Computer simulations and the Laplace demon Alessandro Laio, SISSA (Trieste) Capability to predict the futureCapability to predict the future Lots of demon-like features Super-human capabilities not to get bored with numbersSuper-human capabilities not to get bored with numbers Requires continuous attentions and sacrifices. Otherwise it gets angry.Requires continuous attentions and sacrifices. Otherwise it gets angry.

Computer simulations:... deriving from simple equations complex and realistic predictions... Simple equations, althogh beautiful, contain the description of our world only virtually

Given a potential energy surface: 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 Electrostatic Van der Waals

Schrödinger equation The accurate option: dealing with the electrons Newton equation + = Car-Parrinello molecular dynamics

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

Quantum potentialsQuantum 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 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= 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= 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 virus P.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. Azulene Naftalene? 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”

Azulene Naftalene 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 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 observed with QM/MM and steering MD S. 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 membrane C.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 Stirling Simone Raugei Michele Parrinello Paolo Carloni Pilar Cossio Fabrizio Marinelli Fabio pietrucci Stefano Piana Mike Klein