Force Fields

Force Fields

Summary

Force Fields

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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

There many different types of force fields:Quantum Chemistry -> Molecular dynamics (the MoaFF) (Seminar 6)Electrostatic calculations; self consistent field; finite differencesStatistics; Chou and Fasman type FF;Other

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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 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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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.

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.

And the function is very simple!

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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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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.

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%Glu 6.086Phe 4.822Gly 7.339His 989Ile 6.550Lys 8.127

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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 null-model, 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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Come to the rescue, one long dead physicist

This is at the basis of:ΔG = ΔH - TΔSΔG = -RTln(K)

And of Vriend’s rule of 10...

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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...