Calculating strategies for data collection

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1 Calculating strategies for data collection Alexander Popov A.Popov 1

2 Data quality Completeness, Resolution, Statistics Detector Size Size N.of N.of pixels pixels T T readout readout Noise Noise Sensitivity Sensitivity Dynamic Dynamic range range Crystal Space group Space group Cell parameters Cell parameters Orientation Orientation B-factor B-factor Mosaicity Mosaicity Anisotropy Anisotropy Radiation damage Radiation damage Crystal-to-detector Crystal-to-detector distance distance Resolution Resolution I I p /I b spot p /I overlap b spot overlap X-ray source Intensity Intensity Divergence Divergence Wavelength Wavelength Beam Beam size size Starting Starting angle angle and and total total rotation rotation range range Completeness Completeness Multiplicity Multiplicity d.c. d.c. time time Rotation Rotation width width I I p /I b, spot p /I overlap, b, spot overlap, total total d.c. d.c. time time Exposure time statistics overloads total d.c. time

3 Z. Dauter Data-collection strategies,1999, Acta Cryst. D55, A.Popov 3

4 Multiplicity (statistic, d.c. time) A.Popov 4

5 A.Popov 5

σ I p Accuracy Main uncertainties of the observed intensities are determined by counting statistics ( m n) m + = I p + Ib n G I b where m and n are number of pixels in the peak and background region

6 σ I p Accuracy Main uncertainties of the observed intensities are determined by counting statistics ( m n) m + = I p + Ib n G I b where m and n are number of pixels in the peak and background region of the measurement box respectively. G is the detector gain, which converts pixel counts to equivalent X-ray photons. K ins is a proportionality constant for the instrument-error term I p I p I b A.Popov 6

$The probability density function for diffraction$ According to Wilson statistic p c p a ()= J ()= J 1ˆ J 1

7 The probability density function for diffraction intensity magnitudes follow the Wilson distribution According to Wilson statistic p c p a ()= J ()= J 1ˆ J 1 π J ˆ J 1/ exp Jˆ J exp Jˆ J Acentric reflections Centric reflections

s, Space Group : C 1 1 Cell : 148.7 53.6 76.5 90.

8 ALCOHOL DEHYDROGENASE ID3-1, λ=0.973 Å, Flux= resolution =1.45 Å, Δφ=1º, t exposure=0. s, Space Group : C 1 1 Cell : Mosaicity : 0.40 degree φ=0º φ=90º A.Popov 8

9 ALCOHOL DEHYDROGENASE A.Popov 9

10 ALCOHOL DEHYDROGENASE 1,9 Relative Intensity VS. PHI 1,8 1,7 Relative Intensity 1,6 1,5 1,4 1,3 1, 1, PHI, dg A.Popov 10

11 ALCOHOL DEHYDROGENASE 6 5,5 5 /<Sigma(I)> per every 5 dg. Vs. Phi no radiation damage Resolution shell Ǻ φ_start - φ_finish =90º - 30º Completeness = 100% Δφ= 1º, Exposure time = 0.6 s /<Sigma(I)> 4,5 4 3,5 3, PHI, dg A.Popov 11

12 /<Sigma(I)> per every 5 dg. Vs. Phi 4,5 4 ALCOHOL DEHYDROGENASE Resolution shell Ǻ φ_start - φ_finish =90º - 30º Completeness = 100% Δφ= 1º 3,5 /<Sigma(I)> per 5 dg 3,5 1,5 exposure per image 0.s 0.6s 1 0, Phi, dg. A.Popov 1

13 3,5 ALCOHOL DEHYDROGENASE Resolution shell Ǻ φ_start - φ_finish =90º - 30º Completeness = 100% Δφ= 1º /<Sigma(I)> 1,5 1 I/sigma Rfactor Rfactor/ N.of I/Sigma> 3, % 0,5 I/Sigma> ,1 0, 0,3 0,4 0,5 0,6 0,7 0 Exposure, s A.Popov 13

14 /<Sigma(I)> 3,5 3,5 1,5 1 ALCOHOL DEHYDROGENASE Resolution shell Ǻ φ_start - φ_finish =90º - 30º Completeness = 100% Δφ= 1º BEST Optimal Plan of data collection N Phi_start N.of.images Rot.width Exposure Rfactor/ N.of I/Sigma> 3, % 0, ,1 0, 0,3 0,4 0,5 0,6 0,7 Exposure, s 0 A.Popov 14

