Announcements1. Grades (for Mid-term) in Web portal2. 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.

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

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

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

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.

Gayle Wittenberg 2003

Notice where blue and red dots totally interfere: only at Layer line 4/P. Therefore no signal there.

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

Bottom wave travels extra 1λ

Top wave travels extra 1λ

Both waves travel same distance

Young’s Double Slit: Diffraction and Interference

The phase problem: Coherence length

Recall that the phase between two (or more) points must be well-defined in order to have interference.

The phase problem: Coherence lengthIf 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. Ina 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!!

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.

For Copper electrode, 1.54A

They are not a laser!

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.

Equipment for x-ray diffraction data collectionOf 3-D crystals

Or use synchrotron radiation

Notice that you need the ability to rotate the crystal!

Structure determination by X-ray diffractionNot 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

• 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, andthe greater the electron-density that scattered it

Detection of X-ray diffraction

(X-ray film or electronic) Diffraction pattern

• 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 scatteredX-rays from each of the protein’s ~1,500 atoms

What does the diffraction pattern tell us?