1. Goals for Today Introduce automated refinement and validation.
Evaluate Rwork and Rfree for your ProK model.
Refine ProK
Validate ProK (web server)
Awards
Refine ProK-PMSF complex
Go forth wielding the tools of X-ray crystallography and discover the secrets of other biological macromolecules.

2. Real Space Refinement with manual intervention
positive negative
density density
A simplistic target
Atoms move into closest electron density
Manual adjustments improve radius of convergence

3. REAL vs RECIPROCAL Real Space Reciprocal Space Manual Local
Atomic movements are guided by the phases
Improvement in the model is limited by the quality of the phases
Reciprocal Space
Automatic
Global
Phases not used in the refinement. They change.
Improved phases will lead to improved maps and improved interpretability and improved model.

4. Radius of convergence Manual adjustments improve radius of convergence
Torsion angle Ca-Cb
Rupp

5. REAL vs RECIPROCAL Real Space Reciprocal Space Manual Local
Atomic movements are guided by the phases
Improvement in the model is limited by the quality of the phases
Large radius of convergence
Reciprocal Space
Automatic
Global
Phases not used in the refinement. They change.
Improved phases will lead to improved maps and improved interpretability and improved model.
Small radius of convergence

6. Reciprocal Space Target function: Edata (R-factor)
Move atoms to minimize the R-factor.
Minimize the discrepancy between Fobs and Fcalc.
Specifically, minimize E
Edata=S w(Fobs-Fcalc)2 Over all hkl.
Least squares refinement.
Maximum likelihood allows for non-random error model. Given this model, what is the probability that the given set of data would be observed.

7. Importance of supplementing the Data to Parameter Ratio in crystallographic refinement.
PARAMETERS
Each atom has 4 parameters (variables) to refine:
x coordinate
y coordinate
z coordinate
B factor
In proteinase K there are approximately 2000 atoms to refine.
This corresponds to
2000*4= 8000 variables.
DATA
At 2.5 A resolution we have 8400 observations (data points) (Fobs).
When # of observations= # of variables
A perfect fit can be obtained irrespective of the accuracy of the model.
At 1.7 A resolution we have 25,000 observations. About 3 observations per variable. The reliability of the model is still questionable.
Adding stereochemical restraints is equivalent to adding observations

8. Automated Refinement Etotal = Edata(wdata)+ Estereochemistry
(distinct from manual building)
Two TERMS:
Etotal = Edata(wdata)+ Estereochemistry
Edata describes the difference between observed and calculated data.
wdata is a weight chosen to balance the gradients arising from the two terms.
Estereochemistry comprises empirical information about chemical interactions between atoms in the model. It is a function of all atomic positions and
includes information about both covalent and non-bonded interactions.

9. Estereochemistry (Geometry)
BOND LENGTHS & ANGLES have ideal values. Engh & Huber dictionary.
-CHIRALITY of a-carbons
PLANARITY of peptide bonds and aromatic side chains
NONBONDED CONTACTS -two atoms cannot occupy the same space at the same time
TORSION ANGLE PREFERENCES side chains have preferred rotamers.
some values of f and y are forbidden. -Ramachandran. Not restrained- used for validation.
loop_
_chem_comp_bond.comp_id
_chem_comp_bond.atom_id_1
_chem_comp_bond.atom_id_2
_chem_comp_bond.type
_chem_comp_bond.value_dist
_chem_comp_bond.value_dist_esd
ALA N CA single
ALA CA CB single
ALA CA C single
ALA C O double e

10. Etotal =Estereochemistry + wdataEdata
Jeopardy clue: The appearance of the atomic model when stereochemical restraints are not included in crystallographic refinement.
Etotal =Estereochemistry + wdataEdata
What is spaghetti, Alex?

11. restrained not restrained

12. Etotal =Estereochemistry + wdataEdata
2nd Jeopardy clue: The value of the R-factor resulting when stereochemical restraints are not included in crystallographic refinement.
Etotal =Estereochemistry + wdataEdata
What is zero, Alex?

