Uncovering protein structure

Proteins are one of the most important classes of molecules for life and underpin the field of biochemistry. To fully understand their role, it is essential to explore both their structure and function and this review focuses on how we uncover protein structure. To understand structure, we explore the chemical nature of amino acids which are the building blocks of proteins. We consider how interactions between amino acids help proteins fold and fluctuate as they adopt a variety of structures. Furthermore, to understand how we experimentally study protein structure, we explore fundamental concepts in physics and associated computational methods. This topic is truly interdisciplinary and in addition to biochemistry, spans the fields of biophysics, structural biology and computational biology.

We start by describing the four levels of protein structure and how a variety of protein domains and architectures exist. Proteins are biological molecules produced in living cells, and we must also consider how a long chain of amino acids that are produced from the ribosome can transition to a folded structure that is central to the protein’s function. As such, we consider protein folding thermodynamics and also what happens when proteins misfold inside a cell. We also explore other universal properties of proteins that include their ability to change their shape known as conformational change. In particular, although proteins usually exist in one dominant conformation, we discuss how proteins actually exist in a population (ensemble) of rapidly interconverting conformations that allow them to be flexible and adapt their shapes required for function. We then discuss in detail the primary techniques used to study protein structure and dynamics that have provided these insights. Given the interdisciplinary nature of this topic, along the way, we have provided some stand-alone boxes to give more details about the fundamental science behind these concepts.

Proteins are one of the four major molecules that direct life that includes nucleic acids (deoxyribonucleic acid (DNA), RNA), lipids (fats) and polysaccharides (sugars). All of these large ‘macromolecules’ are carbon-based covalent compounds that use weak reversible non-covalent interactions to fold and interact with their targets, giving the molecules and their complexes distinct shapes and dynamics. Proteins are polymers of typically hundreds of amino acids joined together by peptide bonds, whereas shorter polypeptides (less than 30 amino acids) are typically referred to as peptides. Each amino acid has a common structure containing a central α carbon atom (C_α) that is joined to an amino group (–NH₂) and a carboxylic acid group (–COOH) both of which are used to form peptide bonds. What is most interesting, is that for 19 of the 20 different amino acids, the C_α group is also bonded to a different R group, giving every amino acid its unique ‘side chain’. The side chain gives the amino acid distinctive structural and chemical properties as side chains differ in size, shape, polarity, charge and hydrophobicity (Figure 1). Amino acids are also chiral and can be configured in two possible mirror images (stereoisomers) as the C_α group is bonded to four unique groups that form a chiral centre. As mirror images, stereoisomers cannot be superimposed, in the same way, your hands are mirror images and cannot be rotated to match. The two stereoisomers for each of the 19 chiral amino acids are denoted as d and l, however only the l-stereoisomer is used in nature to construct proteins (glycine has hydrogen for a side chain and is not chiral).

Once amino acids are linked together to form a polypeptide chain, the sidechains and backbone groups interact with each other through many weak interactions to include van der Waals, hydrogen bonds, electrostatic interactions as well as the hydrophobic effect to bring about a protein’s shape and target interactions (Figure 2). For example, the side chain of lysine has a long hydrocarbon chain which is non-polar, yet the end of the chain is positively charged allowing it to interact with other molecules using any of the weak interactions described above. Glutamic acid on the other hand is a similar size but carries a negative charge and has fewer potential ways of interacting. In addition to the sidechain interactions, the peptide bond carries a dipole due to the electronegative properties of the bound oxygen, allowing it to form hydrogen bonds with backbone and mainchain groups. Since there are 20 different amino acids, and they can be arranged in any order, there are a vast number of possible linear combinations and organisms have evolved tens of thousands of different proteins and peptides. Proteins do not usually exist as extended chains, and through sidechain and backbone interactions they fold in on themselves, leading to a unique shape. Each shape has a way of moving and interacting with other molecules bringing about its function. The range of shapes means proteins are extremely versatile, sometimes acting as enzymes to catalyse chemical reactions, sometimes as a type of messenger that binds to a specific partner to relay a message and other times acting as a structural scaffold within the cell (Figure 3). In contrast, DNA usually adopts the classic double-helical structure regardless of its sequence, which suits its function to store genetic information.

Since almost every function crucial to life is mediated by proteins, any changes to their structure due to damage, mutation or modification explains the cause of the disease at the molecular level. The classic example is that of haemoglobin. When an individual inherits a variant haemoglobin gene where the glutamic acid (R group is charged) at residue position six is changed to valine (R group is hydrophobic), this leads to sickle cell disease. This one amino acid difference changes the surface of haemoglobin by removing the negative charge and forming a hydrophobic ‘sticky’ patch (in the absence of oxygen), causing deoxyhaemoglobin to clump together. Since this protein is in high concentrations in red blood cells, it converts the cells from a standard disc into a sickled shape, which reduces cell lifetimes, leading to anaemia, and can result in the blockage of capillaries leading to tissue damage.

To understand protein structures in more detail, we next explore the four levels that determine their shape.

Protein structure is described at four different levels. The arrangement of amino acids in a polypeptide chain is referred to as its primary structure. Each amino acid in a polypeptide chain is referred to as a residue and the linked series of carbon, nitrogen and oxygen atoms are known as the main chain or protein backbone. The first amino group at the start of the peptide chain is known as the N-terminus, and the end with the carboxylic acid group is the C-terminus. When we count or write the residues in a polypeptide chain, we start with the N-terminus. The location of disulphide bonds that covalently link different parts of the polypeptide chain together are also considered part of the primary structure. These bonds are formed between two cysteine residues via their side chain thiol groups (–SH) and they significantly stabilise protein structures.

Protein secondary structure refers to the way the primary structure of a protein arranges itself as a result of regular hydrogen bonds forming between the backbone C = O and NH groups of each peptide bond. However, the peptide bond itself cannot rotate as it has double bond character due to resonance stabilisation (Figure 4), where the nitrogen donates its lone pair of electrons to the carbonyl carbon, pushing electrons towards the oxygen. This results in the electrons being delocalised over multiple atoms, which increases bond stability and decreases rotation (Figure 5A). Therefore, rotation can only occur about the bond between the C_α and the C = O group, (the phi (φ) angle) and the C_α and the NH group, (the psi (ψ) angle). In effect, the polypeptide backbone chain is composed of a repeating series of two rotatable bonds followed by one non-rotatable (peptide) bond. However, not all 360^o of the psi and phi angles are possible as neighbouring sidechains can clash due to steric hindrance. In effect, for certain angles and amino acid combinations, the atoms cannot be in the same physical place and this partly explains why some amino acids have a higher propensity (likelihood) to form different types of secondary structure. Within these restraints, the two principal local conformations that avoid steric hindrance and maximise backbone–backbone hydrogen bonding are the α-helix and the β-sheet secondary structures (Figure 5).

