We describe simulations of Proteins and artificial pseudo-molecules
interacting and shaping lipid bilayer membranes. We extract protein diffusion
Parameters, membrane deformation profiles and the elastic properties of the
used membrane models in preparation of calculations based on a large scale
continuum model

Gräser, Carsten

Klein, Rupert

Peters, Jan Henning

English

arXiv

We describe simulations of Proteins and artificial pseudo-molecules interacting and shaping lipid bilayer membranes. We extract protein diffusion Parameters, membrane deformation profiles and the elastic properties of the used membrane models in preparation of calculations based on a large scale continuum model

Peters, J.H.

Gräser, C.

Klein, R.

Repository: Freie Universität Berlin (FU), Math Department (fu_mi_publications)

CRC 1114 – ReportMembrane Deformation by N-BAR Proteins:Extraction of membrane geometry and proteindiffusion characteristics from MD simulationsJ. H. Peters, C. Gra¨ser, R. KleinDecember 8, 20171 Membrane Shaping Proteins (N-BAR domain)A good overview of mechanisms shaping biological membranes can be foundin [1]. In a previous study ([2]), membrane bending by a BAR domain wasinvestigating using four models of different resolutions.1.1 Simulation SetupMembrane protein structures are notoriously difficult to determine and henceonly a small number of structures are available, most of which are of lower qual-ity. The N-BAR system used here was based on two crystallographic structures,a lower quality dimer structure (PDB id 4I1Q [3]) and a higher quality monomerstructure (PDB id: 4AVM [4]). While the monomer structure is of higher qualitythan the dimer one, it still is missing a number of atoms, which were using PDB-Fixer (https://github.com/pandegroup/pdbfixer accessed 30.10.2017) but alsoa N-Terminal alpha-helix which is assumed to be essential in membrane binding([5, 2]) and which had to be modelled using PyMOL (https://pymol.org). Twocopies of the corrected monomer structure were then fitted on the two chains ofthe dimer structure to produce a fixed dimer structure to be used in simulation.To reduce interaction between periodic images, the dimer was placed incontact with a big (600A˚x 600A˚) membrane patch. As in previous work [2],the membrane was composed of 70% DOPC and 30% DOPS which carries anet charge of −1e per molecule, as BAR-domain membrane interactions arelikely electrostatic in nature ([2]). To reduce computational cost, the MAR-TINI coarse-grained forcefield [6, 7] was used. The system was set up usingCHARMM-GUI (http://www.charmm-gui.org) [8, 9, 10]. And simulated usingGROMACS 5.1.2 [11].After equilibration, a total of 300 ns were simulated using suggested sim-ulation parameters from CHARMM-GUI: A time step of 20 fs was used and1arXiv:1712.02666v1  [physics.bio-ph]  7 Dec 2017neighbour searching was performed every 10 steps. The Shift algorithm wasused for electrostatic interactions with a cut-off of 1.2 nm. A single cut-offof 1.4 was used for Van der Waals interactions. The V-rescale temperaturecoupling algorithm was used to keep the system at 303.15K and semi-isotropicpressure coupling was done with the Berendsen algorithm.1.2 Simulation results1.2.1 2D diffusion of N-BAR dimerOne possible long-term goal of the collaboration with project C07 of CRC 1114was the design of a dynamic model of proteins diffusing (under consideration ofmembrane-induced interaction potentials) on a membrane. To this end, the 2Ddiffusion coefficient of a N-BAR Dimer on a membrane is of interest.The trajectory of the centre of mass of the N-BAR dimer from 1 ns snapshots(figure 1) corresponds to a random walk on a 2D plane defined by the membrane.Calculating from this the mean squared displacement over time (figure 2),thediffusion constant can be approximated usingFigure 1: Trajectory of the center of mass of the Dimer projected to the XYplane.