结构生物学 结构解析基础
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Intensity measured Phases lost
Methods to solve the phase problem:
MIR MAD Molecular replacement
Oscillation Method
Détecteur
Pilatus 6M
Principle Count Rate Dynamic Range Detective Quantum Efficiency Pilatus Dynamic Range Framing Rate Pixel Size Read-out Time Signal to Noise Ratio Point Spread Function
Number of molecules in the asymmetric unit
• Matthews method (1968)
• Empirically, the ratio between the of the unit cell and the molecular weight is comprised between 1,7 and 3,5Å3/Da
Integrating Detector Charge is accumulated and then converted.
Unlimited
PILATUS Detector X-ray is counted above certain threshold.
Limited to ~1.5 MHz/pixel/s 100%@8 keV, 80%@12 keV, 50%@16 keV 1’048’576 10 - 100 Hz 0.172 mm 5 ms Fluorescent background suppression One Pixel
i It is the phase problem ! a
r
F = structure factor (Complex number) = contribution des atomes àla diffraction
• Electronic density :
= tri-dimension function
Ewald sphere
s s1 s0
Crystal diffraction
M’ points are equivalent to M points by crystal translation
Electron density at M
is non zero if
is an integer for every x, y, z integers
• Experiment determintion
• Crystal density (by density gradient analysis) (r) • Solvent content (by dehydratation analysis) (x)
Diffusion by a point object: phase difference
Unit cell and lattice
Why using crystals?
• Signal increase
– adding signal ofe N molecules
• Order N molecules for diffusion in phase
– > crystalline state
1 ia hkl 2pi ( hx ky lz ) r ( x, y, z ) Fhkl e e V h k l
Coefficients = structure factors = complex numbers. (modulus |F| known from intensities, but phases aare unknown)
• Polarisation P
1 cos2 2q P 2
Lorentz Correction L
A non ideal Ewald sphere has a width Refelctions don’t cross Ewald sphere at the same speed
rotation
Reciprocal lattice
Reciprocal lattice belongs to the same space group as the direct lattice
For a non triclinic lattice:
2D reciprocal lattice
Diffraction Condition
Density r can be calculated if the position of the atoms is known (if the problem is solved…)
|F| a
A structure factor Fhkl is the sum of the contribution of all atoms
(proteins)
High
Mosaicity
Imperfect crystal formed of mosaic blocks 0,25-0,5° —> width Dq of reflection profile (problem of overlaping reflections if mosaicity is high)
<Global technique
B factor
f f 0e
f ~Z
B sin 2 q
Attenuatio factor
2
fo = # electrons (=Z)
I ~ Z2
U diffracts 8500 times more than H
B = atomic displacement parameter (unité: Å2) (Debye-Weller factor)
: mean atomic displacement
# e8
Point atom ( à0 K), B =0
5
(B~5Å2) (B~10Å2) (B>15Å2)
10 20 30
0
5,7 Å 2.8 Å
1,5 Å
1Å "resolution" (if = 1 Å)
q) d (Å)
low
Average
w
tangential
• • • • •
• • • • •
For two equivalent reflections :
• • • • •
direct
• • • • •
• • • • •
I2
w
I~S
I1
S1 >> S2
Rotation geometry : correction L ~ 1/sin w for S1 = S2
2
.
2
.
2
.
.
2
2
.
.
2
2
.
.
2
2
Unit cell
The space group is defined by symmetry elements
Point symmetries
Screw axis
Crystal systems
Système trigonal
a=b a=b =90° g=120° maille hexagonale, axes d’ordre 3 parallèle à c ou a=b=c a=b =y maille rhomboédrique
x
1
Length difference Phase difference of the wave in e2
1
Ewald sphere
Scattered beam
Diffusion vector s Incident beam
Angle between scattered and incident beam is 2q
3D lattice
Unit cell paramters: a, b, c, a, b, g
Each crystal belongs to a space group A space group is a 3D arrangement of point groups
.
