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Analiza structurala prin raze X
Transformata Fourier si cristalografia de raze X
Cea mai mare putere a rezolutiei pentru determinarea structurilor macromoleculelor si complexelor macromoleculare
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Matematic: transformata Fourier si inversa ei convertesc dintre doua
domenii (“spatii”) r (exemplu: spatiu sau timp) si domeniul k
(exemple: momente sau frecvente)
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Transformata Fourier
21( ) ( )2
i r kF k f r e dr
21( ) ( )2
i r kf r F k e dk
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Pierderea fazei prin transformata Fourier inversa unidirectionala
Daca se considera faza corecta
Faza incorecta (=0)
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In doua dimensiuni (xy)
Amplitudine si faza
Aranjare hexagonala a “pick”-urilor
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Unele componente au fost sterse
Se regaseste distributia initiala
Componente de amplitudini mici au continut redus de informatie
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Aplicatie: metoda de reduce a zgomotului
3. Se face transformata Fourier inversa
1. Transformata Fourier a unui obiect zgmotos
2. Se substituie anumite componente de amplitudine mica din transformata Fourier
= 0
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Doar o sectiune prin transformata Fourier
Distorsiune semnificativa daca se
foloseste doar un
numar redus de coordonate pentru
reconstructie
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Exemplu de design experimental
Imaginea de difractie a cristalului este trasformata Fourier a structurii
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Difractia pe un singur punct
0/ /S s s
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Difractia pe doua obiecte punctiforme
0/ /rS rs rs
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• Interferenta constructiva daca rS=0,+1, +2, • Interferenta destructiva daca rS=+1/2, +3/2,
• Imaginea de difractie F(S) este data de:
2( ) i r SF s e
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Pentru un obiect macroscopic constand din mai multe puncte cu diverse puteri de
imprastiere:
2( ) ( ) i r SF S r e dr
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Densitatea electronica a structurii proteinei poate fi
obtinuta din inversa transformatei Fourier a
imaginii de difractie
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In microscopie, inversa transformatei Fourier este facuta de catre lentile!
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• Nu exista microscop de raze X cu rezolutie si sensibilitate suficienta
• Oglinzile de raze nu au rezolutiei suficienta pentru o singura proteina.
• Puterea radiatiei ar trebui sa fie prea mare iar proteina ar fi …. denaturata
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Procedeu general:
• Se inregistreaza imaginea de difractie a cristalului proteic
• Se calculeaza inversa transformatei Fourier
• Dezavantaj: se pierde informatia de faza
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Problema fazelor
• Metode prin care se incearca cunoasterea fazelor
• Cea mai folosita metoda: inlocuirea cu atomi grei
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• Un specific al difractiei pe cristale macroscopice: nu se obtine o image continua ci spoturi de difractie
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Retea cristalina in spatiul real/reciproc
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• Celula unitara: cea mai mica unitate din care se poate genera cristalul doar prin translatii
• Pentru un cristal proteic celula unitara este formata din una sau mai multe molecule
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Cristalografia de raze X a proteinelor
http://www.ebi.ac.uk/thornton-srv/databases/cgi-bin/pdbsum/GetPage.pl?template=highlights.html&pdbcode=n/a&highlights=TRUE
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Producerea unor cristale adecvateMonoscrital cu geometrie si marime potrivita
Neadecvate
Adecvate
In mod obinuit, neadecvate
TransparenteFara neomogenitatiFara culoare sau indice de refractie
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Metoda “picaturii”
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Robot pentru metoda picaturii
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• Se incepe cu o concentratie de proteina de 2-50 mg/ml
• Nu trebuie sa contina contaminanti (alte proteine, virusuri)
• Fara proteine impachetate gresit• Fara aditivi chimic care nu sunt necesari la
stabilitate• Proteinele cu capete mai putin flexibile crsitalizeaza
mai bine• Dimensiunea optima a cristalului: ~0,1 mm
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Exista kituri comerciale petru “screening” de cristalizare
http://www.jenabioscience.com/cms/en/1/browse/631_macromolecular_crystallography.html
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Parametri importanti:
• Concentratia proteinei• Tipurile de sare si concentratia lor• pH• Tipul si concentratia surfactantilor• Temperatura• Viteza de cristalizare
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Detector CCD (charge-coupled device)
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Sursa: anod rotitor sau sincrotron
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Sincrotron
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Imaginea de difractie
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Determinarea fazei, inlocuirea cu atomi grei
Cristalizare in solutie care contine atomi grei
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Calcularea densitatii elecronice si rafinarea structurilor
http://www.netsci.org/Resources/Software/Struct/xray.html