〈x2〉 = dDt2Figure 2: Mean squared displacement (in the XY-plane) of the dimer center ofmass for different time differences. For dt ≤ 100ns statistics are good enoughto be described as normal diffusion.Based on dt < 100ns (the regime for which 〈x2〉 increases linear over timeas would be expected in normal diffusion, figure 2), the diffusion coefficient isD = (0.047±0.002)nm2/ns. Using all data (including the low statistics dt > 250ns), D = (0.039± 0.008)nm2/ns1.2.2 Induced curvatureDuring the whole simulation time, the N-BAR dimer remains attached to themembrane (figure 4).To quantify the effect of the N-BAR dimer, the curvature of the membrane atthe location of the protein has to be calculated. Since the membrane fluctuatesover time (figure 6), an average over a long time (200 snapshots representing 200ns simulation time) results in a clear average membrane deformation (figure 5).To calculate the average, translational movement in the xy plane and rotationalmovement around the z-axis of the N-BAR dimer had to be removed.3Figure 3: 2D diffusion coefficient calculated for different maximal time differ-ences.Figure 4: Membrane deformation by N-BAR Dimer.4Figure 5: Average deformation (for trajectory from 100 ns to 300 ns) of themembrane due to interaction with an N-BAR dimer (indicated in black).Figure 6: Average height profile of the membrane in x-direction and y-directionthrough the N-BAR dimer position. The shaded areas describe the standarddeviation of membrane fluctuations over time.52 Geometric Membrane InsertionsThere are only a small number of fully resolved structure of molecules knownto shape biological lipid membranes, and even fewer of transmembrane proteinsknown to have this effect. For a more systematic investigation of the effectcone-shaped membrane insertions, we are using geometrically defined pseudo-molecules.As protein domains that are inserted into biological membranes usually havecorresponding electrostatic properties (i.e. they have charged or hydrophilicresidues where the protein is in contact with charged or hydrophilic lipid headgroups and hydrophobic where the protein is in contact with hydrophobic lipidtails), such insertions ideally should have similar properties.One simple way to construct such domains is to select atoms from an existinglipid bilayer structure selected to be located along the desired geometry (figure7).Figure 7: Cone shaped membrane insertion with an opening angle of 30◦. Whenposition restraints are used, the cone does retain its initial shape (left). By usingnearest neighbour bonds and bond angles, the cone can be kept at approximatelythe same angle even after longer simulation time (right). In this case, the conecan move through the simulation box.In a simulation, these artificial trans-membrane domains are inserted intoa lipid bilayer domain consisting of DPPC lipids. To have a mobile but stablecone structure, bonds and bond angles between the atoms have been introducedto form cone-shaped ”pseudo molecules” (figure 7).As there is no explicit influence of water in these interactions, we have chosenDryMARTINI [12], the implicit solvent variant of the MARTINI coarse grainedforcefield for these simulations.A total of 500 ns were simulated with a time step of 20 fs. Neighbour search-ing was performed every 10 steps. The Shift algorithm was used for electrostaticinteractions with a cut-off of 1.2 nm and a single cut-off of 1.4 was used for Van6der Waals interactions. Semi-isotropic pressure coupling was done with theBerendsen algorithm. As is common for simulations using the DryMARTINIforcefield, the leap-frog stochastic dynamics integrator implemented in GRO-MACS was used with a reference temperature of 323K (DPPC transitions