This book deals with a truly interdisciplinary subject: protein condensation from solution. We use “condensation” in this book to denote one of several forms of proteins: a dense, protein-rich fluid phase, an amorphous aggregate, a gel, a crystal, or a polymer fiber. All these forms have been observed experimentally and are important in their own right. The primary purpose of the book is to bring to a wide audience the current status of research in the field, which is still evolving at a rapid rate. The bulk of the book deals with issues related to producing high quality protein crystals from solution, in which the bottleneck is crystal nucleation. Here the main challenge is to determine the initial solution conditions so that optimal crystal nucleation occurs. A second and increasingly important subject that we discuss involves diseases that occur due to undesired protein nucleation. A classic example is the nucleation of polymer fibers of sickle hemoglobin molecules within the red blood cells that distorts the cells and produces sickle cell anemia. Another example is that of age-related cataracts produced by the undesired aggregation of γ-crystallin protein molecules within the vitreous fluid of the eye. A third, somewhat different, example involves the role of amyloid β protein in Alzheimer's disease.

Overview

This book deals with the condensation of proteins from solution, including protein crystal nucleation and certain diseases related to undesirable protein condensation. We use the word condensation to describe a variety of possible states of matter, including dense, protein-rich fluids, amorphous aggregates, polymer fibers, gels, and crystals. Much of the book deals with understanding how to grow high quality protein crystals from aqueous solutions of protein molecules. This is of importance in structural biology, which deals with the study of the architecture and shape of biological macromolecules, and in particular with proteins and nucleic acids. Biologists are interested in knowing the structure of proteins, since structure determines function. To determine structure requires high quality protein crystals for use in X-ray crystallography. It is quite difficult to grow high quality protein crystals from solution, however; crystal nucleation is the major bottleneck in protein crystallography. Understanding the dependence of crystal nucleation on the initial conditions of the protein solution is a fundamental problem in statistical physics and is a major theme of this book. Understanding protein crystal nucleation is also important in biomedical research. For example, the sustained release of medications, such as insulin and interferon-α, depends on the slow dissolution rate of protein crystals [1–6].

Introduction

Lysozyme was discovered in 1922 by Alexander Fleming during his search for medical antibiotics. His method consisted of adding various matter to bacterial cultures, hoping to find those that would slow the bacteria growth. One day, while suffering from a cold, he added a drop of nasal mucus to the culture and found that it killed the bacteria, thus discovering one of our own natural protections against disease. Lysozyme has since been isolated in many other sources, including saliva, viruses, bacteria, plants, insects, and birds. The most easily obtained source of lysozyme is chicken hen-egg-white, from which it is extracted. Chicken hen-egg lysozyme is probably the most studied globular protein, with an enormous scientific literature. Its three-dimensional structure was determined by X-ray crystallography in the 1960s.

Lysozyme is a small enzyme that protects humans from bacterial infection. It attacks the protective cell walls of bacteria, breaking the carbohydrate chains in the walls, thereby destroying the structural integrity of the bacteria cell walls. As a consequence, the bacteria explode from their internal pressure. Due to its ability to kill bacteria, lysozyme has been used in pharmaceutical and food applications for many years. It also has many other functions, including inactivating certain viruses by forming insoluble complexes and directing anti-inflammatory activity.

Introduction

The crystallins are an important class of globular proteins whose functions are important in human vision. In particular, one member of this family, the γ-crystallins, has been extensively studied experimentally. The γ-crystallins, along with lysozyme and hemoglobin, are the most studied of the globular proteins. As is the case with lysozyme and hemoglobin, the γ-crystallins exhibit a metastable phase separation curve that has coexisting protein-poor and protein-rich phases. Indeed, when scaled with the appropriate variables, both lysozyme and γ-crystallin have very similar phase diagrams [16]. In this chapter we review what is known about the family of crystallins and their relationship to the formation of cataracts.

