is thefree energy of having an interface which is calculated from the line tension of the interface of two systems with different cholesterol concentration which in unfavorable for domain formation. The size of the domains calculated from these two contributions to the free energy gives the domains of a few nm in size. Though we could not find any such domains by directly looking at our simulations.

  • 3.
    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.

  • 4.
    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.

  • 5.
    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.

  • 6.
    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)
  • 7.
    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.

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