Molecular Replacement (Alexei Vagin s lecture)

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1 Molecular Replacement (Alexei Vagin s lecture)

2 Contents What is Molecular Replacement Functions in Molecular Replacement Weighting scheme Information from data and model Some special techniques of Molecular Replacement

3 Molecular replacement programs and systems Programs Systems Amore MrBump MOLREP Phenix QS BALBES PHASER Many others EPMR CNS URO

4 Molecular replacement programs and systems Programs Systems Amore MrBump MOLREP Phenix QS BALBES PHASER Many others EPMR CNS URO

5 Introduction: Where MR could help? Same protein could be crystallised in different space groups Mutants Complexes Homologous proteins Some structure could be derived using NMR Homology modeling MR works best when similarity (3D similarity) between search and target molecules is high and the search model is relatively big. 4

6 Introduction Molecular replacement (MR) is a phasing technique. It may help to derive initial phases. If the MR is successful then you need to do many cycles of refinement and model building. Its attractive side is that it produces initial atomic model also. However avoiding bias towards model may be difficult especially at low resolution. If there are more than one copies of the molecule in the asymmetric unit then non-crystallographic (NCS) averaging may improve phases and maps. If the resolution high enough (e.g. 2.5 or better) then automatic model building (arp/warp, solve/resolve, buccaneer) may help in model rebuilding. 5

7 Overall results reported in PDB MR SIR MIR SAD MAD Not specified Diagram showing the percentage of structures in the PDB solved by different techniques 67.5% of structures are solved by Molecular Replacement (MR) 21% of structures are solved by experimental phasing

8 Molecular Replacement If we can find the rotation and translation that puts the model in the correct position in the crystal cell, THEN we can calculate phases. unknown structure MGDKPIWEQIGSSFIQHYYQLFDNDRTQLGAIY IDASCLTWEGQQFQGKAAIVEKLSSLPFQKIQH SITAQDHQPTPDSCIISMVVGQLKADEDPIMGF HQMFLLKNINDAWVCTNDMFRLALHNFG origin o H K L F φ etc... known structure PSPLLVGREFVRQYYTLLNKAPEYLHRFYGRNSSY VHGGVDASGKPQEAVYGQNDIHHKVLSLNFSECHT KIRHVDAHATLSDGVVVQVMGLLSNSGQPERKFMQ TFVLAPEGSVPNKFYVHNDMFRYEDE origin o H K L F φ etc...

9 Molecular Replacement If we can find the rotation and translation that puts the model in the correct position in the crystal cell, THEN we can calculate phases. unknown structure MGDKPIWEQIGSSFIQHYYQLFDNDRTQLGAIY IDASCLTWEGQQFQGKAAIVEKLSSLPFQKIQH SITAQDHQPTPDSCIISMVVGQLKADEDPIMGF HQMFLLKNINDAWVCTNDMFRLALHNFG origin o H K L F φ etc... known structure PSPLLVGREFVRQYYTLLNKAPEYLHRFYGRNSSY VHGGVDASGKPQEAVYGQNDIHHKVLSLNFSECHT KIRHVDAHATLSDGVVVQVMGLLSNSGQPERKFMQ TFVLAPEGSVPNKFYVHNDMFRYEDE origin o H K L F φ etc...

Molecular Replacement If we can find the rotation and translation that puts the model in the correct position in the crystal cell, THEN we can calculate phases.

10 Molecular Replacement If we can find the rotation and translation that puts the model in the correct position in the crystal cell, THEN we can calculate phases. unknown structure MGDKPIWEQIGSSFIQHYYQLFDNDRTQLGAIY IDASCLTWEGQQFQGKAAIVEKLSSLPFQKIQH SITAQDHQPTPDSCIISMVVGQLKADEDPIMGF HQMFLLKNINDAWVCTNDMFRLALHNFG origin o H K L F φ etc... known structure PSPLLVGREFVRQYYTLLNKAPEYLHRFYGRNSSY VHGGVDASGKPQEAVYGQNDIHHKVLSLNFSECHT KIRHVDAHATLSDGVVVQVMGLLSNSGQPERKFMQ TFVLAPEGSVPNKFYVHNDMFRYEDE origin o H K L F φ etc...

