An introduction to Molecular Dynamics

Matteo Degiacomi

Mass Spectrometry Group Lectures

26th November 2013

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Why Molecular Dynamics?

• aim: replicate experimental conditions, and observe the behavior of molecules at atomic level

• First attempts in early ’60 by S.Lifson (Weizmann Institute), H.Scheraga (Cornell) and N.Allinger (Wayne State Uni)

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structure and dynamics determine the function

Overview

• How does it work? (~15 min)

• MD in practice (~15 min)

• What information can I get? (~10 min)

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HOW DOES IT WORK?Some molecular dynamics fundamentals

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Exploring the conformational space

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conformational space : ensemble of possible atoms arrangements

conformation : one arrangement of all atoms in the system

atom : sphere with associated charge, size, position x, velocity v

AIM: given a starting conformation, compute position and velocity of every atom after a certain time interval

Atoms exert forces on each other

• Neighbouring atoms interact in covalent and noncovalent ways

• On every atom, the sum of all interactions generates a net force, affecting position and velocity

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Newton’sII law of motion

Bonded interactions

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LIMITATIONS:

- connectivity (aka topology) cannot change

- harmonic potentialapproximatesconditions next to equilibrium

Ubond(r)=k1(r-r0)2

Uangle(a)=k2(θ- θ0) 2

Udih.(d)=σ𝑛 𝑘3 1 + cos(𝑛φ − φ0)

sometimes also Uimproper , UUrey-Bradley, …

U = Ubonded + Unon-bonded

Non-bonded interactions

UVdW(r)=4εσR

12−

σr

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12-6 Lennard-Jones

(other: Morse, Buckingham,…)

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Ucoulomb(r)=1

4𝜋𝜀0𝜀𝑟

𝑞1𝑞2

𝑟

repulsion attraction

Distance cutoff: excludeatoms being far away(usually F → 0 when r>12Å)

(use large cutoff or Particle Mesh Ewald)

cutoff

U = Ubonded + Unon-bonded

The Force Field

Constants in equations (r0 , k1 , θ0,…):

• determine interactions strength and equilibriumdistances for specific groups of atoms

• tuned to reproduce measurable quantities (known bonds and angles, helical pitch, area per lipid…)

• can be temperature sensitive

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equations and associated constants describingatomic interactions

What happens in, say, 3 hours?

(x0,v0)

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?

What happens in, say, 3 hours?

(x0,v0)

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• A trajectory is be decomposed in small uniform steps• Step size depends on energy landscape steepness

(x1,v1)

(x2,v2)

(xT,vT)

Uniform motion: Newton to the rescue

• x0: initial atom positions (e.g.

X-ray structure)

• v0 : initial atom velocities (e.g.

Boltzmann distribution)

• dt: time interval

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v1=v0+F(x0)*dt/m

x1=x0+v0*dt

• m : atoms’ mass

• F : force on atoms (F=-dU/dx)v2=v1+F(x1)*dt/m

x2=x1+v1*dt

…

Sampling time at atomic scale

The sharpest gradient determines the smallest timestep

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• Timestep size is imposed by the fastest phenomenon we want to observe :

– Covalent bond hydrogen-heavy atom (1014 Hz): 0.5 fs

– Covalent bond heavy atom-heavy atom: 1 fs

– Angles fluctuations: 2 fs

• restraining covalent bond distances allows to use 1-2 fs timesteps (restraining methods: SHAKE, RATTLE, LINCS,…)

Thermostats and barostats

• Simulations replicate a specific thermodynamicensemble (typically nVT or nPT)

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• Addition of equations acting as thermostats (scalingatom velocities) and barostats (scaling positions)

– Nose-Hoover

– Berendsen

– Parrinello-Rahman

– Langevin piston

Periodic Boundary ConditionsNeeded for simulating bulk water and lipid bilayers (avoid boundary effects). Not necessary for vacuum.

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……

An MD timestep

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Set initialconditions for

x, v and box sizeCompute forces

Compute new x and v for all atoms

Scale x and v with thermo/barostat

Update x and v (with boundary

conditions)

Apply restraintsto bonds

Biasing your simulation

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1. rotation

2. rearrangement

Note: in presentation, these are movies!

• The way forces are computed can be modified in order to:

– Enhance the sampling of rare events

Biasing your simulation

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steer loopregion

Note: in presentation, these are movies!

• The way forces are computed can be modified in order to:

– Enhance the sampling of rare events

– Reproduce specific physical conditions (stretching, electrical field,…)

Biasing your simulation

• The way forces are computed can be modified in order to:

– Enhance the sampling of rare events

– Reproduce specific physical conditions (stretching, electrical field,…)

– deform your models to match experimental data

20Note: in presentation, these are movies!