$A quantitative approach to data collection strategies semi-empirical model for diffraction intensity vs reciprocal space coordinate Ĵ( h) = 1 Ĵ s ( h ) Exp( h B h semi-empirical model of variance vs$

15 A quantitative approach to data collection strategies semi-empirical model for diffraction intensity vs reciprocal space coordinate Ĵ( h) = 1 Ĵ s ( h ) Exp( h B h semi-empirical model of variance vs integrated intensity (Bragg peak, background - ADU/ADU) σ І (І)=α o +α 1 I+α I factorization on the basis of few initial diffraction images (background and Bragg scattering) and few instrumental parameters (calibration) relationship via diffraction geometry (rotation method) scan speed, oscillation range, mosaicity, spot shape, Lorentz, polarization integration over the scanned reciprocal space + Wilson distribution:data statistics (<I/SigI>/distributions, R merge, R friedel etc.) u T ) optimal data collection parameters : total rotation range, oscillation ranges/frame, exposure time providing required data statisics in a minimal total measurement time or exposure dose Popov & Bourenkov, Acta Cryst. D 003 A.Popov 15

16 Average standard uncertainty of the observed squared structure factors for a sampled volume v is approximated by: N 1 ( ˆ σj( h, ϕ) = k0 i+ k1 i J + k J p( J Ĵ( h i1)) + p( J Ĵ( hi )) )dj N i= 1 o k 0 ( h,ζ,ϕ ) = Gk ΔΦ(ΔS b PA ρ s ω + ρ dark ω + ρ readout ω /Δϕ ) (LPA) k 1 (h,ζ,ϕ) = Gω LPA k = k ins ˆ σ J (h) M 1/ m 1 the contribution of peak counting statistics the contribution of the instrumental error ˆ σ J (h,ϕ j ) Scattering background component After merging symmetry equivalent/redundant observations over a large rotation range subdivided into m equally small intervals centred at spindle positions, and assuming that redundant measurements are uniformly distributed over the rotation range, the expectation values of standard uncertainties can be estimated as: m j=1 M is the mean redundancy of the measurements in the total rotation interval A.Popov 16

17 merging equivalents 1/σ <E > =1/σ 1 +1/σ + + 1/σ n <E > hkl = σ <E > (E 1 /σ 1 + E /σ + + E n /σ n ) 1/σ 1 1/σ 1/σ k -1 1/σ n T Variance E k hkl about <E > hkl σ B RD (D i ) σ B RD (D j ) Corr RD ( D i -D j ) + ½π σ 1 σ -> R merge σ k σ n 1/σ 1 1/σ 1/σ k -1 1/σ n V κ n n ˆ σ ˆ σ = V + = δ δ σ σ + ( σ ˆ damage Vstat ik jk Cij bi bj k σ ) i j σ î σ j R = V damage + V π Iˆ i stat 1/ A.Popov 17

18 A variety of different tasks, crystal characteristics and specific instrument conditions make it impossible to define rigid protocols for data collection that would be applicable in all cases. The appropriate decision has to be a result of a compromise between several competing requirements. Structure refinement resolution and completeness are more important than accuracy. Molecular replacement is usually limited to lowresolution data, for which experimental random errors are not significant. Very sensitive to systematically missing the strongest intensities owing to detector saturation Ligand binding study, Drug Discovery Crystal ranking Experimental phasing is based on measuring differences of same-index (or symmetry-related) reflections. The magnitude of the phasing power is resolution dependent. The phasing-power magnitude can be improved equally well by an increase in phasing signal or by reducing errors associated with the signal. A.Popov 18

19 Initial Images Beamline Flux Crystal contents Absorbed dose Space group, Cell parameters, Orientation, Mosaicity I[(h,k,l), T exposure )], I background The user choice I/Sigma or max Resolution Anomalous Redundancy Geometry Total time or dose Geometry Optimal starting spindle angle and scan range Maximum rotation angle without spot overlap Multiplicity Reconstruction of average intensity vs. resolution Statistics modeling based on Wilson distribution Search for the optimal combination of data collection parameters Statistics calculation Low resolution path

20 Crystallographic phenomenology After high dose... cell dimensions/orientation change * mosaicity increase * R-factors increase * phasing signals washed away * diffraction disappears * what can be reduced will be reduced holes punched warmed-up samples explode... (*irrepoducible) A.Popov 0

