The relevance of small molecule crystal growth theories and techniques to the growth of biological macromolecules

Journal of Crystal Growth 90 (1988) 1—13 North-Holland, Amsterdam

1

THE RELEVANCE OF SMALL MOLECULE CRYSTAL GROWTH THEORIES AND TECHNIQUES TO THE GROWTH OF BIOLOGICAL MACROMOLECULES Robert S. FEIGELSON Center for Materials Research, 105 McCullough Building. Stanford University, Stanford, California 94305-4045, USA

Received 7 January 1988; manuscript received in final form 3 February

Over the past 40 years scientists and engineers working on the crystal growth of small molecule materials have developed a strong theoretical background and an impressive array of crystal growth technologies to aid in the growth of a wide variety of materials having extremely diverse properties. One of the major issues brought up at the First International Conference on Protein Crystal Growth at Stanford University in August 1985 was whether these pre-existing theories and techniques would be applicable to the crystal growth of biologically active macromolecules such as proteins. This lecture explores some of the similarities and differences between the properties of small and large molecule materials and their growth behavior, and looks for any common denominators which may exist and how they can serve as a bridge between the two fields to help facilitate cross-fertilization.

1. Introduction In its broadest sense, the field of crystal growth includes in addition to the growth of crystals, studies on the theoretical aspects of crystallization phenomena and also the characterization of the crystals produced. Theoretical investigations involve studies of the relationship between growth parameters, growth behavior and crystal properties including growth rate studies, heat and mass transport phenomina, interface stability and morphological effects, segregation behavior, etc. Characterization includes structural and compositional analysis and an evaluation of the physical-chemical properties of interest and how crystalline defects effect these properties and growth behavior, The history of small molecule crystal growth dates back more than a thousand years [1]. However, it was not until the middle of the sixteenth century that serious attempts to understand crystallization phenomena were made [2]. Over the intervening period, particularly the last 40 years, a large body of both practical and theoretical knowledge has been developed covering a wide variety of materials having diverse properties. By comparison, the growth of biological macromolecules started only very recently, mostly during the

last decade, although a protein was first separated by a process that probably yielded crystals as far back as 1880 [3]. The recent acceleration of effort in the field of protein crystal growth has been driven by a very strong need to understand their crystal structures for medical and pharmaceutical applications. Because the preparation of large, high quality single crystal samples of many of these materials has been very difficult to achieve, it has now become very important to understand the mechanisms by which biological entities crystallize so that effective growth techniques can be developed. One of the major problems that faces scientists and engineers who are trying to grow large (mmsized) biological macromolecule crystals is the lack of thermodynamic, kinetic and material property data necessary for designing successful growth experiments. This is understandable since the primary goal of biological crystallization research efforts to date has been directed toward obtaining molecular structure information. However, an understanding of how crystals grow and how the properties of the crystal may affect their growth and perfection can lead to better, more reliable, growth techniques for materials which are difficult to prepare in the form of large high quality crystals.

0022-0248/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

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Relevance of small molecule crystal growth theories

The work of Schlictkrull [4], Bunn et al. [5], and Fiddis et al. [6] represents the earliest attempts to understand the mechanisms involved in protein crystallization, The First International Conference on Protein Crystal Growth at Stanford University [7] was the first formal meeting between small molecule crystal growers and the biological macromolecule community. One of the major issues that was raised at this conference was whether the body of knowledge developed in the small molecule field could be applied to the crystal growth of biological macromolecules. This paper explores this issue, including some of the similarities and differences that exist between small and large molecule materials and their growth behavior. The common denominators which exist will be discussed and it is hoped that they will help form a bridge between the two communities to further cross-fertilization. The discussion emphasizes the need to separate, both conceptually and experimentally, the nucleation and growth phases of crystal growth processes in order to facilitate the growth of crystals suitable for their intended applications.

