X-ray Structure Determination

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X-ray Structure Determination

March 2013

[email protected]

1 Tuesday, March 19, 13

Slides are skipped if I’m doing a PDB evaluation lecture too.

Who am I?

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These are also perfectly out of phase, but they have different amplitudes

You can work out what happens when you add 2 waves of the same frequency, but different amplitudes and phases - takes some geometry. You get a new wave of the same frequency, new amplitude and phase.

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Phase difference = 2

π

r

.(

s-s

o

)/

λ

When an electron is hit by an electromagnetic wave, it will oscillate with the frequency of the wave. The oscillating electron will become a source of secondary rays in all directions.

These waves will have the same frequency; Thompson scattering The 2 waves have traveled different distances

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S

=(

s-s

o

)/

λ

Phase difference = 2

π

r

.

S

S =2sin(

θ

)/

λ

s

o

s

(

s-s

o

)

Allow

s

to rotate, what

is the surface of

(s-s

o

)

?

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s

0 is fixed in

direction

Let |

s

| = |

s

0 | = 1/

λ

s

sweeps over the

surface of a sphere

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Scattering from a group of atoms

F

(

S

) =

Σ

f

j

exp(2

π

i

r

j

.

S

)

S

is continuous

Group the electrons together -> atoms -> fj is the contribution from each atom

group the atoms together -> molecule

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What if there are 2?

F

(

S

) =

Σ

f

j

exp(2

π

i

r

j

.

S

)

F

(

S

) =

Σ

f

j

exp(2

π

i(

r

j+

δ

/2

).

S

) +

Σ

f

j

exp(2

π

i(

r

j-

δ

/2

).

S

)

= exp(

π

i

δ

.

S

)

Σ

f

j

exp(2

π

i

r

j

.

S

) +

exp(-

π

i

δ

.

S

)

Σ

f

j

exp(2

π

i(

r

j

.

S

)

= (exp(

π

i

δ

.

S

)+

exp(-

π

i

δ

.

S

) )

Σ

f

j

exp(2

π

i

r

j

.

S

)

= 2cos(

π

δ

.

S

)

Σ

f

j

exp(2

π

i

r

j

.

S

)

= (sin(2

π

δ

.

S

)/sin(

π

δ

.

S

))

Σ

f

j

exp(2

π

i

r

j

.

S

)

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What if there are N?

F

(

S

) =

Σ

f

j

exp(2

π

i

r

j

.

S

)

F

(

S

) = ...

= (sin(N

πδ

.

S

)/sin(

πδ

.

S

))

Σ

f

j

exp(2

π

i

r

j

.

S

)

Transform of

one object

Sampling

function

The transform of an object depends on the object (obviously).

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Plot of sinNy/siny

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13 Fourier Transform

Fourier Transform of single, multiple objects. Sampling as we make a 1D crystal

This is a computer exercise that we do in the crystallography course

So, we have an underlying transform that depends on a single object (a circle here), which then get sampled at a spacing that depends on the separation of the objects. The shape of the sampling gets ‘sharper’ as we get more repeating objects.

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14 Fourier Transform

Fourier Transform of single, multiple objects. Sampling as we make a 1D crystal

This is a computer exercise that we do in the crystallography course

So, we have an underlying transform that depends on a single object (a circle here), which then get sampled at a spacing that depends on the separation of the objects. The shape of the sampling gets ‘sharper’ as we get more repeating objects.

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15 Fourier Transform

Sampling as we make a 2D crystal

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1895 the discovery of X-rays

Crystallography is a mature science.

1830 32 point groups described

1850 the 14 (Bravais) lattices

1891 the derivation of the

230 space groups

1912 X-ray diffraction

Why continue studying it?

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2009

Ramakrishnan,

Steitz & Yonath

Why continue studying it?

Nobel Prize

2003 MacKinnon

1997 Walker

1988 Deisenhofer, Huber, Michel

1985 Hauptman, Karle

1982 Klug

1976 Lipscomb

1964 Hodgkin

1962 Perutz, Kendrew

1962 Crick, Watson, Wilkins

2006 Kornberg

2012 Lefkowitz

& Kobilka

X-ray crystallography is producing scientific results of great importance.

