Download Coarse Grained MD

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 in their native conformation
1.2. for intrinsically disordered proteins (IDPs)
2. Coarse-grained models at intermediate resolution (several beads per residue)
2.1 for folded proteins interacting with other macromolecules
2.2 for IDPs
3. More accurate CG potentials: transferable force fields
3.1 for folded proteins and folding of peptides
3.2 for interacting proteins and IDPs
INTRODUCTION
THE TIMESCALE PROBLEM
Timescale explored in an atomistic molecular dynamics (MD) simulation limited
MD simulation
Calculate particle-particle
interaction potentials
t+t
Integrate equations of
motion (update velocities
and move particles)
Timestep ~ 2 fs. Time range limit: s ( ~ 109 simulation steps)
→ little more than sidechain and loop movements
INTRODUCTION
COARSE GRAINED MODELS: WHAT FOR????
“Normal” MD simulation
(GROMACS, AMBER, etc)
Very accurate
Very slow sampling
(experimental times)
Research in biology:
proteins in their normal,
“operative” conformation
Coarse-grained model simulation
Less accurate
Very fast sampling (100 ns trajectory has
more sampling than 100 ns in experiment)
Research in physics:
Polymers (unfolded proteins
and nucleic acids)
Intrinsically disordered proteins (IDP)
INTRODUCTION
Molecular dynamics simulations
INTEGRATING NUMERICALLY THE EQUATIONS OF MOTION
F 
dV
 ma
dr
a
dv
dt
v
dr
dt
Timestep t such that forces change smoothly between steps.
v(t+t)=v(t)+at strictly true only if acceleration a is constant within the timestep t
The lightest particles (hydrogen) move faster, limiting the length of the timestep
Equipartition of kinetic energy
E 3
1
 kT  mv 2
N 2
2
At T=300K, timestep 2 fs (2·10-15 s)
Simplified models: reduce number of particles, particle with higher mass --->
slower moverment ---> longer timestep
INTRODUCTION
How to reach an extensive sampling:
Coarse-graining:
collapsing groups of atoms in beads. Higher mass, lower speed
→ allows use of timesteps of 40 fs (Marrink's MARTINI force field)
Expands in a factor of 20 the time range that can be explored
Limitation: the secondary structure of the proteins must be constrained
→ useless for disordered proteins or amyloid aggregation
Implicit solvent:
Removes the water molecules.
→ If the viscosity is reduced, the sampling is accelerated
x1000 with the UNRES model of Scheraga's group
(Zhou et al. PNAS 111, 182423 (2014))
Conformational changes can happen much faster than in the reality.
Self assembly of lipid bilayer
INTRODUCTION
Final objective: a potential as transferable as the atomistic force fields.
(transferable = universal)
Higher resolution
Higher accuracy
Lower speed
Structure potentials: derived from the structure of the protein. Low resolution.
Keeps the structure of the protein along the simulation.
It does not allow large scale conformational transitions.
Not transferable
The particle-particle interaction potential can be constructed from the particle-particle
distance distribution functions (next page)
Interaction potentials from particle distance probability distributions
LOW RESOLUTION MODELS
Structure-based potentials: folded proteins
Most popular coarse-grained model: residue-level
representation, use of structure-based potentials
zero transferability
(each structure has a different “force field”)
Residue-residue potentials (CA-CA) up to a cutoff distance of 8 A
Very good results for the flexibility of a protein:
average displacement of each residue, deformation modes
Good sampling of the native conformation
A. Emperador, O. Carrillo, M. Rueda and M. Orozco, Biophys. J. 95, 2127 (2008)
LOW RESOLUTION MODELS
Structure-based potentials: folded proteins
Potentials like those used in elastic network models (ENM).
ENM 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
B-factors (average displacement per residue)
LOW RESOLUTION MODELS
The tube model: intrinsically disordered proteins
Most simplified representation: residue level (only CA)
The peptide is considered a homopolymer
(all residues of the same type)
Formation of backbone hydrogen bonds
depending on geometrical conditions.
