1
Structural Biology
Methods
Fall 2020
Lecture #4
Phase problem
[0;0;0] x
y
z
Patterson function
Phase problem
Patterson map of a macromolecule is a mess!
Isomorphous replacement method
Isomorphous replacement method
Isomorphous replacement method
Determination of heavy atom positions from centric
reflections (centro-symmetric projections)
Scale!
Determination of heavy atom positions from
acentric reflections
Determination of protein phase angles
The “lack of closure" error
Ideal:
Real life:
Phase probability
Anomalous scattering
The anomalous Patterson map
27
Molecular Replacement
Known crystal structure New crystal structure
Given: • Crystal structure of a homologue
• New X-ray data
Determine: • The new crystal structure
28
MR Technique
Method: • 6-dimensional global optimisation
– one 6-d search for each molecule in the AU
>> split further to orientation + translation searches = 3 + 3?
Required: • Scoring
– the match between the data and (incomplete) model
– ideally: the highest score = the correct model
Search model
Known crystal structure New crystal structure
First, consider the model Patterson
We put the model in a large P1 box and calculate the Patterson
from the structure factors of the model in the P1 box.
ROTATION?
model in large P1 box
Patterson of
model in large
P1 box
“search” model
Clusters
separated by
P1 cell
dimensions
ROTATION FUNCTION
ROTATION FUNCTION
The Patterson of our unknown structure contains self-vectors and cross-vectors, but
because the cell was large, the self-vectors and cross vectors are well separated from
one another.
self vector
cross
vector
Just as we generated the Patterson for our model in the first orientation, we can
generate the Patterson for the model in any orientation in any sized box.
model in same large P1 box
in different orientation Patterson of
model in large P1
box
in different
orientation
ROTATION FUNCTION
When the models are in different orientations the Pattersons will not match one
another.
=X
ROTATION FUNCTION
However, when the second model is in the same orientation parts of the Pattersons
will match one another, and we can “solve” the rotation function for the model.
=
ROTATION FUNCTION
If the model were in a different sized box, the Patterson of the intramolecular
vectors, which are located in a sphere centred on the origin, can be overlaid. We can
cut out the peaks corresponding to the inter-molecular vectors from each Patterson
and just compare the central parts of the Pattersons.
``
``
ROTATION FUNCTION
=X
=
Now, the Pattersons of
the intra-molecular
vectors will match
when the model is in
the correct orientation.
ROTATION FUNCTION
Rotation function
Rotation function
Translation function
Phase improvement
When to use:
Refinement of the Model Structure
Parameter to measurement ratio – x, y, z, B (anisotropic B-> 8 parameters)
- other data than |Fobs|: stereochemical data (bond lengths and angles)
solvent flattening
NCS
Constrains x Restrains
The Ramachandran Plot
The Ramachandran Plot
Quality of diffraction data