Practicality of membrane protein simulations…

Dr Phil Biggin

Dept. of BiochemistryUniversity of Oxfordphil@biop.ox.ac.uk

Membrane Proteins – Why?

• Ion channels, transporters, pumps, carriers, enzymes.• Atomic level experimental information scarce (relatively)

• expression• crystallization

• But key drug targets:-

From Terstappen & Reggiani, TIPS. 2001

Outline of Procedure

Obtain protein coordinates

Immerse in bilayer/mimetic

Solvate outside of membrane (and inside any pore regions)

Add counterions (for correct concentration or to satisfyelectrostatic calculations)

Run simulation!

Protein Coordinates…

• PDB :- www.rcsb.org - X-ray/NMRXray missing residues etc NMR which structure?

• Number of human membrane proteins at high resolution= ZERO…

• So have to start from homology model (eg from modeller)

Protein Coordinates…

Starting from X-ray… http://www.rcsb.org/ 1BL8

missing residues incomplete residues mutated residues

oligomer state pH disulphides covalent linkages ions/solutes

Examine header

Prepare/Repair Structure

Fix residues

Graphically by hand (eg Quanta, Insight but these cost $$$)Swissviewer is free but more limited.

Online automated versions (eg What-Ifserver http://www.cmbi.kun.nl:1100/WIWWWI/

Will also perform various stereochemical checks)

Oligomeric stateMacromolecular Structure Databasehttp://www.ebi.ac.uk/msd/

Prior knowledge

• Add polar hydrogens (Quanta, Insight but usually scripted in the other packages like pdb2gmx within the gromacs suite)

• pKa may be important – protonation state of ionizable residues.. – Can do ad-hoc. Look at structure and assign by eye/distance the

protonation state of a particular residue.– Important for binding sites etc– BUT can dramatically effect stability of protein in simulation– For membrane proteins, situation is made more complex by presence of

membrane…

Prepare/Repair Structure

Need different dielectric constants for each region(interface region tricky still) =2-4

=2-6

=78-90

Alignment/Positioning in Box

Things to consider:-

• Existing experimental evidence

• The aromatic “girdle”

• Energetic positioning:-- Assign a hydrophobicity value to each residue (many scales to chose

from!)- Calculate surface exposed area of each residue- Decide on width of hydrophobic zone of membrane (30Å)- Use Monte-Carlo to explore rigid-body movements across four degrees

of freedom (3 rotational, 1 translational along Z, the bilayer normal- Lowest Energy position gives starting “orientation” with respect to box

Z

Choice of mimetic

Full BilayerSlowest but gain fullest information.

Octane Slab(speed but no detail)

MicelleFaster than bilayer. More and more NMR data now.

Choice depends on what questions you want to ask.For example – is my homology model stable?

Inserting into Octane

Is system similar to existing one?

Decide on box size and slab width*

Solvate helix with new octane box

Run simulation!

Fit new protein onto existing protein (and delete existing protein)

minimize

Add water (and ions if needed)

equilibrate

NO

YES

* Make slab thickness slightly more than what you want as it will compress during equilibration.

Inserting in a Micelle

• Easiest way is to build micelle around protein

• May also have experimental data as to the overall size estimate of the micelle.

• Simply build by a script that relies on the geometry of the system

• Solvate – might consider using an octahedral box for this system.

Insertion into Bilayer…

KcsA is a membrane protein so solvation includes bilayer, water and ions (sodium and chlorine for example).

[Cytosolic proteins – immerse in box of pre-equilibrated water and delete overlapping (vdw spheres) molecules]

Sounds a lot easier than it really is!…

Add bilayer Add water/ions

Protein into lipid Problem… need to optimise interactions of lipids & protein

Method 1 – Roux & Woolf – pack lipid around a protein Method 2 – Faraldo-Gomez & Smith - ‘grow’ a hole in a pre-formed bilayer Method 3 – Use genbox (gromacs) and run long equilibration Method 4 – Use VMD plugins (designed primarily with NAMD in mind)

x (Å)

y (Å

)

Change in Lipid Density

FhuA inserted in POPC bilayer

Insertion into Bilayer…

Possible Protocol (to be explored in the practical session)

Obtain box of lipid. Put protein into same box dimensions. Use ‘genbox’ to ‘solvate’ the protein with that box of lipid. Add water with ‘genbox’. Delete waters in middle region of bilayer (perl script). Add any counter ions. Energy minimize. Few hundred picoseconds of restrained MD. Few nanoseconds of unrestrained MD (NPT). Check lipid properties. Perform production run (a few more nanoseconds).

Insertion into BilayerThings will equilibrate in a reasonably short time (a few ns)

SolvationNow add water either side (and anywhere else you fancy)

* Adding bulk is easy - add lots of small repeating boxes of water and delete overlapping atoms (as implemented in for example gromacs)

* For smaller pockets, cavities and channels, you may need other “more accurate” methods:-

* Eg. MMC (a grand-canonical monte-carlo approach) from Mihaly Mezei Voidoo/Flood (from Uppsala) Solvate (Grubmuller)

NOTE: May be better/easier to solvate small cavities first prior to inserting into the membrane.