MD IN PRACTICEWhich software should i use? And force field? And computer?

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What do I need for MD?

Atomic structure (X-ray, NMR, model)

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Molecular Dynamics

Force Field

MD engineComputationalresources

Popular Force Fields for Biomolecules

• Amber (Peter Kollmann, UCSF)

– Glycam parameters cover most sugars (Robert J. Woods, University of Georgia)

• CHARMM (Martin Karplus, Harvard)

– POPC, POPE, DPPC lipids

• OPLS (William Jorgensen, Yale)

• GROMOS (Wilfried van Gusteren, ETHZ)

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Most common force fields for biomolecules feature parameters for standard aminoacids, DNA, common ions, and water

there is no «best force field»!

Preparing system’s topology

• Atomic structure + Force Field = topology + coordinates

– missing atoms added (hydrogens, termini,…)

– extra bonds can be added (e.g. disulfide bridges)

• How do I do it?

– depending on chosen force field, dedicated toolscan be used (VMD, tleap, grompp…)

– sometimes manual work is required

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MD ENGINES

– NAMD

– Gromacs

– Amber (pmemd)

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– LAMMPS

– CHARMM

– DLPOLY

• Common MD engines:

– ACEMD

– HOOMD

• YOU WANT: support for force field of choice, SPEED, easy usage, flexibility

• Often come with additional programs helpingsystems preparations or analysis

Simulation protocol

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• AIM: equilibrate your system• YOU WANT: constant volume, pressure and

temperature, stable Root Mean Square Deviation, healthy Ramachandran plot, no exotic chemistry, bulk water (if used), stabilization of whichever other quantityyou are interested about (e.g. Rgyr, …)

• Example:1. Minimize energy, 1000 steepest descent2. Heat system from 0 to 300 K in 500 ps, nPT,

Berendsen barostat 1 atm. α-carbon restrained with

10 Kcal/mol harmonic potential. 2 fs timestep, SHAKE all bonds,

3. 1 ns nVT equilibration with Langevin dynamics, no atom constrained.

4. Production: 200 ns nPT, Nose-Hoover barostat

Computational power

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Thumb rule: peakperformance with around500 atoms per processor

«on a supercomputer, 24/7, for several weeks»

Execution time affected by:• processor power• number of processors• Interconnect speed

Moore’s law: things get steadily better

Size matters, time too• typical system sizes: 10.000-500.000 atoms (i.e. 300-400

kDa protein in a water box)

• data production: 10-50 ns per day

• typical timescales: 10 ns-10 μs (long enough to at least reach equilibrium!)

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• Current cutting edge:

– 200 μs, K. Lindorff-Larsen et al, Structure and

Dynamics of an Unfolded Protein Examined by Molecular Dynamics Simulation, JACS, 2012

– 64mio atoms , G.Zhao et al, Mature HIV-1

capsid structure by cryo-electron microscopy and all-atom molecular dynamics, Nature, 2013

Timescales in biochemistry

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MD

QM

Sizes in biochemistry

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MD

QM

WHAT INFORMATION CAN I ACTUALLY GET FROM IT?

Ok, I have a trajectory… and now?

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Typical quantities to measure

• Compute Root Mean Square Deviation (RMSD) and Root Mean Square Fluctuation (RMSF)

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Typical quantities to measure

• Compute Root Mean Square Deviation (RMSD) and Root Mean Square Fluctuation (RMSF)

• Residues properties: secondary structure, Ramachandran plot, hydrogen bonds, contact map

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Typical quantities to measure

• Compute Root Mean Square Deviation (RMSD) and Root Mean Square Fluctuation (RMSF)

• Residues properties: secondary structure, Ramachandran plot, hydrogen bonds, contact map

• SASA, Rgyr, CCS, Radial Distribution Function (RDF)

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Highlight molecule’s most relevant motions

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decomposition in a linear combination of eigenvectors

MD simulation

Principal Components

Analysis

First eigenvectors represent system’s most relevant movementsNote: in presentation, these are movies!

Use obtained conformations for something else

• compute binding free energy

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● perform docking with alternate conformations

● Simply obtain a structure relaxed into some desired conditions (physiological or experimental)

Where do I start?

• Tutorials:– VMD/NAMD, www.ks.uiuc.edu/Training/Tutorials– Amber, ambermd.org/tutorials– Gromacs, www.gromacs.org/Documentation/Tutorials

• Workshops– CECAM, www.cecam.org– CCP5, www.ccp5.ac.uk

• Books:– T. Schlick, Molecular Modeling and Simulation: An Interdisciplinary

Guide, 2nd edition– D.Frenkel, B. Smit, Understanding Molecular Simulation, Second

Edition: From Algorithms to Applications

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