2. Crystal growth methods No matter what the type of material being crystallized, crystal growers have a common interest in preparing crystals of the highest possible quality as rapidly as possible and with the re-

quired size and properties needed for the intended applications. Crystal growth methods can be broadly categorized by the types of phases undergoing transformation during growth as follows: solid solid vapor solid —*

-~

liquid (melts or solutions) solid. The choice depends on the properties of the materials involved. For biological or protein crystallization, the choice is limited to liquid solid transformations, where the liquid phase is usually an aqueous solution since the materials decompose at elevated temperatures and contain a large volume fraction of H 20. The growth temperatures used are usually less than 500 C. The basic generic methods for growing small molecule crystals from solution are listed in table 1. Aqueous solution growth methods have been described by Buckley [8], Brice [9], James and Kell [10] and Mullin [11].The methods involving growth by changing temperature, fluid transport at constant temperature, or the use of temperature/ composition gradients have not yet been applied —*

—~

to the growth of biological macromolecules. With the exception of hydrothermal growth which is usually done at temperatures greater than 500 C, all of them are potentially applicable to biological materials. To date the most widely applied method for protein growth is the vapor diffusion technique, a variation of the controlled evaporation method (table 1, 2b) which utilizes a hanging or sitting

Table I Basic solution growth methods Method

Relevant material properties

1. Temperature change

High solubility, large temperature

2. (ralsing Constantortemperature lowering) coefficient of solubility (+ or

b. Controlled a. Fluid transport evaporation c. Temperature/ composition gradient method 3. Gel growth 4. Hydrothermal

GLASS

—)

coefficient of solubility (+ or —) Low solubility, High solubility,small large temperature temperature coefficient of solubility (+ or —) Low solubility and/or heat sensitive

SPOT

MI CRODROPLETS

PLATE

VACUUM

~

—

/

~Ic

Low solubility and/or heat sensitive Solubiity increased under pressure

SANDwICH

PETRI DISH HALF

Fig. 1. Schematic illustration of protein the vapor diffusion method commonly used for growth.

R. S. Feigelson

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3

Relevance of small molecule crystal growth theories

CONC. CONC. CONC.—~

CaC1~

2

TARTARIC ACID

SOLUTION

•

w

~ ~Tc~ I

-

/~~

Cl)

6

* :-:-:-:-:-:-~-

— --

CRYSTAL GROWTH

~

4~---.

GEL CONTAINING CONC. WEAR TARTARIC ACID

:-: -—

-.-

\

:—:....~

(a)

—

—

(b)

DISTANCE

—~

Fig. 2. Illustration of two geometries used for the gel growth of calcium tartrate crystals by the reaction H 2C406(tartaric acid) +CaC12 silica CaC4O6(s) + 2 HC1. From Laudise [12].

drop (fig. 1). The gel growth method which is illustrated in fig. 2 [12] has also been applied to biological macromolecules, but only in a few cases [13—15].Dialysis techniques have been more widely contact thermometer for control

expanded polystyrene

~

____________

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2 xl5W lamps

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______

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,—~

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15Cm crystallizing dish contaIning 4 seeds and 500 ml of SolutIon Fig. 3. Growth by slow evaporation using a simple constant temperature control system. Evaporation rates can be varied by adjusting the temperature or the amount of solution surface exposed (dishes can be partially covered). From Brice [9].

used and can be thought of as a special case of gel growth. Growth by changing temperature has rarely if ever been used because of the widespread belief that protein solutions have zero temperature coefficients of solubility. Figs. 3 and 4 show two simple types of crystallization methods used for the growth of small molecule crystals. Both rely on the thermally controlled evaporation of the solvent medium. A number of other methods are also available which aim to provide enough supersaturation in the solution to drive the crystallization process. By cornparison, the most widely used method for the crystallization of macromolecules involves the equilibration of the chemical potential of a precipitating agent in the drop, and in a reservoir which is in vapor equilibrium with the drop. This points out a significant difference between small and large molecule evaporation techniques which are in current use for crystal growth. The crystallization of small molecule matenals by evaporation relies on exceeding the solubility limit of the crystallizing species whereas the crystallization of macromolecules often utilizes both the increase in .

.

.

.

.

4

R.S. Feigelson

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Relevance of small molecule crystal growth theories

stirring mechanism

gasket

nutrient

water

_______

0- ring — seal co~ed

--—-

Illillil/~ ---.