Now add ions (number according to ionic strength)

Method 1 – Random distribution

Method 2 – based on electrostatic potential

Ready to start?

• First step is usually a minimization of sorts.

• Strategy is ad-hoc really but work from bits you trust backwards.

E.G. Sample strategy for membrane protein.

Constrain protein atoms – minimize waters/lipids

Constrain protein atoms – run MD for 200ps

Constrain C atoms – run MD for 200ps

Run it!

OK – now you are in position to run free MD!

1. Run to equilibrium.

2. Use coordinate frames

beyond that.

3. The more the merrier.C

RM

SD

(Å)

Time (ns)

1

2

4

3

Take frames from here

321

Valid/stable simulation

• Lots of parameters to check but probably single most useful one is – the area per lipid (describes molecular packing and describes degree of

membrane fluidity). – very sensitive to simulation details, considered to be a reliable criterion.

• Remember – it depends what your question is, undulations across large patches require different timescales compared to water-headgroup interactions for example.

Parameters to consider in membrane simulations…

• Periodic boundary conditions (PBCs) – what shape box? – Cubic, truncated octahedron, rhombic dodecahedron– Amount of “surrounding water” – typically more than 10Å margin

• Ensemble - NPT commonest, but there are others (NVE for example)– Also constant surface tension simulations

• Pressure and temperature coupling– E.g. Berendsen weak coupling versus Nosé-Hoover/Parrinello-Rahman

• Electrostatics Treatment– Cut-off (artificial ordering?) – Ewald methods, Particle Mesh Ewald (enhance periodicity) – Reaction Field (ignore heterogenous nature of the membrane)

• Frequency of dump – Large systems now (50,000-200,000 atoms) so files become large rapidly!– Suggested dump every 5ps with currently sizes.

Insights from a recent StudyA recent study systematically addressed some of the key issues in membrane

simulations: “Methodological issues in lipid bilayer simulations”. Anézo et al. J. Phys. Chem B. 2003. 107. 9424-9433.

• Parameters investigated:- electrostatic treatment (cutoff,PME,RF), cut-off radii, partial charge groupings, pressure coupling, timestep, size of system, force-field and amount of hydration water. (22 simulations some individually upto 150ns).

• Treatment of electrostatics has most impact on area but all three schemes can give correct area per lipid. Combination of this and force-field is what is important.

• Equilibration times of upto 25ns required for accurate assessment of properties such as area per lipid. Large area fluctuations occur on 10ns time scale.

• Area per lipid cannot tell you whether force-field or method is OK.– But once area is correct, most others are usually OK (explains why so many different

reports in the literature have bilayers with similar properties• No difference with pressure coupling (though Berendsen might be preferred in

equilibration as it damps oscillations more effectively)

• NO method is perfect! You make your choice!

Where do I get lipids from?

• Scott Feller (wabash college) http://persweb.wabash.edu/facstaff/fellers/POPC, DOPC, DPPC, SDPC

• Helmut Heller (München) http://www.lrz-muenchen.de/~heller/membrane/membrane.htmlPOPC in different phases.

• Mikko Karttunen (Helsinki) http://www.lce.hut.fi/research/polymer/downloads.shtmlDMTAP,DMPC,DPPC

• Peter Tieleman (Calgary) http://moose.bio.ucalgary.ca/Downloads/DPC micelles, POPC, DMPC, DPPC PLPC bilayers (topologies here as well).

• And coming soon… BioSimGrid ‘lite’ http://www.biosimgrid.org/Various bilayers all with complete topology and meta-data. More information about

this site in Friday’s lecture.

• Far easier to start with ready-equilibrated systems and insert protein into that

What if I have strange topology?

Bonds and topology• If have similar existing topologies – can ‘adapt’ those.• Can work out manually (can be tiresome and boring!)• Can use PRODRG (Daan van Aalten)• If using gromacs someone might have already done it and uploaded it!

Charges• Use similar atoms from similar ligands• Calculate from ab-initio (usual to use partial charges that best reproduce the

molecular electrostatic potential (MEP)

Vdw Parameters• Use similar atom types if possible.• Optimize to reproduce a range of themodynamic properties (eg density)

Some references…D.M Hirst “A computational approach to chemistry” Blackwell scientific

publications 1990.

A.R. Leach “Molecular Modelling Principles and Applications” Longman

Second ed. 2002.

Gromacs manual @ http://www.gromacs.org

“Methodological issues in lipid bilayer simulations”. Anézo et al. J. Phys. Chem B. 2003. 107. 9424-9433.

J.M. Haile “Molecular Dynamics Simulation” Wiley 1997

Angwe Chemie 29 992 (1990)