The α-helix is a right-handed coil in which backbone NH group hydrogen bonds to the backbone C = O group of the amino acid located four residues earlier along the protein sequence. This results in a polypeptide chain that twists in a regular coil shape with the R-groups pointing outwards away from the peptide backbone. It takes approximately 3.6 residues to complete a full turn of a helix.

β-sheets are composed of two or more extended polypeptide chains called β-strands that run alongside each other. They can be arranged in either a parallel or antiparallel manner. The residues arrange themselves in a regular zigzag manner with the adjacent peptide bonds pointing in opposite directions. In this arrangement, the NH group and the C = O group of each amino acid is hydrogen-bonded to the C = O group and NH group respectively on the adjacent strands. Chains can run in opposite directions, forming an antiparallel β-sheet, or in the same direction, forming a parallel β-sheet. Sidechains from each of the residues point away from the sheets and alternate in opposite directions between residues. It is common to see a pattern of alternating hydrophilic and hydrophobic residues in the primary structure, giving the β-sheets hydrophilic and hydrophobic faces.

The overall three-dimensional (3D) appearance of a protein is known as its tertiary structure and is brought about by the interactions between the side chains (R groups) and the way in which the secondary structure packs together to fold the protein. Quaternary structure refers to how multiple folded protein chains (called subunits) interact and arrange to form a larger multisubunit protein complex. Examples of the tertiary and quaternary structures were seen in some of the first proteins that had their structures solved using X-ray crystallography, as seen in Figure 3. Protein structures are often viewed as models in which the β-strands are represented as arrows and the α-helix as a ribbon or tube. For example, haemoglobin is an α-helical protein with a quaternary structure comprising four subunits, known as a tetramer. The structure can be seen in Figure 3 as a cartoon covered by a transparent molecular surface of the protein. As more proteins were solved, it became clear that there were many different protein shapes and folds, and they appeared to be organised into distinct units called protein domains. Currently, there are approximately 165000 protein structures, and their tertiary and quaternary structures are classified into groups according to two major classification systems called CATH and SCOP. We will focus on the concept of protein domains in the next section.

A protein’s shape comes from the arrangement of secondary structure elements such as α-helices and β-sheets into recognisable conformations called motifs (or super secondary structure). Motifs are short segments of a protein’s structure, and the same arrangement can be found in many different proteins. For example, the β-turn links β-strands together and consists of four consecutive residues which allow the polypeptide chain to fold back on itself by nearly 180 degrees. The β-α-β motif consists of parallel β-strands that are connected by an α-helix that crosses the two strands. Secondary structure elements and motifs are arranged in individual proteins into compact independent 3D structures called domains. Unlike motifs, domains fold independently of the rest of the full-length polypeptide chain. Larger proteins are often formed of multiple different domains linked together with each domain having a structural or functional role (Figure 6). The arrangement of secondary structure elements that describe a protein domain’s shape is called its fold. For example, a Rossman fold has 2× β-α-β motifs with a shared middle β-strand forming the domain. This particular domain is found in many larger proteins, giving it the ability to bind nucleotides. Remarkably, there are only ∼2200 recognisable protein folds despite the vast number of amino acid combinations possible.

Another way to classify proteins is according to the four main protein ‘types’ which all correlate with characteristic sequence and structural features:

1. Globular (roughly spherical) and soluble proteins (for example, enzymes found in the cytoplasm)

2. Membrane proteins within the cell or organelle membrane (for example, receptors)

3. Fibrous proteins (characterised by the presence of repetitive sequence motifs, for example, collagen)

4. Intrinsically disordered proteins (described later in the text)

There are many other ways to classify protein domains, and two of the most commonly used systems are the CATH and Structural Classification of Proteins (SCOP) systems (Table 1). Both are hierarchical domain classification systems in which proteins are organised into different levels based on the structural and sequence similarities, and each has websites that you can explore.

Over evolution, multicellular organisms have generated new large proteins by mixing and matching existing domains into new combinations. Since each domain has a particular function (such as binding or catalysis or gene activation), these new proteins will have a unique combination of properties depending on the domains they contain. Proteins sharing more than a few common domains are usually encoded by members of evolutionarily related genes. They therefore make up gene families that have a common ancestor and equivalent domains within the family have high-sequence conservation. These domains are called orthologues and the proteins they reside in usually play a similar role in all species. Genes for proteins that share only one or a few domains may belong to a gene superfamily. Superfamily members can have one function in common, but their sequences are otherwise unrelated. Similar domains found in different full-length proteins in the same organism are called paralogues. Often, they diverged from a common ancestor a long time ago and these domains usually only have the most essential structural and functional properties conserved. A large protein with various domains will each need to fold from the initial linear polypeptide chain, and this process is considered next.

A protein domain in its functional and/or assembled form is referred to as being in its native state. This state results from the amino acid side chains present on the polypeptide chain making favourable interactions with each other and stabilising the protein. However, when a protein domain is first translated by a ribosome from mRNA it exists as a linear chain of amino acids which lack structure and is referred to as being unfolded or ‘denatured’. In this state, these interactions are yet to form. If the unfolded protein domain were to randomly search through all possible conformations it could make by testing out all the possible combinations of interactions, the process of finding the native state would take longer than the age of the universe! However, most protein domains can fold spontaneously into their ‘native state’ on the order of 10⁻⁶ to 10⁻¹ s. The process by which the unfolded protein domain gains its compact 3D native state is known as protein folding and is studied by thermodynamics and kinetics [For a reminder of the fundamentals of thermodynamics and kinetics please refer to the Essential Chemistry for Biochemists article in this series and the Thermodynamics Box (Box 1)].

Every spontaneous (favourable) reaction in nature results in lowering its free energy as dictated by the laws of thermodynamics. For example, the folding of protein domains is a spontaneous reaction when a negative change in Gibbs free energy (G) occurs, and the protein domain moves to a lower energy state. Change of Gibbs free energy (ΔG) has two components that are influenced by temperature; change of enthalpy (H, a measure of the formed and broken bond energies in the system) and change of entropy (S, a measure of the change of system ‘disorder’) as seen in (eqn 2) in the Thermodynamics Box (Box 1). The driving force for protein folding is a result of hydrophobic collapse, hydrogen bond formation, electrostatic interactions and van der Waals interactions that lower the free energy. According to (eqn 2), for a negative ΔG and for protein folding to become thermodynamically favourable, the change in these interactions must result in either a favourable change in system enthalpy (ΔH) and/or entropy (ΔS).

