Download simplified models for proteins in coarse

SIMPLIFIED MODELS FOR PROTEINS
IN COARSE-GRAINED
MOLECULAR DYNAMICS SIMULATIONS
Agustí Emperador
Institute for Research in Biomedicine, Barcelona
OUTLINE
0. Introduction
1. Coarse-grained models at residue level resolution (one bead per residue):
1.1. for folded proteins
1.2. for intrinsically disordered proteins
2. Coarse-grained models at intermediate resolution (several beads per residue)
2.1 for folded proteins interacting with the environment
2.2 for intrinsically disordered proteins
3. More accurate CG potentials
INTRODUCTION
Why coarse-graining? it allows to explore larger systems and timescales
It is convenient to have a transferable potential, suitable for different systems
Objective: a potential as transferable as the atomistic force fields.
1- A coarse grained potential can be systematically constructed from atomistic molecular
dynamics trajectories for a given protein with a high level of precision,
but this will not be suitable for another system (no transferability)
Izvekov & Voth, J. Phys. Chem. B 109, 2469 (2005)
2- Intrinsically disordered proteins (IDP) are appropriate to be treated with coarse-grained (CG)
force fields, since there is no native conformation to reproduce and they are prone
to aggregation, so many proteins have to be included in the simulation.
Existing transferable CG potentials work fine for IDP proteins, but not for natively folded proteins.
3- The higher the resolution, the better reproduced the atomistic results (UNRES, OPEP).
But the simulation is slower than with strong coarse-graining
4- Hydrogen bonding (fundamental in proteins) demands a high detail of the structures
(dipole-dipole interaction): high resolution, slight degree of coarse-graining: not so fast simulations
5- Lipids can be strongly coarse-grained without significant loss of precision
because these are mostly non polar (no hydrogen bonds)
Structure-based potentials: folded proteins
Most popular coarse-grained model: residue-level
representation, use of structure-based potentials
Minimum energy when the residue-residue distances
are those of the native conformation.
Good reproduction of the summation of
the forces in the system, BUT zero transferability
(each structure has a different force field)
Residue-residue potentials defined up to a cutoff distance of 8 A
(determined from simulations: shorter cutoff leads to unstable
structures, higher cutoff leads to very rigid structures with low flexibility)
Very good results for the flexibility of a protein:
average displacement of each residue, deformation modes
With this CG potential one can generate easily realistic
trajectories of the protein sampling the native conformation
A. Emperador, O. Carrillo, M. Rueda and M. Orozco, Biophys. J. 95, 2127 (2008)
Structure-based potentials: folded proteins
Potentials like those used in elastic network models (ENM).
Normal Mode Analysis of ENM gives flexibility patterns that reproduce very well
the results of atomistic molecular dynamics.
How can it work so well?
Flexibility depends strongly on the shape and topology
of the protein. Sequence has a minor effect in the global
dynamics of the protein.
Structure-based potentials can be only defined when the
Native conformation is known.
Useless for studying proteins interacting with anything
The tube model: intrinsically disordered proteins
Most simplified representation: only CA.
Formation of backbone hydrogen bonds
depending on geometrical conditions
Achievement: reproduce the hydrogen
bond structure in amyloid fibrils with
a resolution of one bead per residue
The tube model: intrinsically disordered proteins
Phase diagram (changing the parameters of the tube model)
Hoang et al, PNAS 101, 7960 (2004)
No sequence (all residues the same):
homopolymer with hydrogen bonding + hydrophobic interactions
The balance between hydrogen bonding energy and hydrophobicity
produces different phases. (Monte Carlo sampling)
The process of aggregation of IDP is independent of the sequence.
First oligomerization in amorphous aggregates, after rearrangement into amyloid fibrils
Intermediate resolution
INTERACTING PROTEINS: PHYSICAL INTERACTIONS MUST BE INCLUDED
TWO-BEAD MODEL: One particle (bead) for the
backbone and another bead for the sidechain
Structure-based interactions between backbone beads
(maintain the structure of each protein by fixing the dihedrals)
Hydrogen bonds cannot be represented.
BAR domains: extra structure bonds between helixes.
Specific physical interactions between sidechain beads,
based on hydrophobicity and charge.
HIDROPHOBICITY: Water molecules form hydrogen bonds
with polar residues. Nonpolar residues are repelled by water,
and tend to join in hydrophobic cores.
Defining hydrophobicity allows to consider implicitly the solvent
Arkhipov, Biophys. J. 95 2806 (2008)
Marrink's coarse-grained model:
defined for lipids (impressive results)
Marrink, J. Phys. Chem. B 108, 750 (2004)
Lennard-Jones potentials between beads
(hardcore distance 4.7 A between all beads)
Different interaction strengths between different
bead types
Plus electrostactic interactions ( summed charge in the bead)
Explicit solvent: 1 bead (type P) = 4 H2O
Interaction strengths calibrated by trial and error
to reproduce several experimental properties:
- density of water and of alkanes: butane, hexane, octane, etc
- solubility of alkanes and water
- diffusion rates
Translation into proteins: remapping of sidechains
Monticelli et al, JCTC 4, 819 (2008)
Lots of restrictions to prevent unfolding
No hydrogen backbone bonds:
the secondary structure should be restrained.
Fixed backbone dihedrals
AGGREGATION OF MEMBRANE PROTEINS
Periole, JACS 129 10126 (2007)
Simulations made with rigid proteins (only moving sidechains)
Intrinsically disordered proteins with sequence effects
A higher resolution description of the structure allows to define physics-based interactions
Four-bead model: backbone N, Cα, C
and one bead for the sidechains (except Gly)
Allows to define hydrogen bonds between
backbones: secondary structure well described
INTERACTIONS BETWEEN SIDECHAINS:
-HYDROPHOBIC
Dipoles in a hydrogen bond
-ELECTROSTATIC ATTRACTION/REPULSION
Hidrophobic interactions: Kyte & Doolitle hydropathy scale
J. Mol. Biol. 157, 105 (1982)
Weight of the hydrophobic, hydrogen bond and electrostatic terms adjusted
To reproduce experiment: Urbanc et al, PNAS 101, 17345 (2004)
To study the formation of oligomers, a large number of proteins should be included in the simulation.
LARGE SIZE
And aggregation takes place in a very long time scale.
LONG TIME
Therefore, an explicit-solvent atomistic molecular dynamics simulation is unfeasible.
Solution: use simplified models of the proteins and make coarse-grained simulations
(reduced number of particles + implicit solvent)
Aim: study the global behaviour of the proteins, not detailed structural features
Experimental finding: AB42 tends to form higher order oligomers than AB40
Simulations of oligmerization of amyloid-beta peptide
Four-bead model
Backbone hydrogen bonds +
hydrophobic interactions between sidechain beads,
based on an empirical aminoacid hydropathy scale
Cutoff distance: 7.5 A between all CB
Results compare well with the experimental
oligomer size distributions
Urbanc et al, JACS 132, 4266 (2010)
Amyloid fibrils formed by amyloid-beta protein in Alzheimer’s disease.
The oligomers have internal rearrangements transforming in protofibrils
In general protein misfolding is necessary for amyloidogenesis
Discrete molecular dynamics
Oligomerization of amyloid-beta protein driven by hydrophobic
interactions and formation of intermolecular beta-strands
monomer
Stanley, PNAS 101, 17345 (2004)
dimer
The predicted distributions of
oligomer sizes compare well
with the experiment.
Amorphous oligomers obtained
Study which are the key residues
for the aggregation.
pentamer
Shortcoming: deficient representation of the sidechains (one bead CB for all the aminoacids)
If applied to natively folded proteins, the native structure is rapidly destroyed.
An intermediate resolution model for polyglutamine peptides:
Marchut & Hall, Biophys. J. 90, 4574 (2006)
Too many beads, try to simulate larger systems with less beads per protein,
but still a model that includes the physical features of the protein: hydrogen bonds,
sidechain packing, hydrophobic regions.
HIGHER RESOLUTION COARSE-GRAINED MODELS
Almost atomistic (slower simulations than with strong coarse-graining)
High accuracy and transferability
UNRES (United Residue)
Parametrized with trajectories of all-atom MD
simulations, and optimized using a training set of
protein experimental structures.
Liwo et al., J. Phys. Chem. B 111, 260 (2007)
OPEP (Optimized Potential for Efficient peptide structure Prediction)
Derreumaux, J. Chem. Phys. 111 2301 (1999)
Interaction potentials parametrized
with a training set of protein structures
Boucher et al., Proteins 68 877 (2006)
Ideal CG model:
1- Minimum number of beads
2- Allows formation of hydrogen bonds (formation of secondary structure)
3- Sequence-dependent: consider properly the interaction between sidechain beads,
and the size of the sidechains (packing)
Simulation method: DMD
Faster because no need to integrate equations of motion
Linear movement with constant velocity until collision