11 Molecular replacement place a homologous model into the crystal with unknown structure or Atomic Model --> EM map

12 Molecular replacement place a homologous model into the crystal with unknown structure or Atomic Model --> EM map 1) 6 - dimensional search check all orientations and positions

13 Molecular replacement place a homologous model into the crystal with unknown structure or Atomic Model --> EM map 1) 6 - dimensional search check all orientations and positions 2) 3-d + 3-d search orientations positions Conventional Molecular Replacement

14 Functions of molecular replacement Cross Rotation function Self Rotation function Translation function Phased Translation function Fast Packing function

15 Cross Rotation Function map model Patterson P obs P mod RF(Ω) = P obs (r) R Ω { P mod (r)} dr R Ω - rotation operator RF Ω

16 Cross Rotation Function map model Patterson P obs P mod RF(Ω) = P obs (r) R Ω { P mod (r)} dr R Ω - rotation operator RF Ω

17 Cross Rotation Function map model Patterson P obs P mod RF(Ω) = P obs (r) R Ω { P mod (r)} dr R Ω - rotation operator RF Ω

18 Cross Rotation Function map model Patterson P obs P mod RF(Ω) = P obs (r) R Ω { P mod (r)} dr R Ω - rotation operator RF Ω

19 Cross Rotation Function map model Patterson P obs P mod RF(Ω) = P obs (r) R Ω { P mod (r)} dr R Ω - rotation operator RF Ω

20 map B Optimal radius of integration model A Vinter AB BA Diametre of the model and less than smallest cell dimension

21 map Self Rotation Function RF(Ω) = P obs (r) R Ω { P obs (r)} dr RF Ω 0 90

22 map Self Rotation Function RF(Ω) = P obs (r) R Ω { P obs (r)} dr RF Ω 0 90

23 map Self Rotation Function RF(Ω) = P obs (r) R Ω { P obs (r)} dr RF Ω 0 90

24 map Self Rotation Function a RF(Ω) = P obs (r) R Ω { P obs (r)} dr a RF 0 90 a Ω

25 Stereographic projection z(c*) R(θ, ϕ, χ) χ Plot for rotation by χ θ ϕ x(a) - χ R(π-θ, π +ϕ, -χ) y x θ ϕ y

26 Self Rotation Function Space group P2 1 one tetramer

27 Self Rotation Function Space group P2 1 one tetramer

28 Self Rotation Function Space group P2 1 one tetramer

29 Translation Function To find relative position of molecules again Patterson function is used. Correctly oriented molecules are shifted to position r, corresponding Patterson is calculated and it is compared with observed Patterson. Maximum correspondence between two Pattersons indicate potentially correct position. TF(s) = P obs (r) P calc (s,r) dr s - vector of translation

30 Fast Packing Function Estimation of overlap: Packing function: Κ # j

31 Questions How to use X-ray data Maximum resolution limit? Minimal resolution limit? Weighting scheme?

32 Short introduction to Fourier Transformation Operators: addition F addition convolution F product

33 Convolution

34 Convolution

35 Real space Real function Gaussian A Functions F F Reciprocal space Complex function Gaussian 1/A A Grid F Grid 1/A Step function A F Interference function 1/A

36 Crystal and Structure Factors Real space F Reciprocal space F obs (s) s Convolution A 1/A F Product F h h

37 Real space F Reciprocal space Map ρ(r) F F(s) structure factors convolution F product Patterson P(r) F F(s) F * (s) = I(s) intensities

38 High resolution data High resolution limit from Optical resolution Weights for high resolution data

39 Real space Optical resolution σ atm F Reciprocal space F obs (s) σ res Convolution σ product resmax σ res = resmax 2 = 2 2 atm + res σ σ σ

40 Real space Optical resolution σ atm F Reciprocal space F obs (s) σ res Convolution σ product resmax σ res = resmax 2 = 2 2 atm + res σ σ σ

41 Real space Optical resolution σ atm F Reciprocal space F obs (s) σ res Convolution σ product resmax σ res = resmax 2 = 2 2 atm + res σ σ σ

42 Real space Optical resolution σ atm F Reciprocal space F obs (s) σ res Convolution σ product resmax σ res = resmax 2 = 2 2 atm + res σ σ σ

43 Real space Optical resolution σ atm F Reciprocal space F obs (s) σ res Convolution σ product resmax Single peak σ res = resmax 2 = 2 2 atm + res σ σ σ Opt res = 2 σ

44 Optical resolution from origin peak of Patterson Real space Patterson atm patt σ σ Opt res = 2 atm σ atm 2 = ( patt 2 + res 2 )/2 σ σ σ

