1. Starting a crystallography project…
(Traversing the mountain range of structure determination)
crystallization
structure
determination
protein
purification
protein
expression
diffraction
cloning
The journey is worth it, because at the end of the day you have a beautiful view (or structure)!

2. The method }
X-rays

3. 1. Growing protein crystals Principles, methods and optimization
Syllabus
1. Growing protein crystals
Principles, methods and optimization
2. Symmetry
Symmetry elements, point groups and space groups
3. Diffraction
Introduction to diffraction of waves
The reciprocal lattice
Diffraction by crystals; Bragg equation
4. Obtaining the diffraction pattern
Instruments
Data collection strategy/quality
5. Deriving a trial structure
Methods for solving phase problem
6. Refining the structure
7. Analysis of structural parameters - quality

4. Growing crystals

5. Protein Crystallisation
Principles and practice in crystallising biological macromolecules
Firstly and most importantly I would like to thank Dr. Sewell for inviting me to give this course, and also thank Brendon Price for all the work he has done behind the scenes to make it happen.
I ought now to introduce myself. My name is Gweneth Nneji, and I am based at Imperial College in London. My main area of interest is in the crystallisation of novel proteins. For many years I have worked on some very challenging proteins - the crystallisation of alpha crustacyanin and its associated appoprotiens (details) the crystallisation of human cardiac troponin which is a regulatory protein in cardiac muscle and a selection of other proteins including a connective tissue growth factor. However more recently the I have been focusing on the crystallisation of peptides and a membrane proteins.
Within our group at Imperial College there is also a strong focus on the development of new methods in crystallisation, and the development of systematic study. The trial and error approach is inefficient if used on its own. The course will reflect these areas of systematic study.
Since we are a fairly small group here perhaps we could go round in turn and each of you could introduce yourselves, say something about your research and what you hope to gain from the course. Who would like to start?
Now that we all know who we are, I will just say a few words about the structure of this course. I would like to use a fairly informal tutorial style of teaching and I would like to make it interactive, so you will have your part to play. This form of teaching will be confined to the morning sessions. In the afternoons I plan to hold practical demonstrations where you will have to opportunity to apply some of the methods for yourselves under my instruction.
Lastly I would just like to say that the focus will be on the crystallisation of globular proteins.

6. Learning objectives
Understand the principles that govern crystal formation and growth
Have knowledge of the different types of precipitant and how they work
Be familiar with a number of different methods of crystallisation
Be able to choose a suitable method for the crystallisation of your macromolecule and to design a crystallisation strategy
Make decisions about screening results and selecting the best leads to follow
Develop and/or modify existing methods to assist the crystallisation of your macromolecule
I thought it would be useful to list the learning objectives so that you will know what you can expect to gain from this course.
By the end of the course I would expect you to:
Have a grasp of the principles that govern crystal formation and growth and to be able to apply them to your crystallisation projects
Have an understanding of the different types of precipitant and how they work
Be familiar with a number of different methods of crystallisation
Be able to choose a suitable method for the crystallisation of your macromolecule and to design a crystallisation strategy
Make decisions about screening results and selecting the best leads to follow
Develop or modify existing methods to assist the crystallisation of your macromolecule
In doing this I hope you will develop an approach that will enable you work independently to achieve the successful crystallisation of your macromolecule.
Ask for areas of interest.

7. Overview Basic principles of crystallisation Practical methods
Supersatutation
Solubility
Nucleation
Crystal growth
Factors that affect crystallisation
Methods in crystallisation
Precipitating agents
Practical methods
Microbatch and other methods using oils
Protein crystallisation is usually thought of as a magical or ‘black art’ I do not know whether or not you share this opinion but hopefully by the end of this course with the knowledge and understanding of the principles you may see and perhaps have the confidence to convince others that there is a scientific basis to it.
This is an outline of the areas we will cover today.
In the morning we will cover the basic principles governing the crystallisation process which will include:
Supersaturation
Solubility
Nucleation
Crystal growth
Factors that affect crystallisation
Methods in crystallisation
Precipitating agents
and in the afternoon we shall apply some of those principles by way of practical demonstration.
We start by considering some basic principles, supersaturation and solubility.

8. Introduction to the principles of crystallisation
3 steps in crystallisation: nucleation, growth and cessation of growth
Macromolecule Crystallisation is a multi parameter process
The differences between protein crystallisation and the crystallisation of small molecules are:
The physico-chemical properties
Conformational flexibility and chemical versatility
Origin of biological macromolecule
I am sure that you are all aware that there are three steps in crystallisation: nucleation, growth and cessation of growth. I will talk about these steps in more detail as we go through this morning’s session.
Mention crystallisation to anyone and they will give you the impression that crystallisation is an easy process. This seems to be a widely held view, with the general public and also with scientists outside our field. Most people have advise to offer which is often as simple as just dip a piece of string into the solution or add a speck of dust and bingo you get crystals. I think this impression comes from their school days and chemistry lessons.
Although the process of small molecule crystallisation is well understood and predictable it certainly is not the case for proteins and biological macromolecules. So what makes the process of crystallisation so difficult for biological macromolecules?
It is because the crystallisation of biological macromolecules is complicated by the fact that there are many different parameters involved in the process.
These may include a variety of things:
Supersaturation, temperature, pH, time (in the sense of rates of equilibration and rates of growth), the nature of precipitant, buffer and additives; diffusion, convection, the effects of surfaces, vibrations I can list many other biological parameters and parameters relating to the purity of the macromolecule. I guess you have got the idea.
This multi-parametric process is what makes crystallisation of biological macromolecules distinct from that of small molecules. In addition proteins are only stable in a narrow range of temperature, pH and salt concentration.
Protein conformation is generally sensitive to temperature, pH, ionic strength and solvents.
Chemical versatility relates to the complexity of the molecule for example the polyelectrolyte nature of amino acids, hydrophobicity versus hydrophilicity in proteins, the ability of macromolecules to bind ligands (such things as substrates, cofactors, metal ions, or other ions) macromolecular interaction with specific additives making them sensitive to external conditions.
We need to take into account that proteins may degrade and denature with time and also the origin of the biological macromolecule in terms of its function and physiological state in the organism or cell.
To grow crystals molecules have to be brought into a supersaturated, thermodynamically unstable state, this may result in a crystalline or amorphous phase when it returns to equilibrium.
To grow crystals molecules have to be brought into a supersaturated, thermodynamically unstable state, this may result in a crystalline or amorphous phase when it returns to equilibrium

