Studying backbone torsional dynamics of intrinsically disorderedproteins using fluorescence depolarization kinetics

DEBAPRIYA DAS1,3 and SAMRAT MUKHOPADHYAY

1,2,3*1Centre for Protein Science, Design and Engineering, Indian Institute of Science Education and Research

(IISER) Mohali, Punjab, India2Department of Biological Sciences, Indian Institute of Science Education and Research (IISER) Mohali,

Punjab, India3Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Mohali,

Punjab, India

*Corresponding author (Email, mukhopadhyay@iisermohali.ac.in)

Published online: 7 June 2018

Intrinsically disordered proteins (IDPs) do not autonomously adopt a stable unique 3D structure and exist as an ensemble ofrapidly interconverting structures. They are characterized by significant conformational plasticity and are associated withseveral biological functions and dysfunctions. The rapid conformational fluctuation is governed by the backbone segmentaldynamics arising due to the dihedral angle fluctuation on the Ramachandran /–w conformational space. We discovered thatthe intrinsic backbone torsional mobility can be monitored by a sensitive fluorescence readout, namely fluorescencedepolarization kinetics, of tryptophan in an archetypal IDP such as a-synuclein. This methodology allows us to map thesite-specific torsional mobility in the dihedral space within picosecond-nanosecond time range at a low protein concen-tration under the native condition. The characteristic timescale of * 1.4 ns, independent of residue position, representscollective torsional dynamics of dihedral angles (/ and w) of several residues from tryptophan and is independent of overallglobal tumbling of the protein. We believe that fluorescence depolarization kinetics methodology will find broad applicationto study both short-range and long-range correlated motions, internal friction, binding-induced folding, disorder-to-ordertransition, misfolding and aggregation of IDPs.

Keywords. Dihedral angles; fluorescence anisotropy; intrinsically disordered proteins; protein conformational dynamics;Ramachandran map; rotational dynamics

1. General aspects of protein dynamics

In order to understand the function of proteins, the tradi-tional structure–function paradigm could be revised bystructure–dynamics–function paradigm because the dynamicattributes along with the structure govern their functions(Henzler-Wildman and Kern 2007). Proteins can sample anensemble of conformational states centred to their averagestructure. The dynamic characteristics of proteins can bedescribed in terms of energy landscape. Protein dynamics isimplicative in several biological activities whose elaboratedescriptions can be obtained only if its dynamic propertiesare taken into account (Karplus and McCammon 1983). Inorder to monitor the protein dynamics, it is necessary tofollow the time-dependent structural changes that occur on awide range of timescales ranging from femtoseconds toseconds. The dynamic processes occurring on the slowertimescale (microseconds and lower) are mainly the collective

motion, which involves the mobility of large domains, loopformations, protein folding/unfolding, partial folding tounfolding transition, and so on. Slow dynamics of proteinsinvolves displacements of a large number of atoms whichmight be correlated to each other. On the other hand, theprocesses that occur on the faster timescale, ranging fromfemtoseconds to nanoseconds, involve vibrational motion,segmental motion, loop motions, side-chain rotations, rota-tion of small group attached to the backbone and side-chainoscillations (Karplus and McCammon 1983). Among thesedynamic processes, the polypeptide backbone dynamicsinvolving the changes in the torsional angles play a pivotalrole in protein conformational changes (Ramachandran andSasisekharan 1968; Ramakrishnan 2001). For a givenpolypeptide backbone, rotations around two single bonds,namely, N–Ca and Ca–C, are allowed (Carugo and Djinovic-Carugo 2013). The angle of rotation around N–Ca bond andCa–C bond are termed as / and w, respectively. The

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J Biosci Vol. 43, No. 3, July 2018, pp. 455–462 � Indian Academy of SciencesDOI: 10.1007/s12038-018-9766-1

torsional dynamics of the polypeptide backbone is the fun-damental dynamics of any protein which takes place on theRamachandran /–w conformational space. Therefore, all thebiophysical phenomena such as protein folding, unfolding,assembly and their functions are enrooted in the backbonedihedral dynamics in the allowed region of the Ramachan-dran map.

