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Phasing in Macromolecular Crystallography

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Transcript of Phasing in Macromolecular Crystallography
Phasing in Macromolecular Crystallography
What do we do with it now?
Phasing in Macromolecular Crystallography
How do we get from spots on a screen to a pretty picture of our protein?
Heidi’s Gun4 Data and Stucture
BY CALCULATING AMPLITUDES AND PHASES!!
Why Do We Care So Much About Phases?
Diffraction by Xrays
h = 1k = 2l = 0
yx
z dhkl
SOURCE
DETECTORΘ
Θ
k
k0
Bragg’s Lawnλ = 2dsinθ
Diffraction by Xrays
(h,k,l) = (2,1,0)
Crystal
k0
k
SOURCE
The Phase Problem
Φ
A PHASE DIFFERENCE!!
k0
k
Addition of Waves
+
+
f1
f2
f3
Fs
The Phase Problem
f1f2
f3
Fhkl
real axis
imaginary axis
Φhkl
The resulting wave that reaches the detector has a particular phase and amplitude that results from the addition of individual scattering factors from all the atoms in the unit cell, which each have their own phase and amplitude.
Fs = V ∑ fj[cos2π(hx + ky + lz) + isin2π(hx + ky + lz)]N
j=1
The Phase Problem
The Phase Problem:Each reflection we measure during the diffraction experiment tells us the amplitude of a particular Fs, but not its phase.
Addition of Waves
+
+
f1
f2
f3
Fs
Solving the Phase Problem• How do we figure
out the phase of Fs?– Combine Fs (or FP
here) with a wave of known phase (fH) to get a new resultant wave (FPH).
FP(unknown phase)
fH(known phase)
FPH(unknown phase)
+
FPH = FP + fH
Solving the Phase Problem:Harker Constructions
real axis
imaginary axis
FPH = FP + fH
fH
FPH FP
Hurray!! We’ve solved the phase problem!!Well, sort of… Now we actually have two phases to choose from.
Solving the Phase Problem
FPH = FP + fH
How do we actually figure out the amplitude and phase of fH?Amplitude: determined during the diffraction experimentPhase: determine the real space (x,y,z) location of “H” through the use of the Patterson Function
real axis
imaginary axis
fH
FPH FP
The Patterson Method
P(u,v,w) = 1/V ∑ Fhkl2cos2π(hu + kv + lw)h,k,l
The Patterson function is similar to the electron density equation in that they both use amplitudes measured during the diffraction experiment.
However, Patterson functions do not require phases to be computed, just the amplitudes of the (h,k,l) reflections
The Patterson MethodThe Patterson map provides a map of interatomic vectors within the unit cell and the peaks in a Patterson map are proportional to the electron density at a particular position.
12
3
REAL SPACE
12
13
21
23
3132
PATTERSON SPACE
The Patterson MethodThe Patterson function is especially useful
because of two important features:
1. The magnitude of P(u,v,w) is proportional to the product of the atomic numbers of the atoms at the ends of the vector u = (u,v,w).
2. The symmetry within a unit cell is imposed on the peaks in a Patterson map. This means that symmetry related atoms will also have a peak in the Patterson map.
Harker Sections
xz
y
180°(x,y,z)
(x,y,z)  (x,y,z)Should have a peak on the v=0 Harker section of the Patterson map.
= (2x,0,2z) = (u,v,w)
x = u/2, y = 0, z = w/2
(x,y,z)
Harker Sections
v = 0 Harker Section
x = u/2, y = 0, z = w/2(2x,0,2z) = (u,v,w)
Solving the Phase Problem
FPH = FP + fH
How do we actually figure out the amplitude and phase of fH?Amplitude: determined during the diffraction experimentPhase: determine the real space (x,y,z) location of “H” through the use of the Patterson Function
real axis
imaginary axis
fH
FPH FP
Methods for Determining Phases
• Isomorphous Replacement– Single Isomorphous Replacement (SIR)– Multiple Isomorphous Replacement (MIR)
• Anomalous Dispersion– Single WaveLength Anomalous Dispersion
(SAD)– Multiple WaveLength Anomalous Dispersion
(MAD)• Molecular Replacement• Direct Methods
Isomorphous Replacement• The Goal: Modify our crystal by
having it bind a heavy atom.• Why? A heavyatom derivative of
our crystal will create a change in the intensity of observed reflections relative to our native crystal.
