Post on 21-Dec-2015
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X-ray DiffractionOne of the premier techniques of Structural Biology
Can get Angstrom resolution of nearly every atom in biological macromolecules—now- a-days get up to (beyond?) 2 MD (Ribosomes).
1st one: Whale myoglobin--won Nobel Prize, 1962, Max Perutz, Sir John Cowdery Kendrew.
Minor Groove1.2 nm = 3P/8
Major Groove2.2 nm = 5P/8
Diameter 2 nm
Interbase distance0.34 nm = P/10
PeriodP = 3.4 nm
Watson & Crick 1953
X pattern
Fraunhofer X-ray Diffraction
Maximum possible resolution ~λX-rays: 10 – 0.1 nm ~Interatomic distances
X-ray Diffraction is elastic scattering
The scattering is elastic; the scattered X-rays have the same wavelength as the incoming X-ray. By contrast, inelastic X-ray scattering methods are useful in studying excitations of the sample, rather than the distribution of its atoms.
86,817 X-ray crystal structures of proteins, nucleic acids and other biological molecules have been determined
X-rays behave as electromagnetic waves1.They interfere
“In Phase”wavelength λ
amplitude
Constructive Interference(Bright Spot)
Destructive Interference(Dark Spot)
ΔL = λ/2 “Out of Phase”
Interference depends on waves traveling different distances
Constructive interference
Destructive interference
Two-wave Interference Pattern
X-rays behave as electromagnetic waves2.They diffract
Interference!
What if there are two (or more) atoms?
Atom
X-rays
Bottom wave travels extra 1λ
Top wave travels extra 1λ
Both waves travel same distance
Young’s Double Slit: Diffraction and Interference
ΔL = λ/2 DestructiveDark Spot
ΔL = λ/2ΔL = Psinθ
P
Constructive Interference (Bright Spots)
ΔL = Psinθ = nλ n = 0,1,2,...
Destructive Interference (Dark Spots)
2n +1ΔL = Psinθ = λ n = 0,1,2,...
2
θ
ΔL
θ
Question about Crystal diffraction
Phys. 102, Lecture 23, Slide 19
In a NaCl crystal, the spacing between atoms is 0.282 nm. Which of the following wavelengths could be used to see a clear diffraction pattern?
A. λ = 0.1 nm B. λ = 1 nm C. λ = 10 nm
1sinλ
θd
need λ < d
First interference maximum:
Need very short wavelength light: X-rays!
0.282 nm
X-ray crystallography
“Photo 51” Rosalind Franklin
Crystalline fiber of DNA
Given X-ray wavelength λ, diffraction angles θ provide information about distance d between atoms in crystal
θ
As long as λ < d, small features lead to large θ. BUT need regular ordering of atoms – i.e. a crystal!
sin mλ
θ md
Four simple arrays... ...and their diffraction patterns
Notice the inverse relationship between spacingin the array and spacing in the diffraction pattern. The array in (x,y,z) real space and the diffraction space (h,l,m) are Fourier Transform of each other. (Will learn about this.)
Rows of spots are perpendicular to original lines
-1 nλθ = sin
P
2-D crystals...
Question: DNA cross patternYou discover a new structure of DNA in which the diffraction pattern is the same as the “normal” DNA in every respect EXCEPT that the cross makes a more acute angle α
“Normal” DNA New form of DNA
Which statement regarding the new DNA structure must be true?A. It cannot be a helix
B. The helix repeat distance P must be different
C. It must be a wider molecule
α αα
Pα
P
Δθ Δθ
Question: What does increasing the diameter of the helix do to slope of decreases the slope?
E
H
Decreases.
X pattern: Helix
Layer Lines: Helix period P
Angle α: Helix radius
10 layers lines/diamond: Interbase spacing P/10
Missing 4th Layer line?
α
Missing lines → Additional Interference
P
q
Even if Blue is in phase with Blue,
Blue may be out of phase with Red
sin =nλP
For 4th layer line, n = 4This is mathematically the correct answer. However, P/8 would make the atoms collide: 10.4bp/8 = 1.3 bases apart. For 5th layer lines you get 5P/8, but this is the same as 3P/8
Notice that both the red and blue dots are spaced 1P apart, but because they’re offset from each other by an amount q.Two helices identical except the starting point, their phase.