Achievement: construct the hydrogen
bond structure (beta sheet)
of amyloid fibrils with a resolution
of just one bead per residue
LOW RESOLUTION MODELS
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 (accounting for the solvent)
HIDROPHOBICITY:
Water molecules form
hydrogen bonds with
polar residues.
Nonpolar residues are
repelled by water,
and tend to join
in hydrophobic cores.
The balance between hydrogen bonding energy and hydrophobicity
produces different phases (Monte Carlo sampling)
LOW RESOLUTION MODELS
The tube model: intrinsically disordered proteins (IDP)
The general process of aggregation of an IDP is independent of the sequence:
1- oligomerization in amorphous aggregates
1- structural rearrangement into amyloid fibrils
Auer et al. HFSP Journal 1, 137 (2007)
Configurations created with Monte Carlo (not real trajectories, no sampling limitations)
Statistical potentials accounting for the hydrophobicity of each residue can be added.
INTERMEDIATE RESOLUTION MODELS
Intermediate resolution
INTERACTING PROTEINS: PHYSICAL INTERACTIONS MUST BE INCLUDED
TWO-BEAD MODEL: One particle (bead) for the
backbone and another bead for the sidechain.
timestep: 20 – 40 fs!!!
Specific physical interactions between sidechain beads,
based on hydrophobicity and charge.
Structure-based interactions between backbone beads
in the protein: backbone fixed, sidechains free
BAR domains: extra structure bonds between helixes.
Explicit solvent: system constituted by proteins
and the cell membrane phospholipids + water
Arkhipov, Biophys. J. 95 2806 (2008)
INTERMEDIATE RESOLUTION MODELS
Marrink's coarse-grained model:
defined for lipids (impressive results)
Marrink, J. Phys. Chem. B 108, 750 (2004)
Lennard-Jones potentials between beads.
Interaction strengths between different beads
depending on bead type
Self assembly of lipid bilayer
+ electrostatic interactions (screened,  = 15)
Explicit solvent: 4 H2O = 1 bead (type P)
PARAMETRIZATION
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
INTERMEDIATE RESOLUTION MODELS
Translation into proteins: remapping of sidechains
Monticelli et al, JCTC 4, 819 (2008)
Lots of restrictions to prevent unfolding
(fixed structure at level of backbone)
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)
Better for proteins: SIRAH model (Pablo Dans) No structural restrictions on the backbone
INTERMEDIATE RESOLUTION MODELS
Intrinsically disordered proteins with sequence specificity
A description of the structure with a resolution higher than bead-per-residue
allows to define physics-based interactions. Implicit solvent (small charges)
Four-bead model: allows to define hydrogen bonds
between backbones: secondary structure well described
INTERACTIONS BETWEEN SIDECHAINS:
-HYDROPHOBIC
-ELECTROSTATIC ATTRACTION/REPULSION
Dipoles in a hydrogen bond
Hidrophobic interactions: Kyte & Doolitle hydrophobicity 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)
WARNING: The 4-bead model do not conserve the structure of native folded proteins
due to simplicity in the side chain representation. Lack of accuracy.
To study the formation of oligomers, a large number of proteins should be included.
LARGE SIZE
And aggregation takes place in a very long time scale.
LONG TIME
Therefore, an explicit-solvent atomistic molecular dynamics simulation is unfeasible.
Urbanc et al, JACS 132, 4266 (2010)
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
Simulations of oligmerization of amyloid-beta peptide
Backbone hydrogen bonds +
hydrophobic interactions between sidechain beads,
based on an empirical hydrophobicity scale
Results compare well with the experimental
oligomer size distributions
INTERMEDIATE RESOLUTION MODELS
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
INTERMEDIATE RESOLUTION MODELS
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)
Ideal CG model for proteins:
1- Minimum number of beads (and implicit solvent to remove solvent molecules)
2- Allows formation of hydrogen bonds (formation of secondary structure)
3- Sequence-specific: consider properly the interaction between sidechain beads,
and the size of the sidechains (packing)
HIGHER RESOLUTION COARSE-GRAINED MODELS
Almost atomistic (slower simulations than with strong coarse-graining)
High accuracy and transferability. Implicit solvent for fast sampling.