ri (t + tc ) = ri (t ) + vi (t )tc
Collision: conservation of linear momentum and energy
mi vi + m j v j = mi vi '+ m j v j '
1
1
1
1
2
2
mi vi + m j v j = mi vi '2 + m j v j '2 + ∆V
2
2
2
2
Change in velocities:



mi vi = mi vi '+ ∆p



m j v j + ∆p = m j v j '
The DMD algorithm spends 99% of the time looking which will be the next collision.
Number of collisions proportional to number of potential steps
The timestep decreases with the number of discontinuities in the potential
SLOW
FAST
Urbanc et al, PNAS 101, 17345 (2004)
Interaction potentials between sidechain beads
Hydrophobic/hydrophilic cutoff distance: 7.5 A
Electrostatic interactions.
Discrete molecular dynamics
MODELLING PHYSICAL INTERACTIONS IN DMD
A higher resolution description of the structure allows to define physics-based interactions
Four-bead model: backbone N, Cα, C
and one bead for the sidechains (except Gly)
Allows to define hydrogen bonds between
backbones: secondary structure well described
Pseudobonds allow to conserve bond angles
and diedrals (planarity of the peptide bonds)
Due to the use of quantum wells, only short-range
interactions can be included in the model
INTERACTIONS BETWEEN SIDECHAINS:
-HYDROPHOBIC
-ELECTROSTATIC ATTRACTION/REPULSION