COMPUTERSIMULATION OF COMPLEX

Computersimulation of reality

real world experimentexperimental

data

predictionscomputational

methodsmodel

of the world

classificationabstractionsimplificationapproximationgeneralisation

comparingis

testing

Three important turns in science:

Thales 600 B.C.design experiment

observe modelmodelmodel

model model

Galileo 1500 A.D.

Rahman 1980 A.D.mimic reality on a computer

observe

observe

Computersimulation of biomolecular systems

1) Why

2) How

3) What

4) And the future …

do we simulate ?

1) Why

2) How

3) What


do we simulate ?


For which problems are simulations useful ?

Simulation can replace or complement the experiment:

1. Experiment is impossible Inside of starsWeather forecast

2. Experiment is too dangerous Flight simulationExplosion simulation

3. Experiment is expensive High pressure simulationWindchannel simulation

4. Experiment is blind Some properties cannot beobserved on very short time-scales and very small space-scales

Simulations can complement the experiment:

Simulation explains experiments Properties of waterFolding of protein molecules

Simulation suggests Design of drugsnew experiments enzymes

less experimentsbetter chance of success

knowledgenew ideas


The world of molecular simulation and experiment

Simulation and experiment are complementing methodsto study different aspects of nature

experiment simulation

Typical space / time scales

size : 10-3 meter 10-9 meter

time : 103 seconds 10-6 seconds

Resolution*

size : 1023 molecules 1 molecule

time : 1 second 10-15 seconds

*: Single molecules / 10-15 seconds possible (but not both in the liquid phase)

(restricted) (unrestricted)

1) Why

2) How

3) What


do we simulate ?


Definition of a model for molecular simulation

MOLECULARMODEL

Degrees of freedom: atoms are the elementary particles

Forces or interactions between atoms Boundary conditions

Methods to generate configurations of

atoms: Newton

systemtemperature

pressure

Every molecule consists of atoms that are very strongly bound to each other

Force Field =physico-chemical

knowledge

Choose relevant degrees of freedom: elementary particles

. . .. . .

atomic nuclei + electrons

quantummechanics

electrostatics

all atoms(excluding solvent)

classicalmechanics

Force Field(including solvent)

monomers

classicalmechanics

Force Field(statistic)

Particles:

Description:

all atoms

classicalmechanics

Force Field(atomistic)

Interactions:

Broader applicabilityLess model parameters Physical parametersMore expensive

Restricted applicabilityMore model parameters

Empirical parametersLess expensive

=


MOLECULARMODEL




atoms: Newton

systemtemperature

pressure


knowledge

Every molecule consists of atoms that are very strongly attached

Interactions in atomic simulaties : Force Field physico-chemical knowledge

Rotation aroundbond

Planaratomgroups

van der Waalsinteractions

Electrostaticinteractions

-+

-

-

Bond stretching

non-bonded interactions

bonded interactions

Angle bending


MOLECULARMODEL




atoms: Newton

systemtemperature

pressure


knowledge


Situation at time t+t

Classical dynamicsSituation at time t

Force is determined by relative positions

acceleration = force / mass

velocity = acceleration × t

position = velocity × tforce

velocity

position

Determinism …Sir Isaac Newton

1642 -1727

Generating configurations in atomic simulations: molecular dynamics

new positions

Time t

Time (t+t)

positionsvelocities

forces

new velocities

... comparable to shooting a movieof a molecular system...

t 10-15 seconds


MOLECULARMODEL




atoms: Newton

systemtemperature

pressure


knowledge


Boundary conditions in atomic simulations

Vacuum

Droplets

Periodic: rectangular system is surrounded by copies of itself

• Surface effects (surface tension)

• No dielectric screening

• Still surface effects

• Only partial dielectric screening

• Evaporation of the solvent

Advantage:• No surface effectsDisadvantage:

• Artificial periodicity

• High effective concentration

Probably still the best approach…

1) Why

2) How

3) What

4) And the future…

do we simulate ?

Methods Applications

in my research group


1. stable structures binding equilibrium energetically favourable structures between two small

organic molecules

2. Relation between structure and function water transport in the enzymes binding cavity of a

protein (FABP)

3. Motions en mechanisms prediction of the three-

protein folding dimensional structure or

the folding of proteins(polypeptides)

4. Design of new compounds binding strength of design of drugs hormone replacing

molecules to theestrogenreceptor

What do biochemists or molecular biologistswant to know of molecules?

Example 1

Structural interpretation ofthermodynamic properties:

Binding equilibrium between two smallorganic molecules

Applications of molecular dynamics simulation:

Binding equilibrium

Hydrogen bonds

NH2

NH2

HO

HOH

H

OH

N

H

H

H

O

N?Cyclohexane-

diamineCyclopentane-

diol

+ -

- +

Complex :

Experimental MD simulation Benzene CCl4

Gb [kJ/mol] -9.3 -11.5 -10.4

Average binding strength (free enthalpy) :

Many different bindingmodes

Formation of the complex(camera focuses on the diamine)

Diol + Diamine + 252 CCl4 Molecules 2.1 – 2.2.10-9 seconds

Complex formed

Diol + Diamine + 252 CCl4 Molecules 3.2 – 4.0.10-9 seconds

… and a nanosecond later …the molecules are free again…

Hydrogen bonds

O N

N O

NH2

NH2

HO

HO

NH2

NH2

HO

HO

NH2

NH2

HO

HO

NH2

NH2

HO

HO

NH2

NH2

HO

HO

NH2

NH2

HO

HO

54%

21%

8%

7%

4%

3%

Occurrence of different binding modes :

