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X-­‐Ray	
  Diffraction:
Primer
Bernie	
  Santarsiero
Center	
  for	
  Biomolecular	
  Sciences
Department	
  of	
  Medicin...
Overall	
  Process
CrystallizationExtraction,	
  Isolation,	
  and	
  Purification Data	
  Collection
Data	
  ProcessingPh...
Overall	
  Process
• Isolate	
  the	
  compound	
  of	
  interest	
  from	
  a	
  mixture	
  and	
  purify	
  as	
  
much	...
Small	
  Molecule	
  Crystallization
Simplest:	
  slow	
  evaporation
from	
  a	
  single	
  solvent	
  until
saturation	
...
Crystallization
• Evaporation	
  is	
  used	
  to	
  concentrate	
  compound	
  in	
  solution.	
  If	
  
supersaturated,	...
Protein	
  Crystallization
Crystal	
  quality	
  varies	
  with	
  
concentration	
  of	
  solute,	
  
rate	
  of	
  solve...
Protein	
  Crystallization
• Protein	
  crystallization	
  is	
  more	
  complicated	
  for	
  two	
  reasons.	
  
First,	...
Choice	
  of	
  Solvents
Additional	
  typical	
  solvents:	
  isopropanol,	
  
1,2-­‐dichloroethane,	
  THF,	
  DMF,	
  D...
Solvents
• Solvents	
  that	
  evaporate	
  quickly	
  can	
  be	
  used,	
  but	
  reduce	
  
temperature	
  so	
  that	
...
Crystals
Unit	
  Cell	
  Parameters:	
  	
  a,	
  b,	
  c,	
  a,	
  b,	
  g (and	
  V)	
  
Only	
  230	
  ways	
  to	
 ...
Crystals
• Molecules	
  pack	
  together	
  to	
  form	
  crystals	
  in	
  each	
  of	
  the	
  three	
  
directions	
  i...
Crystals
Unit	
  Cell	
  Parameters:	
  	
  a,	
  b,	
  c,	
  a,	
  b,	
  g (and	
  V)	
  
Crystal	
  size	
  vs.	
  Nu...
Crystals
• As	
  unit	
  cells	
  stack	
  together,	
  the	
  crystals	
  grow	
  in	
  size
• Since	
  all	
  atoms	
  a...
Data	
  Collection
• High	
  intensity	
  monochromatic	
  x-­‐ray	
  source
• Cryogenically-­‐cooled	
  sample	
  (100K)
...
Synchrotron
Advanced	
  Photon	
  Source
≈100	
  stations
Sample	
  rotation,	
  x-­‐ray	
  
energy,	
  and	
  sample	
  t...
Crystals
• In-­‐house	
  sources	
  can	
  be	
  useful	
  if	
  large	
  crystals	
  are	
  used.	
  The	
  
intensity	
 ...
Synchrotron	
  Sources
• Synchrotron	
  sources	
  are	
  complicated	
  since	
  data	
  collection	
  is	
  
handled	
  ...
Diffraction	
  Image	
  -­‐ Intensities
• Each	
  spot	
  has	
  a	
  3D	
  coordinate:	
  (x,	
  y,	
  j)
• Each	
  pixe...
Diffraction	
  Image
• Reflection	
  spots	
  occur	
  when	
  the	
  geometry	
  of	
  the	
  incident	
  X-­‐
ray	
  bea...
Diffraction
Diffraction	
  Intensities
• The	
  intensity	
  of	
  the	
  individual	
  reflection	
  spots	
  in	
  dependent	
  
upo...
Intensities	
  and	
  Phases
• Crystal	
  (3D	
  grating)	
  scatters	
  the	
  x-­‐rays	
  (waves)
• Each	
  diffracted	
...
Phases	
  and	
  Phasing
• Note	
  that	
  if	
  the	
  amplitudes (related	
  to	
  reflection	
  intensities)	
  
of	
  ...
Resolution
• The	
  higher	
  the	
  “resolution”	
  (more	
  spots),	
  the	
  
better	
  the	
  electron	
  density	
  m...
Electron	
  Density	
  Maps
• robs or	
  2ro-­‐rc map:	
  peaks	
  where	
  you	
  put	
  
