2. Modeling of small systems

Building the model

What is the optimal conformation of a molecule?

What is the relative energy of a given conformation?

What does the charge distribution look like?

Does a molecule form dimers?

Does molecule A fit into a cavity of molecule B?

How flexible is a molecule in solution?

Sampling methods

Modeling of small systems:building the model

database

(CSD, PDB, ICSD)

molecular editor

(Cerius, Sybyl, Molden)

neighbor

internet

set of atoms

molecule

model

connectivityhybridization

atom typescharges

atom types and chargesdepending on FF

Modeling of small systemswhat is the optimal conformation?

optimal conformation: average geometry at room temperature

optimal conformation: structure with the lowest MM energy

optimizing a structure minimizing the MM energy

E = f (geometry) = f (ratom1, ratom2, ratom3, ratom4,……) [atomic coordinates] = f (bond lengths, bond angles, torsion angles) [internal coordinates]

Modeling of small systemswhat is the optimal conformation?

E = f (ratom1, ratom2, ratom3, ratom4,……) = f (bond lengths, bond angles, torsion angles) [internal coordinates]

d1

d22

d3

t3

3

c.f. QM: Z-matrix

Modeling of small systemsoptimal molecular conformation: energy minimization

energy

geometric parameter

Energy minimization may lead to…..:* the absolute E minimum* a local minimum* a saddle point; maximum* an area of almost constant energy

Modeling of small systemsoptimal molecular conformation: energy minimization

Common applications:

‘Cleaning up’ structures from the CSD( remove errors in e.g. H positions)

Identifying packing effects: what does theconformation of an isolated molecule look like?

Modeling of small systems What is the relative energy of a given conformation?

* calculate E()

Calculate E, while setting to 0, 15, 30, 45, ...‘bumping atoms’ will cause unrealistic, high energy barriers. relax (optimize) rest of structure, given .* How likely is each conformation.* How easily can they interconvert.

Modeling of small systems conformational energy with/without solvent

E()….in water?in vacuum?in benzene?

No solvent included in simulation:* intra-molecular H bonds emphasized* molecule tends to contract

Modeling of small systems What does the charge distribution look like?

* how polar is the molecule?* how large is the dipole moment?* which interactions can be anticipated?

example: alizarine/NaCl

Modeling of small systems Does a molecule form dimers?

does a molecule dock well onto itself?

* geometric fitting / steric hindrance: ‘close contacts’.* favorable electrostatics; H-bonds? energy minimization in vacuo

Modeling of small systems Does molecule A fit into a cavity of molecule B?

ligand -- proteinadditive -- crystal surface

Modeling of small systems How flexible is a molecule in solution?

Simulation of an organic salt in benzene or chloroform

Molecular Dynamics (MD): from still picture to movie.

Atomic positions as a function of time, calculated by applyingNewton’s equations of motion.

r(t+ t) = r(t) + v(t+½t)tv(t+½t) = v(t-½t) + a(t)ta = F/m

Modeling of small systems Simulation of an organic salt in solution

* non-zero temperature atomic motion* system has kinetic + potential energy* equilibrium properties at T, transport properties, conformational or ‘configurational’ search

t-½t t+½tt t+t

r v r?a

v

t~1fs

Modeling of small systems Simulation of an organic salt in solution

* periodic boundary conditionsto go from veeeeeeery smal dropletto ‘bulk’

* external forces/constraints: - nr. of particles - temperature - volume - pressure

NVT, NPT simulations

Modeling of small systemsresults from MD

Sampling methods

* Systematic: every combination of possible values of all DOF’s.* Random: a random subset of the above.* MD: ‘frames’ taken every n ps from an MD run.* MC: ‘frames’ taken from an MC run.

Properties/features:simplicity completeness grid sizespeed efficiency birds’ eye view

Obtaining a representative set of structures from a system withfreedom in conformation/configuration.

Next week: Crystals!

Theorie: hoe zat dat ook al weer met die ruimtegroepen??

Experiment: wat bedoelt René de Gelder met R=6.2%?

Modeling: hoe check ik mijn model in Cerius?