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Force Fields
Force Fields
Seminar 3 in the series…
G Vriend 15-9-2009
Force Fields
What is a Force Field ? Wikipedia:
• 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 costbenefit analysis evaluates monetary factors
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Molecularly speaking, it is about time versus accuracy
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Quantum chemistry
Approximations
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Hybrid methods
Self consistent fields
Molecular dynamics and energy calculations (seminar 6)
Minimisers
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
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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This will not come back at the exam
Force Fields
Quantum chemistry is accurate, but slow
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This will not come back at the exam
Force Fields
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 given the problem you want to solve.
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Next step: Newtonian mechanics
If we want to calculate on molecules that contain thousands of atoms, we
have to totally abandon quantum chemistry, and use Newton’s laws of
motion, treating atoms as macroscopical particles instead of quantum
chemical entities.
The YASARA movie in the practical will explain how this is done.
T

H(T) = H(Tref) +
Cp .dT
Tref
T
S(T) = S(Tref) +

(Cp /T).dT
Tref
ΔH wants to go down ΔS wants to go up
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ΔCp cannot be calculated
This will not come back at the exam
Force Fields
Molecular dynamics using Newton’s ‘rules’
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If it is all still too slow, 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 (or many) positions.
This, of course, is an approximation relative to methods based on molecular
dynamics. Often used in drug design (seminar 5).
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Force Fields
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 (seminar 5).
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This will not come back at the exam
Force Fields
Electrostatic calculations
Electrostatic calculations are based on self-consistent field principles. This
field is different from the force fields we have seen so far. It is a distribution of
potentials digitized on a grid that covers the space in and around the
molecule. Needed for drug design (seminar 5) and some MD (seminar 6).
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Force Fields
Electrostatic calculations
Often physics looks like Chinese typed backwards by a drunken sailor, but
when you spend a bit of time, you will see 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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This will not come back at the exam
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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
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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.
Force Fields
But even this is too time consuming to calculate
So, most MD force fields don’t recalculate atomic
charges, at all...
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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 all frequencies:
P(aa,HSR)=P(aa)*P(HSR)
Calibrate the method
Use it by looping over the amino acids in the protein to be tested and
multiply all chances P(aa,HSR).
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One ‘serious’ example: Chou and Fasman
Example of Chou and Fasman:
We count all amino acids in a dataset of 400 proteins with know structure
(they had many fewer proteins available in 1974, but anyway...)
These 400 proteins in total have 102.197 amino acids.
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Ala
Cys
Asp
Glu
Phe
Gly
His
Ile
Lys
7.123 = 7.0%
1.232 = 1.2%
5.993 etc
6.086
4.822
7.339
989
6.550
8.127
Helix 35.017 = 34.3%
Sheet 27.038 = 26.5%
Rest
40.142 = 39.3%
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What is the null-model?
The null-model is the model that assumes that there is no signal in the input
data. In case of our Chou-and-Fasman example, the null model assumes
that there is no relation between the amino acid type and the secondary
structure.
So, if 7% (0.07) of all amino acids are of type Ala, and ~34% (0.34) of all
amino acids are in a helix, then 7% of 34% (0.07*0.34) is 2.4% (0.024) of all
alanines should be observed in a helix.
And since that isn’t true, we can make a model that differs from the nullmodel, and thus we can make predictions.
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Force Fields
One ‘serious’ example: Chou and Fasman
These 400 proteins in total have 102.197 amino acids.
Ala
7.123 = 7.0%
Helix 35.017 = 34.3%
Cys
1.232 = 1.2%
Sheet 27.038 = 26.5%
Asp
5.993 etc
Rest
40.142 = 39.3%
(Ala,Helix)predicted=0.07*34.3=2.4% or 2505 Ala-in-helix predicted in the data
set of 400 proteins.
But we count 3457 Ala-in-helix; that is 1.38 times ‘too many’.
So chances are ‘better than random to find an alanine in a helix. How do we
quantify this?
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Force Fields
Come to the rescue, one long dead physicist
This is at the basis of:
ΔG = ΔH - TΔS
ΔG = -RTln(K)
And of Vriend’s rule of 10...
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Force Fields
One ‘serious’ example: Chou and Fasman
These 400 proteins in total have 102.197 amino acids.
Ala
7.123 = 7.0%
Helix 35.017 = 34.3%
Cys
1.232 = 1.2%
Sheet 27.038 = 26.5%
Asp
5.993 etc
Rest
40.142 = 39.3%
(Ala,Helix)predicted=0.07*34.3=2.4% or 2505 Ala-in-helix predicted in the
data set of 400 proteins.
But we count 3457 Ala-in-helix; that is 1.38 times ‘too many’.
So the ‘score’ for (Ala,helix) = Pref(A,H)= ln(observed/predicted) =
ln(3457/2505)=ln(1.38)=0.32. The preference parameter Pref(A,H) is
positive. So, here positive is good (unlike ΔG or AIDS tests).
And how do we now predict the secondary structure of a protein?
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Force Fields
One ‘serious’ example: Chou and Fasman
One example could be:
Loop over the sequence to be predicted
Give each residue 3 energy scores (for H, S, and rest, respectively)
Find stretches where the energy for one of the three is higher than the
other two.
Hundreds of recipes can be thought of, and the best one wins (CASP
competition teaches us that the best one is a neural network that uses
multiple sequence alignments as input).
SNDALPIVAKGS Nice helix, but for the PIV.
TSEAAQIALHSG Aha, P is exception, and V too
TNDLLMAVMRGG and I too, so it IS a helix after all.
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Force Fields
And the other way around
ΔG= -RT.ln(K)
ΔG is just over 1kCal/Mole when K=10 and K is the ratio between two
‘somethings’ (can be anything). Swimming into a gradient of a factor 10
costs 1 kCal/Mole. A pH unit difference must be ‘worth’ a kCal/Mole.
A nice exam question would be to think of an example of this ‘law of 10’
that hasn’t been discussed in the course yet...
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