When amino acids form new hydrogen bonds, van der Waals and other electrostatic interactions it results in releasing heat, while breaking these bonds with water results in absorbing heat. Therefore, the relative amount of bond formation to bond breakage in the unfolded and folded states will determine ΔH. However, the basis of the hydrophobic effect (collapse) is an increase in the entropy of protein-associated water and is the most important driving force in protein folding. When a protein domain is present in its unfolded state, water molecules have to order themselves in ice-like structures around the hydrophobic groups of the polypeptide chain which forces order on the system and so has less entropy than the free water molecules. Solvent entropy is increased by the protein domain collapsing and placing the hydrophobic side chains into the middle of the protein (Figure 7A). As a result, the hydration shells around the side chains are no longer required, and these water molecules become disordered (free to sample multiple states and interactions), causing a positive change in entropy for the system (ΔS). It should be noted that as a protein domain folds, the polypeptide chain loses entropy as it adopts a single dominant folded conformation (shape), however this decrease in entropy is often offset by the hydrophobic effect described above.

For any given protein, several different folding pathways exist that allow the same protein to reach its native state by different routes. Experimentally we cannot distinguish these individual ‘microscopic’ pathways and can only monitor the ‘macroscopic’ changes along the reaction coordinate using spectroscopic methods (for example, by measuring the fluorescence or CD signal changes as the protein folds in real time). If we represent the associated free energy of the ‘macroscopic’ ensemble of pathways, we generate a classical energy diagram (Figure 7B) that shows the free energy of the protein as it goes from an unfolded ensemble (left) to a folded ensemble (right). Often, small protein domains of a few hundred amino acids can fold in a single step, passing through a high energy transition state ensemble. However, larger protein domains often pass through a number of intermediate states that are stable but not fully folded, before the process is complete. The classical view is useful to interpret experimental measurements however theoretical and computational studies are now working on the new view of folding that tries to understand and represent the microscopic pathways. Here, proteins are multistate objects that fold through multiple unpredictable routes and intermediate conformations. This folding is represented by a more complex funnel-shaped energy landscape in which the proteins energy and number of conformational states decreases as the protein moves down the funnel.

Protein domains fold because the native state releases water to a more disordered state (increasing entropy) and the new bonds (compared with the old bonds) usually result in heat being released, decreasing the enthalpy. Together, this causes the Gibbs free energy to decrease and makes folding spontaneous. However, just because the folded protein is lower in energy than the unfolded protein, this only indicates that the process is favourable to occur. The speed at which it occurs (the rate of the reaction) is independent of ΔG and instead is governed by the size of the barrier between the energy of the unfolded protein ensemble and the energy of the transition state ensemble (also known as the activation barrier or ΔG^# for folding). The lower the energy of the transition state ensemble, the faster the protein folds, which can be as fast as microseconds. We still do not fully understand how to predict how a protein domain will fold, how favourable it will be and how fast it will proceed. One approach to learn the rules is to study how humans engage in a protein folding game. If you want to get involved and have fun trying to fold your own protein using your computer, please visit the ‘fold.it’ site.

Every domain within a full-length protein will usually fold independently; however, sometimes, one or more domains can misfold, and the protein sometimes gets tangled up, forming a protein aggregate, which is described next.

Most of the time, folded proteins stay folded, however, under certain conditions, normally stable natively folded proteins can partially unfold and assemble into a multisubunit aggregated form known as amyloid. The formation of amyloid is associated with a range of increasingly common human disorders, including Alzheimer’s and Parkinson’s diseases as well as type II diabetes where it builds up in organs and tissues throughout the body. Different proteins can form amyloid and each is associated with its own disease. What is intriguing about amyloid is for a range of protein structures, the final amyloid material they adopt shares a remarkably similar structure.

Under an electron microscope, amyloid looks like long unbranching fibres composed of filaments that wrap around each other like threads in a rope. At the protein structural level, the filaments are made up from parallel extended β-sheets structures, known as cross-β. Individual β-strands are stacked in-register, one on top of the other, running perpendicular to the fibril axis. Sidechains protrude from the sheets, and the hydrogen bonds that hold the sheets together run along the length of the cross-β fibril. Since β-sheets are held together by peptide backbone interactions that all proteins can make, this helps explain why so many proteins can adopt this structure (Figure 8). As well as their similar structures, amyloid fibrils from different proteins all have the ability to bind histological dyes.

Amyloid assembly starts with the protein adopting a partially unfolded conformation. This state is neither fully folded nor unfolded and retains secondary structural elements such as β-sheets and α-helices. However, it loses the defined tertiary structure and tight packing of a folded protein. Experimentally, low pH, high temperature and low concentrations of denaturants are also all known to promote adoption of partially unfolded conformations. Mutations, where one amino acid is swapped for another, can also cause the partially unfolded conformation to be more easily adopted. As people age, there is also a gradual breakdown in the cell’s ability to remove occasionally misfolded proteins and explains why some amyloid diseases like early-onset Alzheimer’s are hereditary and age-related. It was initially thought that the amyloid fibrils were responsible for bringing about disease, but it is now more accepted that it is a structure called an oligomer, populated in the early stages of amyloid formation that is the most toxic entity. Oligomers are flexible and soluble existing in several forms. They bring about a toxic gain of function, and solving their structure remains one of the significant challenges of structural biology. In fact, all folded and misfolded proteins regardless of their structure, have a range of flexibility and dynamics that is central to their function and this is considered next.

Proteins are not static and often appear to change their initial native folded structure to allow binding or catalysis to occur. For example, the enzyme hexokinase (Figure 3) that is involved in the first step of glycolysis (the breakdown of glucose) changes conformation. This enzyme contains two (sub)domains and the active site is found between them. Interfaces between protein domains are an ideal place to create active sites as the two parts can shift relative to each other in response to what happens between them. When the substrate glucose binds to the active site region in the open conformation, the two domains change their position to ‘clamp down’ on the substrate to form a closed conformation. This conformational change allows hexokinase to position its catalytic residues around glucose. Once enclosed in the active site, the substrate is phosphorylated using a molecule of bound adenosine triphosphate (ATP), resulting in the production of glucose-6-phosphate.

