Computer simulations and the Laplace demon

Alessandro Laio, SISSA (Trieste)

•Capability to predict the futureCapability to predict the future

Lots of demon-like featuresLots of demon-like features

•Super-human capabilities not to get Super-human capabilities not to get bored with numbersbored with numbers

•Requires continuous attentions and Requires continuous attentions and sacrifices. Otherwise it gets angry.sacrifices. Otherwise it gets angry.

Computer simulations:

... deriving from simple equations ... deriving from simple equations complex and complex and realisticrealistic predictions ... predictions ...

Simple equations, althogh Simple equations, althogh beautiful, contain the description beautiful, contain the description

of our world only of our world only virtuallyvirtually

NII RRRVRM ,,, 21

Given a potential energy surface:

NRRRV ,,, 21

The dynamics is determined from Newton’s equation:

Molecular dynamics

•Extremely efficient•Parallel and highly scalable implementation •Etc….

Modern MD code

More than 3 decades of work by hundreds of

people!!!

Accuracy: the more accurate the description, the more

computationally expensive.

Size:interesting systems are large

and inhomogeneus

Time-scale: chemical reactions, phase

transitions, conformational changes are “rare events“

Three compeeting demands

Which level of description should one

choose?

Accuracy: the more accurate the description, the more

computationally expensive.

The cheap option:Classical Potentials

Many popular force fields (Amber, Charmm, Gromos, OPLS, etc.) differ only for the value of the parameters (charges, torsions,…) .

Bonded

ElectrostaticVan der Waals

0EH

Schrödinger equation

The accurate option:The accurate option:dealingdealing with the electrons with the electrons

rmV Newton equation

+ =

Car-Parrinello molecular dynamics

•500000 “moves”= 1/1,000,000,000 OF A SECOND IN ONE DAY!!!!!

Simulation of "realistic" systems: what we can afford.

Example:simulation of HIV protease (classical potential)

•50000 atoms (protein+water)•Each atom “interacts” with ~ 100 atoms (its neighbors)•In order to calculate the forces, 50000*100 operations•A computer can perform 5000000 operations in 0.2 seconds•In one day I can “move” the system 3600*24/0.2~500000 times

•Quantum potentials Quantum potentials (electrons are explicitly treated: chemical reactions): 1/100,000,0000,000 of a second for a 100 atoms system

•Classical potentialsClassical potentials (no chemical reactions): 1/1,000,000,000 of a second for a 50000 atoms system

Simulation of "realistic" systems: what we can afford

(one day of simulation)

what we will be able to afford in the future

Blue Gene (IBM):•65,536 "Compute Nodes" and 1024 "IO nodes“.•360 TFLOPS=360000 desktop PCs

•One millisecond of molecular dynamics of a protein in one day!!!!

what they will be able to afford in the future

Blue Gene (IBM):•65,536 "Compute Nodes" and 1024 "IO nodes“.•360 TFLOPS=360000 desktop PCs

•One millisecond of molecular dynamics of a protein in one day!!!!

what they will be able to afford in the future

In Italy:

MD simulation of the satellite tobacco mosaic virusP.L. Freddolino, A.S. Arkhipov, S.B. Larson, A. McPherson & K. Schulten

•1 million atoms!!! • Simulation time: 50 ns, program: NAMD •The simulation would take a single 2008 desktop computer around 15 years to complete!!!

CAPSIDE (60 copies)

•1194 atoms,•10 GUA-CYT pairs•200 water molecules•3960 electrons!!!

A single configuration of the

system occupies ~20 Gbytes of memory!!

Car-Parrinello simulation of Z-DNA(F.L. Gervasio, P. Carloni & M. Parrinello)

Accuracy: the more accurate the description, the more

computationally expensive.

Size:interesting systems are large and

inhomogeneus

Time-scale: chemical reactions, phase

transitions, conformational changes are “rare events“

Time-scale: chemical reactions, phase

transitions, conformational changes are “rare events“

Direct simulation is hopeless, even if you have access to a Blue Gene supercomputer.

AzuleneAzulene NaftaleneNaftalene

??

Time-scale: chemical reactions, phase transitions,

conformational changes are “rare events“

Car-Parrinello molecular dynamics

Simulating rare events requires some „computational

wizardry“

Local elevation, Wang-Landau sampling, metadynamics: in order to observe a

transition, fill the wells with “computational sand”

AzuleneAzulene NaftaleneNaftalene

Molecular dynamics with “computational

sand”

Normal molecular dynamics

Solid

Liquid

Freezing water on a computer (D. Donadio, P. Raiteri & M. Parrinello)

Protein folding:a major challenge for any sampling method

Several possible “order parameters” if you don’t know the folded structure:•Gyration radius.•Backbone-backbone H-bonds.•Hydrophobic contacts.•Fraction of helix.•Fraction of sheet.•Correlation between successive dihedrals.•Contact order.•Number of salt bridges.•…..

Accuracy: the more accurate the description, the more

computationally expensive.

Size:interesting systems are large and

inhomogeneus

Time-scale: chemical reactions, phase

transitions, conformational changes are “rare events“

Size:interesting systems are large and

inhomogeneus

QMMM

MM

•Very fast •Accurate proteins

•50000 atoms

QM

•likes CPUs •Accurate chemistry•100 atoms

Interface

Combining classical MD and quantum MD

QM subregion

© U. Rothlisberger

HIV protease

Decarboxylation reaction in ODCase Decarboxylation reaction in ODCase observed with QM/MM and steering MDobserved with QM/MM and steering MD

S. Raugei, M. Cascella & P. CarloniS. Raugei, M. Cascella & P. Carloni

ODCase is an enzyme involved in the nucleic acids biosynthesis. In the enzyme, the probability to observe the CO2 elimination is 17 orders of magnitude larger than in water!!!!

Describe groups of atoms as single “pseudo-atoms”; parameterize ad hoc their interaction potential.•Much faster than all-atom molecular dynamics•The accuracy is parameterization dependent

Coarse-grained models

Dynamics of model pore insertion into a membraneC.F. Lopez, S.O. Nielsen, B. Ensing, P.B. Moore & M.L. Klein

Accuracy: the more accurate the description, the more

computationally expensive.

Size:interesting systems are large

and inhomogeneus

Time-scale: chemical reactions, phase

transitions, conformational changes are “rare events“

Three compeeting demands

Most demon-like feature: computer can help understanding how “life” works!

Acknowledgements

Andres StirlingSimone RaugeiMichele ParrinelloPaolo CarloniPilar CossioFabrizio MarinelliFabio pietrucciStefano PianaMike Klein