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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)+at 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