1. PowerPoint File available: http://bl831.als.lbl.gov/ ~jamesh/powerpoint/ ACA_SINBAD_2013.ppt

2. Acknowledgements Ken Frankel Alastair MacDowell John Spence Howard Padmore LBNL Laboratory Directed Research & Development (LDRD) ALS 8.3.1 creator: Tom Alber PRT head: Jamie Cate Center for Structure of Membrane Proteins Membrane Protein Expression Center II Center for HIV Accessory and Regulatory Complexes W. M. Keck Foundation Plexxikon, Inc. M D Anderson CRC University of California Berkeley University of California San Francisco National Science Foundation University of California Campus-Laboratory Collaboration Grant Henry Wheeler The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences Division, of the US Department of Energy under contract No. DE-AC02-05CH11231 at Lawrence Berkeley National Laboratory.

3. Simultaneous INverse Beam Anomalous Diffraction

4. SINBAD diffractometer concept Nucleus Synthetic light collecting structure h,k,l -h,-k,-l Detector d = 3.5 Å sample injector Mirrors d = 3.5 Å λ = 5 Å XFEL beam

5. Why SINBAD? I+I- Different crystal volumes New source of error in SFX

6. Why SINBAD? I+I- Different crystal orientations New source of error in SFX

7. Why SINBAD? I+I- Different beam intensities New source of error in SFX

8. Why SINBAD? I+I- Different crystal positions New source of error in SFX

9. Why SINBAD? I+I- Different structures (non-isomorphism) New source of error in SFX

10. Dynamic range Why SINBAD? I+I- New source of error in SFX

11. Why SINBAD? I+I- New source of error in SFX Problem: How to get I+ and I- both on Ewald sphere at the same time? ΔI ano

12. Ewald sphere 2 diffracted ray λ*λ* λ*λ* θ 1 Ewald sphere λ*λ* (h,k,l) diffracted ray λ*λ* θ d* Osculating Ewald Spheres (-h,-k,-l) d*

13. SINBAD diffractometer concept Nucleus Synthetic light collecting structure h,k,l -h,-k,-l Detector d = 3.5 Å sample injector Mirrors d = 3.5 Å λ = 5 Å XFEL beam

14. Tolerances: Time: ~10% of 100 fs Distance: 3 μm Angle: ~1% of mosaicity ~100 μRad

15. Can’t we just use scaling? I spot ≈ |F(hkl)| 2

16. Darwin’s Formula I(hkl)- photons/spot (fully-recorded) I beam - incident (photons/s/m 2 ) r e - classical electron radius (2.818x10 -15 m) V xtal - volume of crystal (in m 3 ) V cell - volume of unit cell (in m 3 ) λ- x-ray wavelength (in meters!) ω- rotation speed (radians/s) L- Lorentz factor (speed/speed) P- polarization factor (1+cos 2 (2θ) -Pfac∙cos(2Φ)sin 2 (2θ))/2 A- attenuation factor exp(-μ xtal ∙l path ) F(hkl)- structure amplitude (electrons) C. G. Darwin (1914) P A | F(hkl) | 2 I(hkl) = I beam r e 2 V xtal V cell λ 3 L ωV cell

17. Darwin’s Formula I(hkl)- photons/spot (fully-recorded) I beam - incident (photons/s/m 2 ) r e - classical electron radius (2.818x10 -15 m) V xtal - volume of crystal (in m 3 ) V cell - volume of unit cell (in m 3 ) λ- x-ray wavelength (in meters!) ω- rotation speed (radians/s) L- Lorentz factor (speed/speed) P- polarization factor (1+cos 2 (2θ) -Pfac∙cos(2Φ)sin 2 (2θ))/2 A- attenuation factor exp(-μ xtal ∙l path ) F(hkl)- structure amplitude (electrons) C. G. Darwin (1914) P A | F(hkl) | 2 I(hkl) = I beam r e 2 V xtal V cell λ 3 L ωV cell

