Macromolecular crystallography Pavel Plevka •Development of crystallography •Waves and radiation •Diffraction •Solution of phase problem •Model building and structure validation • WILHELM CONRAD RÖNTGEN (1845-1923) •1901 Nobel Laureate in Physics • discovery of the remarkable rays subsequently named after him. MAX VON LAUE (1879-1960) •1914 Nobel Laureate in Physics • for his discovery of the diffraction of X-rays by crystals laue img59 Friedrich and Knipping Waves Coherent beam Addition of waves Particles & waves MAX VON LAUE (1879-1960) •1914 Nobel Laureate in Physics • for his discovery of the diffraction of X-rays by crystals laue img59 Friedrich and Knipping Wavelength and diffraction Wavelength comparison of X-rays and visible light 38l 70μm WILLIAM HENRY BRAGG (1862-1942) WILLIAM LAWRENCE BRAGG (1890-1971) •1915 Nobel Laureates in Physics • for the analysis of crystal structure by means of X-rays wh-bragg wl-bragg nl = 2d sinq James Batcheller Sumner (1879-1960) •1946 Nobel Laureate in Chemistry • for his discovery that enzymes can be crystallized FRANCIS HARRY COMPTON CRICK (1916-2004) JAMES DEWEY WATSON (1928) MAURICE HUGH FREDERICK WILKINS (1916-2004) •1962 Nobel Laureates in Physiology and Medicine • for their discoveries concerning the molecular structure of nuclear acids and its significance for information transfer in living material. wcwf03 wcwf02 Rosalind Franklin Maurice Wilkins James Watson and Francis Crick Max Ferdinand Perutz (1914 – 2002) John Cowdery Kendrew (1917 – 1997) •1962 Nobel Laureates in Physics • for their studies of the structures of globular proteins Information from X-ray diffraction experiment [0;0;0] x y z aadensity Representative electron density for amino acid side chains Electron density maps calculated at 1.5 Angstrom resolution. Comparison of microscope and diffraction Wave as a vector •F=Acosa+iAsina •F=Aexp(ia) a A Real axis A- wave amplitude a- wave phase F A X-rays scatter from electrons in all directions Primary beam Secondary beams Adition of waves F=Acosa+iAsina •Scattering from a single molecule is not detectable •If molecules are all oriented in the same way, the scattering from individual molecules will add in certain directions –Which directions? There is no path and PHASE DIFFERENCE when rays reflect from a plane nl = 2d sinq Bragg’s law: There is NO PHASE DIFFERENCE if the path differences are equal to whole number multiplies of wavelength. w sinq = w/d 2w = nl (h, k, l) 14 Bravais Lattices Diffraction pattern from a protein crystal nl = 2d sinq piccat piccatfftm picmanxfft Observed amplitudes Fourier amplitudes and phases Real space cat Fourier transform Circular rainbow scale of phases Linear intensity scale of amplitude size Electron density equation + PHASE PROBLEM •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 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 •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 by: Model building & refinement Model building & refinement 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 Validation •Assesment of model quality: •Is the model in agreement with experimwntal data? •How the geometry of amino acids look like? •Are atoms far / close enough from each other? •Are residues “happy” in their environment? •Are the hydrogen donors/acceptors satisfied? R-factor, Rfreefactor R-factor Rfree factor Ramachandran plot Ψ φ φ Ψ ω Geometry and stereochemistry Bond lengths Dihedral angles Real-space fit Data deposition •Protein Data Bank (PDB) •Some structures are wrong! Summary 1. X-rays have suitable wavelength for study of molecular structures 2. Crystals allow measurement of useful diffraction data because they diffract strongly in certain directions 3. Our goal is to obtain three-dimensional distribution of electron density, because it shows the shape of a molecule 4. Diffraction experiments provide only amplitudes of structure factors => Phase problem 5. Solution of the phase problem: Molecular replacement Isomorphous replacement Anomalous diffraction 6. Model building, refinement, validation, deposition X-ray crystallography •First method to determine structure of molecules with atomic resolution •As of November, 2022 there were almost 200,000 structures available from Protein Data Bank (170,000 by X-ray) •Macromolecular structures are crucial for our understanding of life at the molecular level •28 Nobel prizes Deformed wing virus US_bee_decline_PP.jpg Honeybee colonies in US DWV infected pupae varroa.png fig1.pdf Deformed wing virus iflavirus_genome.png DWV_P_domain.png Alignment.png Thank you! 1.) Jakou část strukturního faktoru můžeme změřit v difrakčním experimentu: a) amplitudu (ve formě intensity) b) fázi 2.) Nejčastější metoda pro získání fází je: a) molekulární nahrazení (molecular replacement) b) isomorfní nahrazení c) anomální diffrakce 3.) Ramachandran plot ukazuje: a.) distribuci úhlů v hlavním řetězci proteinu b.) vzdálenosti mezi atomy c.) konformace postranních řetězců aminokyselin 1. Rentgenové paprsky se používají ke studiu makromolekulárních struktur protože: A.) Mají vlnovou délku podobnou meziatomovým vzdálenostem. B.) Jako jediné elektromagnetické záření interagují s biologickým materiálem. C.) Byly objeveny v době intenzivního zájmu o strukturu makromolekul a z historických důvodů se používají dodnes. 2. To, že makromolekuly tvoří krystaly znamená že: A.) Mají enzymatickou aktivitu B.) Jsou součástí kostry buňky (cytoskeletu) C.) Mají stabilní strukturu. 3. Mapa elektronové hustoty, která je výsledkem rentgenové analýzy krystalů: A.) Ukazuje tvar molekul, které tvoří krystal B.) Má vždy bílou barvu C.) Ukazuje tvar molekuly po denaturaci