Hexokinase and other proteins in general are not just limited to a few conformational states, instead proteins are better thought of as dynamic molecules undergoing exchange between states. They are continually undergoing motions where atoms vibrate, bonds wiggle and at times more significant fluctuations occur as the protein samples other possible conformations. These structural changes and dynamic motions are essential for substrate binding and many other functions. With computer simulations, we are starting to visualise the complete process in real-time, in molecular movies generated by molecular dynamic simulations. These movies highlight why folding, structure, dynamics and interactions are central to understanding protein biology. As we will see, some intrinsically disordered proteins (IDPs) naturally exist unfolded all of the time yet do not form amyloid and are therefore even more dynamic, having many more interactions with other biomolecules.

An interesting consequence of conformational change is that after one ligand has bound to a protein, it may change the shape of a separate binding site such that the binding affinity of another ligand at that distant site also changes. In other words, the second ligand may have a different affinity to its target protein depending on whether the first ligand is bound. This concept is known as allostery and is central to the regulation of proteins and enzymes. For example, in haemoglobin, there are four subunits, each containing a haem group that binds oxygen (Figure 3). Oxygen binding at the four haem sites does not necessarily happen simultaneously. Once the first haem binds oxygen, it introduces small changes in the structure of the corresponding protein chain (subunit). These changes nudge the neighbouring chain causing a subtle rotation into a different shape, which allows further oxygen molecules to bind more easily (Figure 9). This effect is called positive allostery as it makes the next event more likely to occur. Allostery is central to regulating metabolic pathways as enzymes at the start of the pathway can be inhibited when the levels of product rise too high via feedback inhibition. The final product usually causes a conformational change in the first (committed) step enzyme such that its substrate can no longer bind as well to its active site. This process is called negative allostery (Figure 10).

Proteins undergo many other types of motions such as internal vibrations and rotations of methyl groups and collective motions of groups of atoms such as wigwag motions of long sidechains or flipping of short peptide loops. Each of these movements is extremely important and is also often central to the protein’s function (Table 2). As the number of exchanging conformations increases, it is simply not possible to represent a protein with a single structure. Instead, one must describe them as a population of multiple interconverting conformations known as a structural ensemble. Structural ensembles are especially relevant when a protein has a large intrinsically disordered region (IDR) that has a low number of bulky hydrophobic amino acids so that in isolation it remains unfolded despite other parts of the protein being folded. Some proteins are so flexible and dynamic that they are classed as being intrinsically disordered proteins and have no defined secondary structure at all. This is a relatively recent understanding as unfolded proteins were thought to result only from conditions such as extreme heat or acidity or from severe mutations. In fact, there appears to be a continuum for proteins with some, where one structure dominates to others that are fully disordered and better described as a dynamic ensemble of unstructured conformations.

Over the past 20 years, there has been considerable interest in disordered proteins as approximately one-third of human proteins contain disordered regions that are 30 or more amino acid residues long. Due to their fluctuating structures disordered proteins offer many advantages for cellular function. The flexibility of a disordered protein, means that the protein can easily be accessed by enzymes such as kinases that can post-translationally modify them (in the case of a kinase enzyme this would add a phosphate group). In many cases, when a disordered protein or region binds a target, it undergoes a conformational change to a better defined structure (Figure 11). The same protein can act as a molecular hub and bind a range of molecules including small ligands, membrane surfaces or other proteins. Folding on binding does not always have to happen, and multiple binding events can simultaneously work together on a disordered protein to change its structure and dynamics. The disordered protein may need to bind several molecules before it gains a 3D shape. For the correct combination of stimuli, this will create a new specific ensemble that forms an appropriate binding site to bind the next target in a signalling cascade, leading to the correct response. It is, therefore, not surprising that disordered proteins provide a way to regulate cell signalling. In this process, signals that come from outside the cell get converted into responses inside the cell. The same disordered protein can process multiple stimuli enabling quick and flexible responses to the changing conditions that cells face. Disordered proteins are also involved in cell cycle activities, transcription and translation, cargo transport and apoptosis. Another exciting area for disordered proteins is their ability to self-assemble into multiprotein complexes and still maintain a fairly extended, non-globular shape, as would be expected for independently folded proteins. These extended conformations allow disordered proteins to become a molecular glue that has a much larger surface area for contacts between proteins and cements the complex together, as can be seen in the assembly of the yeast ribosome.

Finally, disordered proteins with ‘multivalent’ or ‘multiple interaction’ sites have been shown to engage in rapid dynamic exchanging interactions with each other that can cause liquid–liquid phase separation. In these cases, instead of forming amyloid or a defined large complex, some disordered proteins come together to form a separate liquid phase inside the cell that is enriched with these multivalent molecules. The new liquid phase that is formed is called a biomolecular condensate and allows the cell to organise and concentrate molecules involved in a given biochemical reaction just like classic membrane-bound organelles such as the mitochondria. For this reason, they are often referred to as membrane-less organelles. Some of these liquid phases can be seen directly under the microscope, such as the nucleolus and Cajol bodies and the molecules within them carry out distinct roles in the cell. Disordered proteins are therefore extremely important in the cell and in the future will prove central to further understanding how protein structure explains function.

The insights concerning protein folding, structure, dynamics and interactions have all come from using a range of experimental tools, which we will now explore.

There are a wide number of tools available to the structural biologist to allow protein structure and dynamics to be determined. Basic spectroscopic methods such as circular dichroism (CD) or fluorescence give general information about structure, whereas high-resolution methods such as X-ray crystallography, nuclear magnetic resonance (NMR) and cryogenic electron microscopy (cryo-EM) can provide atomic descriptions of protein structure and dynamics. Each of these tools require pure protein, usually in the form of recombinant proteins. Today a wide variety of different biological organisms can be genetically modified to create the required protein synthetically in large quantities, which has led to huge progress in methods that can study protein structure and dynamics.