Isomorphous Replacement• Why do we use heavy atoms?
– Because they have lots of electrons and scatter xrays more strongly.
N
H1/2
N
H
avg
2avg
ff
NN2I
ΔI NH = number of heavy atomsfH = heavy atom scattering powerNN = number of native atomsfN = avg. scattering power for native atoms
Isomorphous Replacement
f1f2
f3
FP
real axis
imaginary axis
Φhkl
f1f2
f3
FP
real axis
imaginary axis
Φhkl
fH
FPH
NATIVE HEAVYATOM DERIVATIVE
Isomorphous Replacement
f1f2
f3
FP
real axis
imaginary axis
Φhkl
fH
FPH
HEAVYATOM DERIVATIVE
Isomorphous Replacement• Why do we care about intensity
differences in the observed diffraction pattern?
P(u,v,w) = 1/V ∑ ΔF2cos2π(hu + kv + lw)h,k,l
The differences in intensity (ΔF = FPH – FP) can be used as coefficients for the Patterson Function.This is useful because our Patterson Maps and Harker Sections are now giving us information about the locations of our heavyatom derivatives. THIS IS REALLY IMPORTANT!!
Heavy Atoms in Isomorphous Replacement
• How do we make derivatives of our crystal?– Trial and error: add a small amount of the metal
reagent (0.110 mM) to the crystallization condition and soak the crystal (seconds, minutes, hours, days)
Common Heavy MetalsPlatinum Potassium Thiocyanate
Gold CyanidePotassium Tetrachloro Platinate
Thimerasol
Amino Acid LigandsHis (pH>7), Lys (pH>9)
Cys, His (pH>7), Lys (pH>9)Cystines, His (pH>7)
Cys, His (pH>7)
And many more…
Detecting Derivatives• Unfortunately, like most things in
crystallography, just about everything is a variable when trying to get a derivative.– So how do we know when we’ve gotten a
derivative?– Answer: Look for differences in spot
intensity between native and potential derivative crystals, especially at low resolution where heavy atom differences will be strongest
Detecting Derivatives• It must take a long time to find a
derivative!!!Fortunately, we don’t have to collect a full dataset for each derivative
Scaling a few images of a derivative dataset against a native dataset is enough to detect differences in intensity
Detecting Derivatives• First things first: A derivative crystal
should be different than the native crystal.
Detecting DerivativesUse Scalepack to scale a native dataset against a few images (~3°) of a potential derivative
When derivative and native crystals are scaled together, the Χ2 value should be >1.Assuming the cell parameters look good,
If Χ2 is…~50, probably not a derivative (nonisomorphous, wrong indexing, or way too many substitutions)
~10, good chance that you have a derivative
~25, well…I would keep looking for derivatives, but keep this one in mind
1, scales well with native so you’ve probably got a native crystal (no heavyatom substitution)
Isomorphous Replacement:The Good and the Bad
The GoodCan be quick since data collection can be done at homeWorks well for proteins purified from sources other than E. coli (e.g. yeast)Don’t need high quality data (low resolution is okay)
The BadGetting a derivative in the first place is not trivialGetting a derivative crystal that’s isomorphous can be difficultData quality can be poor
The Reality of Isomorphous Replacement
FP
real axis
imaginary axis
Φhkl fH
FPH
FPH = FP + fH
The Reality of Isomorphous Replacement
In reality, there’s some error in our measurement of FPH and the location of the heavy atoms
FP
real axis
imaginary axis
Φhkl fH
FPH,obs
FPH ≈ FP + fH
ε FPH,calc
ε = FPH,obs – FPH,calc
ε = lack of closure
The Reality of Isomorphous Replacment
Harker Construction of a single reflection from an SIR experiment
Phase ProbabilityP(α) = exp{ε2(α)/2E2}
Best Phaseαbest = ∫αP(α)dα
Figure of Meritm = ∫P(α)exp(iα)dα/∫P(α)dα
m = 1, no phase errorm = 0.5, ~60° phase error
m = 0, all phases equally probablyMinimize the phase error by using the centroid of the phase distribution (Best Phase).
The Reality of Isomorphous Replacement
By using multiple heavy atom derivatives, we can get a better estimate of the correct phase
This is Multiple Isomorphous Replacement (MIR)
The Reality of Isomorphous Replacment
SIR MIR
Anomalous Dispersion Techniques
What is Anomalous Dispersion?