18. Darwin’s Formula I(hkl)- photons/spot (fully-recorded) I beam - incident (photons/s/m 2 ) r e - classical electron radius (2.818x10 -15 m) V xtal - volume of crystal (in m 3 ) V cell - volume of unit cell (in m 3 ) λ- x-ray wavelength (in meters!) ω- rotation speed (radians/s) L- Lorentz factor (speed/speed) P- polarization factor (1+cos 2 (2θ) -Pfac∙cos(2Φ)sin 2 (2θ))/2 A- attenuation factor exp(-μ xtal ∙l path ) F(hkl)- structure amplitude (electrons) C. G. Darwin (1914) P A | F(hkl) | 2 I(hkl) = I beam r e 2 V xtal V cell λ 3 L ωV cell

19. Greenhough-Helliwell Formula ΔΦ- reflecting range (radians) 2η- mosaic spread (radians) L- Lorentz factor (speed/speed) θ- Bragg angle λ- x-ray wavelength Δλ- wavelength spread γ HV - horizontal and vertical beam divergence (radians) Greenhough & Helliwell (1983) ΔΦ = L sin2θ (2η + Δλ/λ tanθ) + ((L 2 sin 2 2θ - 1)γ H 2 + γ V 2 ) 1/2

20. Greenhough-Helliwell Formula ΔΦ- reflecting range (radians) 2η- mosaic spread (radians) L- Lorentz factor (speed/speed) θ- Bragg angle λ- x-ray wavelength Δλ- wavelength spread γ HV - horizontal and vertical beam divergence (radians) Greenhough & Helliwell (1983) ΔΦ = L sin2θ (2η + Δλ/λ tanθ) + ((L 2 sin 2 2θ - 1)γ H 2 + γ V 2 ) 1/2

21. Lorentz Factor Ewald sphere spindle axis diffracted ray

22. Darwin’s Formula I(hkl)- photons/spot (fully-recorded) I beam - incident (photons/s/m 2 ) r e - classical electron radius (2.818x10 -15 m) V xtal - volume of crystal (in m 3 ) V cell - volume of unit cell (in m 3 ) λ- x-ray wavelength (in meters!) ω- rotation speed (radians/s) L- Lorentz factor (speed/speed) P- polarization factor (1+cos 2 (2θ) -Pfac∙cos(2Φ)sin 2 (2θ))/2 A- attenuation factor exp(-μ xtal ∙l path ) F(hkl)- structure amplitude (electrons) C. G. Darwin (1914) P A | F(hkl) | 2 I(hkl) = I beam r e 2 V xtal V cell λ 3 L ωV cell