_______ ~porous

TS. --

..—plugs

Cl

_______

~~er

1

L

-seed

resistance heater embedded in silicone rubber

Fig. 4. A common aqueous growth system using the evaporation method for growing small molecule crystals. Seed crystals are mounted on a fixture which is rotated (usually alternately clockwise and counterclockwise) to Stir the solution. Holes in the top plate can be used to control the evaporation rate or as shown, a water cooled coil can be used to condense the solvent which can be collected outside the growth system and used to measure the rate of evaporation. From Brice [9].

concentration of the crystallizing species and the interaction of that species with the increased concentration of a precipitating agent. Figs. 5 and 6 illustrate two other types of crystal growth methods, one involving the use of fluid transport at constant temperature and the other temperature or composition gradients. These methods rely on the temperature coefficient of solubility to provide the driving force for crystallization. Since temperature can be easily controlled

Fig. 6. The temperature gradient growth method. The nutrient is usually held at a higher temperature, the seed crystal at a lower temperature. Since the material is more soluble at the higher temperature, mass transport in the resultant concentration gradient gives nse to growth. From Brice [9].

[16], there are significant advantages to be gained by the use of these techniques. 3. Similarities and dissimilarities between small and large molecule materials Some important factors which affect the number of crystals formed during the solution growth process, their size, quality, growth morphology. and structure are given in table 2. With the exception of gravity, which we have only relatively recently been able to study, the other factors have

nutrient in porous bag

Stirrer Oto~

Table 2 Some important parameters influencing crystal growth —

r ysta

I

—

Supersaturation Concentration of impurities and additives (H

~.

ppt agents.

etc.)

II~ ____________

-

I I

I

-coii heating

Fig. 5. A two-bath crystallizer using fluid flow to bring nutrient at one temperature ( — 42°C for KDP) to the growing crystal at a different temperature ( — 35°C for KDP). From Brice [9].

— Fluid Solution Temperature flow temperature (natural and concentration and andforced coefficient convection gradients of solubility effect both heat —

—

— —

and mass transport) Interface attachment kinetics Surface and bulk diffusion Gravity (sedimentation, fluid flow)

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Relevance of small molecule crystal growth theories

Table 3 Areas where small and large molecule materials are similar _____________________________________________________ 1. Obey the fundamental laws of thermodynamics 2. Belong to the same crystal classes 3. Crystals form by a nucleation process 4. Growth rate varies with process conditions 5. Supersaturation is the driving force for nucleation and growth 6. Crystals have morphologies (habits) determined by atomic or molecular structure and by growth conditions

7. Habit or morphology can be modified by varying processing conditions and/or impurities or change in crystal structure (polymorphism)

been thoroughly investigated, both on an experimental and on a theoretical basis for small molecules. While an assessment of the influence of these various factors on the growth of biological materials has not yet been investigated in depth, it would be surprising, as we will see below, if there were radical differences between the behavior of these two classes of materials. In tables 3 and 4 some of the factors which are important to crystal growth are listed. They have been grouped according to whether they are expected to exhibit similar or dissimilar behavior in macromolecular systems. The most important facTable 4 Areas where large and small molecular materials differ _____________________________________________________

