Nucleation and Crystal Growth

SPC1

July 2007, Hamburg

Jeroen R. Mesters

University of Lübeck, Germany

Flowchart

Protein Solution

Supersaturation

>> Nucleation <<

>> Crystal Growth <<

3D Crystal

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

Phase Diagram

[precipitant]

[pro

tein

]

soluble

labile zonemetastable zone

precipitation

spherulites

C > Ce

C < Ce

phase seperation

C >> Ce

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

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

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

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

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.

Cluster formation

Without precipitant With precipitant

Time, volume and concentration

dependent process

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

Threesome

Nucleation

Growth

Concentration

But, of course, the molecules must play along!

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.

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!!)

Electrolytes

Proteins (most proteins) are poly-electrolytes!P

rote

in s

olu

bil

ity

[salt]

Salting in Salting out

Inverse Salting in

pI and Salts

What is the pI of your protein,

and

what salt are you using and how much of it?

Lysozyme

Wrong salt?

50 to 200 mM sodium acetate!

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

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.

Phase diagram for lysozyme precipitated with 5% NaCl

Courtesy Jan Drenth

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

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

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

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

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?

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

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

Supersaturation and Temperature

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

Building blocks

Growth of the crystal

Crystal morphology and size

The END

..may the crystal force be with you..

thank you all for your patience and attention!