9. Supersaturation
An unstable condition where more solutes (protein) are dissolved in a solvent that can normally be held in solution under given conditions of temperature and pressure.
It can also be defined as when the chemical potential (change in free energy) of the solute is greater in solution than in the crystal (solid).
Supersaturation occurs when a chemical solution is more highly concentrated than is normally possible under given conditions of temperature and pressure.
It can be defined as when the chemical potential of the solute is greater in solution than in the crystal. In other words when the change in free energy of the molecule in solution is greater than that in the solid.
Chemical potential
The "chemical potential m" is a measure of how much the free enthalpy (or the free energy) of a system changes (by dGi) if you add or remove a number dni particles of the particle species i while keeping the number of the other particles (and the temperature T and the pressure p) constant:
dGi  =  ¶G /¶ni  ·  dni
Supersaturation can be achieved by evaporation of the solvent or by varying the parameter that affects the chemical potential of the solute e.g.
Protein concentration
Activity coefficient (salt concentration)
Temperature
Pressure
Activity coefficient - A measure of the extent to which substances, on dissolving in water, form charged ions or associate to form multiple molecules. The amount dissolved influences effects which depend on the quantity of molecules but not on their chemical nature. Such as equilibrium, freezing point depression of solution drops and reaction rates in solution.
From this you can see that supersaturation is the driving force for crystallisation and a key parameter in optimisation.
Summarise the thermodynamic link to supersaturation in simple terms.
The chemical potential, µ, of a component in a solution can be thought of in many ways:
# 1. A measure of the "escaping tendency" for a component in a solution;
# 2. A measure of the reactivity of a component in a solution;
# 3. For a one component (pure) phase, the chemical potential can be thought of as:
µ = U + PV - TS (note, in this equation, µ,U,S,V, as well as T and P, are intensive quantities).
4. The chemical potential of a component in a solution is defined as the rate at which the (extensive) internal energy of the solution increases as the number of moles (extensive) of the component in question increases, for a given entropy and volume of the solution.

10. Supersaturation
Supersaturation can be achieved by evaporation of the solvent or by varying any parameter that affects the chemical potential of the solute e.g.
Protein concentration
Salt concentration
Temperature
Pressure
Supersaturation occurs when a chemical solution is more highly concentrated than is normally possible under given conditions of temperature and pressure.
It can be defined as when the chemical potential of the solute is greater in solution than in the crystal. In other words when the change in free energy of the molecule in solution is greater than that in the solid.
Chemical potential
The "chemical potential m" is a measure of how much the free enthalpy (or the free energy) of a system changes (by dGi) if you add or remove a number dni particles of the particle species i while keeping the number of the other particles (and the temperature T and the pressure p) constant:
dGi  =  ¶G /¶ni  ·  dni
Supersaturation can be achieved by evaporation of the solvent or by varying the parameter that affects the chemical potential of the solute e.g.
Protein concentration
Activity coefficient (salt concentration)
Temperature
Pressure
Activity coefficient - A measure of the extent to which substances, on dissolving in water, form charged ions or associate to form multiple molecules. The amount dissolved influences effects which depend on the quantity of molecules but not on their chemical nature. Such as equilibrium, freezing point depression of solution drops and reaction rates in solution.
From this you can see that supersaturation is the driving force for crystallisation and a key parameter in optimisation.
Summarise the thermodynamic link to supersaturation in simple terms.
Supersaturation is the driving force for crystallisation – as such it is a key parameter in optimisation

11. Solubility Solubility is defined as:
the amount of compound dissolved in a solution in equilibrium with an excess of undissolved compound
There are different ways to define solubility
concentration values may be measured before complete equilibrium is reached
solubility may be measured in the presence of precipitate or crystals
In general solubility is defined as the amount of compound dissolved in a solution in equilibrium with an excess of undissolved compound. In the case of biological macromolecules,
There are different ways to define solubility
Concentration values may be measured before complete equilibrium is reached it can take months to achieve equilibrium
Solubility may be measured in the presence of precipitate or crystals

12. Macromolecular structure
A biological macromolecule is a polymer of amino acids or nucleotides, which is folded into tertiary or quaternary structure held together
mainly by dipole-dipole interaction, H-bonds and van der Waals interactions
by some covalent bonds (S-S bridges)
occasionally by salt bridges
Water soluble proteins have mostly hydrophilic side-chains on their surface
Before we move on to discuss solubility let us consider the structure of the macromolecule.
A biological macromolecule is a polymer of amino acids or nucleotides, which is folded into tertiary or quaternary and structure held in conformation by:
mainly by dipole-dipole interaction, H-bonds and van der Waals interactions
by some covalent bonds in the form of S-S bridges
occasionally by salt bridges
Water soluble proteins have mostly hydrophilic side-chains on their surface.
The structural arrangement and complexity of biological macromolecules leads to the complexity of the crystallisation process and the sensitivity of the molecules to their environment.

