Mesters

Macromolecular Crystallography Jeroen R. Mesters University of Lübeck

3-D structure methods Method

Principle

Needs

Resolution Molecular Weight

X-ray

diffraction from electrons

3D crystals

0.1 nm

NMR

spin transition

Neutron diffraction

diffraction from nuclei

Examples

107

protein virus ribosome

concentrated ? solution (inc. labels)

5·104

protein compounds

big 3D crystals

0.2 nm

107

protein

Electron diffraction Diffraction from electrons

2D crystals

0.3 nm

107

membraneprotein

Electron light microscopy microscope

intact particle

1.5 nm

„no limit“

cell-surface ribosome

Diffraction power 1:100:1000=electron:X-ray:neutron=thin→big sample

Why X-rays? •

Ernst Abbe (1840-1905), german mathematician and physicist, professor at Jena University, worked with Carl Zeiss. Developed modern microscope theory.

•

Abbe's law of limiting resolution: d = λ / (2·NA) (d: spacing, λ: wavelength and NA: limiting numerical aperture of objective, 1 if objective lens is large enough to capture the first-order diffraction): the minimal resolvable distance between two points depends on the wavelength of the light used, Dmin ≅ λ/2 (for visible light 4-8·10-7 m, Dmin ≅ 2·10-7 m)

C – C distance about 1.5 Ǻ Röntgen

Abbe

~105 eV → 0.4–2.5 Ǻ (λ = 12398/E [Ǻ]) 1Ǻ = 0.1 nm = 10-10 m

Why crystals? http://www-structure.llnl.gov/Xray/101index.html

One molecule

More ordered molecules

Very weak diffraction

More discrete diffraction

Historical hallmarks •

The diffraction of X-rays by crystals was first demonstrated by Friedrich, Knipping and von Laue (17 years after the discovery of X-rays by Röntgen in 1895): unknown at the time were the nature of both X-rays (particles or electromagnetic radiation) and crystals (internal periodicity or not).

•

The first small molecule structures of KCl, NaCl, KBr and KI in 1913 (Bragg).

•

First protein crystal (hemoglobin) in 1830, first recorded protein diffraction in 1934, DNA double helix structure in 1953 (Watson & Crick) and first protein structures of myoglobin (Kendrew) and hemoglobin (Perutz) in 1959.

•

Nobel Prices Röntgen 1901; Laue 1914; W. Bragg 1915; Watson & Crick 1962; Kendrew & Perutz 1962; Deisenhofer Huber & Michel 1988.

Crystal growing: all about tampering with the solubility of the protein (“cristallos“ = clear ice)

Solution Properties of Proteins Physicochemical properties: - surface properties → pI, post-translational modifications pH: - pH extremes – fold disruption - if pH = pI → solubility↓ Temperature: - class I – ↑ solubility with ↑ temp., most common - class II – little or no temperature effect - class III – ↓ solubility with ↑ temp. Miscellaneous: - buffers, salts, detergents, organic compounds - ligands, cofactors

Protein/Salt mixtures The Hofmeister Series (1888) Precipitating Power: Anions: sulphate > phosphate > acetate > citrate > chloride > nitrate >> chlorate > thiocyanate Cations:

Li+ > Na+ > K+ > NH4+ > Mg2+ Most stabilizing Salting out

> >

Most destabilizing Salting in

- Negative net charge collagenese (pI 4.1, set up pH 7.2) phosphate > sulfate > citrate > chloride (ammonium sulfate with some sodium chloride) - Positive net charge lysozyme (pI 9.5, set up pH 4.8) thiocyanate > nitrate > chloride > acatate > citrate (inversion of Hofmeister series!!)