Asymmetric unit
• Radiation damage distribution over N molecules in crystal • Fixed conformations
Asymmetric unit
.2
.2
solvent
.2
.2 .2 .2 .2 .2 .2
2
.2
.2 .2 .2 .2 .2 .2 .2
.2
.2 .2 .2 .2
.2
.2 .2 .2 .2
.2
.2 .2 .2 .2
.2
.2 .2 .2 .2
.2
.2 .2 .2 .2
பைடு நூலகம்
.2
.2 .2 .2
.2
.2
.2
a
.2
protein
b.2
.2
.2
.2
* A crystal is made of identical unit cells periodically repeated in space by translation operators * A unit cell can contain several molecules related by point symmetry operators * Arrangment in space of operators is the space group * The asymmetric unit is the smallest volume from which the whole unit cell can be built by symmetry operators * The unit cell volume contains ~60% d protein and ~40% solvent
Lattice types
14 Bravais lattices
Space groups for biological macromolecules (65 authorized over 230 possibilities)
Space group P212121
Asymmetric unit: The smallest volume neede to build the whole unit cell by crystallographic symmetry operators
Structure factor in practice
I -Polarisation - Lorentz Correction - Angular dependance 2q
I F c L.P
Scale factor Lorentz factor
Intensity
Io
Polarisation
Io I
If P is a reciprocal node:
is a integer for every x, y, z integers
Electron density calculation
Electron density: rx,y,z)
I(h,k,l) = F(h,k,l)*F(h,k,l)
rx,y,z) = 1/V SF(h,k,l)e2pi(hx+ky+lz) => 3-D structure
1 r ( x, y, z ) Fhkl e 2pi ( hx kylz) V h k l
Fhkl f j e
j 1 j n 2pi ( hx j ky j lz j )
• For n atomes at {xi, yi, zi} :
diffusion factor of the j atome
I(h,k,l) = |F(h,k,l)|eia(h,k,l)] a(h,k,l) not measured
Phase problem
Phasing
Diffracted beam
X-ray source
Rotating node synchrotron
crystal
detector
Recyiprocal lattice
6M
80%@8 - 12 keV 32’768 - 131’072 0.01 - 0.5 Hz 0.05 - 0.15 mm 1 - 120 s Limited by dark current and noise Several pixels
Diffraction = T.F.
T.F. -1
crystal
Methods to solve the phase problem:
MIR MAD Molecular replacement
Oscillation Method
Détecteur
Pilatus 6M
Principle Count Rate Dynamic Range Detective Quantum Efficiency Pilatus Dynamic Range Framing Rate Pixel Size Read-out Time Signal to Noise Ratio Point Spread Function
Number of molecules in the asymmetric unit
• Matthews method (1968)
• Empirically, the ratio between the of the unit cell and the molecular weight is comprised between 1,7 and 3,5Å3/Da
Integrating Detector Charge is accumulated and then converted.
Unlimited
PILATUS Detector X-ray is counted above certain threshold.
Limited to ~1.5 MHz/pixel/s 100%@8 keV, 80%@12 keV, 50%@16 keV 1’048’576 10 - 100 Hz 0.172 mm 5 ms Fluorescent background suppression One Pixel
i It is the phase problem ! a
r
F = structure factor (Complex number) = contribution des atomes àla diffraction
• Electronic density :
= tri-dimension function
Ewald sphere
s s1 s0
Crystal diffraction
M’ points are equivalent to M points by crystal translation
Electron density at M
is non zero if
is an integer for every x, y, z integers
• Experiment determintion
• Crystal density (by density gradient analysis) (r) • Solvent content (by dehydratation analysis) (x)
Diffusion by a point object: phase difference
Unit cell and lattice
Why using crystals?
