Molecular Dynamics. Molecules in motion

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Eustace McDowell
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1 Molecular Dynamics Molecules in motion 1

2 Molecules in mo1on Molecules are not sta1c, but move all the 1me Source: h9p://en.wikipedia.org/wiki/kine1c_theory 2

3 Gasses, liquids and solids Gasses, liquids and solids differ in the amount of interac1on between par1cles Source: h9p://demonstra1ons.wolfram.com/molecularmo1oninsolidsliquidsandgases/ 3

4 Mo1on in liquids and solids The veloci1es of molecules are distributed in a similar way to gasses, but the assump1ons of the Maxwell-Boltzmann equa1on no longer apply (the par1cles interact strongly and the molecules occupy a large frac1on of the total volume). In solids the molecules vibrate in a fixed posi1ons, but again with a range of frequencies (energies). 4

5 The Boltzmann distribu1on Energy Absoute zero Hot Hotter N i / N j = e (E i E j ) / kt 5

6 The Maxwell-Boltzmann distribu1on for an ideal gas Source: h9p://en.wikipedia.org/wiki/maxwell Boltzmann_distribu1on 6

7 The Maxwell Boltzmann distribu1on Assumes an ideal gas i.e. one that follows the equa1on pv = nrt where: p = pressure v = volume of the system n = number of par1cles R = gas constant T = temperature (K) Ideal means that the atoms have zero volume and interact only by elas1c condi1ons. This is a reasonable approxima1on for a gas at low pressures (like 1 atm) 7

Newton s laws of mo1on (classical mechanics) Par1cles will move uniformly unless they are acted on by an external force (The law of iner1a) A par1cle

8 Newton s laws of mo1on (classical mechanics) Par1cles will move uniformly unless they are acted on by an external force (The law of iner1a) A par1cle will accelerate in propor1on to the force applied and in inverse propor1on to its mass. F = ma For every ac1on there is an equal and opposite reac1on 8

9 Quantum Mechanics Quantum mechanics describes the physical behaviour of very small things (e.g. atoms, electrons, molecules) Objects can be described as waves Energy levels are quan%sed Provides an accurate descrip1on of molecular behaviour The Schrödinger equa1on is difficult (and slow) to solve especially for large molecular systems Erwin Schrödinger in

of the par1cles change Hψ = Eψ William Rowan Hamilton (1805 1865) *

10 The Hamiltonian A Hamiltonian is an operator* that describes how the energy of a system of par1cles (atoms) changes as the posi1ons of the par1cles change Hψ = Eψ William Rowan Hamilton ( ) * An operator is a mathema1cal func1on that modifies another func1on. 10

11 Molecular mechanics force fields E = E bond + E ang bonds angles + E tors + E vdw + E electrostatic torsions atm pairs atm pairs The total poten1al energy of a molecular system is the sum of simple, empirical equa1ons which describe Bond lengths Bond angles Dihedral angles van der Waals forces Electrosta1c interac1ons Each equa1on has a number of parameters which vary depending on the type of atoms that are interac1ng In molecular mechanics the force field is the Hamiltoniain 11

12 Molecular dynamics (MD) Approximate quantum forces with Newtonian mechanics and electrosta1c forces Provides an atomis1c and dynamic model of system The forces on the atom are calculated using the Hamiltonian Give atoms ini1al posi1ons Calculate forces Move atoms (a = m/f) Every 2-5 femtoseconds A femtosecond is to a second what a second is to 31.7 million years. At 2 fs/step we need 5 x 10 8 steps for one microsecond = 500,000,000 12

13 Periodic Boundary Condi1ons System cell is surrounded by iden1cal images Removes boundary between system and vacuum which causes problems (e.g. surface tension) and be9er models bulk solvent Can cause artefacts and cause other issues: No object can be larger than the simula1on cell!! Objects can interact with their own image, causing artefacts 13

14 The thermodynamic state The thermodynamic state of a system is defined by specifying proper1es that can be measured. E.g Pressure Temperature Volume Chemical poten1al Total energy Etc The system is something you can draw a box around. It can be open (ma9er and energy can move in and out), closed (no ma9er can pass in or out) or isolated (no ma9er or energy can be transferred). 14

15 Equa1ons of state For some systems we can define equa1ons that define the state of a system E.g. for an ideal gas: pv = nrt Here pressure, Volume, number of par1cles (n) and the temperature are state variables 15

