computer simulations and the laplace demon alessandro laio, sissa (trieste) capability to predict...
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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.
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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
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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!!!
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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
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Which level of description should one
choose?
Accuracy: the more accurate the description, the more
computationally expensive.
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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
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0EH
Schrödinger equation
The accurate option:The accurate option:dealingdealing with the electrons with the electrons
rmV Newton equation
+ =
Car-Parrinello molecular dynamics
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•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
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•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)
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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!!!!
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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!!!!
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what they will be able to afford in the future
In Italy:
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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)
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•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)
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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“
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Time-scale: chemical reactions, phase
transitions, conformational changes are “rare events“
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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
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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”
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AzuleneAzulene NaftaleneNaftalene
Molecular dynamics with “computational
sand”
Normal molecular dynamics
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Solid
Liquid
Freezing water on a computer (D. Donadio, P. Raiteri & M. Parrinello)
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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.•…..
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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“
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Size:interesting systems are large and
inhomogeneus
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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
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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!!!!
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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
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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
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Most demon-like feature: computer can help understanding how “life” works!
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Acknowledgements
Andres StirlingSimone RaugeiMichele ParrinelloPaolo CarloniPilar CossioFabrizio MarinelliFabio pietrucciStefano PianaMike Klein