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.

Real Space Refinement with manual intervention

• A simplistic target• Atoms move into

closest electron density

• Manual adjustments improve radius of convergence

positive negativedensity density

REAL vs RECIPROCAL

• Real 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.

Radius of convergence

• Manual adjustments improve radius of convergence

Rupp

Torsion angle C-C

REAL vs RECIPROCAL

• Real 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

Reciprocal Space Target function: Edata (R-factor)

Move atoms to minimize the R-factor. Minimize the discrepancy between Fobs and Fcalc.

Specifically, minimize EEdata=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.

Importance of supplementing the Data to Parameter Ratio

in crystallographic refinement.

PARAMETERSEach atom has 4 parameters (variables) to refine:

x coordinatey coordinatez coordinateB factor

In proteinase K there are approximately 2000 atoms to refine.

This corresponds to 2000*4= 8000 variables.

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

DATAAt 2.5 A resolution we have 8400 observations (data points) (Fobs).

When # of observations= # of variablesA perfect fit can be obtained irrespective of the accuracy of the model.

Automated Refinement(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 andincludes information about both covalent and non-bonded interactions.

Estereochemistry (Geometry)–BOND LENGTHS & ANGLES have ideal values. Engh & Huber dictionary.CHIRALITY of -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 and are forbidden. -Ramachandran. Not restrained- used for validation.

e

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 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

Jeopardy clue:

The appearance of the atomic model when stereochemical restraints are not included in

crystallographic refinement.

What is spaghetti, Alex?

Etotal =Estereochemistry + wdataEdata

restrained not restrained

2nd Jeopardy clue:

The value of the R-factor resulting when stereochemical restraints are not included in

crystallographic refinement.

What is zero, Alex?

Etotal =Estereochemistry + wdataEdata

An atomic model should be validated by several unbiased indicators

Low RMS deviations in bond lengths and angles does not guarantee a correct structureRfree 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.

The need for Cross-Validation

Lowest energy angles correspond to -helices and -sheets

-helix

-sheet

Lets focus on recognizing helix and strand features in electron density maps.

Ramachandran plot

O

NH

BACKBONE AMIDE

N O

Asn

H

H

O

NH

BACKBONE AMIDE

2.8 Å

BAD

NO

H

H

O

NH

BACKBONE AMIDE

2.8 Å

Asn

GOOD

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.

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.

Report the fraction of residues with score greater than 0.2

Backwards trace

Correct trace

F

Plan for today: Solve structure of ProK-PMSF complex

O

ProKactive siteSer225

PMSF: Phenylmethylsufonyl fluoride

H

The beauty of isomorphism

protein a (Å) b (Å) c (Å)

ProK 67.9 67.9 101.8 90° 90° 90°

ProK+PMSF 67.9 67.9 102.5 90° 90° 90°

Riso=15.2%What is maximum possible Riso?What is minimum possible Riso?

• Initial phases: phases from native proteinase K structure calc ProK. • Fobs amplitudes: Use |FProk-PMSF| data measured earlier in the course.

Why don’t we have to use Heavy atoms?Why don’t we have to use Molecular Replacement?

x,y,z=1/V*|Fobs|e-2i(hx+ky+lz-calc

)

Fo-Fc Difference Fourier mapx,y,z=1/V*|Fobs-Fcalc|e-2i(hx+ky+lz-

calc)

•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.

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.

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

Name _______________________

Proteinase K from Tritirachium album ProK + PMSF

protein atoms

Errat overall quality factor

Number of least-squares parameters

R R

Cis vs. Trans peptide

C

C

O

N

C

peptide plane

RR

C

O

N

Cpeptide plane

C

Cis OK with glycine or proline

RH

C

C

O

N

C

peptide plane

R

C

C

O

N

C

peptide plane

Steric hindrance equivalentfor cis or trans.

Steric hindrance equivalentfor cis or trans proline

.

R

C

C N

C

peptide planeO

R

C

C N

peptide planeO

C

C

C

C C

CC