21 Radiation Damage Factor I(t)/I(0) ID9 ESRF Oxoanion polyreductase I(t)/I(0) 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0, 0,1 d=3.0 Å d=.0 Å d=1.8 Å d=1.6 Å T_exposure (s) A.Popov 1

$Radiation Damage (Bulk MX, Cryo-T) Diffraction Intensity is a function of dose I(hkl)=scale(Dose, hkl )*I(hkl)+Δ(Dose) overall Debye-Waller factor (B) grows by 1 Å per 1 MGy Luzatti isomorphism$

22 Radiation Damage (Bulk MX, Cryo-T) Diffraction Intensity is a function of dose I(hkl)=scale(Dose, hkl )*I(hkl)+Δ(Dose) overall Debye-Waller factor (B) grows by 1 Å per 1 MGy Luzatti isomorphism factor (Log σ A ) decays by 0.1 Å per 1 MGy Kmetko et al. (006) Owen et al. (006) D ½ = 4.3(±0.3) x10 7 Gy Popov et al. (006) RD factors, A Dose E E E E E E E E E+ 07 β=8π s AD = Å A.Popov

23 Radiation Damage Modelling in BEST 1. Intensity decay: I D dbi dd e Ds e βds 11 I D = 0 Wilson plot, Dose = 0.5 MGy 10 Average Intensity, Dose = 0.5 MGy Wilson plot, Dose = 30 MGy 9 Average Intensity, Dose = 30 MGy ln(intensity) ,0 0,04 0,06 0,08 0,1 0,1 0,14 0,16 0,18 1/d^, 1/Á^ A.Popov 3

Non-specific Radiation Damage model: Atomic Debye-Waller factor variation with Dose 55 B (Å - ) 50 45 40 35 30 5 0 15 0 0. 0.4 0.6 0.

24 Non-specific Radiation Damage model: Atomic Debye-Waller factor variation with Dose 55 B (Å - ) Dose (Gy) Derived from the series of refined structures as a function of constant I/SigI/resolution Not visible in electron density maps (other then blurring) Generates extreme non-isomorphism (>70% in R E ) A.Popov 4

25 Radiation Damage Modelling in BEST. Intensity variance (non-isomorphism) Non-specific Radiation Damage model: Atomic Debye-Waller factor variation with Dose Im F D F D=0 σ a e dbi dd Ds dbi 1/ dd e Ds e αds R I I D= 0 D 1/ 1 I = ( 1 σ a ) I D= 0 I D ϕ D ϕ D=0 Re A.Popov 5

26 5 0 Instrument limit <I/SigI> 15 Absolute limit BEST model, no damage 10 BEST model, damage included 5 0 0,01 0, exposure time [sec/degree] A.Popov 6

27 Expected Intensity Variation / <σ/i> R 1I SAD Dose [Gy], d=.5 Å A.Popov 7

28 Interface:CCP4I BEST A.Popov 8

31 Data Collection with Variable Exposure Time and Oscillation Width BEST optimizes the data collection parameters for each crystal orientation (i.e. spindle position reached after exposure to a certain dose) individually; For convenience of data collection/processing the data collection "plan" is smoothed out to produce a small number sub-wedges with varying exposure/oscillation width Even without taking the Radiation damage into account, this is useful (e.g. severely anisotropic diffraction or long cell edge) For high-dose data collection, BEST suggest to increase the exposure time gradually during the data collection, in order to compensate the loss of the diffraction signal due to the radiation damage (according to the model-based expectations) and keep signal-to-noise at a required level. A.Popov 31

32 Reletive Intensity 1,3 1, 1,1 1 0,9 0,8 0, Phi, degree Rotation width, degree 0,7 0,6 0,5 0,4 0,3 0, 0,1 0 (a) Phi, degree Plan of data collection Rot. velocity, degree/s*10^-3,5,00 1,75 1,50 1,5 1,00 0,75 0,50 0,5 0,00 Permitted angle, degree A.Popov 3

500 000 1500 1000 500 0 XDS, data statistics 70% data 40% dose 40 60 80 100

33 Native data: optimization is based on decay model Total dose Gy BEST, strategy+predictions # strong reflections XDS, data statistics 70% data 40% dose spindle angle ( o ) Chi, R merge calculations involve Non-Isomorphism model A.Popov 33

strong reflections 4500 4000 3500 3000 500

34 Total dose 16 MGy BEST data collection, SCALEPACK Constant rotation, SCALEPACK # strong reflections BEST constant rotation spindle angle ( o ) Pseudo-precession images, I/SigI distribution in {hk0} plane A.Popov 34

