1 Structural Biology Methods Fall 2022 Lecture #4 Phase problem [0;0;0] x y z •Multiple/Single Isomorphous Replacement (MIR/SIR) •source of phases – intensity differences between data from native and derivative (heavy atom containing) crystals •Positions of heavy atoms identified from isomorphous difference Patterson maps Solving the phase problem by: •Multiple/Single-wavelength anomalous diffraction (MAD/SAD) •source of phases – intensity differences between structure factors due to the presence of atom that specifically interacts with X-rays of a given wavelength •Positions of heavy atoms identified from anomalous difference Patterson maps Solving the phase problem 3 Patterson function Phase problem Patterson map of a macromolecule is a mess! Isomorphous replacement method Isomorphous replacement method Isomorphous replacement method Determination of heavy atom positions from centric reflections (centro-symmetric projections) Scale! Determination of heavy atom positions from acentric reflections Determination of protein phase angles The “lack of closure" error Ideal: Real life: Phase probability Anomalous scattering The anomalous Patterson map •Molecular replacement •1. source of initial phases is a model •2. the model is oriented and positioned to obtain the best agreement with the x-ray data •3. phases are calculated from the model •4. The calculated phases are combined with the experimental data • Solving the phase problem by: Molecular Replacement was invented by Michael Rossmann 30 Molecular Replacement pp_with_model.png brick_with_model.png Known crystal structure New crystal structure Given: • Crystal structure of a homologue • New X-ray data Determine: • The new crystal structure 31 MR Technique pp_with_model.png brick_with_model.png Method: • 6-dimensional global optimisation – one 6-d search for each molecule in the AU >> split further to orientation + translation searches = 3 + 3? Required: • Scoring – the match between the data and (incomplete) model – ideally: the highest score = the correct model Known crystal structure New crystal structure First, consider the model Patterson We put the model in a large P1 box and calculate the Patterson from the structure factors of the model in the P1 box. ROTATION? model in large P1 box Patterson of model in large P1 box “search” model Clusters separated by P1 cell dimensions ROTATION FUNCTION ROTATION FUNCTION The Patterson of our unknown structure contains self-vectors and cross-vectors, but because the cell was large, the self-vectors and cross vectors are well separated from one another. self vector cross vector Just as we generated the Patterson for our model in the first orientation, we can generate the Patterson for the model in any orientation in any sized box. model in same large P1 box in different orientation Patterson of model in large P1 box in different orientation ROTATION FUNCTION When the models are in different orientations the Pattersons will not match one another. = X ROTATION FUNCTION However, when the second model is in the same orientation parts of the Pattersons will match one another, and we can “solve” the rotation function for the model. = ROTATION FUNCTION If the model were in a different sized box, the Patterson of the intramolecular vectors, which are located in a sphere centred on the origin, can be overlaid. We can cut out the peaks corresponding to the inter-molecular vectors from each Patterson and just compare the central parts of the Pattersons. `` `` ROTATION FUNCTION = X = Now, the Pattersons of the intra-molecular vectors will match when the model is in the correct orientation. ROTATION FUNCTION Translation function piccat picmanxfft Observed amplitudes Fourier amplitudes and phases Real space cat Fourier transform Circular rainbow scale of phases Linear intensity scale of amplitude size Fourier cat piccat picmanx Observed amplitudes Phases unknown! Unknown structure, unknown orientation Known structure Fourier cat Cat Fourier transform Diffraction experiment picmanx Manx cat Wrong orientation! Calculated amplitudes and phases FT of Manx cat picmanx Observed amplitudes Phases unknown! Known structure Fourier cat Fourier transform, try different orientations picmanx Manx cat Wrong orientation! Calculated amplitudes and phases FT of Manx cat picmanx picmanx picmanx picmanx picmanx picmanx picmanx piccatmanx3 piccatmanx3fft Observed amplitudes (tailed cat), calculated phases (Manx cat) Even the tail becomes visible! Inverted Fourier transform picduck picduckfft piccatduckfft piccatduck Duck amplitudes + cat phases Duck Fourier transform of duck Looks like a cat!! Model Bias Fourier transform Inverted Fourier transform Model building & resolution Fitting of protein sequence in the electron density Easy in molecular replacement More difficult if no initial model is available Unambiquous if resolution is high enough (better than 3.0 Å) Can be automated, if resolution is close to 2Å or better Phase improvement When to use: Refinement of the Model Structure Parameter to measurement ratio – x, y, z, B (anisotropic B-> 8 parameters) - other data than |Fobs|: stereochemical data (bond lengths and angles) solvent flattening NCS Constrains x Restrains R-factor, Rfreefactor R-factor Rfree factor Ramachandran plot Ψ φ φ Ψ ω The Ramachandran Plot Geometry and stereochemistry Bond lengths Dihedral angles Quality of diffraction data