atoms;	
  plus	
  peaks	
  f...
Final	
  Structure
• Tables
– Unit	
  cell	
  information,	
  space	
  group
– How	
  was	
  data	
  collection?
– How	
  ...
H-­‐bonding/Packing
Hydrogen
bonding
Note	
  that	
  hydrogen	
  bonding	
  occurs	
  when	
  you	
  have	
  a	
  H-­‐bond...
ORTEP
There	
  is	
  less	
  
uncertainty	
  about	
  atom	
  
positions	
  at	
  lower	
  
temperatures	
  since	
  
ther...
Flack+Absolute	
  Configuration
Analysis
Flack	
  Parameter
• Two	
  structures	
  are	
  possible:	
  the	
  correct	
  
structure	
  and	
  the	
  inverted	
  st...
Xrd basics2018
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Xrd basics2018

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Primer on X-ray analysis of small molecules prepared by Dr. Santarsiero. See his website at : http://bds.lab.uic.edu/Welcome.html.

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Xrd basics2018

  1. 1. X-­‐Ray  Diffraction: Primer Bernie  Santarsiero Center  for  Biomolecular  Sciences Department  of  Medicinal  Chemistry  and   Pharmacognosy UIC  CENAPT
  2. 2. Overall  Process CrystallizationExtraction,  Isolation,  and  Purification Data  Collection Data  ProcessingPhasing  and  RefinementStructure Bond  Length  Tables   and  Annotation Natural  Product
  3. 3. Overall  Process • Isolate  the  compound  of  interest  from  a  mixture  and  purify  as   much  as  possible • Dissolve  compound  in  one  or  more  solvents  and  evaporate   slowly  to  form  single  crystals • A  single  crystal  are  mounted  in  a  loop  with  an  inert  oil  and   cooled  to  100K;  alternatively,  a  crystal  can  be  glued  to  the   head  of  a  glass  fiber • The  crystal  is  rotated  in  an  X-­‐ray  beam,  and  diffraction  images   are  collected  at  different,  successive  orientations.  The   intensity  (darkness)  and  position  of  each  spot  is  determined. • Diffraction  spot  coordinates  and  intensity  are  “phased”  to   reveal  electron  density  map.  Atom  coordinates  of  a  model  of   the  compound  reveal  structure  in  detail,  including  atom  type,   bond  lengths  and  angles,  and  conformation  in  crystal.  
  4. 4. Small  Molecule  Crystallization Simplest:  slow  evaporation from  a  single  solvent  until saturation  is  reached Slow  evaporation  from  a  multi-­‐solvent system:  most  volatile  solvent  fastest Slow  diffusion  from  a  multi-­‐solvent  system: Second  solvent  diffuses  into  first  solvent, and  increased  insolubility Insolubility  at  solvent  interface Repeat  process  with  same  sample using  different  solvents
  5. 5. Crystallization • Evaporation  is  used  to  concentrate  compound  in  solution.  If   supersaturated,  crystals  form  too  quickly,  and  are  unsuitable.   Microcrystals  form  in  metastable  state,  and  slowly  grow,   packing  molecules  in  a  uniform,  regular  pattern.   • Multiple  solvents  can  be  used  to  reach  metastable  zone  and   supersaturation  slowly  since  they  evaporate  towards  vapor   equilibration   • Slow  equilibration  by  vapor  diffusion  or  solvent  layering   generate  concentration  gradients  in  solution,  so  solutions   must  be  left  undisturbed  for  hours  and  days • If  unsuccessful,  redissolve in  a  different  solvent  and  try  again.   Multiple  crystallization  attempts  can  be  undertaken  using  the   same  sample.  At  times,  air  and  light  need  to  be  avoided  to   prevent  oxidation  or  sample  degradation.  
  6. 6. Protein  Crystallization Crystal  quality  varies  with   concentration  of  solute,   rate  of  solvent  evaporation,   and  choice  of  additives
