Comparing Data from MD simulations
and X-ray Crystallography
• What can we compare?
• 3D shapes (Scalar coupling constants, a.k.a. J-values,
nuclear Overhauser effects)
• Atomic motions (RMSF, Order Parameters)
H
HO
O
NOE
HO
O
HO HO
H
H
HO
HO
O
HO
OH
O
NOE
O
HO HO
H
JCH
HO
NOE intensities may be used to estimate the distance between
hydrogen atoms, separated by less than 4 Å
J-couplings may be used to estimate the torsion angles between
the rings
Sparse, complex data!
http://www.nmr.chem.uu.nl/~abonvin/tutorials/Structcalc-Data/overview.html
NMR structure of CCHF virus Gn tail zinc finger.
NMR structure of CCHF virus Gn tail zinc finger.
Stereoview of the superposition of 20 lowest energy NMR
structures of CCHF virus Gn zinc finger (A).
Estrada D F , De Guzman R N J. Biol. Chem. 2011;286:21678-21686
NMR Scalar Couplings (J-values) Depend on
Torsion Angles
NMR – measure J-value
from spectrum then
derive angle
MD – compute angle
from trajectory then
derive J-value
Nuclear Overhauser Effects
The nuclear Overhauser effect (NOE) identifies pairs of
protons (i,j) that are in close proximity. (A) Schematic
representation of a polypeptide chain highlighting five
particular protons. Protons 2 and 5 are in close proximity
Rij
j
i
Under certain NMR conditions: the magnitude of the NOE
intensity is proportional to 1/Rij6, where Rij is the distance
between the protons.
Therefore, NOEs can also be computed from MD data (by
computing 1/Rij6)
(A) NOESY observations show that protons
(connected by dotted red lines) are close to one
another in space. (B) A three-dimensional
structure calculated with these proton pairs
constrained to be close together
http://www.ncbi.nlm.nih.gov/books/NBK22393/
NMR Order Parameters Relate to Internal Motion
Elapsed Time 
f
Initially the structures will align
closely (highly ordered) and
the angle between any internal
vector will be close to zero but
later the structures will be very
different (disordered).
Order Parameter
versus
Simulation time
For example
– when comparing to x-ray data, it is possible to compare theoretical
atomic positions or interatomic distances with experimental values – but
remember the x-ray data were not measured under the same conditions
as the simulation
– when comparing to NMR data, remember, 3D structures reported from
NMR studies are all models based on fitting to the measured NMR
observables (NOE intensities and couplings).
It may be preferable to compute these NMR observables from the
theoretical data, rather than comparing to a 3D model derived from the
NMR data
Property
X-Ray
NMR
MD Simulation
Atomic Positions
Well Defined
Not Defined
Well Defined
Bond Lengths and
Angles
Well Defined
Not Defined
Well Defined
Inter Atomic
Distances
Well Defined
Partially Defined
by NOEs
Well Defined
Torsion Angles
Well Defined
Partially Defined
by J-values
Well Defined
Internal Motions
Not Defined
Partially Defined
by correlation
times
Well Defined
a.b = |a||b|cosf
1)
2)
3)
4)
5)
1)
2)
3)
4)
P2(x) = ½(3x2 - 1)
Run the MD
monitor the N-H bond vectors
compute C(t)
Derive S2
Compare to S2 from NMR
Run the MD
Monitor the dihedral angles
Compute scalar J-values
Derive a simple relationship to assess
the goodness of fit, X2
5) Compare to NMR
Perfect agreement would give X2 = 0
So which water model is superior?
Why did they increase the system
temperature from 300 to 350 K?
Is a X2 value of 3Hz a big error?
Based on the graph below, what range of torsion values is defined by 3Hz?
Vary the force field parameters and see what set gives best agreement with NMR
But how do you know what parameter to vary?
Why does the C-terminus of
the protein have a low
value for the order
parameter?
Because it is highly
flexible…