• Signal increase
– adding signal ofe N molecules
• Order N molecules for diffusion in phase
– > crystalline state
1 ia hkl 2pi ( hx ky lz ) r ( x, y, z ) Fhkl e e V h k l
Coefficients = structure factors = complex numbers. (modulus |F| known from intensities, but phases aare unknown)
• Polarisation P
1 cos2 2q P 2
Lorentz Correction L
A non ideal Ewald sphere has a width Refelctions don’t cross Ewald sphere at the same speed
rotation
Reciprocal lattice
Reciprocal lattice belongs to the same space group as the direct lattice
For a non triclinic lattice:
2D reciprocal lattice
Diffraction Condition
Density r can be calculated if the position of the atoms is known (if the problem is solved…)
|F| a
A structure factor Fhkl is the sum of the contribution of all atoms
(proteins)
High
Mosaicity
Imperfect crystal formed of mosaic blocks 0,25-0,5° —> width Dq of reflection profile (problem of overlaping reflections if mosaicity is high)
<Global technique
B factor
f f 0e
f ~Z
B sin 2 q
Attenuatio factor
2
fo = # electrons (=Z)
I ~ Z2
U diffracts 8500 times more than H
B = atomic displacement parameter (unité: Å2) (Debye-Weller factor)
: mean atomic displacement
# e8
Point atom ( à0 K), B =0
5
(B~5Å2) (B~10Å2) (B>15Å2)
10 20 30
0
5,7 Å 2.8 Å
1,5 Å
1Å "resolution" (if = 1 Å)
q) d (Å)
low
Average
w
tangential
• • • • •
• • • • •
For two equivalent reflections :
• • • • •
direct
• • • • •
• • • • •
I2
w
I~S
I1
S1 >> S2
Rotation geometry : correction L ~ 1/sin w for S1 = S2
2
.
2
.
2
.
.
2
2
.
.
2
2
.
.
2
2
Unit cell
The space group is defined by symmetry elements
Point symmetries
Screw axis
Crystal systems
Système trigonal
a=b a=b =90° g=120° maille hexagonale, axes d’ordre 3 parallèle à c ou a=b=c a=b =y maille rhomboédrique
x
1
Length difference Phase difference of the wave in e2
1
Ewald sphere
Scattered beam
Diffusion vector s Incident beam
Angle between scattered and incident beam is 2q
3D lattice
Unit cell paramters: a, b, c, a, b, g
Each crystal belongs to a space group A space group is a 3D arrangement of point groups
.
Asymmetric unit
• Radiation damage distribution over N molecules in crystal • Fixed conformations
Asymmetric unit
.2
.2
solvent
.2
.2 .2 .2 .2 .2 .2
2
.2
.2 .2 .2 .2 .2 .2 .2
.2
.2 .2 .2 .2
.2
.2 .2 .2 .2
.2
.2 .2 .2 .2
.2
.2 .2 .2 .2
.2
.2 .2 .2 .2
பைடு நூலகம்
.2
.2 .2 .2
.2
.2
.2
a
.2
protein
b.2
.2
.2
.2
* A crystal is made of identical unit cells periodically repeated in space by translation operators * A unit cell can contain several molecules related by point symmetry operators * Arrangment in space of operators is the space group * The asymmetric unit is the smallest volume from which the whole unit cell can be built by symmetry operators * The unit cell volume contains ~60% d protein and ~40% solvent
Lattice types
14 Bravais lattices
Space groups for biological macromolecules (65 authorized over 230 possibilities)
Space group P212121
Asymmetric unit: The smallest volume neede to build the whole unit cell by crystallographic symmetry operators
Structure factor in practice
I -Polarisation - Lorentz Correction - Angular dependance 2q
I F c L.P
Scale factor Lorentz factor
Intensity
Io
Polarisation
Io I
If P is a reciprocal node:
is a integer for every x, y, z integers
Electron density calculation
Electron density: rx,y,z)
I(h,k,l) = F(h,k,l)*F(h,k,l)
rx,y,z) = 1/V SF(h,k,l)e2pi(hx+ky+lz) => 3-D structure
1 r ( x, y, z ) Fhkl e 2pi ( hx kylz) V h k l
Fhkl f j e
j 1 j n 2pi ( hx j ky j lz j )
• For n atomes at {xi, yi, zi} :
diffusion factor of the j atome
I(h,k,l) = |F(h,k,l)|eia(h,k,l)] a(h,k,l) not measured
Phase problem
Phasing
Diffracted beam
X-ray source
Rotating node synchrotron
crystal
detector
Recyiprocal lattice
6M
80%@8 - 12 keV 32’768 - 131’072 0.01 - 0.5 Hz 0.05 - 0.15 mm 1 - 120 s Limited by dark current and noise Several pixels
Diffraction = T.F.
T.F. -1
crystal