35 Good native data Poor anomalous data SAD optimization Minimum of R Friedel =< <E + > - <E - > > is a target noise only, no anomalous scattering itself: decay, non-isomorphism exact pair-vice dose differences for Bijvoet mates A.Popov 35

36 merging equivalents 1/σ <E > =1/σ 1 +1/σ + + 1/σ n <E > hkl = σ <E > (E 1 /σ 1 + E /σ + + E n /σ n ) Variance <E + > hkl about <E - > hkl -> R Fridel ±1/σ 1± ±1/σ ± ±1/σ k± ±1/σ n± T σ B RD (D i ) σ B RD (D j ) Corr RD ( D i -D j ) + σ 1 σ σ k σ n ±1/σ 1± ±1/σ ± ±1/σ k± ±1/σ n± n n ˆ σ i j ( Δ ) = + + C σ σ + ( ˆ σ ˆ σ ) anom k i j σ i ˆ σ σ j ij bi bj π + R anom = 1 N Δ Iˆ anom, i A.Popov 36

37 ΔE =E Dose -E Dose=0 as a function of dose for a bunch of reflections in a narrow resolution shell, calculated from series of refined structures. Stationary stochastic process (exponential distribution at any Dose) ΔE Variance: σ B RD 1-Exp[ D s ] Correlation (D 1,D ): Corr RD Exp[-10-8 D 1 -D s ] E E E E+07.0E+07.5E E+07 Dose D, (Gy) A.Popov 37

38 Total rotation range Predicted average relative error versus resolution for data collections with the same total radiation dose and different data redundancies The choice of the starting and final angles of rotation range must assure the desired completeness of the data set. The smallest rotation range gives the data set with minimum redundancy. Two perfect experiments with the same total exposure dose used for different rotation ranges would provide the same data statistics. However, in the presence of the systematic error increasing the exposure dose per frame may not increase for strong signals over a certain limit. In our model, the contribution of the systematic error to the total intensity error equals 3% of intensity, i.e. for a single observation. Independent redundant measurements can improve the data statistics above this limit. On the other hand, increasing the number of frames by collecting redundant data results in stronger effects of the readout noise on weak signals. A.Popov 38

39 SAD optimization Minimum of R Friedel =< <E + > - <E - > > is a target Dose> MGy Dose>30 MGy Garman limit RFriedel [%] site-specific damage processes the radiation damage may start affecting anomalous signal Multiplicity= Multiplicity= Multiplicity=6 Multiplicity= Multiplicity=6 Multiplicity= E E E+08 Dose [Gy] A.Popov 39

40 Testing: multiplicity dependency 0.5 Last Shell Statistics Correlation ( DANO, FH calc ) Correlation R Friedel, data R Friedel R Friedel, BEST Å 11 SeMet/400 a.a. Total Dose Gy Constant rotation phasing fails BEST optimum phasing successful A.Popov 40

41 SAD optimization Minimum of RFriedel = < <E+/w>-<E-/w> > is a target noise only, no anomalous scattering itself: decay, non-isomorphism exact pair-vice dose differences for Bijvoet mates Resolution RFriedel(%) I/Sigma Redundancy A.Popov 41

42 Rfriedel vs. resolution Á Rfriedel, % Á 0 0 0,0 0,04 0,06 0,08 0,1 0,1 0,14 0,16 0,18 1/d^, A.Popov 4

43 RFriedel, [%] SAD optimization Minimum of R Friedel = < <E + >-<E - > > is a target Dose, [Gy] 0.E+00 5.E+06 1.E+07.E+07.E+07 3.E+07 3.E+07 4.E Multiplicity RD model ON RD model OFF Gradualy increasing exposure time (overall decay compensation) 7% 9% A.Popov 43

44 Testing: Dose dependency/decay compensation 0.19 Simulation, constant rotation Data collection, constant rotation Rfridel, last shell E E+06 1.E E+07.E+07.7E+07 3.E+07 Data collection, + compensation Simulation, + compensation Dose, [Gy] Data set 1 Correlation DANO, FH calc last shell, 3.3Å overall, 0-3.3Å A.Popov 44