Understanding the molecular basis of vision is obviously of great importance. Long ago, nearsightedness was corrected using refractive lenses; today, newer scientific advances allow surgical procedures to eliminate nearsightedness. Other disorders and diseases, however, can impair our vision. Cataract disease is one example; it is often associated with aging and usually manifests itself sometime in late adulthood in certain individuals. Other forms of the disease occur in individuals at a much earlier age, even afflicting young adults and infants, often called juvenile cataracts. In both types of cataracts, blindness can occur if the disease is left untreated.

Another important globular protein that has received significant experimental and theoretical investigation is sickle hemoglobin. The reason it has received so much attention is that it is related to sickle cell anemia. This disease results from the polymerization of sickle hemoglobin molecules via a complex two-step homogeneous/heterogeneous nucleation process to form fibers in solution. Although this non-equilibrium fiber state eventually will form a crystalline state, for all practical purposes it is a long-lived pseudo-equilibrium state. This polymerization of sickle hemoglobin molecules does not occur in globular proteins such as lysozyme or the γ-crystallins. Thus its crystal nucleation process differs from most known globular proteins.

Sickle cell anemia is a genetic disorder that affects red blood cells, which become hard and pointed instead of soft and round. More than 70 000 residents of the USA have sickle cell anemia; about 250 000 babies are born with this disease each year worldwide. The genetic nature of the disease is that two genes for the sickle hemoglobin must be inherited in order to have the disease. If only one mutated gene is inherited and another gene is normal, the person has a so-called “sickle cell trait.” People who have this sickle cell trait will not develop the disease, but they can pass the sickle cell gene to their children.

Introduction

As noted in earlier chapters, intensive studies were carried out in the early 1990s to determine the effects on the phase diagrams of adding salt, decreasing temperature, or changing the pH towards the isoelectric value. These studies were typically performed on globular proteins with low molecular weight (such as lysozyme and the γ-crystallins). The reader should not think, however, that lysozyme or the γ-crystallins are typical of globular proteins. There is in fact a wide variability in the behavior of globular proteins. To illustrate this, we summarize the properties of a few additional proteins. We begin by presenting some results of an experimental study of the role of liquid–liquid phase separation in the crystallization of glucose isomerase. This study shows the possible complexity of crystallization processes, including its sensitivity to the choice of initial conditions in the phase boundary, as well as to the physicochemical properties of the system. It also illustrates the role of protein-rich liquid droplets in crystallization.

We also discuss results for α-crystallins, urate oxidase, bovine pancreas trypsin inhibitor (BPTI), and apoferritin, to illustrate the diversity of possible behavior. Most oligomeric proteins are not compact, which increases the repulsive hard core contribution to the interactions and correspondingly decreases the relative contribution of the short range van der Waals attractive interaction.

Crystal nucleation is the first stage of the protein crystallization process; it is usually considered the bottleneck in growing high quality protein crystals. Also, it not easy to measure crystal nucleation rates directly. The earlier indirect experimental studies of nucleation were performed using quasi-elastic light scattering (QELS) [246], dynamic light scattering [247–249], and also X-ray and neutron scattering. By using the diffusion approximation, one can extract from the scattering data the distribution of particle (molecules and aggregates) sizes. One peak in the scattering intensity corresponds to the molecule's size. The second peak corresponds to the aggregate size. Observing the second peak can provide some information about the nucleation kinetics. The disadvantage of such methods is that they require various assumptions about particle shapes and the scattering intensity distribution that are difficult to verify.

In this chapter we review several experimental studies of homogeneous nucleation. We note at the onset that it is notoriously difficult to avoid heterogeneous nucleation in experimental measurements. In fact, there is still an ongoing debate as to whether the observed nucleation for lysozyme, discussed in Section 8.1, is homogeneous or heterogeneous. We do not discuss this issue here; an excellent review of heterogeneous nucleation and its possible relevance to lysozyme is given in ref. [619].

