G Vriend 2-11-2004
Force Fields
G Vriend master series 2-11-2004
Force Fields
It is all about time versus accuracy
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Quantum chemistry
Approximations
Force Fields
Hybrid methods
Self consistent fields
Molecular dynamics and energy calculations
Minimizers
Yasara-Nova
G Vriend master series 2-11-2004
Force Fields
Quantum chemistry is accurate, but slow
G Vriend master series 2-11-2004
Force Fields
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.
G Vriend master series 2-11-2004
Force Fields
Quantum chemistry is accurate, but slow
Actually, pure quantum chemistry cannot be applied in our (protein) world.
Which is good, because quantum chemistry is much too difficult (for me). But
many of the results are very useful. For example, all atoms in proteins display
sp2 - sp3 hybridization.
Pictures obtained from Clifford J Creswell
G Vriend master series 2-11-2004
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.
G Vriend master series 2-11-2004
Force Fields
So, we will use Newtonian mechanics
If we want to calculate with 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 following (YASARA) movie will explain how this is done.
T
H(T)
=

H(Tref) +
Cp .dT
Tref
T
S(T)
=
S(Tref) +

Tref
ΔH wants to go down
ΔS wants to go up
and ΔCp cannot be calculated
(Cp /T).dT
G Vriend master series 2-11-2004
Force Fields
What can we do with EM and MD?
Despite all its shortcomings, MD can be used to calculate binding constants
of ligands in active site pockets with reasonable accuracy.
This is done with so-called thermodynamic integration which works because
binding a ligand is a state-function (the path is not important, only the endpoints; so non-realistic paths are allowed):
Just take any closed cycle you want. Calculate the easy difference, and since
the cycle is closed, you obtain also the value of the difficult cycle.
G Vriend master series 2-11-2004
Force Fields
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 position.
This, of course, is again an approximation relative to the thermodynamic
integration method. Examples: LUDI or GRID.
G Vriend master series 2-11-2004
Force Fields
And one more approximation step....
Lets go yet one step further along the drug binding path. 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. So,
one more approximation step....
G Vriend master series 2-11-2004
Force Fields
Other force fields
So far we discussed molecular dynamics force fields and ‘approximated’ them
into ‘experience based’ drug design.
Many other force fields exist. For example, many force fields exist for the
purpose of validating protein structures or models. Example ProSa:
1)
2)
3)
4)
Measure Cα distance distributions
Score good proteins per residue
Normalize the scores
Score protein of interest
G Vriend master series 2-11-2004
Force Fields
Other force fields
Force fields do not need to be based on relative positions of atoms. A very different
concept would be a secondary structure evaluation force field.
Recipe:
Take 4000 different proteins and determine their secondary structure.
Determine how many residues are H, S, or R
Determine for each residue type how often it is Helix, Strand, Rest (HSR)
Determine the preference parameters for the 20 aa in the 3 states
P(aa,HSR)=P(aa)*P(HSR)
Pref(aa,HSR)=Ln (observed/predicted)
observed is simply counting (aa,HSR) in the 4000 proteins
predicted is P(aa,HSR) * (total number of aa in the 4000 proteins)
Callibrate the method with a Jack-Knife procedure
Loop over the aa in the protein to be tested and add up all Pref(aa,HSR)
Express the outcome in energy or standard deviations (Z-score)
G Vriend master series 2-11-2004
Force Fields
Electrostatic calculations
Electrostatic calculations are based on self-consistent field principles. This field is
not a force field like we have seen so far, but a distribution of charges over a grid
that covers the space in and around the molecule.
G Vriend master series 2-11-2004
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):
G Vriend master series 2-11-2004
Force Fields
Electrostatic calculations
The Poisson Boltzman equation normally is worked out digitally, i.e., make a grid,
and give every voxel (grid-box) homogeneous values for charge and dielectricum.
Now make sure all neighbouring grid points have the correct pairwise relations. If
one voxel has ‘too much charge’ it should give some charge to the neighbours.....
This is done iteratively till self-consistent.
And the
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 under a bridge in the
Waal, optimize catalysts in mufflers, optimize the horse powers of a car given a
certain amount of gasoline (turbo chargers), etc.
G Vriend master series 2-11-2004
Force Fields
Force Fields
So, what is a force field? There are so many different ones for totally different
things (car design, electrostatics, nuclear bombs, tornados, etc)...
A force field is a set of rules that can predict the ‘optimal constellation’ of a system
in the absence of external forces.
So, in case of electrostatic calculations, the field can be calculated in the absence
of molecular motion, and new ‘things’ entering the system. But for a weather
forecast one can only take small steps in a dynamic system as the sun adds
energy to the system.
Most force fields can be used to optimize/minimize the system, and here we run
into the multiple minimum problem.
G Vriend master series 2-11-2004
Force Fields
Multiple minimum problem
But this is a very simple, one-dimensional case. How many dimensions and how
minima do you think can be found in crambin (326 heavy atoms)?
G Vriend master series 2-11-2004
Force Fields
Back to proteins and MD/EM
During an MD simulation atoms don’t move very far.
A) Because molecules normally aren’t very mobile
B) Because we cannot run the simulations long enough
C) Because the forcefields are far from precise enough
We can use this to do MD differently....
G Vriend master series 2-11-2004
Force Fields
Back to proteins and MD/EM
We have seen that the few forces that we (think that we) understand mainly are of
2
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?
G Vriend master series 2-11-2004
Force Fields
MD with CONCOORD
In the CONCOORD software, all distances between atoms are forced at x0 plus or
minus ‘a little bit’. This little bit is determined by the nature of the force between the
atoms. In a way, concoord works a bit like NMR structure determination.
G Vriend master series 2-11-2004
Force Fields
MD with CONCOORD
All x-es are close to their x0 in each CONCOORD structure. So a movie based on
the CONCOORD structures shows a path of low energy, or a path along the X0 in
2
Q=k*(x-x0)
Molecular dynamics
k
CONCOORD
x0