Describe correctly the native conformation of folded proteins, folding of peptides
UNRES (United Residue)
Liwo et al., J. Phys. Chem. B 111, 260 (2007)
Ab initio folding
Parametrized with trajectories of all-atom MD
simulations, and optimized using a training
set of protein experimental structures.
HIGHER RESOLUTION COARSE-GRAINED MODELS
UNRES: Conformational change and aggregation of and amyloid- peptide
due to interaction with an amyloid fibril
HIGHER RESOLUTION COARSE-GRAINED MODELS
OPEP (Optimized Potential for Efficient peptide structure Prediction)
Derreumaux, J. Chem. Phys. 111 2301 (1999)
Interaction between sidechain beads parametrized
with a training set of protein structures
Lots of adjusted parameters
Simulation of the native conformation of folded proteins
Also:
PaLaCe model (Lavery)
Pasi et al, J. Chem. Theory Comput. 9, 785 (2012)
PRIMO model (Feig)
Kar et al, J. Chem. Theory Comput. 9, 3769 (2013)
Kapoor et al, Proteins 81, 1200 (2013)
Hills et al, PloS Comput. Biol. 6, e1000827 (2010)
The PACSAB protein model
Pairwise
Additive
Coarse-grained
Sidechain and
Atomistic
Backbone
MARTINI sidechain mapping
of Marrink's group
(Monticelli JCTC 2008)
Atomistic backbone
(PRIMO, OPEP, PaLaCe...)
Interactions:
- hydrogen bonding between backbone NH and CO
- van der Waals + implicit solvation between sidechain beads
Parametrization: V = solv Vsolv + VdW VVdW
VvdW: addition of CHARMM19
atomistic vdW terms
Vsolv: addition of EEF1
implicit solvation terms
Particle packing
correction
MISFOLDING AND AGGREGATION
Villin: 37 residues
Simulations at 8.5 mM (beginning of aggregation observed in the experiments)
Explicit solvent simulations →fast aggregation of the native state
due to inaccuracies in explicit solvent force fields
(calibrated to produce good results in simulations of ONE protein)
With PACSAB:
The native state does not aggregate
The misfolded state aggregates
Simulations of ubiquitin (1UBQ), concentration 5 mM. In experiment, 50% monomeric.
Explicit solvent simulation
Implicit solvent, low viscosity simulation
Intermolecular distance
t (ns)
Dissociation rate 1000 times higher!!!
Selective binding:
STABLE
UNSTABLE
Experimental
interface
MISFOLDING IN UBIQUITIN
The misfolded state does not aggregate... neither form dimers
Ubiquitin binds its partners always with the same interface. If the interface disappears,
it has a very low binding affinity
→ the structure of ubiquitin is optimized to bind just one protein
Aggregation of amyloid- peptides
Strongly hydrophobic disordered proteins.
Low solubility (fast aggregation)
Kd ~ 20 M (as determined from experiments)
apolar environment
(lipid): native structure
polar environment
(water): disorder
Stationary state (association/dissociation equilibrium) reached in less than 10 s
thanks to the fast diffusion of the peptides in the PACSAB implicit solvent model
Higher concentration → higher collision rate → aggregation
Experimental finding: using ligand molecules that bind to the A peptide
and stabilize its secondary structure, its aggregation propensity is reduced
(Nerelius PNAS 2009)
Restrained simulations enforcing the -helical conformation
in the 13-26 residues segment
Aggregation is blocked
-helix structure increases strongly
the dissociation rate, contributing
association/dissociation equilibrium
also at higher concentrations