13. Solubility
Solubility is additionally defined by the characteristics of the solvent
The additional chemicals contained in the solvent can affect the solubility of macromolecules by either:
interacting with the different functional groups of the protein, perhaps modifying the conformation
modifying the properties of the solvent e.g., altering the pH or disrupting salt bridges
Solubility is additionally defined by the characteristics of the solvent
The additional chemicals (buffer, salts and additives) contained in the solvent can affect the solubility of macromolecules by either:
interacting with the different functional groups of the protein, perhaps modifying the conformation.
modifying the properties of the solvent e.g., altering the pH may have the effect of modifying the net charge of the protein and affecting the nature of the protein, or if salt bridges are disrupted by ??? Again this may change protein conformation or even denature the protein.

14. Solubility and the solid phase
aqueous solution
crystal
When protein molecules are fully solvated they are surrounded by a sheath of water molecules. Protein, which is the solute, is in equilibrium with the solvent. The energy of the system is at a minimum. Under these circumstances crystallisation, which can be described as the ordered aggregation of protein molecules, will not occur as it is thermodynamically unfavourable. To achieve the solid phase the molecules have overcome the energy barrier to interact and form bonds with each other.
This is where the supersaturation becomes important, as only in the supersaturated state will the equilibrium be shifted in favour of the formation of intermolecular bonds.
How do thermodynamic factors govern crystallisation
Crystallisation is:
The transfer of molecules from the liquid phase (aqueous solution) to an ordered solid phase
Thermodynamic factors govern the solubility
This is where the supersaturation becomes important, as only in the supersaturated state will the equilibrium be shifted in favour of the formation of intermolecular bonds.

15. Solubility and temperature
Entropic effects - An increase in temperature increases the disorder of solvent molecules
During a temperature rise vapour will distil away from a drop increasing the degree of supersaturation - shower of xtals
Decreases in temperature result in vapour condensing on the drop diluting it and increasing the volume (use microbatch or sitting drop)
Protein solubility varies with temperature.
Macromolecular crystals are stabilised by interactions similar to those that stabilise protein tertiary and quaternary structure. There is a degree of hydration associated with each level of the structure from tertiary to quaternary to lattice packing. In crystal lattices complementary electrostatic forces play an important role stabilising the lattice. Such electrostatic forces as hydrogen bond and ion-pairing are mediated by either water or counterions.
Many interactions within and between macromolecules in water are temperature dependent because they involve significant entropy changes. Increases in disorder in the solvent molecules within and between macromolecules?? Macromolecules tend toward association – nucleation?? It is worthwhile varying the temperature over the range that the molecule is stable. Does it mean that at higher temperature solvation persists and maintains stabilisation of the molecule???
During a temperature rise vapour will distil away from a drop increasing the degree of supersaturation – may give shower
When the temperature decreases more vapour condenses onto the drop diluting the protein solution. It can be observed in drops using low salt or PEG as a precipitant an increase in the volume of the drop. Use of microbatch or sitting drop methods reduces these problems.

16. Solubility and pH
pH changes affect both solute and solvent but have a greater effect on the solute, potentially protonating or deprotonating the macromolecule
Charged groups on the surface of the molecules may be affected by protons and different ions in the solution
Solubility and pH
What role does the pH play in crystallisation?
How does the pH affect the solubility of a protein?
Charged groups on the surface of the molecules may be affected by protons and different ions in the solution.

17. Solubility and ionic strength
Salts are responsible for the ionic strength of a solution and affect macromolecular electrostatic interactions by charge shielding
This is achieved by acting in the following ways:
Forming direct electrostatic interactions with charged residues
Forming interactions with dipolar groups (e.g. peptide bonds, amino, hydroxyl or carboxyl groups)
Non-polar interactions of hydrophobic residues with organic salts
Association with binding sites
What is ionic strength?
Why is it relevant? – it explains the effects of salting-int.
Salts are responsible for the ionic strength of a solution and affect macromolecular electrostatic interactions by charge shielding - in that way they minimise the repulsion between molecules.
This is achieved by acting in the following ways:
Salts may form direct electrostatic interactions with charge residues at the surface of proteins through non-specific monopole-monopole interactions; that is interaction of anions or cations with amino acid side chains.
Salts may act by monopole-dipole interactions with dipolar groups of the macromolecule, (e.g. peptide bonds, amino, hydroxyl or carboxyl groups) such interactions may lead to the partial denaturation of the protein.
Non-polar interactions may occur between solvent-exposed hydrophobic residue and the hydrophobic part of organic salts (i.e. carboxylate, sulphonate or ammonium salt). There interactions are also involved in the solublisation of solvent-exposed hydrophobic residue by the hydrophobic tail of an ionic detergent.
Salts may associate with binding sites.