  7. 7. Protein  Crystallization • Protein  crystallization  is  more  complicated  for  two  reasons.   First,  proteins  are  less  stable,  so  multiple  attempts  of   crystallization  are  not  possible.    Second,  supersaturation  is   more  difficult  to  achieve,  so  dozens  to  thousands  of  trials   must  be  attempted  to  generate  single  crystals. • The  majority  of  crystallization  conditions  are  aqueous-­‐based,   so  that  limits  options  available.  Salts,  organic  molecules,  and   oils  are  added  to  solutions  to  help  protein  molecules  pack   together  and  form  single  crystals.   • Unlike  small  molecules,  protein  crystals  can  pack  together  in   many  ways,  so  the  free  energy  of  packing  interactions  is  very   small;  still  depend  on  hydrogen  bonds  and  salt  interactions. • Proteins  are  not  always  stable  at  high  concentration,  so   additives  help  reduce  solubility.  
  8. 8. Choice  of  Solvents Additional  typical  solvents:  isopropanol,   1,2-­‐dichloroethane,  THF,  DMF,  DMSO,  or   dilute  HCl,  acetic  acid,  or  formic  acid SOLVENT VP Water 18 Toluene 29 Ethanol 59 Acetonitrile 97 Ethyl  acetate 97 Benzene 101 Methanol 128 Hexane 160 THF 200 Chloroform 210 Acetone 240 Dichloromethane 475 Pentane 573 Diethylether 587 Volatility  of  various  solvents:  the  solvent with  the  higher  VP  will  diffuse  into  the   solvent  with  the  lower  VP   “Some  thoughts  about  single  crystal  growth of  small  molecules,”  B.  Spingler,  S.  Schnidrig, T.  Todorova,  and  F.  Wild,  Cryst.  Eng.  Comm., 14,  751-­‐757  (2012). Layering:  more  soluble  in  one  solvent,  layer with  second  solvent,  e.g.,  dichloromethane layered  with  diethyl  ether  
  9. 9. Solvents • Solvents  that  evaporate  quickly  can  be  used,  but  reduce   temperature  so  that  evaporation,  and  there  saturation,  is  slow • Examine  if  solvent  pairs  are  miscible  or  immiscible.  Can  help   to  produce  layering  and  concentration  at  the  interface • Ideally  the  compound  is  insoluble  in  one  solvent  and  only   slightly  soluble  in  a  second  solvent.  As  the  solvents  mix,  the   compound  is  less  soluble  in  the  solvent  mixture,  and  starts  to   form  crystals  in  supersaturation • Choice  of  solvent  can  also  help  in  filling  packing  voids,  or  by   helping  increase  hydrogen  bonding  or  hydrophobic  packing  of   one  molecule  up  against  another • Small  molecules  generally  pack  with  little  or  no  excess  space
  10. 10. Crystals Unit  Cell  Parameters:    a,  b,  c,  a,  b,  g (and  V)   Only  230  ways  to   pack  objects  in  3D Any  number  of molecules  in  a unit  cell
  11. 11. Crystals • Molecules  pack  together  to  form  crystals  in  each  of  the  three   directions  in  space • Since  they  are  stacked  in  three  directions,  three  unique  axes   can  be  defined,  labeled  a,  b,  and  c (cell  parameters)  for  the  x-­‐,   y-­‐,  and  z-­‐directions.  Multiple  triads  of  directions  can  be   determined,  but  the  smallest  lengths  of  cell  parameters  can   always  be  defined.   • In  2-­‐dimensions,  one  can  visualize  various  dyads  that  form  a   2D-­‐cell  of  equivalent  area.   • The  angles  between  the  cell  parameter  lengths  include  non-­‐ orthogonal  unit  cells.  The  volume  V  of  the  unit  cell  can  be   defined,  and  will  hold  an  integral  number  of  molecules.   • Symmetry  relates  some  molecules  to  others,  and  simplifies   the  way  that  molecular  packing  can  be  described
  12. 12. Crystals Unit  Cell  Parameters:    a,  b,  c,  a,  b,  g (and  V)   Crystal  size  vs.  Number  of  molecules: 1mm  × 1mm  × 1mm  =  1018 molecules  =  10mg 1µm  × 1µm  × 10µm  =  1010 molecules  =  1ng   Number  of  atoms  in  a  unit  cell U.C.  Volume  =  Total  number  of  atoms  × 11Å3 U.C.  Volume  =  Number  of  non-­‐H  atoms  × 20Å3 Most  typically  r ≈  1  gm/cm3 but  %solvent  can  be  as  high  as  50%