Robert Lefkowitz & Brian Kobilka "for studies of G-protein-coupled receptors". RSY - ribosome

Kornberg - molecular basis of eukaryotic transcription

MacKinnon - structural and mechanistic studies of ion channels

Walker -elucidation of the enzymatic mechanism underlying the synthesis of adenosine triphosphate (ATP) DHM reaction centre

H&K - direct methods

Klug - crystallographic electron microscopy and his structural elucidation of biologically important nucleic acid-protein complexes Lipscomb - structure of boranes illuminating problems of chemical bonding

Hodgkin - for her determinations by X-ray techniques of the structures of important biochemical substances - penicillin PK - hemoglobin & myoglobin

CWW - DNA structure

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Structure

Function

Drug discovery

Applications:

Designer enzymes

Structure is the key to Function. Applications are extensive.

The pictures are the active site of an enzyme, DXR, from M. tuberculosis (Henriksson et al, 2007). This enzyme is the target for an anti-malarial drug, fosmidomycin Are there any designer enzymes that you use? Washing powder: temperature and substrates (cellulases, lipases, proteases) (Proctor & Gamble)

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f (2stv = STNV) was solved by Lars Liljas, Torsten Unge and me. The 3rd virus structure to be solved, first to be refined, whole capsid in the asymmetric unit. Quite a job in 1982-3

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21 60046 entries on 090910

Electron crystallography Neutron diffraction Fiber diffraction FT-IR SAXS

76%

85%

14%

68840 entries on 101101

71516 entries on 110307

79521 entries on 120223

88325 entries on 130219

Still increasing, thru 60k autumn 2009, 70k New Year 2011

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PDB by

country

1

2

3

4

5

7

6

Sweden was beating Italy when I made this snapshot.

But Sweden is doomed to fall behind as the new superpowers ramp up their biotechnology.

How long before Sweden is overtaken by Singapore? Singapore has more crystallographers per sq. meter than any other country. These statistics are no longer easily available at the PDB

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Material

Crystals

Data Collection

Phasing

Model

Refinement

Publication

The Crystallographic Pipeline

DNA revolution ....

Nano-drops,

robotics

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CONSTRUCTS

AZ C-term

AZ N-term

DXR_1

DXR_2

DXR_4

DXR_3

DXR_5

DXR_6

No inhibitor so ....

cDNA CONSTRUCTS

Getting DXR crystals for drug discovery

DXR_4 construct gave crystals but the fosmidomycin inhibitor was not visible in the electron density map. However, we saw no density for a few residues at the C-terminus. The next construct _6, deleted them, material gave a new space group, we could see the anti-malarial drug bound to the M. tb enzyme

Pictures show the manganese iron at the active site, with protein side-chains to the ion, Lys to the phosphonate of the drug, Trp from the ‘lid’, and the NADPH co-factor. Surface is a volume to fill in potential new inhibitors.

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T-2 Phase diagram

Crystallization Phase Diagram

Make a

new crystal

Enlarge a crystal

- seeding

Crystal Phase Diagram.

Crystals are formed in the area labelled Nucleation

1 & 2 are vapour diffusion, 2 is a crystal that has been added after equilibration 3 is a microbatch experiment where a crystal is added to the sealed volume

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T-1 Vapor diffusion

Hanging drop, vapour

diffusion experiment

Use robotic liquid handling.

Hanging drop experiment - this is not rocket science,

The precipitant is at the bottom of the beaker (& usually mixed with the drop containing the protein). Slowly, as things equilibrate, small crystals can form, and grow,

Liquid handling systems have been developed to speed things up Robotic-optical systems to monitor crystal growth.

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Volumes ~300 nanoL

SInce 2004, we have had a simple liquid handling system (Douglas Instruments Oryx) for setting up droplets Why are small volumes good?

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Mosquito robot

Crystallization Hotel

& drop imager

Since end of 2012

Mosquito robot, 100nl+100nl volumes Disposable tips - no contamination Fast 96 well plate takes 2 minutes

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Seeding and the phase diagram

No

seeds added

Seeds

added

Small crystals can also be used to ‘seed’ bigger ones ‘Mighty oaks from little acorns grow’

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30 Protein

Crystals

Good, Bad & Ugly results

Sometimes the drop has a mixture of classes, example 1 (top left) where we have very thin needles (BAD) and one big crystal that is suitable for crystallographic work (GOOD)

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31 Home X-ray source

Radiation damage

For macromolecular crystals, crystallographers use copper anodes. Why?

The picture is the first 2D electronic detector we ever had, a multi-wire proportional counter made by an American company called Nicolet-Xentronics - Autumn 1987. Terese Bergfors and I sat on it for 2 months and solved our first structure with it on 13th Dec 1987, I missed Tonegawa’s Nobel lecture at the BMC.