18. The effect of salts on solubility
The change in protein solubility with increasing salt concentrations is described in terms of:
Salting-in – increasing solubility at low salt concentration
Salting-out – protein solubility is decreased at high ionic strength
Explain so that the meanings of both of these are very clear.
The change in protein solubility with increasing salt concentrations is described in terms of:
Salting-in – increasing solubility at low salt concentration up to a limit beyond which the protein becomes insoluble. Electrostatic interaction between charged protein and ionic species. Low salt is often required to keep protein in solution.
Salting-out – protein solubility is decreased at high ionic strength – where the effects of the salt have a shielding effect on the macromolecule in that way minimising the repulsion between molecules – solubility is governed here by the hydrophobic effect.
Adding a salt, its ions neutralize the electric charges on the surface of the proteins and act against their aggregation.
Reducing the concentration of salt (this means increasing ionic force) the effect will be an excess of charges that, after having saturated the protein, competes with the protein for what concerns water.
Ok, so if I understand correctly, in salting-in, the salt is added and and therefore neutralizes the electric charges on the protein. Because the proteins don't have charges, they don't bind, and so they are dissolved with the water.
If so, why, after adding more and more salt, the solubility of the proteins decrease? Is it because the salt starts to compete with the proteins for the water molecules?
Thanks a lot for your help.

19. How can we take advantage of these factors?
In order to initiate crystallisation we need to achieve supersaturation, effectively reducing the solubility of the protein.
This can be done practically in a number of ways:
Increase the concentration of protein
Alter the ionic strength of the solvent
Alter the pH of the solvent
Change the temperature
In order to initiate crystallisation we need to reduce the solubility of the protein. This can be done in a number of ways:
Increase the concentration of protein in solution to reduce solubility. By increasing the concentration of protein the molecules can no longer be fully solvated and this state is thermodynamically unfavourable, the solution has to move to a new equilibrium. The molecules associated with each other and form intermolecular bonds and nuclei form. It is an equilibrium so the molecules associate and disassociate going in and out of solution.
Alter the ionic strength of the solvent
Alter the pH of the solvent
Change the temperature
Knowledge of solubility is essential in designing experiments.
Solubility data must come from experimentation.
Solubility behaviour is complex and best described by phase diagram.

20. The phase diagram
Metastable zone
The phase diagram is a two-dimensional solubility diagram in which solubility is measured as a function of one parameter, all other parameters being kept constant.
The supersolubility curve separates the undersaturated and supersaturated zones. The curve represents an equilibrium of saturated solution with crystallised protein such as at the end of crystal growth or the dissolution of crystals in an undersaturated solution.
The region below the super solubility curve is undersaturated and the biological macromolecule will never crystallise.
The area above the supersolubility curve is the supersaturated zone and can be divided into 3 regions depending on the kinetics to reach equilibrium and the level of supersaturation. The level of supersaturation is defined as the ratio of biological macromolecule concentration over the solubility value.
The precipitation zone is where excess protein immediately separates from the solution in an amorphous state.
The nucleation zone is where excess protein separates in crystalline form. Near the precipitation zone it may occur as a shower of microcrystals which can also contain precipitate.
The metastable zone is where no nucleation takes place unless the solution is shocked or a nucleant is added. This zone is ideal for the growth of crystals without the nucleation of new crystal nuclei.

21. Overview Basic principles of crystallisation Supersaturation
Solubility
Nucleation
Crystal growth
Factors that affect crystallisation
Methods in crystallisation
Precipitating agents
So far we have established that :
crystallisation is the transfer of molecules from the liquid phase to an ordered solid phase controlled by thermodynamic factors
to achieve crystallisation we have to first achieve supersaturation
knowledge of solubility is essential
however solubility data must come from experimentation.
since solubility behaviour is complex it is best described by phase diagram.
Moving on to nucleation

22. Nucleation
the creation of a new (solid) phase – the formation of ordered aggregates.
It is essentially the coming together of solute molecules within a solution and requires that the energy barrier – the activation energy – is overcome before the formation of intermolecular bonds can occur.
Nucleation is the first step in crystallisation. It can be defined as the creation of a new (solid) phase – the formation of ordered aggregates. It is essentially the coming together of solute molecules within a solution and requires that the energy barrier – the activation energy – is overcome before the formation of intermolecular bonds can occur.
To achieve nucleation supersaturation must be induced. As I mentioned earlier supersaturation is a metastable condition where the solvent holds more protein in solution that it would at the minimum free energy. This state can be created by a variety of methods such as the salting-out effects of high ionic strength salts like ammonium sulphate, the entropic segregation caused by polymers such as PEG, the solvent effects of organic molecules such as MPD, and by varying other conditions such as pH and temperature.
The formation of ordered nuclei is a process that may be competing for protein with irreversible processes that produce amorphous aggregates such as precipitates and protein skins which constantly lower the degree of supersaturation of the macromolecule. As supersaturation is decreased the chance of forming a stable nucleus is reduced. Since the occurrence of spontaneous nucleation depends on the relative rates at which these various competing events take place, crystals may never form even under conditions which might otherwise support crystal growth.
Spontaneous nucleation is a process of negative feedback. As a nucleus is formed its growth reduces the degree of supersaturation of the solution and the probability that another nuclei will form. To take advantage of this and induce nucleation supersaturation must be achieved slowly with the degree of supersaturation at a level to produce a small number of nucleation centres.
There is a lower energy requirement in adding to an existing crystal surface than in creating a new nucleus. The consequence of this is to bias the production of a large number of small nuclei in favour of large crystals.
There is an close relationship between supersatuation, nucleation and the free energy in a system. Even though a solution is supersaturated it exists in an equilibrium state. For nucleation to occur the level of super saturation is critical. If super saturation is too low the energy barrier cannot be overcome and molecules cannot associate and form intermolecular bonds. Effectively no nucleation occurs - this defines the metastable zone. At higher levels of super saturation the solution is forced out of equilibrium and the free energy associated with solute molecules is sufficient to overcome the energy of activation and allow the formation of intermolecular bonds. Nucleation can occur.