2. Intrinsic disorder in proteins

For many decades, it has been widely accepted that theprotein kingdom follows the traditional sequence–structure–function paradigm, which states that a biologically activeprotein must possess a well-defined ordered structure inorder to accomplish its specific function. However, recentstudies have demonstrated the existence of intrinsicallydisordered proteins (IDPs) that do not possess well-definedstructures (Uversky 2013). The biological functions of suchproteins are found to be originating from their inherentconformational flexibility and their ability to adopt a varietyof structures (Fink 2005). Several bioinformatics studiesindicate that IDPs are highly abundant in any given pro-teome. Recent studies revealed that * 25–30% of eukary-otic proteins are intrinsically disordered, of which morethan * 50% eukaryotic proteins bear long regions ofintrinsic disorder, and more than * 70% proteins, involvedin signalling, contain long intrinsically unstructured regions.Analysis of a large number of protein sequences revealedthat the combination of low mean hydrophobicity and highnet charge are the main driving forces, which direct theprotein to be in the disordered or less compact state (Uver-sky 2002; 2013). An abundance of disorder-promotingamino acids within the sequence is also responsible for itsdisorder under native conditions. IDPs are typically involvedin important cellular processes, which include cell division,cell signalling, bacterial translocation, protein degradationand cell cycle control (Uversky 2002). The conformationalplasticity of IDPs could also be detrimental, because it helpsthe polypeptide chain to adopt misfolded amyloidogenicconformations which are implicated in several neurodegen-erative diseases such as Parkinson’s, Alzheimer’s andHuntington’s (Uversky 2003).

IDPs exhibit considerable conformational heterogeneitydue to the lack of ordered three-dimensional structure. Thefree energy landscape of an IDP shows a large ‘hilly plateau’confirming the existence of dynamic ensemble of readilyinterconverting conformations (Uversky 2013). Due to thelack of any order in the structure, IDPs behave as highlyfrustrated systems bearing rapidly fluctuating backboneRamachandran dihedral angles. It is not possible to definethe conformational state of an IDP with a singleRamachandran dihedral coordinate within the availableenergy space at a particular time point. This type of time-

dependent fluctuation is also observed for a structured pro-tein, but the range of fluctuations is notably smaller ascompared to the disordered proteins.

IDPs are deficient in hydrophobic residues and are enri-ched in polar and charged amino acid residues. Therefore,the conformational preferences of an IDP are modulated bythe amino acid compositional bias in different polar solvents.IDPs that behave as strong polyelectrolytes/polyampholytesbecause of the high content of charged residues have apropensity to adopt an expanded coil-like structure due tosolvation of the charged residues in aqueous medium. On theother hand, IDPs which are enriched in polar but unchargedresidues generally tend to form collapsed globule structuresin water. Therefore, the intrinsic preference of an IDP toadopt either collapsed or extended coil-like structure isdependent on the net charge per residue of the protein andalso the solvent microenvironment (Mao et al. 2010). It hasalso been observed that the increase in the net charge perresidue allows globule ? coil transition. Furthermore, it hasbeen shown that even the IDPs lacking nonpolar or polarside chains also tend to form collapsed unstructured globulesin water. This observation clearly indicates that the collapsein IDP might originate from the conformational preferencesof the polypeptide backbone in water. Thus, water behavesas a poor solvent for polypeptide chain that favours chain–chain interactions over the chain–solvent interactions, lead-ing to the formation of collapsed globules (Arya andMukhopadhyay 2014). The counterpoise between the chain–chain and chain–solvent interaction dictates the thermody-namically approachable conformations of IDPs. In order tomonitor the conformational preferences, polymer physicstheories provide important scaling parameters such as radiusof gyration, mean end-to-end distance, hydrodynamic radiias a function of the chain length, amino acid compositionand stiffness. An ideal heterogeneous IDP adopts differenttypes of conformations that are chimeras of collapsedglobule, expanded coil, rods and semi-compact hairpin (Daset al. 2015).