A phenomenon which occurs when electrons absorb and reemit Xrays having an energy close to that of the electron’s nuclear binding energy.
What’s the result of this absorption?
The xray’s reemitted have the same wavelength as the incident radiation, but now are phase shifted by 90°.
Effects of Anomalous Dispersion
Radiation scattered by an atom is actually composed of two components:
1. “Normal” Thompson scattering (no phase change relative to incident radiation)
2. A minor anomalous component phase shifted by π/2
f(λ) = f0 + Δf'(λ) + if''(λ) = f'(λ) + if''(λ)
FPH+
FPH
fH+
fH
FP+
FP
F+ = F Friedel’s Law
fH+
fH
FP+
FP
FPH+
FPH
f''
f''
F+ = F Breakdown in Friedel’s Law
Bijvoet Differences(That’s Bifoot)
Wavelength Dependence ofAnomalous Dispersion
Anomalous Signal Increases With Scattering Angle
Using Anomalous Dispersion to Solve the Phase Problem: MAD
P(u,v,w) = 1/V ∑ (F+  F)2cos2π(hu + kv + lw)h,k,l
Choosing Appropriate Wavelengths
Peak(f'')
Inflection (f')
Remote
MAD Requirements• Strong anomalous signal (at least 1
Se per 17 kDa of protein)• Tunable xray source (synchrotron)• Preferably the ability to measure the
absorbance spectrum of your protein• High solvent content• Best data possible high resolution
and low Rmerge
Single Wavelength Anamalous Dispersion (SAD)
Solve the phase ambiguity by evaluating the quality of the maps for both solutions using density modification programs.
Basic Requirements:•Strong anomalous signal (usually at least 1 Se per 17 kDa of protein)•As usual, best data possible (resolution and error)•High solvent content (>50%)•Accurate measurement of phasing errors
Sulfur Anomalous Phasing
Sulfur Anomalous Phasing
Sulfur Anomalous Phasing
Ramagopal et al. Acta Cryst. (2003) D59, 10201027
Detecting Anomalous Signals
1. Using Scalepack, scale data as normal, except turn on the ANOMALOUS flag (writes out F+ and F separately in a .sca file).
2. Rescale this .sca file, but this time with the anomalous flag turned off. This compares F+ and F.
3. Examine the X2 values. Presence of an anomalous signal should give X2 > 1 (or could indicate absorption or detector problems). Useful for also examining the resolution cutoff of the anomalous signal.
The Good and the Bad of MAD/SAD Structure
Determination• Essentially eliminate the isomorphism problems of
SIR/MIR. Generally better phases.• Ability to use molecular biology to derivatize your
protein (SeMet).– May also be able to use naturally bound anomalous scatters
(Zn, Fe, Ca, etc.)• Usually need to go to synchrotron
– However, there’s often an anomalous signal with CuKα; could be useful in SIRAS/MIRAS methods.
• The potential of sulfur anomalous phasing essentially eliminates the need to derivatize your protein– Method can be limited to especially good data
• Due to availability of synchrotron resources, anomalous phasing is the primary method of choice for phasing
Calculation of Protein Phases
After solving the real space location of the heavy atom through isomorphous or anomalous difference Patterson’s, determine the protein phases:
•Refine the xyz coordinates of the heavy atom through cycles of refining the occupancy and Bfactor•Determine the protein phases from the refined heavy atom coordinates and refine these phases•Look at the initial map and see how you did•Then go and talk to Devin to see where to go from here
•Programs that can do these steps include PHASES and MLPHARE (available in the CCP4 package)
Automated Methods: SOLVEFortunately, there are automated processes available to do everything from scaling data, solving the location of heavy atoms, and determining protein phases. One such program is SOLVE.
Works by converting each decision making step into an optimization problem through scoring and ranking of possible solutions
1. Locate and refine heavy atom sites through difference Patterson’s or direct methods and generate phases. Converts MAD data to pseudoSIRAS.
2. Score potential heavy atom sites by four criteria:A. Agreement between calculated and observed Patterson
mapsB. Crossvalidation of the heavyatom sites through
difference Fourier analysis delete a site in a solution and recalculate phases
C. Figure of Merit (m)D. Nonrandomness of the electron density map identify
solvent and protein regions and score based on connectivity in solvent and protein region.
Tutorial
Use Heidi’s Gun4 MAD data to calculate and analyze Patterson Maps and Harker Sections to determine the real space coordinates of the Selenium within the structure.