23. Nucleation Nucleation is the first step in crystallisation
To achieve nucleation supersaturation must be induced
At supersaturation spontaneous nucleation is a dynamic process
Nucleation is the first step in crystallisation. It can be defined as the creation of a new (solid) phase – the formation of ordered aggregates. It is essentially the coming together of solute molecules within a solution and requires that the energy barrier – the activation energy – is overcome before the formation of intermolecular bonds can occur.
To achieve nucleation supersaturation must be induced. As I mentioned earlier supersaturation is a metastable condition where the solvent holds more protein in solution that it would at the minimum free energy. This state can be created by a variety of methods such as the salting-out effects of high ionic strength salts like ammonium sulphate, the entropic segregation caused by polymers such as PEG, the solvent effects of organic molecules such as MPD, and by varying other conditions such as pH and temperature.
The formation of ordered nuclei is a process that may be competing for protein with irreversible processes that produce amorphous aggregates such as precipitates and protein skins which constantly lower the degree of supersaturation of the macromolecule. As supersaturation is decreased the chance of forming a stable nucleus is reduced. Since the occurrence of spontaneous nucleation depends on the relative rates at which these various competing events take place, crystals may never form even under conditions which might otherwise support crystal growth.
Spontaneous nucleation is a process of negative feedback. As a nucleus is formed its growth reduces the degree of supersaturation of the solution and the probability that another nuclei will form. To take advantage of this and induce nucleation supersaturation must be achieved slowly with the degree of supersaturation at a level to produce a small number of nucleation centres.
There is a lower energy requirement in adding to an existing crystal surface than in creating a new nucleus. The consequence of this is to bias the production of a large number of small nuclei in favour of large crystals.
There is an close relationship between supersatuation, nucleation and the free energy in a system. Even though a solution is supersaturated it exists in an equilibrium state. For nucleation to occur the level of super saturation is critical. If super saturation is too low the energy barrier cannot be overcome and molecules cannot associate and form intermolecular bonds. Effectively no nucleation occurs - this defines the metastable zone. At higher levels of super saturation the solution is forced out of equilibrium and the free energy associated with solute molecules is sufficient to overcome the energy of activation and allow the formation of intermolecular bonds. Nucleation can occur.
There is a lower energy requirement in adding to an existing crystal surface than in creating a new nucleus

24. Types of nucleation There are different types of nucleation:
Homogeneous – occurring within the solution
Heterogeneous – occurring on solid particles or surfaces
Primary – within a system containing no crystalline matter
Secondary – when new nuclei originate from an existing nucleus (to produce twinning or bunching)
Nucleation is described as Homogeneous when it occurs in the solution. It is considered as Heterogeneous when it occurs on solid particles such as dust or fibres or when it occurs on surfaces. Primary nucleation is that which occurs within a system containing no crystalline matter and Secondary occurs when new nuclei originate from existing nuclei.
I should mention epitaxial nucleation as an example of nucleation which occurs on surfaces.

25. Epitaxial nucleation
Epitaxial nucleation is where the regularity of the surface facilitates nucleation.
Glass although siliconised can act as an adhesion surface
The strength of interaction with the glass can be stronger that the forces that bond the crystalline lattice
Crystals or micro-crystals can also be nucleated on cellulose fibres which are accidentally present in the protein/precipitate drop
The nucleation of crystals from aggregates and oils can be considered a case of epitaxial nucleation.
Epitaxial nucleation is where the regularity of the surface facilitates nucleation.
Crystals do preferentially attach to glass surfaces although siliconised. (The strength of interaction with the glass can be stronger that the forces that bond the crystalline lattice.)
In crystallisation trials it is possible to find many instances in which crystals or micro-crystals can be nucleated on cellulose fibres which are accidentally present in the protein/precipitate drop.
In most cases micro-crystals are also observed spontaneously nucleating under other conditions away from foreign particles. The nucleation of crystals from aggregates and oils can be considered a case of epitaxial nucleation. Here ordered surfaces may present within random aggregation of macromolecular which come out of solution as oils and precipitates. These surfaces may provide platforms suitable for macromolecular nucleation, and may possibly support 3-dimensional crystal growth.

