Lab 12 - DNA Diffraction
Physics 42 - Fall 2009
DNA Diffraction
Introduction
In this lab, you will determine the structure and size of hydrated DNA (B-DNA). The first student to
publish the results wins a Nobel Prize.
Brief History
In 1952, James Watson and Francis Crick had been trying to solve the DNA structure puzzle for some time,
and had a large store of information from many different sources. That year, Rosalind Franklin made the
following X-ray diffraction photograph of B DNA (hydrated DNA), known as Photo 51:
DNA was known to be long fibers, and Franklin was able to align the fibers vertically (relative to the
pattern shown above).
Watson saw the photograph in January, 1953. Watson and Crick completed their model of DNA shortly
afterward, on March 7. Franklin saw the model in April, and felt it was too speculative. However, that
month, Watson and Crick published the original paper in Nature describing the structure of DNA.
In 1962, the Nobel Prize in Physiology or Medicine was awarded to Francis Harry Compton Crick, James
Dewey Watson, and Maurice Hugh Frederick Wilkins “for their discoveries concerning the molecular
structure of nucleic acids and its significance for information transfer in living material”. Rosalind
Franklin had died in 1958 from ovarian cancer. A Nobel Prize is shared by at most three people, and is
awarded only to living people.
A dehydrated form of DNA, called “A-DNA”, has a shortened structure. Rosalind Franklin thought it was
not a helix at all, and after making one particular X-ray photograph that was inconsistent with a helix,
distributed the following cards:
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Lab 12 - DNA Diffraction
Physics 42 - Fall 2009
It is now known that both A-DNA and B-DNA are similar, right-handed, double-helix structures. Another
form, Z-DNA, has a left-handed double-helix structure. These three forms of DNA are thought to be the
biologically active forms.
Theory
Recall from double-slit diffraction theory that a pair of features will diffract a coherent light source,
creating an interference pattern with a maximum at intervals:
(1)
d sin φ = nλ
⇒
d=
nλ
nλ
≈
sin φ s / L
screen
screen
φ
d
constructive
interference
s
φ
L
d sin φ
(Left) Top view of diffraction.
(Right) Diagram showing how to achieve constructive interference.
Besides putting transmitting slits into an opaque background, one can also get a diffraction pattern by
putting opaque lines onto a clear background (below):
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Lab 12 - DNA Diffraction
Physics 42 - Fall 2009
screen
target
d
bright central
spot
top view
view from screen
into laser
constructive
interference
screen
(Left) Top view of diffraction by opaque lines. (Middle) Looking from screen, through
target, into laser source. (Right) Diffraction pattern on screen.
The equation relating the line spacing is the same as for double-slit diffraction: d sin θ = nλ.
This is one-dimensional diffraction: a small beam is diffracted into a line on the screen. By putting more
lines on the target, one generates 2D diffraction patterns (below). Notice that wider spaced lines produce
closer-spaced dots on the screen. Also, when the bright spots from two targets don’t overlap, combining
the targets into one target produces a pattern on the screen that is just the sum of the bright spots that would
be produced by each pattern separately.
d
layer line 3
layer line 1
view from screen
into laser
screen
(Left) 2D target. (Right) Diffraction pattern on screen.
In general, 2D diffraction patterns from targets with perpendicular structures form rectangular arrays of
dots. Each row of dots is called a layer line. The layer lines are numbered, with 0 being the central bright
spot.
[Aside: In principle, one can compute the diffraction pattern from any target with a 2D Fourier Transform.
The Fourier Transform is a mathematical tool with a huge range of applications, including heat flow,
differential equations, communications, and optics.]
Sending a beam of X-rays through DNA molecules to make a diffraction pattern is approximately like
flattening the molecules into a target plane, and examining the diffraction of X-rays through that flat target.
Therefore, a helix gets flattened into a sinusoid (below left):
approximation
of sinusoid
period, p
amplitude, A
(Left) A single sinusoid, and its approximation by lines.
(Right) Pattern of multiple identical sinusoids with random spacing.
A large number of molecules would act like a large number of sinusoids randomly stacked (above right).
