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Nucleation and Crystal Growth
SPC1
July 2007, Hamburg
Jeroen R. Mesters
University of Lübeck, Germany
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Flowchart
Protein Solution
Supersaturation
>> Nucleation <<
>> Crystal Growth <<
3D Crystal
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Solution
Solution:Liquid phase containing solute- and solvent-particles
Equilibrium concentration (Ce) or solubility:The concentration of solute in a solvent at equilibrium with undissolved solute,
at a given temperature and pressure.
Saturated solution: C = Ce
Supersaturated solution: C > Ce
Undersaturated solution: C < Ce
Crystal growth does not occur unless C > Ce
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Phase Diagram
[precipitant]
[pro
tein
]
soluble
labile zonemetastable zone
precipitation
spherulites
C > Ce
C < Ce
phase seperation
C >> Ce
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Nucleation is a phenomenon whereby a “nucleus”, such as a
dust particle, a tiny seed crystal, or more commonly in
protein crystallography, a small protein aggregate, starts a
crystallization process.
Nucleation can occur in the labile zone, a zone not
optimal for crystal growth!
Nucleation poses a large energy barrier, which is easier to
overcome at a higher level of supersaturation.
Nucleation
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Nucleation barrier energy
Surface energy contribution
Volume energy contribution
G* or nucleation barrier energy
Fre
e en
ergy
Cluster radius
Nucleation is a process
in which the first tiny
solid aggregates are
formed. Two types of
energy govern this
process:
1) Attraction
2) Surface
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The Kossel crystal: The growth unit displays six unsaturated bonds
located perpendicular to each face of the cube.
a =1a = 2
The cohesion of the cluster is proportional to the number de internal saturated
bonds versus the number of bonds facing towards the mother solution
Kossel Crystal
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G is proportional to the cluster’s volume, the
probability to disaggregate is proportional to the cluster’s surface.
1 6 *12 13
2 6 *22 23
3 6 *32 33
4 6 *42 43
5 6 *52 53
6 6 *62 63 critical size
7 6 *72 73
8 6 *82 83
9 6 *92 93
10 6 *102 103
a FS=6*a2 FA=a3
Critical size
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Addition of precipitant
If no precipitant has been added, the
protein molecules whirl around in the solution,
described by Brownian motion. The molecules
repel each other. The system is in equilibrium.
After addition of precipitant the protein
molecules more often form small groups
of loosely linked molecules. They attract each
other. The system is no longer in equilibrium.
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Cluster formation
Without precipitant With precipitant
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Time, volume and concentration
dependent process
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1. If supersaturation is too high, too many nuclei form,
hence a shower of tiny crystals will appear
2. Bad “nuclei” may stimulate formation of amorphous
precipitate
3. In supersaturated solutions that don’t experience
spontaneous nucleation, crystal growth often only occurs
in the presence of added nuclei or “seeds”
Common difficulties
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Threesome
Nucleation
Growth
Concentration
But, of course, the molecules must play along!
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Solution Properties of Proteins
Physicochemical properties:
- surface properties, shape
- 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.
Cosolvents:
-salts, polymers, alcohols, etc.
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Protein/Salt mixturesThe Hofmeister Series (1888)
Precipitating Power (negatively charged ovalbumin):
Anions: sulphate > phosphate > acetate > citrate > tartrate > bicarbonate
>chloride > nitrate >> chlorate > thiocyanate
Cations: Li+ > Na+ > K+ > NH4+ > Mg2+
Most stabilizing >> Most destabilizing
Salting out >> 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!!)
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Electrolytes
Proteins (most proteins) are poly-electrolytes!P
rote
in s
olu
bil
ity
[salt]
Salting in Salting out
Inverse Salting in
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pI and Salts
What is the pI of your protein,
and
what salt are you using and how much of it?
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Lysozyme
Wrong salt?
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50 to 200 mM sodium acetate!
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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!
Protein purity/concentration
HIV Pr crystals on dialysis membrane
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Cessation of growth
Caused by the development of growth defects or theapproach of the solution to equilibrium.
Mother liquor
The solution in which the crystal exists - this is oftennot the same as the original crystallization screeningsolution, but is instead the solution that exists after
some degree of vapor diffusion, equilibration throughdialysis, or evaporation.
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Phase diagram for lysozyme precipitated with 5% NaCl
Courtesy Jan Drenth
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Modern view on the nucleation
of proteins
• The small unstable aggregates of the classical theory arenot solid particles but are fluctuations in the proteinconcentration. Their amplitude increases gradually
• Locally, high regions of protein concentration are formed.Imagine these regions as minidroplets. If they reach asufficiently high concentration a real solid nucleus formsinside that minidroplet.
• Rapid nucleus formation is easy in a concentrated proteinsolution. It requires overcoming the surface energy andthat is low in a concentrated solution
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Phase separation curves for lysozyme
at three NaCl concentrations
• Phase separationdepends on the strengthof the interaction betweenthe protein molecules
• It is weak for 3% NaCland the curve is at a lowposition.
•
• It is strong for 7% NaCl;this curve is high in thediagram
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Fluctuations as oscillations
• Fluctuations express themselves as oscillations in the phase diagram
• When they reach the phase separation curve real phase separation happens in avery tiny volume (microdroplet). Nucleation follows very soon
• This can only happen below Tc
• Above Tc the fluctuations do not meet the phase separation curve; they have to goa long way before they are sufficiently large for nucleation. Nucleation above Tc isvery slow
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A Lysozyme experiment
• The induction time for
crystallization is plotted
as a function of the
temperature
• A sharp rise happens
near the critical
temperature Tc = 22.5 oC
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Optimal crystallization
conditions• Crystallize to the right
of the solubility curve
but not inside the
phase diagram curve
• The best conditions
are at the level of Tc
• How to determine Tc?
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Determination of an approximate value for Tc
If the induction time is extremely long one is above Tc
Action: Lower the temperature or move Tc upwards by increasing the precipitantconcentration
If crystals appear very fast one is below Tc
Action: Increase the temperature or move Tc downwards
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The other phase diagram
• The metastable zonecorresponds to the slowregion above Tc
• The nucleation zone is theregion below Tc to the left ofthe phase separation curve
• The precipitation zonecorresponds to the regioninside the phase separationcurve
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Supersaturation and Temperature
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Conclusions
• Precipitating agents transfer the protein solution from anunsaturated to a supersaturated state
• On the road to the crystalline state an intermediate stateis formed
• In this intermediate state fluctuations in the proteinconcentration grow
• When they reach a sufficiently high level nuclei form
• Above the critical temperature Tc of liquid/liquid phaseseparation this process takes a long time
• Below Tc the formation of nuclei is fast
• Optimal crystallization conditions are at the level of Tc
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Building blocks
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Growth of the crystal
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Crystal morphology and size
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The END
..may the crystal force be with you..
thank you all for your patience and attention!