26. The results of nucleation
Crystal–like precipitate
the nuclei form regular 3-dimensional structures. (Shower of tiny crystals – too much nucleation but ordered)
Non-crystalline precipitate
the solute molecules associate in a random fashion by non-specific van der Waals forces.
Can be either gel-like precipitate or an amorphous precipitate - there is nucleation in both cases, but it is random
When nucleation occurs it can result in either a crystal–like precipitate or a non-crystalline precipitate.
In a crystal–like precipitate the nuclei form regular 3-dimensional structures.
A shower of tiny crystals indicates that too much nucleation has occurred however the fact that it is crystalline suggest that the nuclei are ordered and there are a number of techniques that can be employed to improve crystal size.
In a non-crystalline precipitate the solute molecules associate in a random fashion by non-specific van der Waals forces. This can appear as either gel-like precipitate, amorphous precipitate or a flocculate. Nucleation is excessive and is a random aggregation of the solute molecules.
It is usually necessary to manipulate the conditions to control nucleation. We will come to them shortly.

27. The phase diagram
Metastable zone
The region of supersoulbility curve just beyond the metastable zone within the area of the nucleation zone is where crystalline precipitate may form. The regions beyond that may be where non-crystalline precipitate may form.
As an illustration the region between the dashed line and the supersolubility curve within the nucleation zone is the region where crystal-like precipitation is likely to occur. The remainder of the are in the supersaturation zone beyond the super solubility curve is where non-crystalline precipitate is likely to occur.

28. Methods to induce nucleation
Alter the protein and/or precipitant concentration
Use an additive or add a nucleant
Use evaporation techniques
Use methods to separate nucleation and growth (e.g. transfer methods)
There are various methods to control nucleation. I will mention just a few. And broadly categorise them into groups where the overall effect is either to induce nucleation or to reduce it.
Alter the protein and/or precipitant concentration
This can be done by altering individually each of the precipitants in turn whilst keeping the others constant if there is more than one precipitant and even the pH in a systematic way. Have to look at your precipitant and decide which component needs to be more concentrated to give you the desired effect.
Use of an additive screen.
Add a nucleant or a seed crystal – you would have to be in the metabstable zone for this to work.
Use methods that involve dilution of protein and/or precipitant solutions
Use evaporation techniques – generally start with metastable conditions
Use methods to separate nucleation and growth (transfer methods)

29. Methods to reduce nucleation
Slowing of equilibration:
with dialysis set-ups
by altering the major parameters of the vapour diffusion technique
Use of silica based gels
Use methods that involve dilution of protein and/or precipitant solutions
Seed into the metastable zone
In dialysis set-ups the major parameters affecting the equilibration rate are temperature, osmotic gradient, dialysis membrane and surface area of exchange. Slowing down the equilibration rate can be achieved by introducing a second dialysis membrane.
The major factors that influence equilibration in the vapour diffusion set-up are: drop volume, dilution of drop and temperature. These factors influence the kinetics of supersaturation.
The phase transitions that force a system back to equilibrium in a supersaturated solution might be:
A second liquid phase (if the concentration is very high)
An amorphous phase
A crystalline phase
It is not possible to predict which phase is reach first kinetically.

30. Factors that affect nucleation
Effect on nucleation
Seeding
Limit/reduce nucleation
Epitaxy
Induce nucleation
Charged surfaces ??
Magnetic/electric fields
Mechanical e.g. vibration, pressure
Induce nucleation in the metastable zone
Precipitant/protein/additive concentration
Effect control on nucleation
Container walls
Induce heterogeneous nucleation
Kinetics (rates of equilibration)
Induce or reduce
This is an exercise for the students to do they can fill in the effects on nucleation and say why. In this way I have an exercise for them to do and a way to assess the understanding.
Factor Effect on nucleation
Seeding limit/reduce nucleation
Epitaxy induce nucleation
Charged surfaces ??
Magnetic/electric fields ??
Mechanical e.g. pressure, vibration induce nucleation in the metastable zone
Precipitant/protein/additive concentration effect control on nucleation
Container walls induce heterogeneous nucleation
Kinetics induce or reduce - effect control on nucleation

31. Overview Basic principles of crystallisation Supersatutation
Solubility
Nucleation
Crystal growth
Factors that affect crystallisation
Methods in crystallisation
Precipitating agents
We have considered what crystallisation is and why it is difficult to achieve. We have also considered solubility and the relationship between supersaturation and nucleation. We are now in a position to consider crystal growth.

32. Principles of crystal growth
To bring the system gradually into a state of supersaturation by:
modifying the properties of the solvent
altering a physical property such as temperature