intothe gel phase below 314K) and an inverse friction constant of 4.0 ps.Membrane insertions are known to have a weaker effect on membrane cur-vature than memberane-attached proteins the BAR domain ([1]). Again, sys-tematic membrane deformation can best be observed by averaging over longertrajectories. Also, since the membrane insertions are rotationally symmetric,the height profile was averaged radially (figure 8).Figure 8: Average deformation of the membrane due to interaction with a cone-shaped insertion. the shaded areas describe the standard deviation of the mem-brane fluctuations.3 Mapping from Molecular Dynamics to Con-tinuum ModelEliott Et. Al. [13] have developed a variational approach to model the in-teraction between membranes and membrane-shaping particles based on theCanham-Helfrich continuum model [14, 15, 16], which requires the bendingrigidity to describe the response of the membrane to interaction.Both for membrane stiffness calculations (section 4) and for comparison withcontinuum models, it is helpful to map the particle representation of the mem-brane to a continuous model of the form h(x, y) = z. Radial basis functions area mesh-free model of the formh(x, y) =N∑ncnf(√(x− xn)2 + (y − yn)2)By using the coordinates of N atoms (xn, yn, zn) as anchor points of the rbf,the function can be constructed in a way to satisfyh(xn, yn) = zn7for all points by selecting the correct cn through a simple set of linear equa-tions.To account for statistical fluctuations in atom positions, we divide the mem-brane into a number of layers (using the same atom from each lipid molecule),construct an rbf for each of them (after centring them in z-direction) and thenaverage over these models.84 Bending Stiffness CalculationsAn approach to calculate the membrane bending stiffness from equilibrium sim-ulations (in contrast to non-equilibrium simulations like vesicle closing simu-laitons) has been developed by Khelashvili Et. Al. ([17, 18]). While the origi-nal implementation ([18] requires a solvent density to calculate the membranesurface (and from it the surface normal which is required for the calculation ofthe bending stiffness), our Rbf-based membrane fitting approach can also beapplied to implicit solvent systems where no water density is available.Following the method described in [18], we have calculated bending rigidityof an unperturbed DOPC/DOPS membrane using the explicit solvent MARTINIcoarse grained forcefield (corresponding to the membrane used in the N-BARdomain simulations, section 1) and a DPPC membrane using the implicit solventDryMARTINI forcefield (corresponding to the membrane used in the geometricinsertion simulations, section 2 ). The resulting bilayer bending moduli arelisted in table 1.membrane system bending rigidityDOPC/DOPS (16.8± 0.8)kBTDPPC (20.2± 0.8)kBTTable 1: Bending rigidities calculated for unperturbed membrane systems95 ConclusionsAcknowledgementsThis research has been funded by Deutsche Forschungsgemeinschaft (DFG)through grant CRC 1114, project C01. The authors acknowledge the North-German Supercomputing Alliance (HLRN) for providing HPC resources thathave contributed to the research results reported in this paper. We would liketo thank Prof. Roland Netz for his suggestions leading to the simulation ofcone-shaped membrane inclusions.10References[1] I. K. Jarsch, F. Daste, and J. L. Gallop, “Membrane curvature in cellbiology: An integration of molecular mechanisms,” J Cell Biol, vol. 214,pp. 375–387, Aug. 2016.[2] A. Arkhipov, Y. Yin, and K. Schulten, “Four-Scale Description of Mem-brane Sculpting by BAR Domains,” Biophysical Journal, vol. 95, pp. 2806–2821, Sept. 2008.[3] M. J. Snchez-Barrena, Y. Vallis, M. R. Clatworthy, G. J. Doherty, D. B.Veprintsev, P. R. Evans, and H. T. McMahon, “Bin2 Is a Membrane Sculpt-ing N-BAR Protein That Influences Leucocyte Podosomes, Motility andPhagocytosis,” PLOS ONE, vol. 7, p. e52401, Dec. 2012.