23. Integral under curve intensity “Full” Spot

24. Integral under curve intensity Spot on “Still”

25. What is "partiality"? 100%

26. What is "partiality"? 50%

27. What is "partiality"? 50%

28. What is "partiality"? 90%

29. What is "partiality"? 15%

30. What is "partiality"? 1%

31. What is "partiality"? 0.9%

32. What is "partiality"? 0.8%

33. What is "partiality"? 0.5%

34. What is "partiality"? 0.2%

35. What is "partiality"? 1%

36. What is “partiality”? Ewald sphere diffracted ray d* λ*λ* λ*λ* F(h,k,l)

37. What is “partiality”? Ewald sphere diffracted ray d* λ*λ* λ*λ* F(h,k,l)

38. What is “partiality”? Ewald sphere diffracted ray d* λ*λ* λ*λ* F(h,k,l)

39. What is “partiality”? Ewald sphere diffracted ray d* λ*λ* λ*λ* F(h,k,l)

40. What is "partiality"? 100% !

41. What is "partiality"? 90%

42. What is "partiality"? 80%

43. What is "partiality"? 50%

44. What is "partiality"? 20%

45. Bragg, James & Bosanquet (1921). Philos. Mag. Ser. 6, 41, 309–337.

46. What is “partiality”? Ewald sphere diffracted ray d* λ*λ* λ*λ* F(h,k,l) F(0,0,0) Partiality is always 100% !

47. What is “partiality”? Ewald sphere diffracted ray d* λ*λ* λ*λ* F(h,k,l) F(0,0,0) Partiality is always 100% !

48. What is “partiality”? Ewald sphere diffracted ray d* λ*λ* λ*λ* F(h,k,l) F(0,0,0) Partiality is always 100% !

49. What is “partiality”? Ewald sphere diffracted ray d* λ*λ* λ*λ* F(h,k,l) F(0,0,0) Partiality is always 100% !

50. Why SINBAD? I+I- Different crystal orientations New source of error in SFX

51. F(h,k,l) Ewald sphere spectral dispersion λ1*λ1* λ2*λ2* F(0,0,0) 100% ~90%

52. F(h,k,l) Ewald sphere spectral dispersion λ1*λ1* λ2*λ2* F(0,0,0) 100% ~45%

53. Ewald sphere spectral dispersion λ1*λ1* λ2*λ2* F(0,0,0) F(h,k,l) 100% 0%

54. F(h,k,l) F(0,0,0) beam divergence Ewald sphere diffracted ray d* λ*λ* λ*λ*

55. beam divergence Ewald sphere λ*λ* λ*λ* F(0,0,0) d* diffracted ray

56. Ewald’s “mosaic” picture

57. F(0,0,0) mosaic spread Ewald sphere diffracted ray λ*λ* λ*λ* d* F(h,k,l)

58. F(0,0,0) Ewald sphere diffracted ray λ*λ* λ*λ* d* F(h,k,l) mosaic spread

59. F(0,0,0) mosaic spread Ewald sphere diffracted ray d* λ*λ* λ*λ* F(h,k,l)

60. F(0,0,0) Ewald sphere diffracted ray λ*λ* λ*λ* d* F(h,k,l) mosaic spread

61. F(0,0,0) mosaic spread Ewald sphere diffracted ray λ*λ* λ*λ* d* F(h,k,l)

62. F(0,0,0) mosaic spread Ewald sphere λ*λ* d* F(h,k,l)

63. F(0,0,0) mosaic spread Ewald sphere diffracted ray d* λ*λ* λ*λ* F(h,k,l)

64. F(0,0,0) mosaic spread Ewald sphere λ*λ* d* F(h,k,l)

65. mosaic spread = 0 º

66. mosaic spread = 0.1º

67. mosaic spread = 0.2º

68. mosaic spread = 0.4º

69. mosaic spread = 0.6º

70. mosaic spread = 0.8º

71. mosaic spread = 1.0º

72. mosaic spread = 1.5º

73. mosaic spread = 2.0º

74. mosaic spread = 2.5º

75. mosaic spread = 3.2º

76. mosaic spread = 6.4º

77. mosaic spread = 12.8º

78. Ewald’s “mosaic” picture What is this stuff?

79. Darwin’s original picture

80. “mosaicity” with visible light

81. 10 atoms 0.1 μm Scattering: line of atoms 50 atoms 0.5 μm 100 atoms 1 μm 200 atoms 2 μm 300 atoms 3 μm 400 atoms 4 μm 500 atoms 5 μm 1000 atoms 10 μm position on detector (mm) intensity (photons/SR/atom)

82. Scattering: line of atoms peak intensity (photons/SR) number of atoms in line “coherence length” depends on detector distance !!! integrated intensity never changes peak intensity depends on size

83. 10 atoms 0.1 μm Integral under curve 50 atoms 0.5 μm 100 atoms 1 μm 200 atoms 2 μm 300 atoms 3 μm 400 atoms 4 μm 500 atoms 5 μm position on detector (mm) intensity (photons/SR/atom) Spot Intensity