To study proteins, we use electromagnetic radiation (see Box 2, Properties of Light Box) to probe their structural and functional properties using a fundamental experimental technique called spectroscopy. Spectroscopy is the study of the interaction of electromagnetic radiation (light) with matter, in our case proteins. Several closely related events can occur depending on the amount of energy that the radiation carries. In the first example of absorption, electromagnetic radiation is captured by a protein sample, which converts the energy of the photon into internal energy. Atoms within proteins are composed of a nucleus containing neutrons, protons and dispersed electrons. Electrons, however, are not merely floating within the atom but are instead fixed within electron orbitals. There are multiple electron orbitals within an atom, and each has its an energy level associated with it. Since the energy levels of matter are quantised, only light of energy that can cause transitions from one existing energy level to another will be absorbed. The amount of energy carried by a light photon depends on wavelength. The shorter the wavelength, the higher the energy carried by a photon; hence, ultraviolet (UV) light carries more energy than visible light. When a molecule absorbs a photon of the correct energy, an electron is promoted from its ground state to an excited state. This occurs if the energy of the photon, corresponding to the energy gap between the ground state and an empty higher energy level (the excited state). After absorption, the energy is then lost to the solvent as heat (thermal energy) when the electron drops back to the ground state. An absorption spectrum measures the amount of light that passes through a sample at a variety of wavelengths. The spectrum depends on the type and arrangement of atoms in the sample and can make absorption spectra useful for identifying different molecules. In this way, absorption spectroscopy can be used to reveal some very basic information about the structure and conformational states of a protein.

For a given wavelength, if the extinction coefficient (ε) is known then by measuring the amount of light that a protein sample absorbs (A) and using the known pathlength (l), we can work out its molar concentration (c).

Circular Dichroism (CD) spectroscopy is a form of UV light absorption spectroscopy that is used to determine the secondary structure of proteins. To understand how the process works, we must investigate the properties of light. Each wavelength of light has associated time-dependent electric and magnetic fields that oscillate between peaks and troughs in the direction of travel. The intensity of the light (amplitude) is a measure of the relative height of the wave. Wavelength is a measurement of the distance between the peaks in metres. Light waves are said to be in phase if the peaks and troughs of the waves line up (see Box 2, Properties of Light Box). It is possible, by use of filters, to generate plane polarised light with an electric field that oscillates in just a single plane. If you are looking into the path of this light and could see it coming towards you, vertically polarised light would oscillate up and down in a single plane. If you combine in-phase horizontally polarised light with vertically polarised light, you will generate plane polarised light wave that oscillates back and forth at 45 degrees (average of the two) (Figure 12A). Something exciting happens when you combine two perpendicular plane polarised light waves of equal amplitude, but that differ in phase by a quarter as they generate circularly polarised light. The result is an electric vector that rotates either clockwise (left) or anticlockwise (right) as it propagates. In this case, if you could see the peak of the electric field as the wave came towards you, it would appear to rotate (Figure 12B). This circularly polarised light is shown as a spiral and referred to as left- and right-circular polarised light (LCP or RCP in Figure 12C). To view some excellent movies that illustrate how circularly polarised light is generated from combining plane polarised light, see the references in further reading.

If left- and right-circularly polarised light are superimposed, and after absorbance, the amplitudes are equal, the result is back to generating plane polarised light (Figure 12D, left). However, if the amplitudes are unequal because one absorbs more than the other as the light passes through a protein sample (as seen in Figure 12C), the resulting light is elliptically polarised light (Figure 12D, right). The angle made by the big axis of the ellipse with respect to the original polarisation plane is measured in degrees (θ) which are the units seen on a raw CD spectrum. Since this value is usually quite small, it is often quoted in millidegrees (1/1000 of a degree). Symmetrical molecules absorb left- and right-circularly polarised light equally. Non-symmetric/chiral molecules such as proteins that contain secondary structure interact with the light and absorbed left- and right-circularly polarised components differently. Differences in the absorption of left- and right-handed circularly polarised light by the secondary structural components of a protein over a range of wavelengths give rise to a CD spectrum.

When working with proteins, mean residue molar CD (Δε_MR) is used which reports the molar CD for individual protein residues instead of the whole protein. This allows direct comparison between proteins of different sizes. To do this the mean residual concentration (Molarity multiplied by number of of amino acids) is used in place of the Molarity in the above equation, essentially treating the protein as a solution of its free amino acids.

$$CD spectroscopy is well suited to proteins as the peptide bonds that dictate secondary structure are optically active. Different secondary structures types absorb left- and right-circularly polarised light to different amounts meaning α-helix and β-sheets have different Far UV-CD spectra with recognisable shapes (Figure 13). An α-helical protein, for example, will have a positive peak at ∼190 nm and negative peaks at 222 and 208 nm giving a characteristic double-humped spectrum in the far UV wavelength range (between 180 and 260 nm). These spectra can be compared to reference spectra that exist for proteins that are 100% α-helix, β-sheet or random coils (Figure 13), as well as more complex libraries of protein with mixed structures. A mathematical process known as deconvolution can then be used to work out the relative fractions of each secondary structural type by summing different combinations of these reference spectra. Another common use of CD with proteins uses the absorbance of the side chains of Phe, Tyr and Trp in the near UV wavelength range (250–350 nm) to give limited information about the tertiary structure of a protein. The absorption of the side chains tells us how well the secondary structure elements are packed together as well as indicating interactions with ligands that bind to the protein surface.

CD is widely used to see if proteins are folded following purification and before attempting more involved techniques such as X-ray crystallography. CD gives detailed information about a protein’s secondary structure, but it does not tell us about the precise 3D structure, and for that, we need more complex methods such as X-ray crystallography, NMR and cryo-EM.

Although CD spectroscopy indicates the secondary and tertiary structure of a protein in solution, it does not provide structural detail at the atomic level. X-ray crystallography however reveals the accurate structure of biomolecules held within crystals. X-rays are used as they have a wavelength that closely approximates the length of covalent bonds. This means they are ideal for resolving atoms separated by these distances. Modern crystallography methods are usually performed at cryogenic temperatures allowing large (between 2 and 100 nm) complex structures to be determined. One of the most important structures determined was that of the ribosome and led to the award of the Nobel Prize in 2009 (Chemistry) to Ada Yonath alongside Venkatraman Ramakrishnan and Thomas A. Steitz. Such discoveries and innovation have transformed our understanding of biology by allowing access to the atomic detail of biomolecules.

The hanging drop vapour diffusion method is a common method used to form crystals. The process begins by using a highly concentrated pure protein in a buffered solution. The protein sample is suspended as a drop over a liquid reservoir of buffer in a sealed container. The drop contains a lower concentration of buffer components than the reservoir. Equilibrium between the drop and the reservoir is achieved by the water vapour leaving the drop and moving to the reservoir. The movement of water between the drop and the reservoir increases the concentration of the protein until it becomes supersaturated and starts to form a crystal.