Main Salt Classes Kosmotropes – strong H2O interactions water-structure makers singly- or multiply-charged ions high charge density SO42-, HPO42-, Mg2+, Ca2+, Li+, Na+, H+, OHChaotropes – weak H2O interactions water-structure breakers large, singly-charged ions low charge density SCN-, H2PO4-, HCO3-, I-, Cl-, NO3-, NH4+, Cs+, K+, (NH2)3C+ (guanidinium)

Chaotrope

Kosmo- and Chaotropes Prot

Prot

1st hydration shell (dense)

Bulk water

Prot Prot Kosmotropic effect • ordering the bulk water

- 1st hydration shell is ordered and dense (~20% denser than bulk water) - regions of high water density (low entropy) termed 'icebergs‘. - icebergs help maintain folded state - icebergs keep protein molecules separated from each other

Prot Prot Chaotropic effect • disordering hydration shell (melting the icebergs)

Protein solubility

Solubility diagram f([salt]) Salting in

Salting out

Inverse Salting in

[salt]

Protein solubility

Solubility diagram f(pH) ← Salts - PEG – Salts → Crystallization slot (!?) 1-2 pH units away from pI

pI pH

Phase Diagram [protein]

growth nucleation precipitation

soluble

labile zone metastable zone [precipitant]

[protein]

Concentrated Protein Solutions For NMR and Xtallography alike:

soluble [precipitant]

In order to prepare a highly concentrated solution that keeps the protein happy in solution, one needs to screen (!) for the best starting conditions with respect of the right buffer, pH and salt etc. There is no thing like „one buffer fits all“.

Trouble already starts at the level of cell disruption! ) sparse matrix screening

Crystallization methods • Vapor diffusion • Dialysis • Batch • Capillaries

Protein purity/concentration Naturally, both as high as possible but, sufficient amount left to screen with……. If concentration via centrifugation or dialysis („protein sticks to membrane“) does not work, immediately check for aggregation!

Precipitants Salts: (NH4)2SO4 NaCl K/Na-phophates Malonate/Tartrate Polymers: Poly-ethelene-glycol (different MW: 400 -20.000) Organic solvents: 2-Methyl-2,4-pentanediol Ethanol Acetone Buffers: Acetate Citrate Tris Hepes Cacodylate Detergents: ß-octylglycoside Triton-X100 LDAO Additives: EDTA Spermin MgCl2 ATP CaCl2 Zn-acetate Ligands Inhibitors etc.

Vapor diffusion

Phase diagram [protein]

growth precipitation

phase separation (oil droplets)

nucleation

soluble

spherulites labile zone metastable zone

[precipitant]

Vapor modification Oil layer: Al‘s oil or silicon oil

Speed of equilibration: -Salts fast (~2 days) -Polymers slow (4-7 days) Oils work best for salts Courtesy: JuanMa García-Ruiz, http://lec.ugr.es

Protein with or without sugars? • Glycosylation leads to heterogeneities • Deglycosylation (or expression in E. coli) often leads to inactivation 94 67 43 30 20 14,4

Garlic

12,5% SDS-PAGE Gel of the protein stock solution.

1

2

3

4

5

IEF-PAGE gel (pH 3-9) of protein stock solution and different crystals.

E. Bartholomeus Kuettner, Rolf Hilgenfeld and Manfred Weiss, J. Biol Chem. 277, 46402-46407.

H9

N328-A

N328-B

N276 K280* H6

H11

H11

H5

Y174

N146-A

H5

R169* K173*

S10

S10

N146-B

N146-A

A149

T148

Space group P212121 Resolution range 20 - 1.53 Å R factor of 19.3% (free 22.9%) Sugars (N146) involved in monomer-monomer contacts within the homodimer. E. Bartholomeus Kuettner, Rolf Hilgenfeld and Manfred Weiss, J. Biol Chem. 277, 46402-46407.

One more example PAP-S, isolated from the seeds of pokeweed, belongs to the family of the type-1 ribosome inactivating proteins (site specific depurination of the αsarcin/ricin loop in rRNA). Crystals of PAP-S were grown from a heterogeneous mixture of two isozymes, approximately 29 and 30 kDa.

pokeweed Tanis Hogg et al., Acta Cryst. D58, 1734-1739.

