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.

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

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

REAL vs RECIPROCAL Real Space Reciprocal 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.

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.

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

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.

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 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

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?

restrained not restrained

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?

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.

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.

O N H BACKBONE AMIDE

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

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

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.

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

Plan for today: Solve structure of ProK-PMSF complex H O F ProK active site Ser225 PMSF: Phenylmethylsufonyl fluoride

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?

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.

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.

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

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

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!

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

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