Goals for Today

1
Goals for Today

• Introduce automated refinement and validation.
• Evaluate Rwork and Rfree for your ProK model.
• Refine ProK (automatic)
• Validate ProK (web server)
• Awards
• Automatic refinement
• 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
Radius of convergence

• Manual adjustments improve radius of convergence

Torsion angle Ca-Cb
Rupp
4
REAL vs RECIPROCAL

• Real Space
• Manual
• Local
• Large radius of convergence
• Atomic movements are guided by the phases
• Improvement in the model is limited by the
  quality of the phases

• Reciprocal Space
• Automatic
• Global
• Small radius of convergence
• Phases not used in the refinement. They change.
• Improved phases will lead to improved maps and
  improved interpretability and improved model.

5
Reciprocal Space Target function Edata (R-factor)
Move atoms to minimize the R-factor. Minimize
the discrepancy between Fobs and
Fcalc. Specifically, minimize E EdataS
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.
6
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 20004 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
7
Automated Refinement
(distinct from manual building) Two
TERMS Etotal Edata(wdata) Estereochemistry Ed
ata 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.
8
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.ty
pe _chem_comp_bond.value_dist _chem_comp_bond.valu
e_dist_esd ALA N CA single
1.458 0.019 ALA CA CB single
1.521 0.033 ALA CA C single
1.525 0.021 ALA C O double
1.231 0.020
e
9
Jeopardy clueThe appearance of the atomic
model when stereochemical restraints are not
included in crystallographic refinement.
Etotal Estereochemistry wdataEdata
What is spaghetti, Alex?
10
restrained not restrained
11
2nd Jeopardy clueThe value of the R-factor
resulting when stereochemical restraints are not
included in crystallographic refinement.
Etotal Estereochemistry wdataEdata
What is zero, Alex?
12
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.
13
Lowest energy f,y angles correspond to a-helices
and b-sheets
b-sheet
a-helix
Ramachandran plot
Lets focus on recognizing helix and strand
features in electron density maps.
14
(No Transcript)
15
BAD
2.8 Å
O
N
Asn
16
GOOD
2.8 Å
H
O
N
H
Asn
17
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.
18
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
19
Plan for today Solve structure of ProK-PMSF
complex
O
H
F
ProK active site Ser225
PMSF Phenylmethylsufonyl fluoride
20
The beauty of isomorphism
r(x,y,z)1/VSFobse-2pi(hxkylz-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 67.9 101.8 90 90 90
ProKPMSF 67.9 67.9 102.5 90 90 90
Riso15.2 What is maximum possible Riso? What is
minimum possible Riso?
Why dont we have to use Heavy atoms? Why dont
we have to use Molecular Replacement?
21
Fo-Fc Difference Fourier map
r(x,y,z)1/VSFobs-Fcalce-2pi(hxkylz-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.

22
Plan for today (continued)

1. Remove waters from autobuilt ProK model.
2. Use this as a starting model to refine against
   ProK-PMSF data.
3. 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.
4. Validate structure. Fill out Refinement
   Statistics table.

23
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

24
Name _______________________
Proteinase K from
Tritirachium album ProK PMSF
Number of least-squares parameters
protein atoms
Errat overall quality factor
25
Cis vs. Trans peptide
26
Cis OK with glycine or proline
O
peptide plane
C
N
Ca
Ca
R
Steric hindrance equivalent for cis or trans.
27
Steric hindrance equivalentfor cis or trans
proline
O
peptide plane
Ca
Cd
Cb
Cg
C
N
Cg
Cb
Cd
Ca
R
.