Automated Refinement (distinct from manual building) Two TERMS: E total = E data ( w data ) + E stereochemistry E data describes the difference between observed and calculated data. w data is a weight chosen to balance the gradients arising from the two terms. E stereochemistry 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.
E data (R-factor) Move atoms to minimize the R-factor. Discrepancy between F obs and F calc. Specifically, minimize E E= w(F obs -F calc ) 2 Over all hkl. Least squares refinement. Atoms shift toward positive density in a difference Fourier electron density map. x =1/V* |F obs -F calc |e -2 i(hx- calc ) positive negative density Radius of convergence is limited
E stereochemistry (Geometry) –BOND LENGTHS & ANGLES have standard 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.
Jeopardy clue: The appearance of the atomic model when stereochemical restraints are not included in crystallographic refinement. What is spaghetti, Alex? E total =E stereochemistry + w data E data
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. 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 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.
2 nd Jeopardy clue: The value of the R-factor resulting when stereochemical restraints are not included in crystallographic refinement. What is zero, Alex? E total =E stereochemistry + w data E data
An atomic model should be validated by several unbiased indicators R free 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. therefore
N O Asn H H O N H BACKBONE AMIDE 2.8 Å BAD
N O H H O N H BACKBONE AMIDE 2.8 Å Asn GOOD
ERRAT plot examines the geometric relationship between non-bonded atoms. Looks at the fraction of non-bonded contacts with C, N, O as a function of distance.
RuBisCo chain traced backwards Verify 3D plot –Gives an indication if the sequence has been improperly threaded through the backbones. Each of the 20 amino acid types has a characteristic (1) Surface area buried (2) fraction of side-chain area covered by polar atoms (3) local secondary structure. Verify 3D plots correlation between ideal and your model. Compatibility of a model with its sequence.
Plan for today 1)The refinement of native proteinase K is assumed to be complete thanks to ARP/wARP. 2)You will refine the structure of the proteinase K- PMSF complex using the |Fobs| data measured earlier in the course. 3)The starting model for the refinement will be the native proteinase K structure. 4)Begin 5 cycles of automated refinement. This will only move atoms. It will not add new atoms. 5)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. 6)Validate structure. Fill out Refinement Statistics table.
Difference Fourier map x =1/V* |F obs -F calc |e -2 i(hx- calc ) Here, Fobs will correspond to the ProteinaseK-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.
R R Cis vs. Trans peptide CC C O N CC peptide plane R R C O N CC CC
Cis OK with glycine or proline R H CC C O N CC peptide plane R CC C O N CC Steric hindrance equivalent for cis or trans.
Steric hindrance equivalent for cis or trans proline. R CC CN CC peptide plane O R CC CN O CC CC CC CC CC CC CC
Name _______________________ Proteinase K –PMSF complex