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The methods listed below represent only a small number of available methods to study protein disorder. These methods can be considered as initial experiments to assess ID. More information about these methods and additional experiments are found in the review articles given in Ref. [150,155,176] and references therein.

1.6.1. Computational methods

Due to their unique structural characteristics computational algorithms have been developed to recognise ID. Two prominent examples are PONDR [177] and DisEMBL [178]. Hydrophobic cluster analysis (HCA) identifies the presence or absence of hydrophobic clusters and thus might indicate regions of order or disorder [179]. Additionally, charge-hydrophobicity plots can be used to identify IDPs. In contrast to globular folded proteins, IDPs occupy a distinct space marked by high mean net charge and low mean hydrophobicity [144,180].

1.6.2. Biochemical methods

A first indication for ID can be gained from sodium dodecyl sulfate - polyacrylamide gel electrophoresis (SDS-PAGE). As IDPs tend to bind less SDS compared to globular folded proteins due to a depletion in hydrophobic amino acids, IDPs are marked by an abnormal electrophoretic mobility resulting in high apparent molecular weights (MWs). The SDS-PAGE

determined MWs are often 1.2-1.8 times larger than can be expected from the amino acid

sequence. In contrast to IDPs, globular proteins tend to aggregate upon heat or acid denaturation due to exposure of buried hydrophobic residues. As IDPs are depleted in hydrophobic residues, they exhibit increased thermal and acid resistance that has been successfully used to purify IDPs. As mentioned above, IDPs are hypersensitive to protease digestion. Folded segments in contrast to disordered regions sequester their protease cut sites and are thus cleaved at a much lower rate. Limited proteolysis assays may therefore be used to identify possible regions of ID (optimally combined with the analysis of possible fragments by mass spectrometry) [155].

1.6.3. Methods to assess the protein dimension and shape

In contrast to globular proteins, IDPs are marked by varying degrees of extended conformations. A critical parameter that can be determined in this respect is the hydrodynamic

radius or Stokes radius (RS). Consistent with the above mentioned IDP characteristics, the

globule, pre-molten globule to coil-like states. Based on their hydrodynamic properties it is therefore possible to discriminate between these states [181]. Size exclusion chromatography (SEC) for instance is a simple method to assess the hydrodynamic properties of proteins. Due to

their increased hydrodynamic radii IDPs produce higher apparent MWs by SEC compared to

globular proteins of similar chain length. However, similar high apparent MWs are also observed

for well-ordered but asymmetrically (i.d. non-globular) shaped proteins. Similarly, RS values can

be obtained from dynamic light scattering (DLS) experiments that allow distinction between

globular proteins and IDPs. An alternative method for the determination of RS values has been

described for pulsed-field-gradient nuclear magnetic resonance (PFG-NMR) diffusion experiments [176].

Hydrodynamic properties of proteins can also be assessed by analytical ultracentrifugation,

which determines the apparent sedimentation coefficient. This value is related to the MW and

shape of the molecule, allowing MW estimates for proteins or protein complexes. A more

powerful method for assessing the dimension and shape of proteins is small-angle X-ray scattering (SAXS). The shape of a protein may be determined by SAXS if it is well defined. Otherwise, the maximum dimensions can be obtained from the distance distribution function, which is the histogram of all interatomic distances within the molecule. Furthermore, the

forward scattering intensity is proportional to the MW of a protein and thus allows the

determination of the oligomeric state. This, in conjunction with the experimentally determined

radius of gyration (Rg), allows the discrimination between globular, pre-molten globule and coil-

like states. The Rg value is the root-mean-square distance from the centre of gravity of the

molecule weighted by the electron density. Typically large Rg values are obtained for IDPs [155].

1.6.4. Methods for the assessment of secondary structure

One of the simplest methods to determine the secondary structural content is provided by far- UV CD spectropolarimetry. The CD effect relies on the interaction of circular polarised light with chiral compounds. For protein spectroscopy the interaction with the peptide bond proved to be crucial. As the CD signal reflects the symmetry of the peptide bond, it is dependent on the conformation of the two participating residues and thus gives information about the secondary structure [182]. CD measures the overall secondary structural content and does not allow the localisation of certain secondary structural elements to specific regions in the protein sequence. Furthermore, the obtained spectrum represents the population-weighted average of all structures in the conformational ensemble. CD spectra of IDPs are typically marked by a large negative

ellipticity at 200 nm, a negligible negative ellipticity at 222 nm, and an ellipticity close to zero at 185 nm. Other optical analysis methods to assess residual secondary structure are provided by Raman spectroscopy [150,155].