  13. 13. Crystals • As  unit  cells  stack  together,  the  crystals  grow  in  size • Since  all  atoms  are  around  the  same  size,  and  bond  lengths   are  generally  around  the  same  length,  as  estimate  can  be   made  from  the  volume  of  the  unit  cell  on  how  many  atoms   occupy  the  unit  cell.  Another  way  to  visualize  this  is  that  the   density  of  an  organic  molecule  doesn’t  vary  greatly. • If  we  know  the  number  of  atoms  in  the  molecule,  we  can   estimate  the  number  of  molecules  in  the  unit  cell • The  estimate  can  be  uncertain  if  solvent  is  also  incorporated   into  the  crystals • Estimation  of  the  number  of  molecules  helps  to  define  the   unit  cell  parameters,  and  the  type  of  symmetry  involved  in  the   packing  of  molecules
  14. 14. Data  Collection • High  intensity  monochromatic  x-­‐ray  source • Cryogenically-­‐cooled  sample  (100K) • Orientation  of  sample  over  various  angles • Large  detector  near  sample  (100  µm)   0-­‐1° 1-­‐2° 2-­‐3° 3-­‐4° 4-­‐5° Detector  converts  x-­‐rays   photons  into  electrons  or   something  that  is  counted
  15. 15. Synchrotron Advanced  Photon  Source ≈100  stations Sample  rotation,  x-­‐ray   energy,  and  sample  type In-­‐house  system X-­‐Ray Source Crystal Holder Low-­‐temp  stream
  16. 16. Crystals • In-­‐house  sources  can  be  useful  if  large  crystals  are  used.  The   intensity  of  the  diffraction  spots  is  dependent  upon  the   intensity  of  the  X-­‐ray  beam  and  number  of  molecules  involved   in  the  diffraction  process. • Synchrotron  sources  at  hundreds  to  thousands  as  times   intense  and  smaller  as  in-­‐house  sources.  Therefore,  very  small   crystals  can  be  used  to  collect  diffraction  images. • With  synchrotron  sources,  data  collection  is  faster  and  can   accommodate  very  small  crystals.  Low-­‐temperature  reduces   problems  with  intense  irradiation  of  crystalline  samples. • Synchrotron  sources  also  provide  a  way  to  change  the  energy   or  wavelength  of  the  incident  source,  which  can  be  useful  in   modifying  the  way  the  data  is  collected
  17. 17. Synchrotron  Sources • Synchrotron  sources  are  complicated  since  data  collection  is   handled  remotely.    Also,  with  smaller  X-­‐rays  beams,  more   instrumentation  is  packed  in  a  smaller  area • The  synchrotron  source  is  channeled  and  isolated  in  a  small   area  with  various  shutter  mechanisms • The  crystal  is  surrounded  by  a  low-­‐temperature  stream  of   nitrogen  gas,  controlled  by  a  mechanism  to  rotate  it  in  several   directions,  optics  to  view  the  crystal,  and  a  detector  (gray  box   on  the  right)  to  collect  the  diffraction  image  at  various  crystal-­‐ to-­‐detector  distances • All  devices  are  motor-­‐driven  to  operate  from  outside  of  the   workstation
  18. 18. Diffraction  Image  -­‐ Intensities • Each  spot  has  a  3D  coordinate:  (x,  y,  j) • Each  pixel  on  image  summed  to  a  net  intensity • 3D  position  is  related  to  crystal  building  blocks • (h,  k,  l),  intensity,  sint
  19. 19. Diffraction  Image • Reflection  spots  occur  when  the  geometry  of  the  incident  X-­‐ ray  beam  and  orientation  of  the  crystal  satisfy  the  “Bragg”   condition,  as  defined  by  Bragg’s  Law. • Bragg’s  Law  involves  the  incident  energy  or  wavelength  of  the   X-­‐ray  beam,  the  unit  cell  parameters,  and  the  crystal   orientation • As  noted  above,  each  diffraction  image  can  be  indexed  with  a   unique  set  of  coordinates,  relating  to  the  position  on  the   image  (x,  y)  and  what  angle  the  crystal  was  rotated  to • The  diffraction  spot  is  a  collection  of  small  spots—pixels—that   can  be  estimated  as  the  brightness  above  a  common  dark   background;  this  is  the  intensity  of  a  reflection  spot • Each  diffraction  spot  is  defined  by  its  coordinates,  intensity,   and  an  estimate  of  that  intensity
  20. 20. Diffraction
