Force Fields Summary Force Fields What is a

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 Moa. FF) (Seminar 6) Electrostatic calculations; self consistent field; finite differences Statistics; Chou and Fasman type FF; Other 2

Force Fields Back to proteins and MD/EM We have seen that the few forces that we (think that we) understand 2 mainly are of the form Q=k*(x-x 0) In this equation x 0 is known with great precision, while k can easily be wrong by a factor of two or more. Can we use the precision of x 0? 3

Force Fields 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): 4

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 5 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. 6

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). 7

Force Fields 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. 8 Ala Cys Asp Glu Phe Gly His Ile 7. 123 = 7. 0% 1. 232 = 1. 2% 5. 993 etc 6. 086 4. 822 7. 339 989 6. 550 Lys 8. 127 Helix 35. 017 = 34. 3% Sheet 27. 038 = 26. 5% Rest 40. 142 = 39. 3%

Force Fields 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. 9

Force Fields 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. 10

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. . . 11

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? 12

Force Fields And the other way around ΔG= -RT. ln(K) ΔG is just over 1 k. Cal/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 k. Cal/Mole. A p. H unit difference must be ‘worth’ a k. Cal/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. . . 13