It is mentioned earlier that all the physiochemical dynamicprocesses in proteins take place on the timescale whichranges from ps to ms and involves various backbone motionssuch as short-range conformational fluctuations, long-rangecorrelated dynamics, local motion of the amino acid sidechain and segmental dynamics of polypeptide chain. Thefundamental backbone dynamics in IDPs arises due to theRamachandran dihedral angle fluctuations. IDPs are usefulmodels to study the short-range segmental mobility ofbackbone as they lack an ordered structure under physio-logical conditions (Jain et al. 2016). Several theoretical andexperimental approaches are being used to study the con-formational preferences and dynamics of IDPs such as NMRtechniques, especially, 15N NMR relaxation, isotropicreorientational eigen mode dynamics, relaxation methods,paramagnetic relaxation, molecular dynamics simulation,

456 D Das and S Mukhopadhyay

fluorescence correlation spectroscopy and fluorescencedepolarization measurements.

3. Methods to study the conformational distributionand dynamics of IDPs

IDPs are known to exhibit extensive conformational flexi-bility and exist as a structural ensemble. It is therefore verychallenging to characterize the structural and dynamicattributes of IDPs. X-ray crystallography is not suitable toelucidate their structure because of their conformationalheterogeneity (Konrat 2014). In order to study the structureand dynamics of IDPs, several physical methods need to beemployed.

First, the presence or absence of secondary structure canbe monitored by using several spectroscopic techniquesincluding far ultra-violet–circular dichroism (UV-CD),optical rotatory dispersion (ORD), Fourier transform infraredspectroscopy (FTIR) and Raman optical activity (Uversky2003). Hydrodynamic parameter can be measured by usingdifferent scattering techniques such as small-angle X-rayscattering (SAXS), small-angle neutron scattering (SANS)and dynamic light scattering (DLS), which elucidate thestructural compactness of the concerned protein (Uversky2003). NMR techniques offer a unique opportunity to studythe structural dynamics of IDPs. H-exchange rate, chemicalshift and residual dipolar coupling (RDC) are used to probethe local short-lived secondary structural elements at atomiccoordinate (Konrat 2014). NMR studies furnish detailedinformation about the dynamics in a site-specific manner,

which includes rapid backbone motion of the polypeptidechain and also the slow motion which is expected to be theoutcome of long-range contacts and folding-upon-bindingevents (Eliezer 2009). RDC provides information on thelocal dynamics related to the different inter-nuclear bondvectors encompassing the backbone of the protein andincludes transient long-range interactions (Konrat 2014). Inan anisotropic media, N–H bond vectors of the backbonealigned themselves orthogonally to the polypeptide chainwhen the conformational ensemble is largely in the extendedstate. Local dynamics taking place on the ps-to-ns timescalecan be probed by hetero-nuclear NMR relaxation method,which provides information on the timescale of intercon-versions, as supported by chemical shifts and RDC (Jensenet al. 2013). Local dynamics, including amide backbone andside-chain motion, are assumed to be faster than the overallglobal tumbling of the protein and can be detected bysolution NMR (Henzler-Wildman and Kern 2007). Param-agnetic relaxation enhancement (PRE) is described to be themost relevant tool to probe long-range correlated dynamicsin IDPs (Parigi et al. 2014). In random coil structure, theresidues are present in increasingly distant positions from thespin label (artificially introduced to the cysteine moiety ofthe protein) and are expected to show monotonicallydecreasing degrees of line broadening. Any deviation fromthis usual pattern reflects the stability and preferentiality oflong-range interactions. Several models are used to analysethe PRE data, such as molecular dynamics (MD) andextended model-free analysis for time-dependence study.The position of the spin labelling should be chosen carefullyin order to avoid any perturbation in the tertiary contacts.

Figure 1. Schematic of fluorescence anisotropy. (a) Schematic of rotational dynamics of a fluorophore (green) bound biomolecule (red).When attached to the biomolecule, fluorophore undergoes fast local motion results in rapid depolarization of initial fluorescence anisotropyand the entire biomolecule experiences an overall global tumbling that is related to the hydrodynamic property of the biomolecule.(b) Time-resolved fluorescence anisotropy decay of Trp in a globular protein showing local and global dynamics. Trp has a much lowerintrinsic anisotropy (* 0.20). The raw anisotropy decay plot is indicated by a blue line, whereas the fitted decay is shown by a solid blackline.