45 Optical Resolution Å Opt res = 2 σ 2 = ( atm 2 + res 2 ) )/2 σ σ σ 10 Optimal high resolution 5 Å Resolution

46 Optical Resolution ( by sfcheck )

47 Weights for high resolution data and similarity

48 Map 1 2 F obs (s) Model 1 2 2σ

49 Map 1 2 F obs (s) Model 1 2 2σ

50 Map 1 2 F obs (s) Model 1 2 2σ

51 Map 1 2 F obs (s) Model 1 2 2σ PTF

52 Map 1 2 F obs (s) Model 1 2 2σ PTF

53 Map 1 2 F obs (s) Model 1 2 2σ PTF

54 Map 1 2 F obs (s) Model 1 2 2σ PTF

55 Map 1 2 F obs (s) Model 1 2 2σ PTF

56 Map 1 2 F obs (s) Model 1 2 2σ PTF

57 Map 1 2 F obs (s) Model 1 2 2σ PTF

58 Map 1 2 F obs (s) Model 1 2 2σ PTF

59 Map 1 2 F obs (s) Model 1 2 2σ PTF not possible to find solution

60 Map 1 2 F obs (s) Model 1 2 2σ PTF not possible to find solution Map (blurred) 1 2 F obs (s) Exp(-Bs 2 ) π σ B=1/4 2 2

61 Map 1 2 F obs (s) Model 1 2 2σ PTF not possible to find solution Map (blurred) PTF F obs (s) Exp(-Bs 2 ) π σ B=1/4 2 2 Clear solution

62 Low resolution data Weights for low resolution data and size of model

63 Soft minimal resolution cut-off Real space F Reciprocal space F obs (s) Rad model s

64 Soft minimal resolution cut-off Real space F Reciprocal space F obs (s) s Exp(-Bs 2 ) Exp(-r 2 /2 σ 2 ) B=1/4 π 2 2 σ = Rad model / 6 Rad model σ convolution product: Exp(-Bs 2 ) F obs

65 Soft minimal resolution cut-off Real space F Reciprocal space F obs (s) s Exp(-Bs 2 ) Exp(-r 2 /2 σ 2 ) B=1/4 π 2 2 σ = Rad model / 6 Rad model σ convolution product: Exp(-Bs 2 ) F obs subtraction (1-exp(-Bs 2 ) )F obs

66 Weighting scheme F used = (1 - exp(-b off s 2 ) ) F obs exp(-bs 2 ) 1 - exp(-boff s2 ) 1 exp(-bs 2 ) s

67 Weighting scheme F used = (1 - exp(-b off s 2 ) ) F obs exp(-bs 2 ) 1 - exp(-boff s2 ) 1 exp(-bs 2 ) 1/Rmin s Rmin = 2B off = 2 model σ model = Rad model / 6 Rmin Rad model π σ

68 Weighting scheme F used = (1 - exp(-b off s 2 ) ) F obs exp(-bs 2 ) 1 - exp(-boff s2 ) 1 exp(-bs 2 ) 1/Rmin 1/Rmax s Rmin = 2B off = 2 model σ model = Rad model / 6 Rmin Rad model π σ B=1/4 π 2 2 σ Model similarity Rmax = 2B

69 Weighting scheme Two filters in Image processing: Gaussian highpass filter Gaussian lowpass filter F used = (1 - exp(-b off s 2 ) ) F obs exp(-bs 2 ) We can consider this weighting scheme as an approximation to the likelihood approach

70 Information in X-ray and Model must overlap 1 1/Rmin 1/Rmax (fom model size) (fom model similarity) s 1/Resmax_used (fom opt. resolution) 1/Resmin_X-ray 1/Resmax_X-ray

71 Can we find solution? Weight of high resolution grows Low high Model size Weight of low resolution grows Low high Model Similarity Very likely Very unlikely

72 Can we find solution? Weight of high resolution grows Low high Model size Weight of low resolution grows Low high Model Similarity Very likely Very unlikely Small model with low similarity

73 Can we find solution? Weight of high resolution grows Low high Model size Weight of low resolution grows Low high Model Similarity Very likely Very unlikely Small model with high similarity Small model with low similarity

74 Can we find solution? Weight of high resolution grows Low high Model size Weight of low resolution grows Low high Model Similarity Very likely Very unlikely Small model with high similarity Small model with low similarity Big model with low similarity

75 What do you need to do before MR 1) Examine the data 2) Examine the model

76 Examine the data (e.g by sfcheck) Completeness of data Signal-to-noise Anisotropy (make correction?) Pseudo-translation Twinning Resolution

77 Sfcheck 1

78 Sfcheck 2

79 Pseudo-translation Cell P0 Patterson P0 Pst-vector

80 Examine the model Look at the molecular shape and flexibility Check the sequence similarity Estimate the model size Choose the method of the model correction Estimate number of copies