Life time :

• Average life time of the complex: 2.10-10 sec (max. 3.10-9 sec)• Average life time of a hydrogen bond: 5 .10-12 sec

Results of the simulation (over 10-7 sec) :

Experimentally hardly (or not) possible !



organic molecules


protein (FABP)






Boundaries: membranes consist of lipids with pores of proteins

Hereditary information in the nucleus: DNA

Proteins: e.g. haemoglobin

for oxygen transport

Carbohydrates:storage of energyand molecularstamps

Biomolecules

• Important to understand enzymatic reactions: the dynamics of the binding cavity

• Simulation allows one to follow the movements of individual molecules

Example 2The watertransport in the binding cavity of a protein (FABP)




organic molecules


protein (FABP)






Example 3

Protein folding the challenge

Proteins consist of chains of amino acids (primary structure)

In an organism proteins only function if they have been correctly folded three- dimensionally. (secondary and tertiary structure)

• What is the relation between amino acid sequence and folded spatial structure?• How does the folding process take place?

20 kinds


• Proteins are too large systems to simulate the slow folding process.

• Smaller model compounds can be correctly folded on the computer.

Information about folding mechanisms and the unfolded state:

surprise

Foldingsimulation

t [ns]

RM

SD

[nm

]

00 50 100 150 20000

0.1

0.2

0.3

0.4

Unfolded structures

all different?how different?

321 1010 possibilities!!

Folded structures

all the same

Surprising result after simulations of many polypeptides

number of amino acids in

the protein

10

100

Folding time (exp/sim) in

seconds

10-8

10-2

possible structures

320 109

3200 1090

relevant (observed) structures

103

109

number of

peptide

protein

The number of relevant unfolded structures is much and much smaller than the number of possible unfolded structures

Assuming that the number of relevant unfolded structures is proportional to the folding time, only 109 protein structures need to be simulated instead of 1090 structures.

Folding mechanism is simpler than generally expected: searching through only 109 structures

Protein folding on a computer is possible before 2010

Simulations can complement the experiment:

Simulation explains experiments Properties of waterFolding of protein molecules

Simulation suggests Design of drugsnew experiments enzymes

less experimentsbetter chance of success

knowledgenew ideas




organic molecules


protein (FABP)






Example 4Design of drugs

testing compounds with the computer

Enzymes work according to the “lock and key”-principle

Applications of molecular dynamics simulations:

the “key hole”: the active site in the

protein

containing a “fitting key”: the active site with an active molecule

the active and a new molecule (to

be tested) superimposed

a “new key”?: The active site with the molecule to be

tested

HO

Cl

Cl

HO

Cl

Cl

HO Cl

Cl

Cl

HO Cl

ClCl

Cl

HO

Cl ClCl

Cl

Cl

Cl

HO

Cl

Cl

Cl

ClCl

Cl

HO

Cl

Cl

Cl

Cl Cl

HO

Cl

Cl

Cl

Cl

Cl

HO

Cl

Cl

Cl

Cl

Cl

HO

Cl

Cl

Cl

Cl

Cl

HO

Cl

ClCl

Cl

HO

Cl

Cl

Cl

16 hydroxylated PCB’s

Unphysical reference state

Polychlorinated biphenyls

Binding to the estrogen receptor

16 hydroxylated PCB’s: 10 < kBT 2.5 kJ mol-1

13 < 1 kcal mol-1

Average deviation: 2.5 kJ mol-1

Variation exp. values: 4.2 kJ mol-1

1) Why

2) How

3) What



Year molecular system: type, size length of the simulation in seconds

1957 first molecular dynamics simulation (hard discs, two dimensions)

1964 atomic liquid (argon) 10-11

1971 molecular liquid (water) 5 .10-12

1976 protein (no solvent) 2 .10-11

1983 protein in water 2 .10-11

1989 protein-DNA complex in water 10-10

1997 polypeptide folding in solvent 10-7

2001 micelle formation 10-7

200x folding of a small protein 10-3

History: classical molecular dynamics simulationsof biomolecular systems

And the future ...

2001 Biomolecules in water (~104 atomen) 10-8 sec

2029 Biomolecules in water 10-3 sec

2034 E-coli bacteria (~1011 atoms) 10-9 sec

2056 Mammalian cell (~1015 atoms) 10-9 sec

2080 Biomolecules in water 106 sec

2172 Human body (~1027 atoms) 1 sec

As fast as nature !

Protein folding sooner?

Standard classical simulations :

Computer speed increases with a factor 10 about every 5½ year!

• Upper limit to computer speed ?• Accuracy of classical models and force fields ?• Better approximations and simplifications

But :

Computersimulation of reality

real world experimentexperimental

data

predictionscomputational

methodsmodel

of the world

classificationabstractionsimplificationapproximationgeneralisation

comparingis

testing

Acknowledgements

Gruppe informatikgestützte Chemie (igc) http://www.igc.ethz.ch

Dirk Bakowies (Germany)

Riccardo Baron (Italy)

Indira Chandrasekhar (India)

Markus Christen (Switzerland)

Peter Gee (England)

Daan Geerke (Holland)

Daniela Kalbermatter (Switzerland)

Alice Glättli (Switzerland)

David Kony (France)

Chris Oostenbrink (Holland)

Daniel Trzesniak (Brasil)

Alex de Vries (Holland)

Haibo Yu (China)

COMPUTERSIMULATION OF COMPLEX

Documents

configurations of atoms

world of molecular simulation

time t force

molecules1 molecule

elementary particlesforces

meter time

protein molecules simulation

short time scales