Torsional dynamics using fluorescence depolarization kinetics 457

Cross-correlated relaxation (CCR) is also a powerful noveltool to probe the dihedral angle distribution along thepolypeptide backbone of IDPs and provides useful infor-mation about the structure and dynamics (Konrat 2014).IDPs are known to exhibit substantial b-turn (I, II) andpolyproline II helical conformations. CCR appears to be asuitable tool to assess these conformations. In addition,dynamics of interchain loop formation has been observed bytriplet–triplet energy transfer (TTET) in different unfoldedchains consisting of polyserine and poly (glycine-serine)(Fierz et al. 2007). It has also been established that themechanism of loop formation involves complex kinetics andtakes place on the timescale of 50–500 ps within the localwell of the energy landscape (Fierz et al. 2007). Slowermotions show exponential kinetics and occur on the time-scale of 10–100 ns and it is mostly diffusive in natureexploring the complete conformational space. In order tostudy the structural dynamics of IDPs, single-moleculeForster resonance energy transfer (FRET) methodologies

appear to be extremely useful. Single-molecule techniquesallow quantification of the conformational sub-populationsand dynamic distributions that are generally hidden in atypical ensemble experiments (Mukhopadhyay et al. 2007;Schuler et al. 2012). Although single-molecule FRET is arobust tool to capture the microscopic conformationaldynamics, it is difficult to probe the dynamics faster than 50microseconds (ls). In order to probe faster fluctuations, acombination of single-molecule FRET and fluorescencecorrelation spectroscopy can provide information about thedynamic features of IDPs (Mukhopadhyay et al. 2007).

4. Fluorescence depolarization kinetics to study chaindynamics

Time-resolved fluorescence anisotropy decay (depolarizationkinetics) measurements offer a unique and sensitive tool todirectly probe the dynamics of biomolecules. Fluorescence

Figure 2. Representative time-resolved fluorescence anisotropy decay analysis (for Trp-39 variant of a-syn). (a) The raw anisotropy dataare indicated by blue line, whereas, the fitted decay is shown by solid black line. (b) The global analysis of Ik (t) (red) and I\(t) (green) and

corresponding fits are shown using solid black lines. (c) and (d) are the residual plot and the autocorrelation function for Ik (t), respectively.

(e) and (f) are the residual plot and the autocorrelation function for I\(t), respectively (Reproduced with permission from Jain et al. 2016Direct observation of the intrinsic backbone torsional mobility of disordered proteins. Biophys. J. 111 768–774).

458 D Das and S Mukhopadhyay

depolarization kinetics captures the rotational events occurringduring the excited-state lifetime of the fluorophore (Miller1996; Krishnamoorthy 2012; Jain and Mukhopadhyay 2014;Bhattacharya andMukhopadhyay2016). This technique allowsus to study the site-specific polypeptide chain dynamics at a lowprotein concentration under native conditions (Jain et al. 2016).When a certain population of fluorophore (intrinsic tryptophanor extrinsic fluorophore labelled on the protein) is excitedwith alinearly polarized light, fluorophores having the absorptiontransition moment parallel to the electric vector of the incidentlight are promoted to the higher excited state known as photo-selection (Valeur 2001; Lakowicz 2007). Depolarization of theemission transition dipole can occur due to various processesduring the lifetimeof thefluorophore, suchas torsionalmotions,rotational diffusion, energy transfer and so forth. Fluorescenceanisotropymeasurements are carried out in two formats: steady-state and time-resolved anisotropy measurements. When afluorophore is attached to a protein, it can exhibit its own fastlocal motion, and the entire biomolecule will experience globaltumbling, which is slower than the local motion (figure 1A)(Jain et al. 2016). Steady-state anisotropy (polarization) pro-vides information about the overall size or dynamics of the

protein, whereas time-resolved anisotropymeasurement allowsus to discern the local, segmental and global motions.

