284 7.5  Making Crystals

Indeed, the trick for obtaining homogeneous crystals as opposed to amorphous

precipitated protein is to span the metastable zone between supersaturation and undersatur­

ation by making gradual changes to the effective precipitant concentration. For example,

crystals can be simply formed using a solvent evaporation method, which results in very

gradual increases in precipitant concentration due to the evaporation of solvent (usually

water) from the solution. Other popular methods include slow cooling of the saturated solu­

tion, convection heat flow in the sample, and sublimation methods under vacuum. The most

common techniques, however, are vapor diffusion methods.

Two popular types of vapor diffusion techniques used are sitting drop and hanging drop

methods. In both methods, a solution of precipitant and concentrated but undersaturated

protein is present in a droplet inside a closed microwell chamber. The chamber also contains

a larger reservoir consisting of a precipitant at higher concentration than the droplet but no

protein, and the two methods only essentially differ in the orientation of the protein droplet

relative to the reservoir (in the hanging drop method the droplet is directly above the reser­

voir, in the sitting drop method it is shifted to the side). Water evaporated from the droplet is

absorbed into the reservoir, resulting in a gradual increase in the protein concentration of the

droplet, ultimately to supersaturation levels.

The physical principles of these crystallization methods are all similar; in terms of the

phase diagram, a typical initial position in the crystallization process is indicated by point

I on the phase diagram. Then, due to water evaporation from the solution, the position of

the phase diagram will translate gradually to point II in the supersaturation zone just above

the metastable zone. If the temperature and pH conditions are optimal, then a crystal may

nucleate at this point. Further evaporation causes crystal growth and translation on the phase

diagram to point III on the saturation curve. At this point, any further water evaporation then

potentially results in translation back up the phase transition boundary curve to the supersat­

uration point IV, which again may result in further crystal nucleation and additional crystal

growth. Nucleation may also be seeded by particulate contaminants in the solution, which

ultimately results in multiple nucleation sites with each resultant crystal being smaller than

were a single nucleation site present. Thus, solution and sample vessel cleanliness are also

essential for generating large crystals. Similarly, mechanical vibration and air disturbances

can result in detrimental multiple nucleation sites. But the rule of thumb with crystal forma­

tion is that any changes to physical and chemical conditions in seeding and growing crystals

should be made slowly—​although some proteins can crystallize after only a few minutes,

most research grade protein crystals require several months to grow, sometimes over a year.

Nucleation can be modeled as two processes of primary nucleation and secondary nucle­

ation. Primary nucleation is the initial formation such that no other crystals influence the

process (because either they are not present or they are too far away). The rate B of primary

nucleation can be modeled empirically as

(7.2)

B

N

t

k

C

C

n

sat

n

1 ⁼

=

−

(

)

d

d

where

B1 is the number of crystal nuclei formed per unit volume per unit time

N is the number of crystal nuclei per unit volume

kn is a rate constant (an on-​rate)

C is the solute concentration

Csat is the solute concentration at saturation

n is an empirically determined exponent typically in the range 3–​4, though it can be as

high as ~10

The secondary nucleation process is more complex and is dependent on the presence of

other nearby crystal nuclei whose separation is small enough to influence the kinetics of fur­

ther crystal growth. Effects such as fluid shear are important here, as are collisions between

preexisting crystals. This process can be modeled empirically as