All proteins are linear polymers of amino acids, large sequences of which constitute a peptide chain. Our focus is on globular proteins, whose peptide chain has a folded structure. In general, they are soluble in water and in other polar solvents. Although their structure is complex, we will see in this chapter that they often assume similar forms and that their shapes, sequence, and conformation can be understood by considering some fundamental aspects of their structure.

Amino acids and primary structure

The fundamental unit (monomer) of the protein molecule is the α amino acid. It consists of an acidic carboxyl group and an amino group attached to a single carbon atom, referred to as the α-carbon, and a hydrogen atom. This is illustrated in Fig. 2.1. A side-chain of molecules, designated as “R,” is also attached to the amino acid. This side-chain is specific to each amino acid and is what differentiates them from each other. The side-chains can vary in complexity; examples are simple hydrogen atoms, an extra amino group, an extra carboxylic group, a sulphydryl group, a hydroxyl group, or a simple hydro-chain or hydro-carbon ring. There are 20 biologically important amino acids listed in Table 2.1. The table also lists some proteins and their amino acid composition.

In this chapter we provide a brief summary of some of the methods used to study the physical properties of proteins in solution. This is not meant as a thorough discussion of experimental techniques, but rather as an introduction with sufficient references to provide the interested reader with a guide to the literature.

Methods to determine three-dimensional protein structure

As noted earlier, knowing the structure of a protein molecule is crucial to understanding its biological function. Over the past century, efforts have been focused on methods which allow protein structure to be determined. X-ray crystallography and NMR studies are two popular techniques, the former being predominant.

X-ray crystallography

X-ray crystallography [13, 14] of protein crystals is a well known technique, which we briefly summarize here. Its use for protein crystals, of course, depends upon the regular arrangement of protein molecules on a crystal lattice. When electromagnetic radiation of a given wavelength, such as X-rays, is incident upon a grating of appropriately sized spacings, the waves interfere constructively and destructively in a process known as diffraction. The diffraction pattern is a three-dimensional image of the crystal in reciprocal space and can be used ultimately to determine the real structure of the lattice; it represents the scattering of the X-rays by the electrons of the atoms in the crystal.

Classical nucleation theory

In this section we give a brief review of nucleation theories sufficient for understanding the following chapters. Very good reviews of nucleation theories can be found in refs. [208]–[212].

Nucleation is a stochastic process by which droplets of the new (stable) phase are formed in the background of the metastable phase. The stochastic nature of fluctuation means that the supersaturated system does not switch to the new stable state immediately; before this, a sufficiently large fluctuation with properties of the new phase should occur. This fluctuation is called a critical nucleus or critical droplet, and the formation of the droplet is called a nucleation event. Each nucleation event occurs randomly. The average rate of the nucleation events per unit of time per volume is called the nucleation rate. Homogeneous nucleation is the occurrence of nucleation events in the bulk, with no surfaces or impurities involved. Heterogeneous nucleation is nucleation that occurs on surfaces or impurities. Homogeneous nucleation is an intrinsic property of a system, whereas heterogeneous nucleation is not.

In the case of liquid condensation from vapor or crystallization from dilute solution, it is straightforward to identify the clusters of new phase, as they differ in density. However, this is not always the case.

Introduction

A major stumbling block in developing a first principles understanding of crystal nucleation is the lack of a detailed understanding of the forces that exist between protein molecules in solution. Proteins are complex molecules whose surfaces consist of amino acid residues that possess charged and uncharged regions and in general have complicated interactions with the surrounding electrolyte. The forces between protein molecules in solution include, for example, screened repulsive Coulomb interactions and attractive van der Waals interactions. In addition, protein–ion dispersion forces and hydrophobic and hydration forces play an important role. To further complicate matters, subtle mutations on the surface of these molecules (e.g. sickle hemoglobin, gamma crystallin) can have profound effects on their intermolecular interactions. One can imagine, therefore, how difficult it is, in principle, to determine a realistic model of protein–protein interactions. Progress to date has been based on rather simple models which are spatially isotropic, with short range attractive interactions. Clearly, more realistic models are needed to obtain a more quantitative understanding of the protein phase diagram, nucleation rate, and subsequent growth. One important aspect of the interactions between globular protein molecules, which is only recently being considered by theorists, is that many of the interactions are highly directional.