The steady-state fluorescence anisotropy can be expressedas follows:

rss ¼ Ik � GI?� �

= Ik þ 2GI?� �

ð1Þ

where rss represents the steady-state anisotropy, Ik and I\ are

the parallel and the perpendicular fluorescence emissionintensities, respectively, and G factor is introduced to correctthe perpendicular components. Being a ratiometric readout,anisotropy is a dimensionless parameter and does not dependon the concentration. The steady-state fluorescence anisotropyprovides an average indication of rotational flexibility and isinadequate to distinguish between the local dynamics of thefluorophore and global tumbling of the entire biomolecule(Bhattacharya and Mukhopadhyay 2016), whereas the depo-larization kinetics obtained from the time-resolved fluores-cence anisotropy measurements can distinguish thecontributions from both local and global motions. A typicalbiexponential kinetics accounts for the two kinds of motions(figure 1B). Time-dependent anisotropy, [r tð Þ], can be analysed

Figure 3. Representative time-resolved fluorescence anisotropy decays of single-Trp mutants of a-syn: (a) Trp-39, (b) Trp-78 and (c) Trp-140. The insets show the fittings of parallel [Ik (t)] and perpendicular [I\(t)] intensity components. (d) Trp-107 (inset shows the overlay of

the decay fits for Trp-78 and Trp-107 in the log scale indicating a slower decay for Trp-107). The fits are indicated by black solid lines(Reproduced with permission from Jain et al. 2016 Direct observation of the intrinsic backbone torsional mobility of disordered proteins.Biophys. J. 111 768–774).

Torsional dynamics using fluorescence depolarization kinetics 459

by globally fitting Ik (t) and I\(t) and can be expressed by the

following biexponential decay function as follows:

Ik tð Þ ¼ I tð Þ 1þ 2r tð Þ½ �3

ð2Þ

I? tð Þ ¼ I? tð Þ 1� r tð Þ½ �3

ð3Þ

r tð Þ ¼ r0 bfastexp �t=/fast

� �þ bslowexp �t=/slowð Þ

� �ð4Þ

where r0 is the intrinsic (time-zero) anisotropy (should beclose to 0.4 according to the photo-selection rule), ufast rep-resents the local motion of the fluorophore and uslow is relatedto the global motion of the entire protein. bfast and bslow rep-resent the amplitude of the local and global motions, respec-tively, which measures the extent (degree) of rotationalfreedom of the probe. Fluorescence depolarization techniquescan discern several dynamic events at a low (nanomolar tomicromolar) concentration and on the ps–ns timescale.

5. Direct observation of the intrinsic backbone torsionalmobility

In order to study the backbone dynamics, we used a-synu-clein (a-syn), which is an IDP under physiological condi-tions. a-syn is one of the well-studied IDPs and itsmisfolding and aggregation is implicated in Parkinson’sdisease. It is a short 140-residue protein and does not possessany stable local interactions within the polypeptide. Thischaracteristic allowed us to speculate that the fluorescencedepolarization kinetics of a-syn would capture the backbonesegmental dynamics resulting from the dihedral angle fluc-tuations on the /–w space (Jain et al. 2016). In order tomonitor fluorescence depolarization, we took the advantageof non-occurrence of Trp in a-syn sequence and created tensingle tryptophan (Trp) mutants along the polypeptide chain.These mutations retained the general conformational char-acteristics of a-syn (Jain et al. 2013). DLS experimentsrevealed that hydrodynamic radius of the monomer is * 3nm, and using Stokes–Einstein’s law, the timescale of globaltumbling of the entire protein was estimated to be * 25 ns.

We monitored the fluorescence depolarization kinetics ofthe ten residue positions using picosecond time-resolvedfluorescence anisotropy decay measurements and analysedthe results by globally fitting (Eqs. 2 and 3) (figure 2A–F).Depolarization kinetics yielded two well-separated rotationalcorrelation time components (Eq. 4). The faster sub-nscomponent with an amplitude of * 50% indicated the localmobility of Trp. The slower component (* 1.4 ns) wasnearly similar for nine residue positions (figure 3A–C). Thiscomponent was slower than the local motion but much fasterthan the overall global tumbling of the protein (* 25 ns).Therefore, the time constant of * 1.4 ns is an intrinsictimescale of the polypeptide chain that could arise due torandomization of emission dipole due to the backbone

Figure 4. Capturing the intrinsic torsional dynamics of an intrinsi-cally disordered protein monitored by time-resolved fluorescencedepolarization of tryptophan that experiences the segmental mobilityover a length scale spanning several residues. (Adapted with permissionfrom Jain et al. 2016 Direct observation of the intrinsic backbonetorsional mobility of disordered proteins. Biophys. J. 111 768–774).

