Force Fields

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Force Fields

• G Vriend 2-11-2004

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It is all about time versus accuracy
G Vriend master series 2-11-2004
Force Fields

• Quantum chemistry
• Approximations
• Force Fields
• Hybrid methods
• Self consistent fields
• Molecular dynamics and energy calculations
• Minimizers
• Yasara-Nova

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Quantum chemistry is accurate, but slow
G Vriend master series 2-11-2004
Force Fields
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Quantum chemistry is accurate, but slow
G Vriend master series 2-11-2004
Force Fields
The largest thing that can realistically be
worked-out using the Schödinger equation is
hydrogen. Other applications are the particle in
a box that is mainly of theoretical importance,
the postulates of quantum chemistry, etc.
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Quantum chemistry is accurate, but slow
G Vriend master series 2-11-2004
Force Fields
Actually, pure quantum chemistry cannot be
applied in our (protein) world. Which is good,
because quantum chemistry is much too difficult
(for me). But many of the results are very
useful. For example, all atoms in proteins
display sp2 - sp3 hybridization.
Pictures obtained from Clifford J Creswell
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Approximations, faster, less accurate
G Vriend master series 2-11-2004
Force Fields
Approximations can make quantum chemistry
software faster, but at the cost of accuracy. A
major part of all efforts in quantum chemistry is
to think about short-cuts that have an optimal
price/performance ratio.
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So, we will use Newtonian mechanics
G Vriend master series 2-11-2004
Force Fields
If we want to calculate with molecules that
contain thousands of atoms, we have to totally
abandon quantum chemistry, and use Newtons laws
of motion, treating atoms as macroscopical
particles instead of quantum chemical entities.
The following (YASARA) movie will explain how
this is done.
?H wants to go down ?S wants to go up
and ?Cp cannot be calculated
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What can we do with EM and MD?
G Vriend master series 2-11-2004
Force Fields
Despite all its shortcomings, MD can be used to
calculate binding constants of ligands in active
site pockets with reasonable accuracy. This is
done with so-called thermodynamic integration
which works because binding a ligand is a
state-function (the path is not important, only
the end-points so non-realistic paths are
allowed)
Just take any closed cycle you want. Calculate
the easy difference, and since the cycle is
closed, you obtain also the value of the
difficult cycle.
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We can turn the thing inside-out
G Vriend master series 2-11-2004
Force Fields
Other approaches are also possible. Rather than
calculating the energy lost or gained to actually
move an atom somewhere, we can calculate the
potential energy for atoms at a certain position.
This, of course, is again an approximation
relative to the thermodynamic integration method.
Examples LUDI or GRID.
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And one more approximation step....
G Vriend master series 2-11-2004
Force Fields
Lets go yet one step further along the drug
binding path. Assume we have a series of docked
molecules. We superpose them, and determine what
they have in common. The next drug should have
those same characteristics. So, one more
approximation step....
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Other force fields
G Vriend master series 2-11-2004
Force Fields
So far we discussed molecular dynamics force
fields and approximated them into experience
based drug design. Many other force fields
exist. For example, many force fields exist for
the purpose of validating protein structures or
models. Example ProSa

• Measure Ca distance distributions
• Score good proteins per residue
• Normalize the scores
• Score protein of interest

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Other force fields
G Vriend master series 2-11-2004
Force Fields
Force fields do not need to be based on relative
positions of atoms. A very different concept
would be a secondary structure evaluation force
field. Recipe Take 4000 different proteins and
determine their secondary structure. Determine
how many residues are H, S, or R Determine for
each residue type how often it is Helix, Strand,
Rest (HSR) Determine the preference parameters
for the 20 aa in the 3 states P(aa,HSR)P(aa)P(H
SR) Pref(aa,HSR)Ln (observed/predicted) observe
d is simply counting (aa,HSR) in the 4000
proteins predicted is P(aa,HSR) (total number
of aa in the 4000 proteins) Callibrate the method
with a Jack-Knife procedure Loop over the aa in
the protein to be tested and add up all
Pref(aa,HSR) Express the outcome in energy or
standard deviations (Z-score)
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Electrostatic calculations
G Vriend master series 2-11-2004
Force Fields
Electrostatic calculations are based on
self-consistent field principles. This field is
not a force field like we have seen so far, but a
distribution of charges over a grid that covers
the space in and around the molecule.
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Electrostatic calculations
G Vriend master series 2-11-2004
Force Fields
Often physics looks like Chinese typed backwards
by a drunken sailer, but when you spend a bit of
time, you will that things actually are easy.
Take the Poisson Bolzmann equation that is used
for electrostatic calculations
which can be converted into
This looks clearly impossible, but after a few
days of struggling, it becomes rather trivial
(next slide)
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Electrostatic calculations
G Vriend master series 2-11-2004
Force Fields
The Poisson Boltzman equation normally is worked
out digitally, i.e., make a grid, and give every
voxel (grid-box) homogeneous values for charge
and dielectricum. Now make sure all neighbouring
grid points have the correct pairwise relations.
If one voxel has too much charge it should give
some charge to the neighbours..... This is done
iteratively till self-consistent.
And the function is very simple!
The same technology is used to design nuclear
bombs, predict the weather (including the future
path of tornados),
design the hood of luxury cars, predict how water
will flow under a bridge in the Waal, optimize
catalysts in mufflers, optimize the horse powers
of a car given a certain amount of gasoline
(turbo chargers), etc.
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Force Fields
G Vriend master series 2-11-2004
Force Fields
So, what is a force field? There are so many
different ones for totally different things (car
design, electrostatics, nuclear bombs, tornados,
etc)... A force field is a set of rules that can
predict the optimal constellation of a system
in the absence of external forces. So, in case
of electrostatic calculations, the field can be
calculated in the absence of molecular motion,
and new things entering the system. But for a
weather forecast one can only take small steps in
a dynamic system as the sun adds energy to the
system. Most force fields can be used to
optimize/minimize the system, and here we run
into the multiple minimum problem.
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Multiple minimum problem
G Vriend master series 2-11-2004
Force Fields
But this is a very simple, one-dimensional case.
How many dimensions and how minima do you think
can be found in crambin (326 heavy atoms)?
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Back to proteins and MD/EM
G Vriend master series 2-11-2004
Force Fields

• During an MD simulation atoms dont move very
  far.
• Because molecules normally arent very mobile
• Because we cannot run the simulations long enough
• Because the forcefields are far from precise
  enough
• We can use this to do MD differently....

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Back to proteins and MD/EM
G Vriend master series 2-11-2004
Force Fields
We have seen that the few forces that we (think
that we) understand mainly are of the form
Qk(x-x0) In this equation x0 is known with
great precision, while k can easily be wrong by a
factor of two or more. Can we use the precision
of x0?
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MD with CONCOORD
G Vriend master series 2-11-2004
Force Fields
In the CONCOORD software, all distances between
atoms are forced at x0 plus or minus a little
bit. This little bit is determined by the nature
of the force between the atoms. In a way,
concoord works a bit like NMR structure
determination.
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MD with CONCOORD
G Vriend master series 2-11-2004
Force Fields
All x-es are close to their x0 in each CONCOORD
structure. So a movie based on the CONCOORD
structures shows a path of low energy, or a path
along the X0 in Qk(x-x0)
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Molecular dynamics
k
CONCOORD
x0