  21. 21. Diffraction  Intensities • The  intensity  of  the  individual  reflection  spots  in  dependent   upon  the  atoms  in  the  structure  (number  of  electrons),  their   distance  and  orientation  to  each  other,  and  how  they  are   arranged  in  the  crystal • Uranium  atoms  contribute  more  than  hydrogen  atoms   because  they  have  90  times  the  number  of  electrons.  Thus  a   structure  with  uranium  atoms  will  have  more  intense  spots   than  a  structure  with  lighter  atoms,  if  the  crystals  are  the   same  size • All  atoms  in  the  structure  and  crystal  contribute  to  the   generation  of  reflection  intensities,  but  contribute  differently   due  to  changes  in  orientation  as  you  collect  diffraction  images • Consider  differences  in  the  orientation  of  a  card  as  you  rotate   it,  and  the  cross-­‐sectional  viewing  of  the  card
  22. 22. Intensities  and  Phases • Crystal  (3D  grating)  scatters  the  x-­‐rays  (waves) • Each  diffracted  x-­‐ray  related  to  every  atom • Each  wave  has  an  amplitude and  phase • r(xyz)  =  (1/V)SFhkleijhkle-­‐2pi(hx+ky+lz)
  23. 23. Phases  and  Phasing • Note  that  if  the  amplitudes (related  to  reflection  intensities)   of  the  “duck”  are  used  with  the  phases of  the  “cat”,  the   resulting  image  looks  like  a  cat;  phases  are  important. • We  can  measure  intensities  directly,  but  not  phases. • We  can  guess  at  phases,  and  if  we  make  good  guesses,  we  can   phase  the  amplitudes  to  create  an  image  of  a  molecule • Karle,  Hauptman,  and  Karle  developed  ways  to  make  good   guesses  of  the  phases  by  looking  at  which  intensities  were   weak  and  which  were  strong;  so-­‐called  “direct  methods.” • Once  we  approximately  phase  each  reflection  intensity,  we   start  to  recognize  the  molecule  (six  membered  rings,  etc).   Forcing  atoms  to  have  reasonable  chemical  bonds  and  angles   then  helps  refine  the  phases,  and  more  of  the  molecule  is   revealed  by  creating  an  electron  density  map.
  24. 24. Resolution • The  higher  the  “resolution”  (more  spots),  the   better  the  electron  density  map  will  look   1Å 2Å 3Å
  25. 25. Electron  Density  Maps • robs or  2ro-­‐rc map:  peaks  where  you  put   atoms;  plus  peaks  from  missing  atoms • ro-­‐rc “difference”  map:  perfect  map  would  be   flat  with  no  peaks  or  valleys,  missing  atoms   are  peaks,  extra/wrong  atoms  are  valleys
  26. 26. Final  Structure • Tables – Unit  cell  information,  space  group – How  was  data  collection? – How  well  was  structure  refined? – Atom  coordinates,  occupancy,  “B-­‐factors” – Bond  lengths,  angles,  torsion  angles,  planes – Absolute  stereochemistry?     – Calculated  and  observed  SFs (F’s)  with  wΔ2 • Structure – Packing?  H-­‐bonding?  Unusual  features?
  27. 27. H-­‐bonding/Packing Hydrogen bonding Note  that  hydrogen  bonding  occurs  when  you  have  a  H-­‐bond  donor   (hydrogen  atom)  and  H-­‐bond  acceptor  (electron  pair  on  O,  N,  etc.).   The  acceptor  and  donor  distance  is  around  2.8Å.  Hydrogen  bonding   creates  networks  of  molecules  linked  to  each  other  in  2-­‐ and  3-­‐ dimensions.  Hydrophobic  packing  also  help  build  a  3D  network  of   molecules  with  little  or  no  voids  of  empty  space.  
  28. 28. ORTEP There  is  less   uncertainty  about  atom   positions  at  lower   temperatures  since   there  is  less  vibration. Each  non-­‐hydrogen   atom  is  depicted  as  a   “football”  to  indicate   uncertainty  or  motion   in  each  of  three   possible  directions.
  29. 29. Flack+Absolute  Configuration Analysis
  30. 30. Flack  Parameter • Two  structures  are  possible:  the  correct   structure  and  the  inverted  structure   • It  doesn’t  matter  is  there  is  1  or  more   stereochemical centers  in  the  molecule • The  Flack  parameter  is  determined  for  an   enantiomerically pure  structure,  with  a  value near  zero  for  the  correct  structure,  and  near  1   for  the  inverted  (wrong)  structure • An  estimation  of  the  uncertainty  of  the  Flack   parameter  provides  a  measure  of  confidence   in  the  assignment  of  an  absolute  structure.

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