Differences

1. System size

Small molecule

Proteins

Centimeter

Very small

to meter 2. Bonding type

All types and mixed

Predominantly molecular, H~

3. Electrostatic charge

Rarely

Could be

effect

important

4. Biological degradation

Not likely

Can be very important

5. Solution structure (morphology and size

Complex

Complex

Only as

Integral

of growth units) 6. Contains free water

entrapped solvent

5

tor, the thermodynamic behavior of the crystallizing system, is listed first. It is generally agreed that all materials behave according to the basic laws of thermodynamics. This fundamental parameter which allows us to analyze the properties of all materials in a self-consistent fashion and compare materials with different properties should form the bridge between the small and large molecule crystal growth fields. From an understanding of the thermodynamic behavior of a material system, whether it involves inorganic or biological materials, will come the ability to effectively developed processes by which different types of materials can be synthesized and fabricated into various forms. Following from this initial premise and experimental evidence, one can then postulate that crystals containing large biological molecules will form by nucleation processes essentially similar to that of small molecule materials, and that in solution growth systems supersaturation will provide the driving force for both nucleation and growth as will be discussed later. A crystal grown without physical or thermal restraints will exhibit a growth habit, that is an external shape or morphology which depends on (1) the internal arrangements of the atoms or molecules making up the crystal lattice and (2) the growth conditions employed. Atoms or molecules arrange themselves in space with structures related by a limited number of symmetry operations which are common to all crystalline solids. This results in an external form which is bounded by flat faces (facets). The angle between these facets take on only a few discrete values for a particular crystal system since this morphology is consistent with the symmetry of the point and space groups involved. As a crystal grows, the fast growth faces will grow out leaving only the slowest growing faces. This gives a morphology which is bounded by a small number of equivalent planes, for example the { 100 } faces which form the cubic shape of NaC1 crystals. Both inorganic and biological crystals exhibit morphologies which result from the above factors and this represents a major area where biological materials resemble small molecule inorganic solids. A composite photograph in McPherson et al. [17] clearly shows the extensive morphology van-

6

R. S. Feigelson

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Relevance of small molecule crystal growth theories

~

~

Ifl III

‘

l]~ i—i

L~J.5J

,-

nil

m

S

C

C ~1 II~

m

S

Fig. 7. Various habit modifications found for KCLO

3 crystals. From Buckley [8].

ations exhibited by crystals of various biological materials. The variations in morphology of small molecule crystals is equally extensive. Fig. 7 shows a variety of morphologies found for crystals of just one inorganic compound, KC1O3. Even a trained crystallographer would find it difficult to determine which type of material (inorganic or biological) was which, based solely on observations of crystal morphology, While the external crystal morphology is determined by the internal atomic or molecular arrangement, it can be radically altered in both small and large molecule growth systems by changing various crystallization parameters including growth rate, impurities or dopants, pH, mechanical constraints, fluid flow etc. Fig. 8 shows the change in morphology brought about by solution additives in the potassium chlorate system. In the case of proteins, different external morphologies were found by Ataka and Tanaka [18] for orthorhombic crystals of lysozyme grown at temperatures above 25°C compared with the usual

tetragonal phase grown below that temperature. McPherson and Spencer [19] obtained three different morphologies of canavalin by starting the crystallization at different pH’s and by the addition of EDTA to the growth solution. There are six areas where biological macromolecules are significantly different from their small molecule counterparts (table 4). Probably the most important with respect to growing large crystals for structural analysis is the size of the crystallizing system. The volume of a small molecule growth system is usually in the range of 50 ml to over 40 liters, while a large proportion of biological materials are grown in droplets of 20—30 ftl or less. The reason for the small size of the biological samples is the general lack of availability of pure material in large quantities. This is due, in large part, to the difficulty in separating and purifying them from the various substances in which they are found. Working with these very small samples makes it very difficult, though not impossible, to apply most of the small molecule

R..S. Feigelson / Relevance of small molecule crystal growth theories

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so,.

aW —

..

—,-

~

__

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•

i.• ~

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Fig. 8. Effect of impurities on the morphologies of KC10

1 crystals: a hor~ix(4.5 ~ I. (hi Pyronine U (I .5 ~ I and Ic) l’ontac~lViolet

(‘413 (1.5

‘.

I. From Buckles

[SI.

8

R. S. Feigelson

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Relevance of small molecule crystal growth theories

crystal growth methods described earlier. Controlling fluid flow, maintaining desirable temperature and concentration gradients for example, are challenging problems in small liquid droplets. Another significant difference between small and large molecule materials is the way the atoms and molecules are bonded. Hydrogen bonding, often involving bridging water molecules, is common in biological compounds while inorganic materials typically exhibit predominately ionic or covalent bonding. It is not clear whether the weaker bonding will have a significant effect on the nucleation and growth kinetics of these materials, but since large molecules are usually in an electrolyte solution, electrostatic and dcctrodynamic effects are more likely to play a role in the crystallization process. These effects probably do not have as significant an influence on the growth of most inorganic crystals. Biological matter can degrade in a number of ways which are very different from the behavior of inorganic materials. For example, starting materials and solutions are susceptable to attack by other biological species. Some of these materials cannot even be crystallized if either the starting materials or the solutions have become contaminated or have decomposed. While the crystallization behavior of inorganic compounds can be strongly influence by impurities also (as shown in fig. 8), the crystallization process is rarely inhibited by biological contaminants. Many impurities in inorganic and biological systems can be effectively removed by a number of purification techniques, but the damage done by biological contamination or dehydration effects in protein solutions are usually difficult to reverse, Finally, the role of water in these two systems is remarkably different. In small molecule crystals, water is either a structural component of the crystal or an impurity usually in the form of solvent inclusions. In biological crystals, on the other hand, water is found both as structurally bound water, and in the form of a more loosely held water whose quantity can vary roughly between 30% and 70% and whose role is not yet fully understood. It is surprising that with so much “free” water in these crystals the morphologies are not significantly different from those of anhydrous crystals.

