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Force Fields
Force Fields
Summary
Force Fields
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
There many different types of force fields:
Quantum Chemistry -> Molecular dynamics (the MoaFF) (Seminar 6)
Electrostatic calculations; self consistent field; finite differences
Statistics; Chou and Fasman type FF;
Other
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Force Fields
Back to proteins and MD/EM
We have seen that the few forces
that we (think that we) understand
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mainly are of the form Q=k*(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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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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Force Fields
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/sec (turbo chargers), etc.
Force Fields
Other force fields
Force fields do not need to be based on concepts of physics. You can also
base a FF on statistics. The idea being that if you see it often, it must have
a high probability.
So, a variant on the sequence rule:
If it is important, you see it often.
And now we will do an experiment counting sheep.
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Force Fields
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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Chou and Fasman; null-model
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. This is the null-model.
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?
So there is an above average preference for Ala to be in a helix.
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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. This is the null-model.
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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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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