Crystals are a highly ordered arrangement of individual protein molecules. When an X-ray beam is focussed on a protein crystal, the electric component of the electromagnetic X-ray waves interacts with the atom’s electron clouds surrounding the nuclei of the atoms leading to diffraction (Figure 14). The diffracted X-rays generate spots (also called reflections) on a detector (digital camera) that have an intensity. The spots are the result of reflections of the crystal at a certain angle (2θ) relative to the original beam according to the geometric laws of constructive interference in crystals first described by Bragg (see Box 3, Bragg’s Law box). The waves that generated the measured reflections can be represented as a periodic cosine wave by; y = Acos(x + θ. A is the amplitude, which can be calculated from the intensities of the diffraction spots (square root of the intensities) and θ, which is the phase of the wave and unfortunately cannot be recorded. Due to the flat nature of the detector, only a subset of diffraction spots are recorded at any given X-ray-to-crystal angle. Therefore, the experiment is repeated with the crystal rotated to multiple different orientations which allow the angle of the incoming X-rays to change with respect to the crystal providing new reflections. After all diffraction patterns are recorded, for any given protein, a dataset of spots is collated that corresponds to many of the possible constructive interference diffraction events for the crystal. Unlike visible light microscopy, there is no lens to refocus these rays and we need the mathematical power of a computer to convert the X-ray data into electron density which allows us to form an image of the protein. X-ray crystallography thus requires four main components: an X-ray source, a protein crystal, a detector and a computer.

Ordered crystals act to amplify diffraction and convert a very weak scattering that would result from one protein molecule into a strong diffraction pattern described by Bragg’s Law (see Box 3, Bragg’s Law box). The intensity of each spot in a diffraction pattern from a crystal is determined by how many electrons lie on a particular set of imaginary parallel planes called Bragg planes that cross through the crystal. Each set of planes is named by having a unique integer value for the letters h, k and l, which describe the spacing and direction of these planes in three dimensions. There are billions of copies of protein molecules in a crystal which are arranged in a regular lattice, which means that the parallel Bragg planes cross the same place in the protein for every copy. For any given set of planes, this allows all copies of the protein to contribute to the same given diffraction event through constructive interference, increasing the signal of the spots on the detector.

Ultimately, it is the electron density around all the protein atoms in a crystal that scatters X-rays to form the diffraction patterns. The electron density and diffraction patterns are converted between each other by a mathematical operation called a Fourier Transform (Figure 15). To convert a set of reflections into an electron density map, we need the amplitudes of each reflection as well as the phase. The amplitude is measured as the square root of the spot intensity; however the phase is unknown. It is also possible to back-calculate an estimate of the amplitude and phase of possible diffraction peaks from the known electron density (atomic positions).

As the phase information of the reflections cannot be measured, we do not have the complete mathematical description of these functions and therefore we cannot apply a Fourier Transform to them to get to the electron density. This is known as the phase problem. One way to solve this is called Molecular Replacement, where we use a model protein structure (previously determined) that we assume is very similar to the unknown structure for which we have a set of measured diffraction intensities. A computer program tries all possible positions and orientations of this model in the unknown crystal to find a match between the measured diffraction pattern and the pattern predicted for each model orientation being tested (calculated by a Fourier Transformation). When the correct orientation has been found, we assume the model has crystallised in the unknown crystal with this orientation and borrow the phase values generated from this model for the unknown phases. With these phases solved by molecular replacement and the experimentally observed amplitudes, an initial map of the unknown structure is now possible by Fourier transformation.

Using features of the initial electron density map, we start to build an atomic model by threading the known polypeptide chain sequence into the density. Once we have built an initial model, we can calculate all the theoretical reflections and phases that would result from the model structure being in the crystal. This is done in a computer by applying a Fourier transform to a series of simple functions that represent the electron positions in that crystal. We use these new theoretical phases and combine them with the experimental intensities to apply another Fourier transform that creates a new and improved electron density map. The phases improve because the original phases were based on an estimate from a similar structure (using molecular replacement), however, now we can build into the map and define solvent molecules, bound ligands and avoid building into a density that appears to be noise. Thus, applying a Fourier Transform to this model will give a new set of wave functions with more accurate phases than the starting set of reflections. The process of model building, calculating new phases, creating an improved electron density map and making an improved model, which overall, is the process of refinement, continues until no further improvements can be made. At this stage of the refinement, different electron density maps are calculated that allow crystallographers to see any mistakes made in the model that are not consistent with the experimental reflections, locate missing atoms and make adjustments to the final structure. In Figure 16, where the final electron density map has been calculated, there is clear evidence of the peptide backbone and sidechains and the primary amino acid sequence is easily fitted into this map.

Once the structure has been fully refined, the x, y, z coordinates of each of the atoms within it are shared with other scientists by depositing them into a global database called the Protein Data Bank (PDB). X-ray crystallography finds the structure of proteins fixed in the crystal lattices. The crystals can contain 20–80% solvent, and protein molecules are generally observed to be in the active state as has been demonstrated for many enzymes. However, structures tend to represent a snapshot of the protein, like taking a photo of an object, and some dynamic information is missing. We will next review the process of studying the structure of proteins using Nuclear Magnetic Resonance (NMR), which studies proteins completely free in solution.

NMR can reveal the structure and dynamics of biomolecules in solution, which is how they exist inside cells. In fact, NMR has been used to directly study proteins in the cell, even if they are unfolded. We will see that NMR can be used to reveal all the atomic positions within proteins and how these move and change in real-time when interacting with other molecules such as other proteins or drugs. Such information can tell the structural biologist how a protein can exert its function inside the cell. With this information, we can better understand how proteins lose function in disease, how to engineer them to be more effective or how to design drugs to alter their behaviour.

NMR is based on the observation that certain atomic nuclei have a property called a spin magnetic moment. A common analogy is that each nucleus behaves as if it were a tiny bar magnet pointing in a particular direction. Only magnetically active atoms with a spin value of ½ can be observed by NMR, for example, ¹H, ¹⁵N, ¹³C. A typical protein sample at millimolar concentrations will contain 10¹⁷ molecules and therefore 10¹⁷ copies of each given atom (Figure 17). The ‘bar magnets’ that represent many identical copies of these atoms point in all directions and on an average, they cancel out any net magnetic moment/dipole. However, something special happens when this sample is placed in an NMR superconducting magnet, as the spin ½ nuclei are now exposed to a very strong external magnetic field (B₀). After a short time (few seconds), equilibrium is reached and the bar magnets start to rotate (or precess) around the external field all at the same resonance (or Larmor) frequency, although at a range of different angles, like a large collection of spinning tops that are tilted to various degrees from the ground (second column in Figure 17). However, instead of cancelling out, there are now slightly more in an orientation parallel to the external magnetic field (B₀). This occurs as this orientation has the lowest energy with the external magnetic field (B₀). This slight bias within the group produces on average, a slight net upward magnetic moment, which we call bulk magnetisation. At equilibrium this magnetisation is stationary pointing along the z-axis, and no net magnetisation is present in the x–y plane and the spins are out of phase and do not precess together in synchrony.