The picture that emerges when both the similar and dissimilar properties and crystallization behavior of small and large molecule materials are compared is one in which the fundamental aspects of crystal growth (the thermodynamic, nucleation, kinetic behavior, etc.) should not be very different. This indicates that it should be possible, and useful, to apply the fundamental crystal growth concepts and technologies developed for small molecule crystal growth to the growth of biological macromolecules. In some cases modifications to these theories and techniques will be necessary depending on the specific properties of the particular material being crystallized.

4. Phase equilibria The success of a crystal growth project involves not only achieving the desired result but also doing so at the minimum expenditure of time and money. The growth of crystals by solution techniques is greatly facilitated if data on the solubility, phase relationships, solution hydrodynamics, metastability limits and nucleation characteristics are known. In many inorganic systems, a relatively large amount of data has been accumulated, particularly in the area of phase equilibria, which provides information on the number and type of phases present under equilibrium conditions for various values of temperature, pressure and cornposition. This information is not available for most biological materials because the small quantity of material available makes it difficult to measure their properties. The difficulty in time involved both in making extra material for these measurements and making the measurements themselves may in many cases make it more practical for workers in this field to continue to use empirical approaches. While it is clear that many workers neither will have the time, background, experience, or financial resources to permit them to exhaustively study the phase relations for the materials they plan to crystallize, they can, by referring to previous studies on other systems, find information which will help guide them in the growth of their compound. It is important that they know what information is

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Relevance of small molecule crystal growth theories

available and how to apply it to their specific crystal growth problems. One of the most important pieces of information needed to help effectively determine the most appropriate crystal growth conditions is the solubility data for a given species in H20 at various

7C

60

—

temperatures and concentrations of precipitating agent and as a function of pH. Such data has just

50

—

started to become available for a few proteins. Howard and co-workers [20] cently published the solubility and phase for lysozyme. Dc Mattei and Feigelson shortly be doing the same for canavalin.

common have rerelations [21] will

5. derstood Nucleation Small molecule that and crystallization growth crystal growers is a two have steplong process uninvolving: (1) the nucleation of small crystallites following by (2) the growth of these nuclei to macroscopic size suitable for the intended application. The nucleation and growth behavior of small molecule materials have been extensively studied and some excellent recent reviews are available [9,11,22—25]including the concise review by Boistelle and Asteir [26] which can be found in these proceedings. Although under certain conditions they may occur simultaneously, it is common practice to separate these two parts of the crystallization process because the supersaturation conditions necessary for nucleation is usually quite different (often much higher) than those necessary for stable, controlled growth. Most of the batch techniques used for protein crystallization, such as the hanging drop method, do not discriminate between the two processes and often lead to the formation of large numbers of small crystals clustered and intergrown into aggregates. Often the growth rate of the crystals is erroneously calculated by including the incubation time for nucleation which is usually many times longer than the time to grow the crystals to macroscopic dimensions.

