Transcript X-ray sources are incoherent!!

Announcements
1. Grades (for Mid-term) in Web portal
2. Review your Mid-term today or tomorrow in 328/326 LLP.
(Worthwhile top review test so you can see what you
should know for final.)
Homework
1. Read chapter on DNA and X-ray Diffraction. (It was assigned last Tuesday.
2. There will be a quiz next Tuesday, in class.
3. Written homework will be assigned by the end of Friday. Do next Thursday.
Watson & Crick 1953
Interbase distance
0.34 nm = P/10
X pattern
Minor Groove
1.2 nm = 3P/8
Period
P = 3.4 nm
Major Groove
2.2 nm = 5P/8
Diameter 2 nm
X pattern: Helix
Layer Lines: Helix period P
Angle α: Helix radius
α
10 layers lines/diamond:
Interbase spacing P/10
Missing 4th Layer line?
ΔL = λ/2 Destructive
Dark Spot
θ
P
θ
ΔL = λ/2
ΔL = Psinθ
Destructive Interference (Dark Spots)
ΔL = Psinθ =
 2n +1
2
λ
n = 0,1,2,...
Constructive Interference (Bright Spots)
ΔL = Psinθ = nλ
n = 0,1,2,...
Missing lines → Additional Interference
Even if Blue is in phase with Blue,
q
P
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.
nλ
sin =
P
Blue may be out of phase with Red
For 4th layer line, n = 4
This 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 3 P/8
Gayle Wittenberg 2003
Notice where
blue and red dots
totally interfere:
only at Layer line
4l/P. Therefore
no signal there.
X pattern: Helix
Layer Lines: Helix period P
Angle α: Helix radius
α
10 layers lines/diamond:
Interbase spacing P/10
Missing 4th Layer line?
Young’s Double Slit: Diffraction and Interference
The phase problem: Coherence length
Bottom wave
travels extra
1λ
Both waves
travel same
distance
Top wave
travels extra
1λ
Recall that the phase between two (or more) points must be
well-defined in order to have interference.
The phase problem: Coherence length
If the phase of a light wave is well defined at all times
(oscillates in a simple pattern with time and varies in a smooth
way in space at any instant), then the light is said to be
coherent.
If, on the other hand, the phase of a light wave varies randomly
from point to point, or from moment to moment (on scales
coarser than the wavelength or period of the light) then the
light is said to be incoherent.
For example, a laser produces highly coherent light. In
a laser, all of the atoms radiate in phase.
An incandescent or fluorescent light bulb produces incoherent
light. All of the atoms in the phosphor of the bulb radiate with
random phase. Each atom oscillates for about 1ns, and
produces a wave about 1 million wavelengths long.
X-ray sources are incoherent!!
They are not a laser!
Only the most sophisticated synchrotrons are slightly coherent.
So how did Franklin et al. produce their diffraction pattern?
They used a lead and also somewhat monochromatic light.
Coherent over a length of P.
Equipment for x-ray diffraction data collection
Of 3-D crystals
Or use synchrotron radiation
Notice that you need the ability to rotate the crystal!
The basic equipment necessary to conduct an X-ray diffraction experiment
consists of an X-ray source, a means for orienting the crystal and a means
for detecting (measuring) the diffraction spots.
Structure determination by X-ray diffraction
Not just 1dimensional crystal, but three dimensional
Strategy & objectives
Determine location and intensities of electron densities in crystal
Model the positions of atoms in 3 dimensions.
(You have the 1d amino acid or nucleotide sequence.)
Thread it through the electron density.
In general, can’t see H’s but know heavier atoms: C, O, N, P
Detection of X-ray diffraction
(X-ray film or electronic)
Diffraction pattern
• Each diffraction spot is the result of interference of all X-rays with the same
diffraction angle emerging from all atoms
• The stronger the signal, the more intense the scattered beam, and
the greater the electron-density that scattered it
What does the diffraction pattern tell us?
• Each spot contains a small amount of information about the position of each
atom in the unit cell
• To produce all possible spots, X-rays must be allowed to strike the crystal
from many different directions: crystal is rotated in the X-ray beam
• Positions & intensities of each spot are the basic experimental data
• The ~ 25,000 diffracted beams diffracted by myoglobin contain scattered
X-rays from each of the protein’s ~1,500 atoms