Nuclear magnetic resonance (NMR) spectroscopy allows, unlike CD spectropolarimetry, the determination of secondary structure down to the atomic level. Thus, secondary structural elements can be located within the protein sequence. A detailed description of NMR would be beyond the scope of this section, therefore only important concepts will be provided. NMR

measures the magnetic properties of susceptible atoms such as 1_H, 13_{C and} 15_{N. As the latter two}

are not naturally occurring in biologic samples, proteins can be enriched in these atoms with specific labelling techniques (Chapter 2.5.). In strong external magnetic fields these atoms, or more accurate spins, can be excited through absorption of energy, a phenomenon called resonance. Energy is provided through irradiation of radio wave pulses. NMR follows the return of the excited spins to equilibrium, which yields characteristic resonance frequencies for each spin. These resonance frequencies depend on local magnetic fields and thus on the local chemical environment. As the local chemical environment is influenced by neighbouring atoms, resonance frequencies are therefore reflective of the local secondary structure [183].

Due to their flexibility and rapid interconversion between multiple conformers, residues in IDPs experience similar local chemical environments. This results in similar resonance frequencies, especially of protons, and thus in a narrow spectral dispersion. As mentioned for CD spectropolarimetry, the observed resonance frequencies therefore represent a population- weighted average over all structures in the conformational ensemble [155]. For comparison with residues in secondary structural elements, these resonance frequencies have been termed random coil chemical shifts. Secondary structure induces a deviation from the random coil shifts termed the secondary chemical shift. As a result of secondary structure, an increased dispersion of the

resonance frequencies is usually observed. Especially, 13_{C resonances such as the alpha and beta}

carbons (Cα _{and C}β_{), or the carbonyl of the peptide bond (C’) are sensitive to the secondary}

structure induced shifts. Therefore, the secondary chemical shift values of these residues can be used for the identification of secondary structural elements. Secondary structure can further be identified from specific proton-proton distances. These distances are measured by NOE (nuclear Overhauser enhancement) experiments.

Measurements of amide proton exchange rates by NMR can further provide information about the compactness of a protein. In folded segments the amide exchange rate is reduced due to a possible involvement in hydrogen bonds or due to burial in a hydrophobic core, whereas in

disordered regions the rate is increased as the amides are solvent exposed and unprotected. Finally, NMR determined dynamics of a residue can provide information about secondary structure, with residues in flexible segments having distinct dynamics than residues in ordered regions [150,155,176].

1.6.5. Methods to assess tertiary structure

Various methods can be applied to gain information about the presence of tertiary structure and, under certain conditions, of residual secondary structure. Differential scanning microcalorimetry (DSC) produces heat absorption curves, which shape is characteristic for the presence or absence of tertiary structure. Alternatively, extrinsic fluorescence compounds such as ANS may be used to identify residual hydrophobic core-like structures in a given protein. ANS binds to hydrophobic pockets that may be present in molten globule or pre-molten globule states resulting in a fluorescence increase. In this way molten globule or pre-molten globule states can be easily discriminated from extended coil-like states. Various other fluorescence techniques have been described to assess the degree of tertiary structure in IDPs, most importantly Förster resonance energy transfer (FRET) techniques. Due to the low abundance of tryptophan in IDPs this residue type is commonly used as donor in fluorescence experiments [150,155]. Information about the local environment of aromatic amino acid residues, in particular the tertiary structure around them, can be gained by near-UV CD spectropolarimetry (250-350 nm). Near-UV CD spectra of IDPs typically display a low complexity and intensity due to a lack of ordered structure. The aforementioned limited proteolysis assay is another method useful for the identification of possible regions of order.

NMR spectroscopy can also provide useful information about the tertiary structure of a protein. Long range NOE contacts over distances up to ~10 Å can indicate the proximity of certain regions within an IDP. However, these NOEs may be difficult to detect in IDPs as the contacts may be to short lived due to the inherent flexibility of the molecule. Therefore, a different NMR technique has been proven more useful in the determination of tertiary contacts within IDPs. Paramagnetic relaxation enhancement (PRE) involves the introduction of a paramagnetic label, commonly by coupling to free cysteine groups, which drives the enhanced relaxation of nearby nuclei. This method is more sensitive and enables the detection of contacts up to ~20-25 Å apart [150,155,176].

As IDPs are marked by fast interconversion between various structures the gathered structural information has to be interpreted as ensemble-average values. Despite computational approaches

a unique representation of the conformational ensemble has seldom been achieved. This is, however, of great importance for the analysis of the biological function, as only a small population of the ensemble might represent the biologically active state [176].