I

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~ 5)

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30

—

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I I’ -

-

20 10 56

54

,_ 52

—

50

48

46

Fig. 9. Cooling curves for NaNO1 and the formation of a metastable region. From Miers and Isaac [27].

crystallization behavior of NaNO3 in aqeuous solutions and their results are shown in fig. 9. The controlling variable studied was temperature (NaNO3 has a temperature dependent solubility in H20). The concentration of some other suitable variable such as precipitating agent, pH. etc. could also be similarly studied. When the temperature was decreased for solutions containing a range of NaNO3 concentrations they found that crystallization did not occur at the saturation temperature, but rather when the temperature reached a value defining the critical supersaturation necessary for nucleation. When the temperature at which nucleation took place was plotted as a function of composition, it yielded a “supersolubility” curve which nearly paralleled the solubility curve and below which crystalline solids (amorphous solids or colloids for certain materials) will always form. When this critical supersaturation value was reached, and nuclei had formed, the NaNO3 concentration in solution rapidly decreased at con-

5.1. Nucleation

The nucleation process was elegantly studied by Miers’ group [27] in 1907. They studied the

stant temperature, either by growth on existing nuclei or by producing more nuclei. This type of situation is not conducive to controlled growth of

10

R.S. Feigelson

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Relevance of small molecule crystal growth theories

solubility (c/s). Techniques for measuring super-

~_—Solubility curve

\.

saturation are discussed by Mullin [28]. B’

A

5.2. Growth kinetics

~TURATI0N ~ SUPERSATURA~0N~B

.~

labile

metastable

The standard approach for growing crystals of

C) 0.

~E

material new material is available) from solution is to nucleate (if enough and grow starting some

Superslity~~~~ curve

%

NaNO

3, decreasing

~

Fig. 30. Division of the solubility field according to Miers and Isaac [27].

large, high quality crystals, although in large crystallizers such crystals have sometimes been harvested. Fig. 10 illustrates the relationship between supersaturation and solubility as developed by Miers and Isaac [27] from their work on NaNO3. In the undersaturated region, crystals introduced into the solution will dissolve. Below the solubility curve is the supersaturated region which is divided by the supersolubility curve into a metastable and labile region. In the metastable region, growth can occur on a preexisting nucleus or crystal by increasing the supersaturation by either reducing temperature (A—D) or by evaporation (A—C). However, if the solution is mechanically shocked while in this region a shower of fine crystals can result. Otherwise this is the ideal region in which to grow crystals using seeding techniques, and seeding is almost always used in the aqueous solution growth of small molecule crystals. Spontaneous nucleation can occur if the labile region is entered even during seeded growth so it is to be carefully avoided. Table 5 gives some values for the undercoolings of a number of different types of cornpounds. It can be seen that these values differ widely and the design of a good crystal growth experiment would be greatly facilitated by having this information available for the material being grown. Biological materials would also be expected to have a range of values. The same type of table could be constructed using supersaturations in the form of bulk concentrations divided by

crystals by a batch method, and then use the best crystals available as seeds for a growth run where the supersaturation can be carefully controlled (in the rnetastable region). The subsequent growth will be controlled by controlling the supersaturation either through temperature changes, solvent evaporation or chemical additions to the solution. Fig. 11 shows some typical growth rate curves for several compounds dissolved in H20. Also shown, in fig. lic, is the dependence of growth rate on crystallographic orientation (growth anisotropy) which leads to the growth habits commonly observed. These curves can be compared

Table 5 Maximum undercooling for aqueous solutions of certain matenals Solute

Saturation

Maximum

temperature

undercooling

T(K)

~T(°C)

KI KNO3 K2SO4 K2Cr2O7 KHC4H4O,

328 279 323 301 323 313 357 310 354 303

3 6 8 20 14.9 8 3 37 46.3 12

NaNO~

353

60

NH4NO,

357

(NH4)2C2O4-H2O NiSO4

290

17

323

20

1-lydroquinone Pyrocatechol

313 313

3

Trinitrocresol

323

20

Urea

307

3

H2C204 KBr KCI

5.5

7

Values of ~T/T in the literature range from 0.008 to 0.2 with a median of about 0.03 For comparison, values of 4T/T for

melts range from about 0.05 to 0.5 with a median of about 0.2. From Brice [9].

R. S. Feigelson

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0’

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Relevance of small molecule crystal growth theories

I,

400p.m,° I

42~...

4.+

nr2

2-

o_____o_

-

—

{iio}

/1+1

9. n=l.67~.~.~/ ~

-~

1

~

/8

05-

-~

...-~°

to

.