81 Automatic correction of the model using sequence alignment PHE VAL Initial model Search model Sequence

82 without alignment correction with alignment correction P models in a.u.c. Identity 27% --- Rotation function --- Rf Rf/sigma RF RF * RF RF RF RF TF Rfac Score can not find solution Rf Rf/sig RF RF RF * RF RF * --- Translation function --- RF TF Rfac Score with fixed model

83 Model improvement Set atomic B values according to accessible surface area B=15 B (A 2 ) = 15 (A 2 ) + 10 SA (A 2 ) SA surface area

84 Expected number of copies

85 Time to have a break

86 NMR model Rotation function Use as single model or Averaged individual RF Averaged intensities Translation function Use as single model or Averaged individual TF

87 Special techniques of molecular replacement Locked Rotation function Multi-copy search Use phases after Refinement Spherically Average Phased Translation function

88 Self rotation and locked RF Peaks selected from the self rotation function can be used for locked cross rotation function. Locked rotation function is averaged RF according to NCS Sol_ Space group : H 3 Sol_--- Rotation function --- theta phi chi Rf Rf/sig RF RF RF RF Sol_--- Locked Rotation function --- theta phi chi Rf Rf/sig RF RF RF RF

89 Multi-copy search Cell Model1 Model2 F 1 F 2 Patterson F 1 F * 2 Structure Factors F 2 F * 1 F 1 F 1 * + F 2 F* 2 Real function

90 Difficult case Space group H3 Resolution 1.8A One molecule in a.u.c Identity 35% 1. Using complete model - failed 2. Using domains separately - failed 3. Multi-copy search - success

91 Initial model

92 RF & TF complete model RF TF Score domain 1 RF TF Score domain 2 RF TF Score

93 Domain : Multi-copy search multi-copy Search R1 R2 STF TF PFmax PFmin Score domain1 (rf7), domain2(rf24)

94 Initial model and MR solution MR initial

95 MR solution and final structure MR final

96 Use Phases after Refinement

97 Example: Domain motions - 1tj3 unknown structure (1tj3) search model with sequence identity 100% Search for the whole molecule using standard MR protocol failed because of domain flexibility. Search by domains using standard MR protocol failed because of small size of the second domain. Structure was then solved manually in three steps: 1) standard MR search for larger domain; 2) refinement of the partial model; 3) search for smaller domain in the masked map (generated from REFMAC s FWT and PHIWT)

Example: Domain motions - 1tj3 unknown structure (1tj3) search model with sequence identity 100% Search for the whole molecule using standard MR protocol failed because of domain flexibility.

98 Example: Domain motions - 1tj3 unknown structure (1tj3) search model with sequence identity 100% Search for the whole molecule using standard MR protocol failed because of domain flexibility. Search by domains using standard MR protocol failed because of small size of the second domain. Structure was then solved manually in three steps: 1) standard MR search for larger domain; 2) refinement of the partial model; 3) search for smaller domain in the masked map (generated from REFMAC s FWT and PHIWT)

99 Fitting model into X-ray or EM map 1. find orientation (RF) 2. find position (PTF) Alternative approach: 1. find position 2. find orientation

100 Spherically Averaged Phased Translation Function (SAPTF) Map ρ (r) radial distribution ρ m (r) s Model SAPTF(s) = ρ s (r) ρ m (r) r 2 dr

101 Spherically Averaged Phased Translation Function (SAPTF) Map ρ (r) radial distribution ρ m (r) ρ m (r) s Model SAPTF(s) = ρ s (r) ρ m (r) r 2 dr

102 Spherically Averaged Phased Translation Function (SAPTF) Map ρ (r) radial distribution ρ s (r) ρ m (r) ρ m (r) s Model SAPTF(s) = ρ s (r) ρ m (r) r 2 dr

103 SAPTF as Fourier series By expanding SAPTF into spherical harmonics it is possible to represent it as a Fourier series SAPTF(s) = ρ s (r) ρ m (r) r 2 dr = π = h A h exp(2 i hs) A h = n F h c 00n (R) j 0 (2 Ra) b π 00n

104 Algorithm 1. Find position: Spherically averaged phased translation function 2. Find orientation: Local phased rotation function 3. Check and refine position : Phased translation function

Direct Method. Very few protein diffraction data meet the 2nd condition

$Direct Method. Very few protein diffraction data meet the 2nd condition$ Direct Method Two conditions: -atoms in the structure are equal-weighted -resolution of data are higher than the distance between the atoms in the structure Very few protein diffraction data meet the 2nd