In this chapter we review some of the existing theoretical studies of models for the phase diagram of globular proteins. Almost all studies to date treat the multicomponent solution as a quasi-one-component solution, with a potential energy of interaction (e.g. potential of mean force) between the protein molecules that is usually assumed to be spatially isotropic. Typically, the interactions consist of a repulsive hard core and a short range attractive interaction. The majority of these studies involve simulation techniques, particularly the Gibbs ensemble Monte Carlo method, although studies based on thermodynamic perturbation theory, finite size scaling theory, and various theories for the radial distribution function also exist. These models have in common the feature that, for sufficiently short range attractive interactions, the fluid–fluid coexistence curve is metastable. Their phase diagrams look qualitatively similar to experimental diagrams, such as that shown in Fig. 4.4. In addition to these studies, we discuss a theoretical estimate for the rather narrow window of values for the range R of the attractive interaction within which the boundary between stable and metastable fluid–fluid transitions is located. We also discuss recent theoretical studies of spatially non-isotropic models that are more realistic descriptions of protein–protein interactions.

The idea that the range of the attractive interaction between protein molecules should be small as compared with the molecular size has its roots in the seminal observation by George and Wilson [25] that for several globular proteins the optimal window of crystallization corresponds to small negative values of B2.

Introduction

Another globular protein, amyloid β protein (Aβ), plays an important role in Alzheimer's disease (AD). This is a devastating disease that, if left unchecked and untreated, threatens to affect over 13 million Americans by the year 2050 [520]. About one in ten people over the age of 65 and as many as five out of ten people over the age of 85 are affected by AD. In the twentieth century, it was found by looking at deceased patients suffering from Alzheimer's that the brains of such individuals contained plaques and neurofibrillary tangles [521–523]. Over the past 20 years, we have gained a more molecular understanding of the causes of AD. Indeed, the primary protein component of these plaques was sequenced [524, 525]; in addition, the protein that is the building block of the neurofibrillary tangles has now been sequenced. Such knowledge has obviously led to a focused concentration on these phenomena. Indeed, at first it was believed that these plaques and tangles were the prime causes of the disease. Recent studies, however, point to another possible cause. In this chapter we summarize our progress in understanding AD. Although our understanding of the disease is still developing, the mechanisms causing AD are better understood.

Introduction

Membrane proteins play a significant role in biological processes, including biological energy conversion and photosynthesis. They also can act as signal receptors and transmitters of hormones, light, or chemicals. However, there is far less structural information about these proteins than about globular proteins. A major factor is their insolubility in aqueous solutions. As a consequence, far fewer membrane protein structures are known than for globular proteins; the number of successfully crystallized membrane proteins is well below 100.

Membrane proteins are different from globular proteins in one main respect: the former are usually “anchored” to a membrane lipid layer. Two predominant types of interactions are responsible for the overall structure observed in a membrane: hydrophobic and hydrophilic interactions. Other non-covalent interactions are present as well, such as hydrogen bonding and electrostatic interactions. However, hydrophobic and hydrophilic interactions are the main forces responsible for the overall structure of a membrane and its attached proteins [350]. Hydrophobic interactions are responsible for keeping a non-polar object away from polar groups such as water. The well known example of the immiscibility of hydrocarbons (i.e. oil) and water applies. An object is termed hydrophobic if it prefers to be oriented away from water. More specifically, it would require a significant expenditure of free energy to transfer a hydrophobic particle from a non-polar environment to a polar one.