Simulationen von Lipidmembranen

Transcription

1 Simulationen von Lipidmembranen Thomas Stockner

2 Summary Methods Force Field MD simulations Membrane simulations Application Oxidized lipids Anesthetics

3 Molecular biology Molecular modelling

4 Introduction: How to describe a molecule in a computer?

5 Computer description of molecules Mathematical functions are used to describe molecular properties: Size/Volume Interaction energies (enthalpy) Conformational freedom (entropy) Description of a molecule at the atomic level: Bond length Angles Torsion dihedral Charge (Coulomb s law) Size (van der Waals radius) The functions must be fast to compute. Experimental results should be reproduced.

6 Interactions through bonds Atom-atom distances E= k i (r i r i,0 ) 2 Angle bending E= k i (q i q i, 0 ) 2

7 Interactions through bonds Dihedral angles Torsion angles Planarity of rings Chirality E= k i (1+ cos(nω d))

8 Interactions through bonds Dihedral angles Torsion angles Planarity of rings Chirality E= k i (1+ cos(nω d))

9 Non-bonded interactions Van der Waals interactions Dominant interactions in the protein interior and membranes Atoms size Molecular volume Atom - Atom interactions N E = i=1 N 4ϵ j =i+ 1 ij(( σ )12 ij r ij ( σ ij r ij )6)

10 Non-bonded interactions Distances dependency of the dominant interaction energy term of polar atoms: Electrostatic interactions Charge-Charge Charge-Dipole Dipole-Dipole Very difficult to handle, because long ᅠ range by nature Truncate at some distance ᅠ ᅠ Continuum models are used beyond cutoff to mitigate error 1 r 3 1 r 2 1 r N E = i=1 N j =i+ 1 q i q j 4π e 0 r ij

11 Neutral charge groups Distance dependence of electrostatic interactions Charge - charge Charge - dipol Dipol - dipol ᅠ ᅠ ᅠ Neutral charge group concept used to reduce cutoff problems at the boundary 1 r 3 1 r 2 1 r

12 Force field Intramolecular interactions Bond Angle Dihedral Intermolecular interactions Electrostatic Van der Waals

13 Introduction: How can we connect a microstate with a macrostate?

14 How can we connect a microstate with a macrostate?

15 Microstate

16 Microstate

17 Microstate

18 Microstate

19 Microstate

20 Microstate

21 Microstate

22 Microstate Partition function Free Energy Q= e E k B T dr dp A= k B T ln Q

23 Introduction: How do molecule move in a computer?

24 Simulations Requirements Starting coordinates Macromolecular parameter Force field Solving Newton s equation of motion Results Dynamics: time evolution of a system; e.g. ligand binding to a receptor All properties that depend on coordinates can in principle be calculated N E= bond N + dihedral N + i =1 N k i (r i r i,0 ) 2 + k i (q i q i, 0 ) 2 angle k i (1+ cos(n ω d)) N 4 ϵ j =i+ 1 ij(( σ ij r ij ( )12 σ ij r ij )6 + q i q j 4 π ϵ 0 r ij )

25 Simulations Requirements Starting coordinates Macromolecular parameter Force field Solving Newton s equation of motion Results Dynamics: time evolution of a system; e.g. ligand binding to a receptor All properties that depend on coordinates can in principle be calculated N E= bond N + dihedral N + i =1 N k i (r i r i,0 ) 2 + k i (q i q i, 0 ) 2 angle k i (1+ cos(n ω d)) N 4 ϵ j =i+ 1 ij(( σ ij r ij ( )12 σ ij r ij )6 + q i q j 4 π ϵ 0 r ij )

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27 Membranes: How can we simulate membranes

28 Membranes environment Many cellular functions occur in or around membranes: energy productions, protein synthesis, clearance, communication,... Lipids in membranes Number of different types of lipids can exceed 1000 in cell membranes Membranes are fluid: lipid are not covalently bound In membranes, domains (rafts) are formed consisting of particular proteins and lipids

