Force Fields

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Force Fields

• G Vriend 20-9-2005

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What is a Force Field ?

• A force field is a set of equations and
  parameters which when evaluated for a molecular
  system yields an energy
• A force field is a specific type of vector
  field where the value of a given force is defined
  at each point in space. Examples include
  gravitational fields  and electrostatic fields
• In the fictional Star Trek  universe, force
  shields are the defenses most commonly used to
  protect a starship. The physics of a shield is
  extracted from the physics of a force field ..
  etc.
• The space around a radiating body within which
  its electromagnetic oscillations can exert force
  on another similar body not in contact with it
• Force field analysis evaluates non-monetary
  factors, just as cost-benefit analysis evaluates
  monetary factors

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It is all about time versus accuracy

• Quantum chemistry
• Approximations
• Force Fields
• Hybrid methods
• Self consistent fields
• Molecular dynamics and energy calculations
• Minimizers
• Yasara-Nova
• We will first travel from quantum chemistry to
  brownian motion and after that we will look at a
  series of other Force Fields.

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Quantum chemistry is accurate, but slow
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Quantum chemistry is accurate, but slow
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
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
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
If we want to calculate on 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 ?Cp cannot be calculated
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What can we do with EM and MD?
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)
Take any closed cycle. Calculate the easy
differences, and since the cycle is closed, you
obtain also the value of the difficult
transitions.
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We can turn the thing inside-out
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....
Lets go yet one step further. 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. This
approximation step is known as QSAR (more precise
in DD course).
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Other 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 distances
• Score good proteins
• Normalize the scores
• Score protein of interest

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Electrostatic calculations
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
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
The Poisson Boltzman equation is worked out
digitally, i.e., make a grid, and give every
voxel (grid-box) a charge and a dielectricum. Now
make sure neighbouring grid points have the
correct relations. If a 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 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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Other force fields
Force fields do not need to be based on atoms. A
very different concept would be a secondary
structure evaluation force field Take many
different proteins and determine their secondary
structure. Determine how many residues in total
are H, S, or R, and do the same for each residue
type. Determine preference parameters. P(aa,HSR)
P(aa)P(HSR) Pref(aa,HSR)Ln (observed/predicted)
observed 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 outcome in energy or
standard deviations.
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Force Fields
So, what is a force field? There are so many
different ones for totally different things car
design, electrostatics, nuclear bombs, tornados,
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.
But for a weather forecast one can only take
small steps in a dynamic system as the sun adds
energy to the system, so every time unit
everything has to be recalculated days in
advance. 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
But this is a very simple, one-dimensional case.
How many minima do you think can be found in
crambin (326 heavy atoms)?
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Back to proteins and MD/EM

• During an MD simulation atoms dont move very
  far.
• Because molecules normally arent very flexible
• 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
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
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
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