The above crystal has had holes drilled through it by (more powerful) synchrotron x-ray beams.

It is not quite so dramatic usually, the crystal just looses the capacity to diffract the x-rays as the long range order breaks down. Why? Bonds broken, free radical produced, ...

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32 Synchrotron radiation

When high energy electrons or positrons travel around in a storage ring, they emit an enormous amount of x-radiation.

Unlike home source, they have a more continuous wavelength spread so you can build stations (beam-lines) that are ‘tuneable’ The bottom pictures are insertion devices, wigglers or undulators, which are even more powerful.

The x-ray beam can be orders of magnitude more intense than home sources. Some rings are dedicated to producing just X-rays.

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Brilliance &

wavelength

tuneability

Dedicated

ESRF

Paul Ellis (SLAC)

European Synchrotron Research Facility in Grenoble

Is there any point in producing such intense beams since the crystals will just get destroyed faster? Would have been useless without freezing - liquid nitrogen temperatures.

A snap-shot of PDB depositions.

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A DXR diffraction image, displayed with a computer program called Mosflm, runs on your laptop, but not your iPhone.

The x-ray camera is more or less the same as 30 years ago, but the detector is electronic, images are sucked into a computer and either processed interactively, or written to storage for taking home.

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Crystals have symmetry within the 3D unit cell and this repeats through space to make up the complete lattice.

The detailed positioning of different symmetry elements that get applied to the building block of the crystal defines the so-called space group Not all space groups are equally common

The computer software makes suggestions for the possible space groups during the processing N.B. macromolecules cannot be crystallized in space groups that have mirrors or inversions! Why?

The crystal building block does not necessarily correspond to a single molecule, it too can have symmetry.

BUT this symmetry is local - non-crystallographic symmetry - the insert is a ‘spherical’ virus (STNV) where the whole virus capsid is the so-called asymmetric unit. We collected the data at home, with film ...

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Material

Crystals

Data Collection

Phasing

Model

Refinement

Publication

The Crystallographic Pipeline

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FFT

Cat amplitudes,

Horse phases?

Fourier Transform

The x-ray diffraction pattern is a sampled, complex number, but we can only measure the amplitudes. How important are the phases?

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FFT

Cat amplitudes,

Horse phases?

Fourier Transform

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Material

Crystals

Data Collection

Phasing

Model

Refinement

Publication

The Crystallographic Pipeline

MIR/MIRAS

MAD

SAD

MolRepl

Phasing may be via experimental techniques, or by the molecular replacement method. • Max Perutz invented the MIR method

Wayne Hendrickson invented the SAD/MAD method

Experimental methods work by introducing new scattering into the asymmetric unit, either a heavy atom soaked into it, or by modifying how a particular atom interacts with the x-rays (by changing the wavelength)

• Michael Rossman, David Blow and Walter Hoppe are the fathers of the Molecular Replacement method. In this method, we use somebody else’s structure to solve ours.

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Phasing Statistics Today

Snapshot

May-July 2003

Paul Ellis, SLAC

Structural Genomics

MAD/SAD have taken over from MIR

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Phasing Statistics Today

Snapshot

May-July 2003

Paul Ellis, SLAC

Structural Genomics

MAD/SAD have taken over from MIR

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42 Molecular Replacement Method

Unknown

Known

This illustrates how we use a known structure (top cat, say), to solve the structure of the unknown, but related structure (an earless, tailless

variant)

The success of the method depends on the similarity of the 2 objects, for macromolecules we need an RMS on CA atoms of < 1.5Å, otherwise it

gets hard.

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P2 Myelin Protein (1988)

Founding members of 2 protein

families

Retinol Binding Protein (1984)

Here are founding members of 2 families of proteins that I worked on.

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0

1

2

3 RMSD

Search for similarity to 1CBS with Dali

(cellular retinoic acid binding protein, scores Z-sorted to RMSD=2.0)

P2 myelin is #67

RBP is #314

~180 in family

Liisa Holm

Hard to solve

Easy to solve

Here is a DB search for a member of the P2 family, cRABP

The family now has ~200 members, of which almost all have been solved by MR - like the family relationships linking the royal families of Europe

in the 1800-1900’s.

The results for the search start to merge the 2 families so RBP also pops up with other members of its family.

Dali is a structural similarity search program, available via a web server, developed by Prof. Liisa Holm.