Space group I222 Resolution range 30 - 1.7 Å R factor of 18.1% (free 21.9%)

No less than two direct and two water-mediated hydrogen bonds are formed. Tanis Hogg et al., Acta Cryst. D58, 1734-1739.

Microdialysis(-button/-rod)

Easy to adjust/correct! Good idea to start with….

Phase diagram [protein]

growth nucleation precipitation labile zone metastable zone

soluble [precipitant] Remember, easy to adjust/correct! Good idea to start with….

(Micro-)batch under oil

Phase diagram [protein]

growth precipitation

phase separation (oil droplets)

nucleation

soluble

spherulites labile zone metastable zone

[precipitant] Only true for evaporating dropslets (silicon or Al‘s oil)

Membrane proteins under oil Oil has an advantage ….slowly absorbing the detergent thereby promoting crystal growth….

Capillary

gel Courtesy: JuanMa García-Ruiz, http://lec.ugr.es

Nail Polish

Precipitant + glycerol + heavy metals

Protein and low concentration agarose

Nail Polish

Crystal properties •

Mechanical, electrical and optical properties, symmetry, etc.

•

In general, a crystal is an anisotropic body with anisotropic properties like ist dielectrical constant, ist polarization and ist refraction index: Optical activity: triclinic, monoclinic and orthorhombic crystals polarize light along all axis trigonal, hexagonal and tertagonal crystals are isotrope // C cubic crystals are isotrope

•

Due to the high water content (30-80%), protein crystals can be soaked with heavy metal compounds and dyes, but also substrates (ribosome crystals with tRNA).

•

A protein crystal is soft whereas a salt crystal is „rock hard“ (needle test).

Salt or protein - Birefringence - IZIT - Needle test - Ultimately, X-ray diffraction

Crystal gallery

Beauty is only skin deep, appearances can be deceiving (big crystal, no diffraction) Micro- and macro-seeding for growing bigger crystals (cat whiskers) Epitactical growth of protein crystals on an amorphous surface

X-ray sources • Sealed tube • Rotating anode • Synchrotron

Sealed tube Cu anode

Ni-filter

X-rays

e-

M level

cathode

Kα1 1.54051 Å Kα2 1.54433 Å Kß

1.39217 Å

L level

1.54178 Å Ni-filter

Kα2 Kα1

Kß K level

Synchrotron X-rays

e-

Very intense light with tunable wavelenght

http://unisgi2.desy.de/x13.html

Diffraction Pattern

Interference of waves +

A

+

λ

=

2A

=

λ

„in phase“ (constructive) path difference = n·λ

„completely out of phase“ destructive interference path difference = (n+½)·λ

Bragg‘s law Path difference between waves 1 and 2 is equal to OA + OB. In the case of constructive interference, OA + OB = n·λ

1

θ

2

θ d A

B

O

Since OA = OB = d · sinθ it follows that (OA + OB =)

n·λ = 2d · sinθ Bragg‘s law

θ θ

Number of reflections How many reflections are possible at a given λ is equivalent to asking how many lattice points lie within the limiting sphere Volume of limiting sphere is 4/3 · π · r3 = 4/3 · π · (2/λ)3 (because r of limiting sphere is 2·r of reflection sphere) Number of reflections N = 4/3 · π · (2/λ)3 · 1/(reciprocal cell volume) N = 33.51 · (volume direct cell) / λ3 Example: P222 (1 r.l.p. per U.C.) with a = 150 Å, b=100 Å and c=40 Å λ= 1.54 Å ) λ= 0.80 Å )

N = 33.51 · 600000 / 3.6523 = 5.505.024 reflections N = 33.51 · 600000 / 0.512 = 39.269.531 reflections

Luckily, these are not all unique reflections and do not all need to be measured!

