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The Miers diagram18 (Figure 1.10), was traditionally used by crystal growers to illustrate the effects of temperature on crystallization. The diagram is divided into 3 regions
1) The stable zone, an area where protein solubility is may be termed undersaturated.
2) The metastable zone, where protein concentration is greater than the solubility limit. Existing crystals may grow within this zone but generally no crystal nucleation occurs here.
3) The labile zone, where supersaturation is high and spontaneous nucleation and a small amount of crystal growth can occur.
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Figure 1.10 The Miers diagram indicating three main zones on the temperature/protein phase diagram. Figure from ref. 18
A more generic phase diagram for protein crystallization studies exists22. The generic diagram is shown in Figure 1.11. By adding various precipitants19 (for example ammonium sulphate, ethanol or polyethylene gycol), as one usually does when crystallizing a protein, the extent of the anisotropic short range protein-protein
interactions are be altered19, 28. As a result, zone widths and zone boundaries, as indicated in Figure 1.11 may also be altered. The alteration is due to the nature of the precipitant and cannot be predicted easily22.
Figure 1.11 Generic phase diagram proposed by Muschol22 and co-workers. Panel (a) indicates a phase
diagram for proteins with conventional solubility behaviour. Panel (b) indicates phase diagram for proteins with retrograde solubility. Solution conditions above the solubility curve in (a) and below the solubility curve in (b) are metastable with respect to crystallization. Zone II indicates an area of liquid-liquid phase
separation. Gelation is common in Zone III and indicative of very high protein concentrations. Cross hatched area on the border between Zone I and Zone III is an area of amorphous precipitate formation. The best position for protein crystallization is in Zone I, just outside the cross hatched area and near Zone II19, 28.
Figure taken from ref.22
A phase diagram which is of more practical utility is a protein/precipitant phase diagram, elucidated at constant temperature (Figure 1.12). Again the three main zones are indicated on this phase diagram.
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Figure 1.12 The lysozyme/NaCl phase diagram at pH 4.5 taken from Iwai and co-workers44. An arbitrary
solution starting condition is indicated by a red-dot on the diagram. Figure taken and adapted from ref.44
Within this thesis and Chapter 2 in particular, we have made extensive use of lysozyme-NaCl phase diagrams compiled by Iwai et al.44. This diagram was compiled by crystallizing lysozyme over a wide range of different pH conditions. Specifically, the phase diagrams were compiled using crystals grown via the dialysis method, using a 50 µl micro-dialysis button with a membrane which had a cut-off weight of 1000 Daltons.
The borderline between the metastable and the nucleation zone was determined in the following way. The concentration of precipitant (in this case NaCl) was increased incrementally in steps of 0.1 (w/v) % for a specific protein concentration at a specific pH. With each incremental step, the solution was left for a period of 8 days at 293 K.
Solutions were checked to see if any crystallization had occurred. If a crystallization event was indeed observed, a point was thus marked on the diagram which gave the corresponding precipitant and protein concentrations (at a specific pH) which led to the crystallization event. The borderline between the metastable zone and the nucleation zone was thus compiled by joining these points on the diagram as shown in Figure 1.12.
The solubility curve was determined by dissolving previously grown crystals within a dialysis button. Specifically, precipitant concentrations were decreased in increments of 0.1 (w/v) % per day. At the end of each day, an observation was made to see if crystals had completely dissolved. If complete dissolution had occurred, a point was marked on the lysozyme-NaCl diagram. If complete dissolution had not occurred, the precipitant concentration was further lowered by 0.1 (w/v) % and the process continued until complete dissolution was achieved. The solubility curve (at different pH) was compiled by joining the points on the phase diagram.
Based on 3 years of experimental experience with lysozyme crystallization in the presence of NaCl under ‘batch’ type conditions, and by using bulk solution conditions (of the type featured within Chapter 2), we have found these phase diagrams (Figure 1.12) to have reasonable accuracy with regards the prediction of a crystallization and a non- crystallization event. Specifically, we have found that under ‘crystallizing’ conditions (such as those found within the nucleation zone at a particular pH) a crystallization event would occur within a 1-4 hour time period (depending on level of supersaturation). At higher levels of supersaturation one can achieve lysozyme crystallization within as little as 45 minutes. Under non-crystallizing conditions (such as those depicted within the metastable zone in Figure 1.12) no crystallization event would be achieved during a 1-4 hour period.
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Figure 1.13A lysozyme-NaCl diagram compiled at pH 4.2 and 20 degrees Celsius, with a temporal element. The figure has been taken from ref. 45. Lines A and B refer to ‘paths’ taken across the diagram via dialysis and vapour diffusion crystallization experiments respectively. Times to lysozyme crystallization at various
lysozyme-NaCl compositions are indicated on the phase diagram.
These experience-based observations can be corroborated via reference to a ‘temporal’ lysozyme-NaCl diagram45 (Figure 1.13). One notes that on this diagram at pH 4.2 and using crystallization conditions of the type found within Chapter 2, lysozyme crystallization may be achieved after an approximately a 1 to 6 hour period.
For a complete picture of the entire lysozyme crystallization process, which would incorporate all reasonable protein and precipitant concentrations at different pH values, one would need an impossible-to-visualize multi-dimensional plot (4 dimensions
minimum). This type of plot has never been compiled and is not currently in existence. In fact a suggestion in this regard was made at a recent international conference on
macromolecular crystallization. The suggestion was unfortunately met by derisory laughter.
In terms of the relevance of these types of diagrams to experimental work presented within this thesis, they are currently of high relevance. This is mostly due to the fact that these types of diagrams are not easily available or have never been compiled at all. Therefore this is all there is to go on at present. More sophisticated and efficient compilation of such diagrams would require a dedicated experimental set-up with robotic assistance.