Force Fields

Force Fields

G Vriend 30-11-2008

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 • 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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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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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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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.But we count 3457 Ala in helix; that is 1.38 times ‘too many’.So chances are ‘better than random to find Ala in a helix. How do we quantify this?

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Come to the rescue, one long dead physicist

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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.But we count 3457 Ala in helix; that is 1.38 times ‘too many’.So chances are ‘better than random to find Ala in a helix. How do we quantify this?

So the ‘score’ for (Ala,helix) = Q(A,H)= ln(observed/predicted) = ln(3457/2505)=ln(1.38)=0.32. The preference parameter Q(A,H) is positive.

And how do we now predict the secondary structure of a protein?

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One ‘serious’ example: Chou and Fasman

One example could be:Loop over the sequence to be predictedGive 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 tooTNDLLMAVMRGG and I too, so it IS a helix after all.

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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 Vriend’s law of 10 that hasn’t been discussed in the classroom yet...