We can approximate the sinusoids as slanted lines, as shown in the diagram.
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Lab 12 - DNA Diffraction
Physics 42 - Fall 2009
Pre-Lab Exercise
1.
Sketch the diffraction pattern produced by each target pattern, using the same scale for all patterns.
target
2.
target
target
Show that the slope of the line approximating a sinusoid is related to the ratio of amplitude to
period of the sinusoid, by |slope| = p/2πA.
Equipment
The simulated DNA diffraction studies use a helium-neon (HeNe ) laser, and a patterned target slide, much
like the single-slit diffraction lab performed earlier. The target slide has 12 different targets, each intended
to demonstrate an important feature relevant to DNA structure. The 12 targets are labeled A - L (below
left).
Institute for Chemical Education
C
D
E
F
G
H
I
J
K
L
C
B
I
A
Institute for
Chemical Education
This side
toward screen
target
laser slide
E
L
Side view
(Left) The target slide with 12 targets.
(Right) Setup for making the diffraction patterns.
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screen
Lab 12 - DNA Diffraction
Physics 42 - Fall 2009
Sideways view of slide targets.
Procedure
Orient the slide in the holder as shown in the Equipment section, above. The ICE lettering faces the laser,
the other side of the slide is labeled to be facing the screen.
1.
Look through the slide at white light. What do you see? What is the slide doing to produce this
image? Which color is bent the most? The least?
2.
Set up the laser, slide, and screen as shown.
3.
Shine the laser through the 12 different targets, and look quickly at each pattern, to get a feel for
the range of patterns we will be studying. Note that moving the slide slightly, or changing the
angle slightly, will clarify or blur the diffraction pattern. At each step below, adjust the slide for
the cleanest pattern you can reasonably get.
4.
Measure the distance from the slide (diffraction target) to the screen, L.
5.
Measure the spacing of the layer lines, s. The ratio of s/L will determine the size of the mock
DNA (the image on the slide).
6.
Targets A - C consists of short lines. Within each target, the lines are all at the same angle. For
each target, determine the angles of the lines (with uncertainties).
7.
Targets D, E, G, and H are sinusoids. Estimate the ratio of amplitude to period for each (without
uncertainties).
8.
Target J is the closest approximation to real DNA. Compare its diffraction pattern to that of Photo
51. Which layer line is missing from both patterns?
9.
A missing layer line suggests that the two helices in DNA are not equally spaced. Targets H, F, L,
and I have helices with offsets of 0/8, 2/8, 3/8, and 4/8 of a period, respectively. Which pattern
matches that of Photo 51 and target J?
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Lab 12 - DNA Diffraction
Physics 42 - Fall 2009
10. Look carefully at the diffraction pattern from target J. There is a feature of the pattern that has a
large period (many layer lines). Can you find it? [Hint: it appears as only two bright dots.] How
big is it (measured in layer lines)? How big is the corresponding molecular feature, compared to
the period of the helix? What molecular feature might account for this diffraction pattern feature?
Post-Lab Questions
Assume that your laser were really an X-ray source, with a wavelength of 0.054 nm. [The “Bohr radius” of
a hydrogen atom is 0.053 nm.]
1.
What is the period of the DNA helix?
2.
What is the width of the DNA helix?
3.
What is the offset of the two helices, in fractions of a period?
4.
What is the spacing of the base pairs (along the axis)?
Draw some conclusions on your own about things we didn’t specifically ask. Notice anything unusual?
Odd? Different? Unexpected?
References
[ICE] Institute for Chemical Education, Shanks, Kathleen editor, Simulating DNA Diffraction, University
of Wisconsin-Madison, 1999. ICE Pub. 99-001.
[Nob] The Nobel Prize in Physiology or Medicine 1962,
http://nobelprize.org/nobel_prizes/medicine/laureates/1962/index.html
[Say] Sayre, A., Rosalind Franklin and DNA, Norton, New York, 1975.
[Wat] Watson, J. D., The Double Helix, Atheneum, New York, 1968.
[WC1] Watson, J. D. & Crick, F. H. C., Nature 1953, vol. 171, p. 737.
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