When a very short, yet carefully chosen length, radiofrequency (RF) electrical pulse is applied through a wire coil close to the sample but wrapping around the x-axis, it generates a weak varying magnetic field (B₁) that is perpendicular to B₀. This transverse RF magnetic field tips the bulk magnetisation away from the vertical axis exactly into the x–y plane. This happens as the RF-pulse is oscillating at the same Larmor frequency which ‘excites’ the spins, causing them to precess together in synchrony. Following the pulse, spins start to precess out of phase again, and the bulk magnetisation returns to align with the z-axis in a corkscrew motion, precessing around this z-axis at its distinctive resonance (Larmor) frequency (Figure 17). The x-component of the rotating bulk magnetic field that is generated immediately after the pulse causes a simple oscillating electrical current with exponentially decaying amplitudes that is recorded as a time-dependent free-induction decay (FID) in the same coil that generated the pulse. The key to this experiment is measuring the oscillating signal away (perpendicular) from the B₀ field, which is much stronger and would mask this signal if you tried to measure along the z-axis. For clarity, Figure 17 only shows multiple copies of the same atom, however a protein contains many different atoms and so the FID we record is a mixture of different oscillations at different frequencies. Fourier transformation of this complicated FID by a computer generates a frequency-dependent spectrum consisting of signals separated by the Larmor frequencies of the atoms in the molecule. The number of signals is equal to the number of magnetically different atoms in the molecule. The position of signals is called the chemical shift and is measured in ppm (parts per million) units relative to the frequency of a standard chemical included in the sample. Using the ppm scale instead of a Larmor frequency scale makes spectra independent of the B₀ magnetic field used for a given NMR spectrometer. For a protein, when using an RF-pulse designed to only perturb hydrogens, there could be as many as 1000 ¹H nuclei within the combined amino acids.

Each ¹H atom in a protein is surrounded by a unique chemical environment from electrons in nearby atoms in the biomolecule that leads to a slightly different Larmor frequency compared with other ¹H atoms. These nearby electrons have the effect of shielding the nuclei from the full strength of the external B₀ magnetic field, which in turn affects its rate of precession (Larmor frequency). For example, if electrons are pulled away from a hydrogen, the Larmor frequency for that hydrogen is shifted downfield as the atom is less shielded, which causes the chemical shift to increase. This is seen for amide hydrogens which are attached to nitrogen, an electronegative atom (Figure 18).

Although studying one nucleus from one atom in a protein can be informative, in order to study all of them, we must know which chemical shift belongs to which atom in the protein. This requires a series of experiments that measure multiple different types of magnetically active nuclei (¹H, ¹³C, ¹⁵N) on recombinant proteins that have incorporated ¹³C and ¹⁵N isotopes. With these labelled proteins, we can determine how atoms are connected together using experiments that are designed to transfer bulk magnetisation from one atom to another through ‘coupled’ or connecting bonds in the protein, ultimately telling us the chemical shift of every atom.

A simple H-N two dimensional (2D) spectrum can be recorded on a recombinant protein that has incorporated the relatively inexpensive ¹⁵N isotope. After our assignment experiments described above, we can label each peak in this spectrum as an amino acid according to the chemical shift value for its backbone amide nitrogen and hydrogen. This is very useful as it provides a unique “fingerprint” identification of the protein in an experiment that takes less than 30 min to run (Figure 19). The simple H-N 2D spectrum is incredibly powerful, as it is an excellent check on the condition of a protein, before embarking on lengthy experiments (such as structure determination). It can tell you if the protein is folded, by checking if the peaks are well dispersed in the spectrum and not simply concentrated in the middle of the spectrum (between 7.8 and 8.8 ppm), which would indicate an unfolded or intrinsically disordered protein. It can tell you if the protein is aggregated by examining the shape of the peaks if they are spread out and broadened then that could indicate some form of self-association. It can also indicate if parts of your protein are dynamic as usually these peaks are missing in the spectrum. Crucially, H-N 2D spectra are frequently used to look at interactions with other proteins, ligands or drugs. Binding partners often are unlabelled (contain the natural ¹²C and ¹⁴N isotopes) to ensure they will not contribute to the spectra. However, when they are added to a labelled protein, we can quickly tell which of its amino acids are involved in binding, as these peaks will shift due to the new environment created by the binding partner. This allows us to map the binding surface on to the protein and estimate the strength of binding by titrating the binding partner into the protein and recording a series of 2D spectra to follow the peak positions.

To gain the full 3D structure of a protein, we need to assign all atoms to chemical shift values. This information is then used to determine which atoms are close together in space (not through bonds) through a variation of NMR experiment called Nuclear Overhauser Effect SpectroscopY (NOESY) experiment. In this experiment, the transfer of magnetisation from one hydrogen atom to another nearby hydrogen atom in 3D space is recorded. The size or strength of the bulk magnetisation vector after the transfer has occurred in a NOESY experiment tells us how close that atom was to the nearby atom. After identifying all possible Nuclear Overhauser Effects (NOEs) for the protein, we produce a series of atom–atom distances that connect the polypeptide to itself and help define its fold. We use a computer to find the fold that is consistent with all of these measured distances by doing a series of molecular dynamics simulations which is repeated approximately 100 times. With enough NOE restraints, most of the simulations will ‘converge’ on an ensemble of equivalent and similar low energy structures that all ‘fit’ with the distance restraints used.

Protein NMR spectroscopy is powerful as once an ensemble of structures is determined, further experiments are performed that detail the dynamics of each atom and the bonds they form. NMR thus gives information about how the protein moves in solution and combined with additional molecular dynamics techniques (Table 3), it is possible to estimate its conformational ensemble. NMR dynamics experiments can also be performed on assigned proteins which do not have an NMR structure determined, and the results simply mapped on to a model determined previously making the process quicker. As such, NMR can quickly provide a wealth of information as soon as protein has been purified. NMR is an essential tool as protein motions are central to function inside the cell as we saw when we considered how proteins fold and their associated dynamics.