27.5 C

.,.—“

~

~_‘“~‘

0.1

1

0

0.1 05

/ 300~sm

,~///

0 2

/0

/

/

1.0

C

-

I

a I

1

I

I

2 ~T(C)

5

b

//

10

0.1 1 0.2

I I 0.5 1 Supersaturation

I I

5

2

0.5

1.0

4C (g/lOOml)

2

~IC

Fig. 11. Growth rate curves as a function of supersaturation or undercooling for (a) ethylene diamine tartrate, (b) sucrose and (c) copper sulphate solution. From Brice [9[.

with figs. 12 and 13 which show some typical data for biological macromolecules. Note the linear relationships found for both types of materials. A study of the growth rate data as a function of supersaturation or undercooling has allowed small molecule scientists to understand the mechanisms

A

2.2

2.0

•1 14

canavalin [21]. In the case of insulin, lysozyme and

~

1.8

involved in crystal growth and such data has helped lead to successful crystal growth processes for many materials. Such studies should also be useful in understanding the behavior of biological materials during crystallization and some preliminary work has confirmed this hypothesis. Investigations to date on the growth rate behavior of biological materials have concentrated on lysozyme [6,29,30], insulin [4,6], rennin [5] and

0

I

/0/

1~ ~

1.~

log

1.6

—a-——

I

0.3 [In (C/C

j.1

0.4

Fig. 12. The (110) face growth rate as a function of the bulk supersaturation ratio for tetragonal lysozyme crystals. From

Fig. 13. Log growth rate as a function of reciprocal log of

Pusey and Nauman [29].

supersaturation for insulin. From Fiddis et al. [61.

12

R.S. Feigelson

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Relevance of small molecule crystal growth theories

Table 6 Growth rate comparison on a 100 lsmX 100 ~m surface

6. Summary

Matenal

Si KDP Canavalin

Growth rate (cm/day)

240.3 0.006

Atomic/ Number molecular of layers radius per hour

Number of atoms/ molecules

Based on the arguments discussed above and the currently available data it would appear likely

(A)

per hour

that the crystallization of biological macromolecule will follow the same general principles as small molecules materials. While there are significant differences in some aspects of the crystallization of biological macromolecules particularly relating to the small size of the growth systems used, the complexity of the growth unit in solution, the water content of the crystals, and electrostatic/ electrodynamic interactions, the crystallization of these materials can probably be understood within the context of our current knowledge of crystal growth. Some phenomena observed may require the adaption of new models such as the colloid stability theory proposed by Young et al. [31]. What is lacking in the biological macromolecule area is the vast body of physical-chemical data that has been so useful to the small molecule crystal grower. The situation is changing rapidly, however, as more researchers become involved in the crystal growth of biological macromolecules and develop an interest in understanding the mechanisms involved in the crystallization process. This trend can clearly be seen in many of the research papers published in this proceedings..

1.17 5.01 37

7 7.80x1018 4.27x10 4.16x 10~ 4.16~1O14 3.38 x iO~ 6.17 x 10°

canavalin, the growth kinetics seem to be dominated by the surface kinetics, It has been generally assumed that biological macromolecule crystals grow at much slower rates than small molecule crystals largely because, as mentioned before, when measurements were made the incubation time for nucleation and the time involved in producing a crystal of a given dimension were not separated. Table 6 compares the growth rates of three different types of materials, Semiconductor grade silicon single crystals, which are pulled from a melt, can be grown at higher growth rates than most other materials. Its growth rate is at least two orders of magnitude faster than KDP (potassium dihydrogen phosphate) which is grown from aqueous solutions and whose growth rates are typical of solution grown crystals. It can be seen from table 6 that the growth rates of KDP and the protein canavalin are not that dissimilar. At the macroscopic level, crystals of proteins whose growth rates have been carefully measured do not appear to grow at rates too different from small molecule materials grown from aqueous solution. The last column in table 6 gives an indication of the number of molecules which attach to the surface per unit time. At this microscopic level, canavalin is approximately 3 orders of magnitude slower “growing” than KDP. Thus in terms of molecular flux, biological macromolecules can be said to be slow growing. However, since these molecules are much larger than small molecule species it takes fewer of them to give the same linear growth rate R (where R NL/t with N, the number of molecules per unit area of length L depositing parallel to the growth direction in time =

t).