29 Lipids

30 Lipids: headgroups Phophatidyl-Ethylamine Phophatidyl-Choline Phophatidyl-Serine Phophatidyl-Inositol

31 Lipids: tails Sphingomyeline Phophoglycerides

32 Lipids: tails Saturated fatty Acid Unsaturated fatty acid

33 Lipids: tails Saturated Unsaturated

34 Lipids: Chain length dependent properties Huang C. and Li S. BBA 1999, 1422, 273

35 Membrane lipids Lipid types Phospholipids, cholesterol, sphingolipids Variable chain properties Chain length, saturation Head groups Choline, serine, ethanolamine, inositol

36 Cholesterol Kaiser HJ et al., PNAS 2011, 108(40),

37 Setup of a Simulations Force field selection Lipids Water Conterions Simulation parameter Starting geometry

38 Membrane Force Fields The choice of the applied force field depends on the question to be answered, the resolution necessary and the computer time available. All Atom Force Fields Charmm Amber United atom Force Field Berger lipids GROMOS Coarse Grained Martini Force field Implicit solvent model

39 System assemply

40 System assemply

41 System assemply

42 System assemply

43 System assemply

44 Periodic boundary conditions Closest image convention Box boundaries distort system behavior Solution: periodic system Approximation of an infinite system No edge effects (e.g. wall) Actual system size can remain relatively small

45 Box Shape Finite system problem On a confined system, most of the atoms are affected by the presence of the wall. Completely fill the volume 5 shapes are available: Cubic, rectangular, rombic, truncated-octahedron, dodecahedron

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47 Box Shape Semi-isotropic pressure scaling to maintain rectangular shape

48 Area per lipid ApL= Area of the membrane patch Number of lipids per leaflet

49 Density profile

50 Membrane thickness Membrane thickness

51 Diffusion Diffusion 6Dt=lim (r r 0 ) 2 t Calculated from the mean square displacement using the Einstein relationship

52 Diffusion Plochberger B et al. Langmuir (2011) 26,

53 Cholesterol Cholesterol has very strong effect on membranes Used by cells to manipulate/adjust the behavior of their membranes to many needs, as temperature changes, fluidity, rafts formation,.. Schematic diagram of cholesterol position Cholesterol distribution Phenyl ring and tail Lipid tail chain ordering caused by 3 different type of cholesterol

54 All atom simulations Formation of a membrane triggered by a transmembrane peptide DPPC lipid, 50 ns System at different timepoints Density profiles

55 Example: Simulation studies of oxidized lipids in model membranes

56 Biological activity oxidized lipids Oxidized lipids are recognized by the immune system Danger signal Induce apoptosis Inflammation Foam cell formations athereosclerotic plaques Disease Atherosclerosis, CNS disorder, liver disease, rheumatoid arthritis

57 Lipid oxidation Formation Radical reaction Enzymatic Biophysical properties Membrane fluidity Membrane thickness Stability of rafts Membrane permeability Influence the activity of membrane inserted proteins

58 Lipid whisker model Reversal of oxidized chain Protrution from the membrane surface Recognition by receptors ME. Greenberg et al. J. Biol. Chem. (2008)

59 Membrane size PGPC POVPC

60 Area per lipid

61 Membrane thickness

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63 8% PGPC 8% POVPC

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66 Model of oxidized lipid geometry PGPC POVPC

67 Area per lipid

68 Membrane Thickness

69 Lipid whisker model Reversal of oxidized chain Protrution from the membrane surface Recognition by receptors ME. Greenberg et al. J. Biol. Chem. (2008)

70 Conclusions Chain reversal PGPC shows complete chain reversal Oxidized chain of POVPC remains in the headgroup region PGPC and POVPC have opposing effects on the membrane properties: Membrane thickness Area per lipid Lipid tail order Diffusion