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Search for similarity to 1CBS with Dali

(cellular retinoic acid binding protein, scores Z-sorted to RMSD=2.0)

P2 myelin is #67

~180 in family

Here is a DB search for a member of the P2 family, cRABP

The family now has ~200 members, of which almost all have been solved by MR - like the family relationships linking the royal families of Europe

in the 1800-1900’s.

The results for the search start to merge the 2 families so RBP also pops up with other members of its family.

Dali is a structural similarity search program, available via a web server, developed by Prof. Liisa Holm.

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Material

Crystals

Data Collection

Phasing

Model

Refinement

Publication

The Crystallographic Pipeline

The fun part of crystallography where you get to sample the fruits of your work. This is where I did some of the early research

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Myoglobin - the first protein structure to be solved & first atomic model, parts still exist in the Science Museum in London.

Bror Strandberg was a young Swedish post-doc who worked with John Kendrew at the end of the 1950s. Here he’s imitating an oxygen molecule One can see the haem, and a long helix on the right.

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Carbonic anhydrase, the first macromolecule to be solved in Sweden by Bror’s group. Bror came back to UU, and set up his group to do macromolecular crystallography.

Another young Swede went to Cambridge in 1961, Carl-Ivar Brändén, who returned, setting up his group at SLU. I was the first thing they shared, in 1979.

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Siemens 4004

PDP-11/VG3400

Frodo

1978

VG3400

This is the 2nd thing Calle & Bror shared.

I started working on graphics in 1976 at MPI for Biochemistry in Munich

This was one of the first computer graphics systems one could buy that was powerful enough Note the input devices. The big box is what we call a graphics card today

The computer (DEC PDP-11) had 64 kilo words of memory, but only 32k could be accessed at a time. You can also see the disks to the left (20 cm radius), they held 1.5 M words

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Cost?

This was a black and white vector drawing device Chicken wire contours of maps

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Skeletons

An alternative map representation.

A piece of string through space

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Jones & Thirup (1986)

A breakthrough paper.

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Material

Crystals

Data Collection

Phasing

Model

Refinement

Publication

The Crystallographic Pipeline

Validation

The first model ALWAYS has errors or is incomplete.

Fixing these problems is called crystallographic refinement

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Model Errors

What sorts of errors do

crystallographers make?

Every sort that can be made!

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It’s good to understand

what can go wrong

Complete trace incorrect

2ry structure recognized, could be wrong

direction

Incorrect connections between 2ry

structure units

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Rainbow colouring from N- to C-termini, red to blue Left as published, Right as corrected

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Secondary structure

elements maintained

Beware if you have a 3 A

poorly phased map

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Out of register error

Most common serious error

All

low resolutions start models will have

this sort of error

Usually a local error; 2 errors can bring

sequence back into register with the

density

Structure has been published where most

2ry structure elements were out of

register

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Out

of

register

errors

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Out of

register - most

common

serious error

Rest are

out of

register

OK

Structural

alignment

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Phasing errors

Resolution

Inexperience

Shortage of equipment

is no longer a problem

Main reasons for making

errors

Most errors can be

fixed during

refinement, but keep

the experimental map

Coupled

Can be treated

Macbook is enough

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64 Fourier Transform

Amplitudes

Phases

Current

model

Perfect

model

This illustrates how we use our current best model to phase, then look at maps to find errors or missing bits. In this case a tail of a cat called Pelle

(note he lacks ears too)

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65 Fourier Transform

This illustrates how we use our current best model to phase, then look at maps to find errors or missing bits. In this case a tail of a cat called Pelle

(note he lacks ears too)

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• The initial model tends to

• Lack bits that should be there (missing domains, loops, side

chains, ligands, water, …)

• Contain bits that shouldn’t be there

• Have bits that should be there but are in the wrong place

• In other words, the model contains random and systematic

errors

• Hence: the initial model is almost always inaccurate

and imprecise and incomplete

Why do we need refinement ?

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Refinement

Quality control

Rebuilding

Final model

Initial model

Biology

Iterate these steps

until the model is

as complete as the

data will allow and

no more

improvement can

be obtained by

further refinement

(“convergence”)

Retraction

Model improvement

Do papers have to me retracted? Some disasters have been made.

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Resolution

This illustrates that our cat becomes less clear as we get less data to make the reconstruction

This is at the heart of resolution

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Resolution

This illustrates that our cat becomes less clear as we get less data to make the reconstruction

This is at the heart of resolution

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