16 Common thermodynamic (sta1s1cal) ensembles used in MD Ensemble Constant proper1es Variable proper1es Canonical Num par1cles, Volume, Temperature Pressure Grand canonical Isobaricisothermal Chemical poten1al* (μ), Volume, Temperature Num par1cles, Pressure, Temperature Num par1cles Volume *The chemical poten1al (μ) is the amount of energy required to add an extra par1cle (molecule) to the system Image source: 16

17 MD thermostats and barostats The Canonical and Isothermal-Isobaric ensembles use algorithms to regulate the temperature and pressure of the systems during the simula1on A thermostat algorithm adds or subtracts energy from the system to maintain a constant temperature A barostat algorithm maintains a constant pressure by changing the size of the simula1on cell in response to the internal pressure. 17

18 MD simula1ons of drug/gpcr binding Simula1ons of Dopamine D2 and D3 receptors with the an1psycho1c drugs clozapine and haloperidol Set of 36 long simula1ons (currently ns) Simula1ons started in an arbitrary posi1on ~5 Å from the entrance to the binding pocket 18

2A, 5-HT 2B, 5-HT 2C Muscarinic M 1 Histamine H 1 extracellular lipid membrane Orthosteric binding

19 G protein-coupled receptors (GPCRs) Characteristic structure Numerous disease states Schizophrenia, Parkinson s disease, obesity Receptors Adenosine A 2A Dopamine D 2, D 3, D 4 Serotonin 5-HT 1B, 5-HT 2A, 5-HT 2B, 5-HT 2C Muscarinic M 1 Histamine H 1 extracellular lipid membrane Orthosteric binding site intracellular β 2 -adrenergic receptor (2RH1) 19 Cherezov, V. et al. Science 2007, 318,

20 Key residues: β 2 -adrenergic receptor Key contacts Phe6.51 Phe6.52 Ser5.42 Ser Asp3.32 Trp6.48 Ser5.46

21 Living systems Mostly liquid 21

electrosta1cs NAMD2 2 fs 1mestep 10 ns/day

22 D 3 or D 2 receptor 80 united atom POPC lipids 4000 TIP3P water molecules Total 22,000 atoms Construc1ng the system All atom receptor/drug United atom lipid PME electrosta1cs NAMD2 2 fs 1mestep 10 ns/day on MASSIVE CPU/ GPU computer (4 CPUS and 4 GPUS) 22

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25 Similar bound poses of clozapine in the D 2 R and haloperidol in the D 3 R 25

26 GPCR docking by MD Drug Receptor Num Simul. Aggregate 1me Dissoc. Loop Region Glu 2.65 Asp 3.32 Fully Bound Clozapine D2 Clozapine D3 Haloperidol D2 Haloperidol D μs μs μs μs Simula1on lengths currently vary from ns. 26

27 MD docking conclusions We can dock drugs into GPCRs by MD MD simula1on of drug binding is limited by the 1mescales we can simulate There are methods available to bias simula1ons to explore the region we are interested in. These are necessary if we wish to thoroughly inves1gate ligand binding. 27

28 MD sosware There are a large number of MD programs available. Widely used programs: NAMD namd/amber AMBER ambermd.org/ Gromacs 28

29 Parallel compu1ng MD simula1ons are very computa1onally intensive Simula1on speed can be improved by using parallel compu1ng (i.e. splitng the job into pieces and alloca1ng to mul1ple CPUs) Current desktop computers have 2-8 CPUs (cores) Supercomputers have 1000s of cores 29

30 Molecular mo1on Classical mechanics What have we covered? Atomic velocity distribu1ons Molecular mechanics force fields The MD algorithm Thermodynamic ensembles Thermostats and barostats The difficulty of simula1ng on a biological 1mescale Big computers MD sosware 30

Molecular dynamics simulation. CS/CME/BioE/Biophys/BMI 279 Oct. 5 and 10, 2017 Ron Dror

Molecular dynamics simulation. CS/CME/BioE/Biophys/BMI 279 Oct. 5 and 10, 2017 Ron Dror Molecular dynamics simulation CS/CME/BioE/Biophys/BMI 279 Oct. 5 and 10, 2017 Ron Dror 1 Outline Molecular dynamics (MD): The basic idea Equations of motion Key properties of MD simulations Sample applications