460 D Das and S Mukhopadhyay

segmental dynamics (Jain et al. 2016). Overall, the charac-teristic timescale of backbone torsional mobility was *1.4 ns, independent of residue position, and is in closeagreement with the estimated reorientation timescale of astatistical (Kuhn’s) segment of a-syn (Parigi et al. 2014).One of the residue positions, 107, that is a pre-prolineresidue, the rotational correlation time was found to beslower (* 1.8 ns), as expected for a restricted pre-prolineresidue (figure 3D) (Schimmel and Flory 1968).

The molecular origin of the 1.4 ns component in thedepolarization kinetics of single-Trp variants of a-syn is therotation around the single bonds N–Ca and Ca–C on the/–w conformational space. The rotation around the singlebonds is a fast process occurring on the ps timescale, thenwhy do we observe the 1.4 ns component? N–Ca and Ca–C bond rotations are restricted in the allowed region of the/–w dihedral space; therefore, a complete fluorescencedepolarization requires several N–Ca and Ca–C bondrotations around the fluorophore (Trp) (figure 4). In otherwords, the torsional relaxation monitored by the fluores-cence depolarization is felt over a number of residues onboth sides of the fluorophore. The 1.4 ns component cap-tures a collective torsional mobility over a characteristiclength segment that is dependent on the persistent length ofthe IDP. Due to the length dependence of this short-rangesegmental motion, fluorescence depolarization techniquewill be insensitive to capture the dynamics beyond itspersistent length. As stated before, this rotational correla-tion time of * 1.4 ns is very close to the estimatedreorientation time of a statistical segment of a-syn, whichwas captured by a low-field NMR relaxation method (Pa-rigi et al. 2014). Results obtained from the MD simulationssuggested that most of the conformational dynamics occurslocally and the estimated timescale is * 1.3 ns (Xue andSkrynnikov 2011). An inspection of MD trajectories alsoindicated that a change in backbone dihedral angles of aparticular amino acid residue generally does not bringabout any major change in global conformational dynam-ics. Rather, this motion is limited at the local (short-range)length scale encompassing the adjacent residues (Xue andSkrynnikov 2011).

6. Conclusion and future directions

Characterization of segmental backbone dynamics is pivotalto elucidate the conformational dynamics of IDPs, particu-larly in the context of coupled binding, disorder-to-ordertransitions and aggregation. Recent studies have also shownthat segmental dynamics of the disordered polypeptide chainis one of the predominant components of internal friction(Echeverria et al. 2014). Therefore, this methodology willallow us to quantify the internal friction arising due todihedral dynamics. We envision that the fluorescence

depolarization technique offers a unique way to characterizethe backbone torsional dynamics of IDPs on theRamachandran dihedral space. The main advantage of usingthis technique lies in its ability to discern several modes ofconformational dynamics in a single measurement. The useof long-lifetime probes will allow us to capture the presenceof long-range conformational dynamics of IDPs. We believethat fluorescence depolarization kinetics methodology willfind broad application to study both short-range and long-range correlated motions, internal friction, binding-inducedfolding, disorder-to-order transition, misfolding and aggre-gation of IDPs.

Acknowledgements

We thank the Department of Science and Technology andthe Ministry of Human Resouce Development, Governmentof India, for the financial support (Centre of Excellence grantto S.M.; INSPIRE fellowship to D.D.).

References

Arya S and Mukhopadhyay S 2014 Ordered water within thecollapsed globules of an amyloidogenic intrinsically disorderedprotein. J. Phys. Chem. B 118 9191–9198

Bhattacharya M and Mukhopadhyay S 2016 Studying proteinmisfolding and aggregation by fluorescence spectroscopy. Rev.Fluorescence 2015. 1–27

Carugo O and Djinovic�-Carugo K 2013 Half a century ofRamachandran plots. Acta Cryst. D 69 1331–1341

Das RK, Ruff KM and Pappu RV 2015 Relating sequence encodedinformation to form and function of intrinsically disorderedproteins. Curr. Opin. Struct. Biol. 32 102–112

Echeverria I, Makarov DE and Papoian GA 2014 Concerteddihedral rotations give rise to internal friction in unfoldedproteins. J. Am. Chem. Soc. 136 8708–8713

Eliezer D 2009 Biophysical characterization of intrinsically disor-dered proteins. Curr. Opin. Struct. Biol 19 23–30

