Mid-term

Mid-term by Question

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 pattern

Layer Lines

Missing 4th layer

Diamond Pattern

“Photo 51” – Rosalind Franklin 1952

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”

ΔL = 0

ΔL = λ

ΔL = 2λ

Constructive interferenceΔL = nλ n = 0, 1, 2, ...

Destructive interference n’ = 0, 1, 2, ...

ΔL = λ/2

ΔL = 3λ/2

ΔL = 5λ/2

2n +1ΔL = λ

2

Constructive Interference(Bright Spot)

Destructive Interference(Dark Spot)

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

Imagine a simple 1-D crystal...

P

X-rays

ΔL = 0 ConstructiveBright Spot

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

θ = 0

-1 λθ = sin

P

-1 2λθ = sin

P

-1 λθ = -sin

P

-1 2λθ = -sin

P

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

Gayle Wittenberg 2003

Θ, λ, P

Can get P

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...

http://mrsec.wisc.edu/Edetc/background/DNA/DNA_OTK.htm

Basic pattern

The first three mask patterns

A helix (flattened into 2 dimensions)is very similar to a zig zag

PeriodicPeriodic

X-shape = Helix!

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.

Continued next class

Class evaluation

1. What was the most interesting thing you learned in class today?

2. What are you confused about?

3. Related to today’s subject, what would you like to know more about?

4. Any helpful comments.

Answer, and turn in at the end of class.