33. Crystal growth Diffusion and convection play a major role - use gels
Kinetic factors govern crystal growth
Events of crystal growth are quite different to nucleation - uncouple growth from nucleation seeding is one such method
To promote growth use an additive, add a nucleant or a seed crystal
Crystal quality is affected by: rates of growth, internal order of the initial nucleus, purity of the sample
Diffusion and convection play a major role in crystal growth. Transfer of mass from the bulk of the solution on to the crystal surface results in a density gradient where the concentration of protein decreases as you approach the surface of the crystal. Diffusion of molecules along this density gradient is a major feature of crystal growth. Density gradients arising in this way induce convection currents within growth solutions. Convection currents can cause problems in crystal growth. Diffusion is the predominant feature when crystallising with gels.
convection movement caused within a fluid by the tendency of hotter and therefore less dense material to rise, and colder, denser material to sink under the influence of gravity, which consequently results in transfer of heat.
Kinetic factors govern crystal growth. These factors relate to the attachment of molecules onto the crystal. Crystallisation requires that protein and precipitating agent equilibrate and induce nucleation. The important issues here are (i) the rate of nucleation, which depends on supersaturation and the way in which it is reached and (ii) the rate of equilibration. Slowing down the rate of equilibration seems to result in fewer larger crystals.
To explain further: as equilibration proceeds supersaturation develops and once the solution has reached the labile region nuclei may result. If nucleation occurs just above the border between the metastable zone and the nucleation zone small crystalline aggregates result, growth takes place and the solution is pushed back into the metastable zone preventing further nucleation. However if equilibrium has not been reached (e.g. the equilibration of a hanging drop with it’s reservoir) the system will be driven further into the labile region and more nuclei may appear. There is a tug-of-war between the growth of existing crystals and the nucleation of new ones. The goal being to decrease the free energy of the system as fast as possible. Ideally for optimal crystal growth after limited nucleation, the rate of equilibration should be slowed to keep the system in the metastable region to prevent further nucleation.
The kinetics of equilibration depends on the experimental arrangement and the method chosen. The events of crystal growth are quite different to nucleation this presents an opportunity to control the process by uncoupling growth from nucleation.
Seeding is a method to uncouple nucleation and growth
Attachment of molecules into the lattice can be considered from a theoretical point of view as either the formation of a perfect crystal or growth out of a screw dislocation. Describe further in terms of the tug-o-war between nucleation and crystal growth (p223).
Events of crystal growth are quite different to nucleation – considered separately
As crystals grow the degree of supersaturation is reduced and protein may be transferred from the various reversible amorphous phases to the soluble phase and bind to the crystal surfaces.
Crystal quality affected by: rates of growth, internal order of the initial nucleus, purity of the sample.

34. Optimising crystal growth
Knowledge of the growth sequence is important
The time span for the first crystal to become visible
Rates of equilibration and nucleation
An idea of an approximate growth rate
Exert some control of the kinetics of supersaturation and nucleation
Choose supersaturation conditions just above the border between metastable and nucleation
Knowledge of the growth sequence is important, with this knowledge we can modify the experimental set-up.
The time span for the first crystal to become visible – achieved by observation
Rates of equilibration and nucleation – what are the means of determination?
An approximate growth rate
To exert some control of the kinetics of supersaturation and nucleation – suggest in what way
The origin of twinning or bunching (is it sedimentation or secondary nucleation) – Is this epitaxy??
Choose supersaturation conditions just above the border between metastable labile in doing this the formation of the nuclei would drive the system back into the metastable region and regular growth would proceed. There are a number of methods which manipulate the reservoir composition as a function of time in the vapour diffusion technique that have been demonstrated to allow crystal growth to be optimised.
A suggestion of some practical methods
Additive screens
Dilution techniques
Microbatch – using gels
Microbatch techniques – oil mixtures to enhance evaporation
Methods to separate nucleation and growth
Evaporation techniques

35. Cessation of crystal growth
There is a limit to crystal growth
Cessation can be caused by:
growth will naturally cease as the protein concentration drops to the solubility limit
the random accumulation of defects as the crystal grows
adsorption of impurities or denatured protein onto the surface – “poisoning” of the surface
There is a limit to crystal growth this is important to consider as there is a minimum crystal size required for x-ray crystallography.
Crystals will naturally cease to grow as the protein concentration drops to the solubility limit. Reference to the solubility curve, the line that separated undersaturated and metastable.
However in some circumstances growth may cease even at high concentration will not restart unless the supersaturation is made very high. This may be brought about by a change in the crystal surface such that attachment becomes unfavourable. The explanation for this includes random accumulation of defects as the crystal grows and adsorption of impurities or denatured protein onto the surface.

36. Overview Basic principles of crystallisation Supersatutation
Solubility
Nucleation
Crystal growth
Factors that affect crystallisation
Methods in crystallisation
Precipitating agents

37. Factors that affect crystallisation
What are the parameters that affect the thermodynamics of interactions between molecules?
What factors affect the stability of proteins?
Which biological parameters are involved?
Do this as an exercise on a flip chart.
What sort of factors affect the thermodynamics of interactions between molecules? The thermodynamic interactions are key in crystallogenesis.
pH,
ionic strength,
level of supersaturation, (conc. of macromolecule and precipitant)
temperature,
volumes,
solid particles, surfaces, walls of vessels (homogenous vs heterogeneous nucleation, epitaxy)
purity, (contamination odd macromolecules, conformational heterogeneity flexible domains)
diffusion and convection,
vibrations,
What factors affect the stability of proteins?
pH and temperature must be in physiological range
presence of cofactors substrates
ageing
contamination by proteases
Which biological parameters are involved?
Methods of preparation
Function of the protein

38. Factors affecting crystal growth
Protein purity and homogeneity
Precipitating solution
The pH of the crystallisation solution
Crystallisation temperature
Chemical or biochemical modifications to the protein
Stability of the protein or macromolecule
Surface charge of the macromolecule

39. Overview Basic principles of crystallisation Supersatutation
Solubility
Nucleation
Crystal growth
Factors that affect crystallisation
Methods in crystallisation
Precipitating agents

40. Methods in protein crystallisation
Batch
Microbatch (by hand and by robot)
Vapour diffusion
hanging drop
sitting drop
Equilibrium dialysis
Free interface diffusion
Which are the most commonly used methods in the group of students present?
Batch
Microbatch (by hand and by robot)
Vapour diffusion
hanging drop
sitting drop
Equilibrium dialysis
Free interface diffusion
Reverse vapour diffusion