84. Can’t we just rotate the crystal? 1 μm 1°1° 100 fs = 90 km/s 9 nm 17.26 km/s (90 km/s) 2 0.5 μm = 1.5 x 10 15 G = 0.5 nN

85. Can’t we just rotate the crystal? NO Why do we want to rotate the crystal?

86. The “nanocrystal advantage” I spot = k N cells Ewald sphere range 2

87. Fraunhofer Formula I pixel - photons/pixel/s I beam - incident (photons/s/m 2 ) r e - classical electron radius (2.818x10 -15 m) hkl- index of pixel (a·(u p +u s )/λ) a- orientation (recip. cell vectors) u p,u s - unit vector pointing at pixel,source λ- x-ray wavelength (in meters!) N- number of cells (each direction) Ω- solid angle of pixel (steradian) P- polarization factor (1+cos 2 (2θ) -Pfac∙cos(2Φ)sin 2 (2θ))/2 A- attenuation factor exp(-μ xtal ∙l path ) F(hkl)- structure amplitude (electrons) Circa 1820s see: Kirian et al. (2010) P A | F(hkl) | 2 sin(πN·hkl) sin(π·hkl) I pixel = I beam r e 2 Ω 2

88. Scattering: atom by atom h index intensity

89. Scattering: atom by atom h index intensity

90. Scattering: atom by atom h index intensity

91. Scattering: atom by atom h index intensity

92. Scattering: atom by atom h index intensity

93. Scattering: atom by atom h index intensity

94. Scattering: atom by atom h index intensity

95. Scattering: atom by atom h index intensity

96. Inter-Bragg spots over-sample unit cell

97. square

98. round

99. Why SINBAD? I+I- Different structures (non-isomorphism) New source of error in SFX

100. Dear James The story of the two forms of lysozyme crystals goes back to about 1964 when it was found that the diffraction patterns from different crystals could be placed in one of two classes depending on their intensities. This discovery was a big set back at the time and I can remember a lecture title being changed from the 'The structure of lysozyme' to 'The structure of lysozyme two steps forward and one step back'. Thereafter the crystals were screened based on intensities of the (11,11,l) rows to distinguish them (e.g. 11,11,4 > 11,11,5 in one form and vice versa in another). Data were collected only for those that fulfilled the Type II criteria. (These reflections were easy to measure on the linear diffractometer because crystals were mounted to rotate about the diagonal axis). As I recall both Type I and Type II could be found in the same crystallisation batch. Although sometimes the external morphology allowed recognition this was not infallible. The structure was based on Type II crystals. Later a graduate student Helen Handoll examined Type I. The work, which was in the early days and before refinement programmes, seemed to suggest that the differences lay in the arrangement of water or chloride molecules (Lysozyme was crystallised from NaCl). But the work was never written up. Keith Wilson at one stage was following this up as lysozyme was being used to test data collection strategies but I do not know the outcome. An account of this is given in International Table Volume F (Rossmann and Arnold edited 2001) p760. Tony North was much involved in sorting this out and if you wanted more info he would be the person to contact. I hope this is helpful. Do let me know if you need more. Best wishes Louise Non-isomorphism in lysozyme