45 Minimal R Friedel vs. Resolution and Orientation Rfriedel, % Random P Rfriedel, % random P ,05 0,1 0,15 0, 0,5 1/d^ 0 0 0,05 0,1 0,15 0, 0,5 1/d^ P P3 1 1 Rfriedel, % Rfriedel, % random ,05 0,1 0,15 0, 0,5 1/d^ 0 0 0,05 0,1 0,15 0, 0,5 1/d^ A.Popov 45

46 ESRF beamline >edna-prototype --flux 1.0e1 --beamsize images ref-my * img Indexing: MOSFLM : Version for Image plate and CCD data 0th August Integration : MOSFLM : Strategy : Summary of Strategy: Strategy : Strategy : Raddose : version 4. // 007/07/05.. Strategy : Raddose : Dose rate : 1.7e+05 [Grays/s] Strategy : Strategy : Strategy : Best : Version d // Strategy : Best : Strategy : Best : Plan for data collection: Strategy : Best : N Phi_start N.of.images Rot.width Exposure Distance Overlap Strategy : Best : No Strategy : Best : No Strategy : Best : No Strategy : Best : Strategy : Best : Attenuation : 1.0 Strategy : Best : Total rotation range : 70.4 [degrees] Strategy : Best : Total number of images : 146 Strategy : Best : Total exposure time : 56.6 [s] Strategy : Best : Total data collection time : 41.6 [s] Strategy : Best : Resolution :. [A] Strategy : Best : Resolution reasoning : Resolution limit is set by the radiation damage Strategy : Best : Ranking resolution :. [A] A.Popov 46

47 Strategy : Best : Predicted statistics: Strategy : Best : Resolution Compl. Average I/Sigma I/Sigma Chi** R-fact Overload Strategy : Best : Lower Upper % Intensity Sigma /Chi % % Strategy : Best : Strategy : Best : Strategy : Best : Strategy : Best : Strategy : Best : Strategy : Best : Strategy : Best : Strategy : Best : Strategy : Best : XDS : SUBSET OF INTENSITY DATA WITH SIGNAL/NOISE >= -3.0 AS FUNCTION OF RESOLUTION RESOLUTION NUMBER OF REFLECTIONS COMPLETENESS R-FACTOR R-FACTOR COMPARED I/SIGMA R-meas LIMIT OBSERVED UNIQUE POSSIBLE OF DATA observed expected %.0% 3.0% % %.% 3.0% % %.1% 3.% % %.0% 3.3% % %.6% 3.4% % % 14.9% 15.0% % % 5.9% 6.3% % % 31.6% 31.9% % total % 4.9% 5.4% % A.Popov 47

48 PROBLEM 1. sample > beam Irradiation crystal volume VS Phi????. Beam profile and crystal shape? A.Popov 48

49 Relative drop of average intensity vs. radiation dose (BEST predictions and SCALA data) 1 d=6.0 Ǻ 0,8 Rel. drop of intensity 0,6 0,4 scala scale scala scale scala scale best model best model d=3.0 Ǻ best model best B and scale estimate best B and scale estimate best B and scale estimate d=1.9 Ǻ 0, ID14-4 ESRF data collection from cytochrome c nitrite reductase (P13, a=194.4 Ǻ) Resolution=1.89 Ǻ, rot.width=0.5, exposure =8 s, flux=6e11,dose_rate=1.9e4 5 (50 images) of rotation provides complite data set 0 0,0E+00,0E+06 4,0E+06 6,0E+06 8,0E+06 1,0E+07 1,E+07 dose, Gy A.Popov 49

50 Acknowledgements: Gleb Bourenkov ESRF Beamlines : Sean McSweeney, Raimond Ravelli RADDOSE: Elspeth Garman Kappa workgroup Johan Unge (EMBL-HH MaxLab, Lund) Sandor Brokhauser (EMBL-Grenoble) Peter Keller, Gerard Bricogne (Global Phasing) EDNA Collaboration ( BEST users, all those who gives samples to us BIOXHIT before Software available for download at: A.Popov 50

Diffraction Geometry

$Diffraction Geometry$ Diffraction Geometry Diffraction from a crystal - Laue equations Reciprocal lattice Ewald construction Data collection strategy Phil Evans LMB May 2013 MRC Laboratory of Molecular Biology Cambridge UK