References [1] M.-H. Jiang, J. Crystal Growth 79 (1986) 33.

[21J. Bohm, Acta Phys. Hung. 57 (1985) 161. [31A. McPherson, Preparation and Analysis

of Protein

Crystals (Wiley, New York, 1982). [4] J. Schlictkrull, Acta Chem. Scand. 10 (1977) 1455, 1459; 11(1977) 291, 299, 439, 484, 1248.

(5] C.W. Bunn, C.P. Moews Soc. (London) B178 (1971)and 245.M.E. Baumber, Proc. Roy. [6] R.W. Fiddis, R.A. Longman and P.D. Calvert. J Chem. Soc., Faraday Trans. 75 (1979) 2753. [71See J. Crystal Growth 76 (1986) 559—718. [8] HE. Buckley, Crystal Growth (Wiley. New York, 1951). [9] J.C. Growth of Crystals From Liquids (Wiley, New Brice, York, The 1973). [10] A. James and R.C. Kell, Crystal growth from aqueous solutions, in: Crystal Growth, Ed. B. Pamplin (Pergamon, Oxford, 1975) p. 551.

R. S. Feigelson

/

Relevance of small molecule crystal growth theories

[11] J.W. Mullin, Crystallization, 2nd ed. (Butterworths, London, 1972). [121 R.A. Laudise, The Growth of Single Crystals (Prentice Hall, Englewood Cliffs, NJ, 1970). [131 MC. Robert and F. Lefaucheux, J. Crystal Growth 90 (1988) 358. [14] L. Loyd, D. Maeder, N. Chayen and M. Buckler, Crystal Growth of Biological Macromolecules, FEBS Advanced Lecture Course, Bischenberg, France, July 1987. [15] S. Narayana Kalkura and S. Devanarayanan, Crystal Growth of Biological Macromolecules, FEBS Advanced Lecture Course, Bischenberg, France, July 1987. [16] J. Shah and H.H. Wills, Creation, measurement and control of crystal growth environment, in: Crystal Growth, Ed. B. Pamplin (Pergamon, Oxford, 1975) p. 326. [171 A. McPherson, S. Koszelak, H. Axelrod, J. Day, L. Robinson, M. McGrath, R. Williams and D. Cascio, J. Crystal Growth 76 (1986) 547. [181 M. Ataka and S. Tanaka, Biopolymers 25 (1986) 337. [191 A. McPherson and R. Spencer, Arch. Biochem. Biophys. 169 (1975) 650. (201 S. Howard, P.J. Twigg, J.K. Baird and E.J. Meehan, Jr., J. Crystal Growth 90 (1988) 94.

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[21] R.C. De Mattei and R.S. Feigelson, to be published. [22] B. Lewis, Nucleation and growth theory, in: Crystal Growth, Ed. B. Pamplin (Pergamon, Oxford, 1975) p. 12. (23] P. Hartman, in: Crystal Growth: An Introduction, Ed. P. Hartman (North-Holland, Amsterdam, 1973). [241A.A. Chernov, Modern Crystallography III: Crystal Growth, Springer Series in Solid State Sciences, Vol. 36 (Springer, Berlin, 1984). [25] R.L. Parker, in: Solid State Physics, Vol. 25, Eds. M. Ehrenreich, F. Seitz and D. Turnbull (Academic Press, New York, 1970) p. 152. [26] R. Boistelle and J.P. Astier, J. Crystal Growth 90 (1988) 14. [271 HA. Miers and F. Isaac, Proc. Roy. Soc. (London) A79 (1907) 322. [28] J.W. Mullin, Bulk crystallization, in: Crystal Growth, Ed. B. Pamplin (Pergamon, Oxford, 1975) p. 289. [29] M. Pusey and R. Nauman, J. Crystal Growth 76 (1986) 593. [30] S.D. Durbin and G. Feher, J. Crystal Growth 76 (1986) 583. [31] C-C. Young, R.C. De Mattei, R.S. Feigelson and WA. Tiller, J. Crystal Growth 90 (1988) 79.