101. Johnson’s ratio Structure factor (e - ) Non-isomorphism in lysozyme

102. Johnson’s ratio Structure factor (e - ) Non-isomorphism in lysozyme

104. RH 84.2% vs 71.9% R iso = 44.5%RMSD = 0.18 Å Non-isomorphism in lysozyme

105. Dear James The story of the two forms of lysozyme crystals goes back to about 1964 when it was found that the diffraction patterns from different crystals could be placed in one of two classes depending on their intensities. This discovery was a big set back at the time and I can remember a lecture title being changed from the 'The structure of lysozyme' to 'The structure of lysozyme two steps forward and one step back'. Thereafter the crystals were screened based on intensities of the (11,11,l) rows to distinguish them (e.g. 11,11,4 > 11,11,5 in one form and vice versa in another). Data were collected only for those that fulfilled the Type II criteria. (These reflections were easy to measure on the linear diffractometer because crystals were mounted to rotate about the diagonal axis). As I recall both Type I and Type II could be found in the same crystallisation batch. Although sometimes the external morphology allowed recognition this was not infallible. The structure was based on Type II crystals. Later a graduate student Helen Handoll examined Type I. The work, which was in the early days and before refinement programmes, seemed to suggest that the differences lay in the arrangement of water or chloride molecules (Lysozyme was crystallised from NaCl). But the work was never written up. Keith Wilson at one stage was following this up as lysozyme was being used to test data collection strategies but I do not know the outcome. An account of this is given in International Table Volume F (Rossmann and Arnold edited 2001) p760. Tony North was much involved in sorting this out and if you wanted more info he would be the person to contact. I hope this is helpful. Do let me know if you need more. Best wishes Louise Non-isomorphism in lysozyme

106. Non-isomorphism = dehydration? = 1 nL 100 μm

107. Anomalous difference is resilient to non- isomorphism Nucleus Synthetic light collecting structure 0 20 40 60 80 100 R iso (%) 1.0 0.8 0.6 0.4 0.2 Correlation Coefficient of ΔF ano 100 x 100 lysozyme PDBs

108. Why SINBAD? New sources of error in SFX: 1.Partiality 2.Dynamic range 3.Jitter 4.Non-isomorphism ?

109. SINBAD diffractometer concept Nucleus Synthetic light collecting structure h,k,l -h,-k,-l Detector d = 3.5 Å sample injector Mirrors d = 3.5 Å λ = 5 Å XFEL beam

110. h,k,l -h,-k,-l Detector λ = 5 Å sample injector Si(111) 52.87deg Si(111) 2 Multilayer mirrors d=2nm, W/B4C KB Horiz focus KB vertical focus ~ 1m

111. How to reflect x-rays at 90° ? λ = 2 d sinθ Silicon: absorbs ~50%/bounce Diamond: Unit cell too small Platinum: Too soft = high mosaic Iridium: high hardness CsI: just miss edge d = 0.7 λ Want: Large structure factor Low absorbance Most promising:

112. Summary http://bl831.als.lbl.gov/~jamesh/powerpoint/ACA_SINBAD_2013.ppt SFX introduces new sources of error Software solutions are tractable, but hard SINBAD could solve them “in hardware” Non-isomorphism can be controlled? Mono xtal has applications for seeding

113. Muybridge’s galloping horse (1878)

114. Muybridge’s multi-camera

115. Hot questions: 21 st century how do molecules work? Beernink, Endrizzi, Alber & Schachman (1999). PNAS USA 96, 5388-5393.

116. a “crystal” of horses

117. realistic “crystal” of horses

118. average structure: galloping horse

119. not enough signal

120. brighter light

121. even brighter

122. very bright light

123. average structure: galloping horse

124. Horse: real and reciprocal

125. Supporting a model with data

126. Molecular Dynamics Simulation 1aho Scorpion toxin 0.96 Å resolution 64 residues Solvent: H 2 0 + acetate Cerutti et al. (2010).J. Phys. Chem. B 114, 12811-12824. using real crystal’s lattice

127. 30 conformers from 24,000

128. Electron density from 24,000 conformers

129. Regular model with real data!

130. Molecular Dynamics vs Observation F obs 1aho.cif1aho.pdb F sim F calc R cryst = 0.137 R cryst = 0.116 R vault = 0.69 refined_vs_Fsim.pdb LSQ rmsd = 0.43Å rmsd = 1.05 Å 1aho 64-residue scorpion toxin in water to 1.0 Å resolution R vault = 0.48 to 4 Å R iso =

131. Molecular Dynamics vs Observation RMSD 1.05 Å

132. Molecular Dynamics vs Observation RMSD 0.45 Å aligned