Generalised structure factor Fourier pair of equations: F(hkl) = V ∫x∫y∫z ρ(xyz) exp[2πi·(hx + ky + lz)]dxdydz ρ(xyz) = 1/V ∑h∑k∑l |F(hkl)| exp[-2πi·(hx + ky + lz) + iα(hkl)] y

y

Discrete

0

1

x

f(x0→1) = x1 + x2 +x3 + x4 + x5 = ∑x f(xn)

Continuous

x

f(x0→1) = ∫0→1 f(x)dx {the area under the function curve}

Information loss From our diffraction pattern we can determine the relative values of F(hkl) because they are proportional to I(hkl). However, we can not determine α(hkl)! Bad news, we can not calculate the structure immediately.

ρ(xyz) → I(hkl) → |F(hkl)|2 {no α(hkl)} ↑ The so-called „crystallographic phase problem“ can be solved by using some cleaver methodologies: MR, MIR, MAD, etc. Ihkl ≡ Io· λ3/ω · Vx · L · p · A/V2 · |Fhkl|2 (C.G. Darwin)

What can be calculated? • We can still calculate a Fourier summation with the intensities as coefficients and all αhkl equal to zero, e.g. a Patterson map. • P(uvw)

= 1/V·∑h∑k∑l |Fhkl|2·exp[-2πi·(hx+ky+lz)] = 1/V·∑h∑k∑l |Fhkl|2·cos[2π·(hx+ky+lz)] ≡ ∫v ρ(x,y,z) ρ(x+u,y+v,z+w) dV

* Note that eix = cos(x) + isin(x).

∫v ρ(x,y,z)ρ(x+u,y+v,z+w)dV Ori

(0.2 0.2)

P(uvw)

ρ(xyz) (0.1 0.5)

(0.5 0.5)

Consequences • Only interatomic vectors in real space show up as peaks in Patterson space since P(uvw) = ∫v ρ(x,y,z) ρ(x+u,y+v,z+w) dV. • The map of a real unit cell with N atoms will contain N2-N peaks in Patterson space outside the origen. Origin will contain N peaks. • Patterson maps contain an additional symmetry element (centrosymmetry). • In simple structures with a limited number of atoms, the atomic positions can be derived fairly straightforward.

Fph = Fp + Fh

MIR

Cosine rule c2 = a2 + b2 -2ab·cos(γ) cos(γ) = - (c2-a2-b2)/2·a·b

Fph

Fh

π−αh αh αp Fp αp

αph

γ = 180º + αp - αh

Harker construction |Fp|

|Fph1|

|Fph2|

cos(180º + αp – αh) = - cos (αp - αh) = - (|Fph |2 - |Fp |2 – |Fh |2) / 2·|Fp|·|Fh| αp= αh + arc cos(|Fph|2-|Fp|2-|Fh|2)/2(|Fp||Fh|) Two solutions for one derivative.

More derivatives will solve the ambiguous result!

Multi-wavelenght Anomalous Dispersion • Normal situation, |Fhkl| = |Fhkl| with αhkl = - αhkl • The most tightly bound electrons in atoms (atom specific, wavelength dependent) cause anomalous scattering of X-rays. From Sulfur onwards, a measurable effect occcurs that causes a difference in intensity in the Bijvoet pairs, |F+|2 and |F-|2. • For anomalously scattering atoms, |Fhkl| ≠ |Fhkl| with αhkl ≠ - αhkl • A synchrotron beamline with tunable wavelenght is needed.

Metals in crystallography Zn

λ=1.28Å 9661 eV CuKα

X-ray anomalous scattering

HK0 layer

X-ray anomalous scattering hkl ≠ hkl

About f‘ and f‘‘ eV

f‘

f‘‘

low

large

small

inflection

minimum large

peak

medium

maximum

high

large

medium

In principle, a 2-wavelength experiment should solve the phase problem.

Peak f‘‘ maximal Inflection point |f‘| maximal

Finale

May the crystal force be with you….. Thanks for your attention!

Rotspon Marzipan