41. Batch crystallisation
The method involves mixing the biological macromolecule and the crystallising solution to achieve supersaturation instantaneously.
Since experiment starts at supersaturation – nucleation tends to be too large
Large crystals can be obtained when working close to metastable

42. Microbatch crystallisation
A batch method where crystallization samples are dispensed as small drops (can be less than 1ml final volume) under oil.
Enables systematic studies on very small quantities – ml scale, of both protein and crystallizing agents.
Applications include:
Screening
Optimisation
Control of nucleation and equilibration

43. Dispensing Drops Under Oil
Chayen (1997) Structure 5,

44. Phycocyanin crystal by microbatch

45. Vapour diffusion
A good method for screening large numbers of crystallisation conditions
Evaporation of water from the sample droplet accompanied by net condensation into the reservoir solution so as to equalise the concentrations of the two solutions
This migration of water from the droplet results in concentration of both the protein and the precipitating agent lowering the solubility of the protein and if the condition are right inducing the formation of crystals

46. Vapour diffusion – by hanging drop
The macromolecule and crystallising agent equilibrate against the reservoir which is at a higher - generally twice - concentration than that of the drop
Equilibration proceeds by evaporation of the volatile species (water or organic solvent) until the vapour pressure in the droplet equals that of the reservoir
Hanging drop
droplet
Reservoir
The droplet contains the macromolecule and crystallising agent.
The macromolecule and crystallising agent equilibrate against the reservoir which is higher (generally twice) than that of the drop.
Equilibration proceeds by diffusion of the volatile species (water or organic solvent) until the vapour pressure in the droplet equals that of the reservoir.
If equilibration occurs by water exchange (from drop to reservoir) it leads to droplet volume change.
Schematic diagram of a hanging drop

47. Vapour diffusion – by sitting drop
droplet
Reservoir
The same principle applies in the hanging drop as in the sitting drop the difference is in the experimental set-up
Vapor pressure is the pressure of a vapor in equilibrium with its non-vapor phases.
Schematic diagram of a sitting drop

48. Crystallization by vapor diffusion
Protein
solution.
Reservoir
(precipitant)

49. Crystallization by vapor diffusion
Sitting drop
Hanging drop

50. Phase diagram for vapor diffusion (no crystals)
Airlie J McCoy, Protein Crystallography course

51. Phase diagram for vapor diffusion (crystals!!!)
Airlie J McCoy, Protein Crystallography course

52. Dialysis
In dialysis the biological macromolecule is separated from a large volume of solvent by a semi-permeable membrane which allows small molecules (such as ions, additives, buffer etc.) to pass through but prevents the passage of the macromolecule
The kinetics of the equilibrium will depend on the membrane cut-off, the ratio of the concentration of crystallising agent on either side of the membrane and the temperature and design of dialysis set up
Crystallisation dialysis set ups usually require large volumes of sample. The process has been adapted to use micro volumes. Membrane separates protein and crystallising agent
Membrane acts as a barrier for the protein only salt can diffuse into the protein
Button set up for smaller volumes.
Microdialysis design by …

53. Free interface diffusion
Also known as the liquid/liquid diffusion method
Equilibration occurs by diffusion of the crystallising agent into the biological macromolecule volume
To avoid rapid mixing:
Less dense solution is poured on more dense (salt usually)
Crystallising agent is frozen and protein layered on top
Use tubes of small inner diameter to reduce convection
Wax
Protein solution
Crystallising solution
May mimic microgravity – reduction of convection.
Diagram of a liquid/liquid set-up

54. Revisiting the Phase Diagram
Relate the methods of crystallisation to crystal growth
Batch
Vapour diffusion
Dialysis
Free interface diffusion

55. Precipitating agents
Chemical precipitants are used to achieve supersaturation in order to induce crystallisation, they can be divided into the following categories:
Salts
Straight chain polymers (e.g. PEG)
Organic solvents
The highest numbers of macromolecular crystals have been obtained using:
Ammonium sulphate, PEGs, Na/K phosphate, sodium chloride, MPD and magnesium chloride
There are two main groups:
Salts
Organic solvents (Polyethylene glycols (PEGs) can be classified as organic solvents)
The highest numbers of macromolecular crystals have been obtained using listed in descending order:
Ammonium sulphate, PEGs, Na/K phosphate, sodium chloride MPD and magnesium chloride
Pegs are long chain polymers Polyethylene glycols – PEGs - can be classified as organic solvents

56. Salts as precipitants
Salts work by disrupting the hydration shell of proteins minimising the attractive protein-solvent interactions and maximising the attractive protein-protein interactions
As a quick recap: Salts work by disrupting the hydration shell of proteins minimising the attractive protein-solvent interations and maximising the attractive protein-protein interactions

57. Organic precipitants
Organic precipitants function primarily by lowering the dielectric constant of the solution to reduce the electrostatic shielding of charged and polar functional groups on proteins
Most commonly used organic solvents are:
2-methyl-2,4-pentanediol (MPD)
Polyethylene glycols (PEGs)
Organic chemistry days crash out with acetone.

58. Poly(ethylene glycol)s (PEGs)
PEGs are very large polymers produced from a mixture of ethylene
Like other organic solvents PEGs lower the dielectric constant of the solution but they also affect the structure of water
PEGs may be contaminated with things such as aldhydes and peroxides – use crystallisation grade PEGs