One of the drawbacks of X-ray crystallography is the need for a crystal to produce the diffraction patterns and a drawback of NMR is there is a limitation on the size of the protein that can be studied. In the 1970s, Nigel Unwin was trying to determine the shape of a protein called bacteriorhodopsin. Unable to produce a crystal of the molecule, electron microscopy (EM) was used to gain the structural outline of this protein, demonstrating how it can move protons across a membrane. Improvements in the methodology enabled Richard Henderson in 1990 to determine the first atomic-resolution images of bacteriorhodopsin using newly developed cryo-EM methods. The development of cryo-EM by Jacques Dubochet, Joachim Frank and Richard Henderson led to the Nobel Prize in 2017. It opened the door to the structural determination and functional understanding of very large complex protein structures without the need for crystallisation. Such is the progress and quality of cryo-EM images that the images now rival those of X-ray crystallography, with all the additional advantages for easier sample preparation.

Transmission EM (TEM) operates on the same basic principles as a light microscope but uses a beam of electrons to examine the structures of cells and tissues. The electron beam has a wavelength of approximately 10⁻¹⁰ m (about the size of an atom) meaning TEM can reveal the internal structure of cells that cannot be seen by the longer wavelength used in light microscopy. The incoming and outgoing lenses of a light microscope are replaced by a series of coil-shaped electromagnetic lenses through which the electron beam travels to produce magnified images. Only parts of the beam are transmitted through the sample depending on their thickness and electron transparency. A final lens then refocusses this and projects an image of the sample onto a camera detector. To help improve the contrast of the very thin samples, heavy metal stains are often used to bind the proteins and stop the transmission of the electrons. The image then shows regions of the specimen where the electron transmission has been prevented. Biological molecules such as individual proteins and complexes are not compatible with the high vacuum needed for TEM as the high energy electrons burn the protein and evaporate the water that surrounds them.

Cryo-EM uses the same principle as TEM but cools the samples to cryogenic temperatures and embeds them in an environment of vitreous ice, allowing protein and protein complexes to be studied. To do this an aqueous protein sample solution is applied to a grid-mesh and plunge-frozen in liquid ethane. The process is so quick that the water molecules do not have time to arrange into a crystalline lattice. In this ‘vitrified’ sample, the water is disordered but the 3D structure of the biomolecules in the sample is retained. Stains are not needed here as the surrounding buffer allows for enough contrast to observe the specimen, to improve contrast multiple images are taken instead. Randomly orientated proteins are struck by the electron beam, producing a faint image on the detector. A computer then decides what is a faint molecular image of the proteins and what is the background. Similar images are then placed (grouped) together. Thousands of similar images are averaged by the computer to generate high signal to noise 2D images (Figure 20) that are used to clean-up the dataset from contamination and other junk particles. Software is then used to calculate how all the good molecular images relate to each other and generates a high-resolution 3D image or density map. The amino acid chain is then threaded into this map in a similar process to X-ray crystallography. Cryo-EM offers a significant advantage in that through the direct acquisition of the images, the specimen can be statistically analysed allowing for the reconstruction of the structural information and different conformations can be determined in the same sample. It is also possible to control the chemical environment, which in turn allows for effective examination of different functional states of different types of molecules. The final major advantage of cryo-EM is that large intact complexes can be studied allowing the 3D structure of ribosomes, proteins and viruses, almost to the atomic scale.

Cryo-EM of proteins and their complexes promises to revolutionise structural biology as many life processes depend on large dynamic macromolecular assemblies, however like all the methods described here there are some naunces. For example, it can be difficult to prepare a grid that has a well-represented number of orientations as sometimes the proteins will preferentially align towards the hydrophobic air–water interface, on occasions the proteins will denature, and screening multiple grids with different conditions can be expensive. Nevertheless, datasets sufficient for high-resolution structures can be recorded in just a few hours or overnight and the amount of protein required is much less than X-ray crystallography or NMR, and the samples do not have to be as pure, all of which helps balance the cost of this incredibly powerful technique.

There are a vast range of other methods that are also used to study protein structure and their interactions, many of which can be performed in just one day and yield complementary information to the techniques mentioned above. Table 3 gives an overview of some of the more common methods and their applications.

Within this essay, we have explored proteins through the eyes of a structural biologist. We have considered the following areas:

• The structural organisation of proteins and their range of shapes and conformations.

• What influences the thermodynamics of protein folding.

• How proteins’ ability to change their shape enables them to bind new partners as well potentially misfold and aggregate, bringing about disease.

• How to experimentally determine protein structures and their interactions at the molecular level.

We hope this will inspire readers to view some of the suggested resources which provide more detail on uncovering protein structure.

CD data for an immunoglobulin was simulated from the pdb code: 1igt using the PDB2CD [Mavridis and Janes (2017) PDB2CD: a web-based application for the generation of circular dichroism spectra from protein atomic coordinates. Bioinformatics33, 56–63]. CD Data for the soluble domain of micro-exon gene 14 protein (CD0004062000) and insulin (CD0000040000) were extracted from the PCDDBID [Whitmore, Miles, Mavridis, Janes and Wallace (2017) PCDDB: new developments at the Protein Circular Dichroism Data Bank. Nucleic Acids Res.45 (D1), D303–D307] [Lopes, Orcia, Araujo, DeMarco and Wallace (2013) Biophys. J.104, 2512–2520]. CD figures were created by use of Szilágyi (2019): EMANIM: interactive visualisation of electromagnetic waves. Web application available at URL https://emanim.szialab.org. All other pdb codes for figures are indicated in their legends.

The authors declare that there are no competing interests associated with the manuscript.

E.J.S. and D.S., both contributed to writing the review and producing figures; however, E.J.S. took the lead in writing while D.S. took the lead in producing the figures.

We acknowledge Marie Phelan, Igor Barsukov, Ed Yates, Lia Ball, Christos Savva, Kathryn Garner, Svetlana Antonyuk and reviewers for critical comments on this work. We also acknowledge Bryan Sutton for providing the electron density figure.

Δ

change in a system

2D

two dimensional

3D

three-dimensional

B₀

magnetic field aligned to the z-axis

CD

circular dichroism

cryo-EM

cryogenic electron microscopy

DNA

deoxyribonucleic acid

EM

electron microscopy

FID

free-induction decay

G

Gibbs free energy

H

enthalpy

Hz

frequency in Hertz

IDP

intrinsically disordered protein

NMR

nuclear magnetic resonance

NOE

Nuclear Overhauser Effect

NOESY

Nuclear Overhauser Effect SpectroscopY

PDB/pdb

Protein Data Bank

ppm

parts per million

S

entropy

T

temperature

TEM

transmission EM

T_m

melting temperature at which 50% of a protein is unfolded

UV

ultraviolet

λ

wavelength