13. An atomic model should be validated by several unbiased indicators
The need for Cross-Validation
Low RMS deviations in bond lengths and angles does not guarantee a correct structure
Rfree is an unbiased indicator of the discrepancy between the model and the data. The data used in this R-factor calculation were not used in determining atomic shifts in the refinement process.
Ramachandran plot is unbiased because phi and psi torsion angles are not restrained in the refinement process.

14. Lowest energy f,y angles correspond to a-helices and b-sheets
a-helix
Ramachandran plot
Lets focus on recognizing helix and strand features in electron density maps.

15. O N H
BACKBONE AMIDE

16. BAD O N H
BACKBONE AMIDE
2.8 Å H O N
Asn

17. GOOD O N H
BACKBONE AMIDE
2.8 Å H O N H
Asn

18. ERRAT examines distances between non-bonded atoms
ERRAT examines distances between non-bonded atoms. Reports the deviations of C-C, C-N, C-O, N-N, N-O, O-O distances from distributions characteristic of reliable structures.

19. Verify 3D plot –Indicates if the sequence has been improperly threaded through the density. It measures the compatibility of a model with its sequence.
For each residue in the structure, measured values of (1) Surface area buried (2) fraction of side-chain area covered by polar atoms (3) local secondary structure are compared to the values preferred for its amino acid type.
Correct trace
Backwards trace
Report the fraction of residues with score greater than 0.2

20. Plan for today: Solve structure of ProK-PMSF complexH O F
ProK
active site
Ser225
PMSF: Phenylmethylsufonyl fluoride

21. The beauty of isomorphism
r(x,y,z)=1/V*S|Fobs|e-2pi(hx+ky+lz-fcalc)
Initial phases: phases from native proteinase K structure fcalc ProK.
Fobs amplitudes: Use |FProk-PMSF| data measured earlier in the course.
protein
a (Å)
b (Å)
c (Å) a b g
ProK
67.9
101.8
90°
ProK+PMSF
102.5
Riso=15.2%
What is maximum possible Riso?
What is minimum possible Riso?
Why don’t we have to use Heavy atoms?
Why don’t we have to use Molecular Replacement?

22. Fo-Fc Difference Fourier map
r(x,y,z)=1/V*S|Fobs-Fcalc|e-2pi(hx+ky+lz-fcalc)
Here, Fobs will correspond to the Proteinase K-PMSF complex.
Fcalc will correspond to the model of Proteinase K by itself after a few cycles of automated refinement.
Positive electron density will correspond to features present in the PMSF complex that are not in the native structure.
Negative electron density will correspond to features present in the native structure that should be removed in the inhibitor complex.
After model building, do more automated refinement and then validate.

23. Plan for today (continued)
Remove waters from autobuilt ProK model.
Use this as a starting model to refine against ProK-PMSF data.
Then manually build the PMSF inhibitor into an Fo-Fc difference Fourier map. Refinement process typically iterates between automated and manual building. Automated refinement has a limited radius of convergence. For example- automated refinement cannot jump between rotamers or flip between cis and trans peptides.
Validate structure. Fill out Refinement Statistics table.

24. 3 Key Concepts
When to use isomorphous difference Fourier to solve the phase problem.
How to interpret an Fo-Fc Difference Fourier map.
RMS deviation from ideal geometry
difference between cis and trans peptides
methods of cross-validation

25. Number of least-squares parameters
Name _______________________
Proteinase K from Tritirachium album ProK + PMSF
Number of least-squares parameters
protein atoms
Errat overall quality factor

26. Cis vs. Trans peptide R Ca C O N C O N Ca R R LOTS OF FREEDOM!
peptide plane C O N Ca
peptide plane R
Steric
CLASH R
LOTS OF FREEDOM!

27. Cis OK with glycine or prolineCa C O N
peptide plane O
peptide plane C N Ca Ca R
Steric hindrance equivalent
for cis or trans.

28. Steric hindrance equivalent for cis or trans prolineCa C N
peptide plane O
peptide plane Ca Cb Cd Cg C N Cg Cb Ca Cd R .