FierzB, SatzgerH,RootC,Gilch P, ZinthW, et al. 2007Loop formationin unfolded polypeptide chains on the picoseconds to microsecondstime scale. Proc. Natl. Acad. Sci. USA 104 2163–2168

Fink AL 2005 Natively unfolded proteins. Curr. Opin. Struct. Biol.15 35–41

Henzler-Wildman K and Kern D 2007 Dynamic personalities ofproteins. Nature 450 964–972

Jain N, Narang D, Bhasne K, Dalal V, Arya S, et al. 2016 Directobservation of the intrinsic backbone torsional mobility ofdisordered proteins. Biophys. J. 111 768–774

Jain N, Bhasne K, Hemaswasthi M and Mukhopadhyay S 2013Structural and dynamical insights into the membrane-bounda-synuclein. PLoS One 8 e83752

Jain N and Mukhopadhyay S 2014 Applications of fluorescenceanisotropy in understanding protein conformational disorder and

Torsional dynamics using fluorescence depolarization kinetics 461

aggregation.AppliedSpectroscopyand theScienceofNanomaterials,Progress in Optical Science and Photonics Ed. P Misra. (Springer)

Jensen MR, Ruigrok R and Blackledge M 2013 Describingintrinsically disordered proteins at atomic resolution by NMR.Curr. Opin. Struct. Biol. 23 426–435

Karplus M and McCammon JA 1983 Dynamics of proteins:elements and function. Ann. Rev. Biochem. 53 263–300

Konrat R 2014 NMR contributions to structural dynamics studiesof intrinsically disordered proteins. J. Magn. Reson. 241 74–85

Krishnamoorthy G 2012 Motional dynamics in proteins and nucleicacids control their function: revelation by time-domain fluores-cence. Curr. Sci. 102 266–276

Lakowicz JR 2007 Principles of Fluorescence Spectroscopy.Springer, New York

Mao AH, Crick SL, Vitalis A, Chicoine CL and Pappu RV 2010Net charge per residue modulates conformational ensembles ofintrinsically disordered proteins. Proc. Natl. Acad. Sci. USA 1078183–8188

Millar DP 1996 Time-resolved fluorescence spectroscopy. Curr.Opin. Struct. Biol. 6 637–642

Mukhopadhyay S, Krishnan R, Lemke EA, Lindquist S and DenizAA 2007 A natively unfolded yeast prion monomer adopts anensemble of collapsed and rapidly fluctuating structures. Proc.Natl. Acad. Sci. USA 104 2649–2654

Parigi G, Rezaei-Ghaleh N, Giachetti A, Becker S, FernandezC, et al. 2014 Long-range correlated dynamics in

intrinsically disordered proteins. J. Am. Chem. Soc. 13616201–16209

Ramachandran GN and Sasisekharan V 1968 Conformation ofpolypeptides and proteins. Adv. Protein Chem. 23 283–438

Ramakrishnan C 2001 Ramachandran and his Map. Resonance 648–56

Schimmel PR and Flory PJ 1968 Conformational energies andconfigurational statistics of copolypeptides containing L-proline.J. Mol. Biol. 34 105–120

Schuler B, Muller-Spath S, Soranno A and Nettels D 2012Application of confocal single-molecule FRET to intrinsicallydisordered proteins. Methods Mol. Biol. 96 21–45

Uversky VN 2002 Natively unfolded proteins: A point wherebiology waits for physics. Protein Science. 11 739–756

Uversky VN 2003 A Protein-Chameleon: Conformational plasticityof a-synuclein, a disordered protein involved in neurodegener-ative disorders. J. Biomol. Struct. Dyn. 21 211–234

Uversky VN 2013 Unusual biophysics of intrinsically disorderedproteins. Biochim. Biophys. Acta 1834 932–951

Valeur B 2001 Molecular Fluorescence: Principles and Applica-tions. Wiley-VCH

Xue Y and Skrynnikov NR 2011 Motion of a disorderedpolypeptide chain as studied by paramagnetic relaxationenhancements, 15N relaxation, and molecular dynamics simu-lations: How fast is segmental diffusion in denatured ubiquitin?J. Am. Chem. Soc. 133 14614–14628

462 D Das and S Mukhopadhyay