[4] C. K. Allerston, T. Krojer, C. D. O. Cooper, M. Vollmar, C. H. Arrowsmith,A. Edwards, C. Bountra, F. Von Delft, and O. Gileadi, “Crystal Structureof the N-Bar Domain of Human Bridging Integrator 2.,” To be Published.[5] J. L. Gallop, C. C. Jao, H. M. Kent, P. J. G. Butler, P. R. Evans, R. Langen,and H. T. McMahon, “Mechanism of endophilin NBAR domainmediatedmembrane curvature,” The EMBO Journal, vol. 25, pp. 2898–2910, June2006.[6] L. Monticelli, S. K. Kandasamy, X. Periole, R. G. Larson, D. P. Tieleman,and S.-J. Marrink, “The MARTINI Coarse-Grained Force Field: Extensionto Proteins,” Journal of Chemical Theory and Computation, vol. 4, pp. 819–834, May 2008.[7] D. H. de Jong, G. Singh, W. F. D. Bennett, C. Arnarez, T. A. Wassenaar,L. V. Schfer, X. Periole, D. P. Tieleman, and S. J. Marrink, “ImprovedParameters for the Martini Coarse-Grained Protein Force Field,” Journalof Chemical Theory and Computation, vol. 9, no. 1, pp. 687–697, 2012.[8] S. Jo, T. Kim, V. G. Iyer, and W. Im, “CHARMM-GUI: A web-basedgraphical user interface for CHARMM,” Journal of Computational Chem-istry, vol. 29, pp. 1859–1865, Aug. 2008.[9] Y. Qi, H. I. Inglfsson, X. Cheng, J. Lee, S. J. Marrink, and W. Im,“CHARMM-GUI Martini Maker for Coarse-Grained Simulations with theMartini Force Field,” Journal of Chemical Theory and Computation,vol. 11, pp. 4486–4494, Sept. 2015.[10] P.-C. Hsu, B. M. H. Bruininks, D. Jefferies, P. Cesar Telles de Souza, J. Lee,D. S. Patel, S. J. Marrink, Y. Qi, S. Khalid, and W. Im, “CHARMM-GUIMartini Maker for modeling and simulation of complex bacterial mem-branes with lipopolysaccharides,” Journal of Computational Chemistry,vol. 38, pp. 2354–2363, Oct. 2017.11[11] M. J. Abraham, T. Murtola, R. Schulz, S. Pll, J. C. Smith, B. Hess, andE. Lindahl, “GROMACS: High performance molecular simulations throughmulti-level parallelism from laptops to supercomputers,” SoftwareX, vol. 12,pp. 19–25, Sept. 2015.[12] C. Arnarez, J. J. Uusitalo, M. F. Masman, H. I. Inglfsson, D. H. de Jong,M. N. Melo, X. Periole, A. H. de Vries, and S. J. Marrink, “Dry Martini, aCoarse-Grained Force Field for Lipid Membrane Simulations with ImplicitSolvent,” Journal of Chemical Theory and Computation, vol. 11, pp. 260–275, Jan. 2015.[13] C. M. Elliott, C. Grser, G. Hobbs, R. Kornhuber, and M.-W. Wolf, “A Vari-ational Approach to Particles in Lipid Membranes,” Archive for RationalMechanics and Analysis, vol. 222, pp. 1011–1075, June 2016.[14] P. B. Canham, “The minimum energy of bending as a possible explanationof the biconcave shape of the human red blood cell,” Journal of TheoreticalBiology, vol. 26, pp. 61–81, Jan. 1970.[15] W. Helfrich, “Elastic Properties of Lipid Bilayers: Theory and PossibleExperiments,” Zeitschrift fr Naturforschung C, vol. 28, pp. 693–703, Dec.1973.[16] E. A. Evans, “Bending Resistance and Chemically Induced Moments inMembrane Bilayers,” Biophysical Journal, vol. 14, pp. 923–931, Dec. 1974.[17] G. Khelashvili, B. Kollmitzer, P. Heftberger, G. Pabst, and D. Harries,“Calculating the Bending Modulus for Multicomponent Lipid Membranesin Different Thermodynamic Phases,” Journal of Chemical Theory andComputation, vol. 9, pp. 3866–3871, Sept. 2013.[18] N. Johner, D. Harries, and G. Khelashvili, “Implementation of a method-ology for determining elastic properties of lipid assemblies from moleculardynamics simulations,” BMC Bioinformatics, vol. 17, p. 161, 2016.12

CRC 1114 - Report Membrane Deformation by N-BAR Proteins: Extraction of membrane geometry and protein diffusion characteristics from MD simulations

Abstract

Similar works

Full text

Available Versions

Repository: Freie Universität Berlin (FU), Math Department (fu_mi_publications)