Guanidine-HCl Dependent Structural Unfolding of M-Crystallin: Fluctuating Native State Like Topologies and Intermolecular Association

Numerous experimental techniques and computational studies, proposed in recent times, have revolutionized the understanding of protein-folding paradigm. The complete understanding of protein folding and intermediates are of medical relevance, as the aggregation of misfolding proteins underlies various diseases, including some neurodegenerative disorders. Here, we describe the unfolding of M-crystallin, a βγ-crystallin homologue protein from archaea, from its native state to its denatured state using multidimensional NMR and other biophysical techniques. The protein, which was earlier characterized to be a predominantly β-sheet protein in its native state, shows different structural propensities (α and β), under different denaturing conditions. In 2 M GdmCl, the protein starts showing two distinct sets of peaks, with one arising from a partially unfolded state and the other from a completely folded state. The native secondary structural elements start disappearing as the denaturant concentration approaches 4 M. Subsequently, the protein is completely unfolded when the denaturant concentration is 6 M. The 15N relaxation data (T1/T2), heteronuclear 1H-15N Overhauser effects (nOes), NOESY data, and other biophysical data taken together indicate that the protein shows a consistent, gradual change in its structural and motional preferences with increasing GdmCl concentration.


Introduction
The phenomenon of protein folding-unfolding and its relevance to diseases [1,2,3,4,5,6] is yet to be understood. Protein folding always starts enthalpically/entropically from a state, which is nonnative or denatured state and goes into a stable state i.e., native state. Deciphering the structural and dynamic basis of how a given protein sequence translates into a folded conformation requires understanding of the intermediate state(s) of the protein during the process of protein folding/unfolding. The information about the structure and dynamics of different protein states is useful to understand the enthalpically or entropically driven folding/ unfolding processes in a given protein, which in turn help in the understanding of the design of protein function. In this endeavor, solution structures are ideally suited for studying such functional states. Earlier studies suggest that proteins exhibit different secondary structural elements under extreme conditions, and sometimes even possesses residual structures [2,7,8,9,10,11,12,13].
On the other hand, the eye-lens, its architecture and its evolution has been subjects of research for quite a long time [14,15]. The transparency of the lens is due to its complex architecture and due to the presence of high protein concentration. The function of the eye-lens is to focus the incoming light on the retina. The lens proteins, namely crystallins, accomplish this task of focusing the incoming light. Eye-lens crystallins are of three kinds; a-, band ccrystallins. The lens a-crystallins are known to act as molecular chaperones, while lens band c-crystallins, which were thought to be structural proteins, were shown recently to have diverse roles in various cellular processes [16,17]. The band c-crystallins are grouped under bc-crystallin superfamily, because of their structural similarity and these proteins comprise of two consecutive Greek key motifs, which together form a stable eightstranded b-sheeted sandwich structure [18,19]. Some of the bccrystallins that include several bacterial homologues have been shown to bind Ca 2+ [20,21,22,23,24]. When the eye-lens becomes opaque, it results in cataract, a disorder of the eye. Causes of cataract include: mutation in one of the lens-crystallin proteins, ageing process, diabetes, and environmental factors (i.e., change in the pH, temperature and UV-exposure). During these processes, unfolding of any crystallin protein may occur and lead to protein aggregation or altered interaction/association between native crystallins, due to insolubility of proteins. Therefore, it is important to study the complete unfolding pathway of these proteins, which could aid in understanding cataract related problems.
In this backdrop, we have used M-crystallin, a putative bccrystallin protein (accession NP_617429) from the genome of an archaea Methanosarcina acetivorans, as a model protein to study the folding/unfolding behavior of this oldest relative of bc-crystallins ( Figure S1) [25]. We have earlier solved the 3D structure of M-crystallin in its Ca 2+ -bound form by NMR [25]. A temperature dependent oligomerization of this protein has been reported to have significance in the cataract [26]. The 15 N relaxation data (T 1 /T 2 ), heteronuclear 1 H- 15 N Overhauser effects (nOes), NOESY data, and other biophysical data of M-crystallin taken together indicate that the protein shows a consistent, gradual change in its structural and motional preferences with increasing GdmCl concentration.

Results and Discussion
Resonance assignments of M-crystallin in 4 and 6 M GdmCl The backbone 1 H, 13 C and 15 N resonance assignments of Mcrystallin in 4 and 6 M GdmCl were carried out to an extent of 94 and 96%, respectively, using a suite of 3D experiments (HNCACB, HN(CO)CACB, HNCO and HN(CA)CO), as reported earlier [27,28]. Inherent spectral overlaps caused by the chemical shift degeneracies in 1 H and 13 C spins could be resolved using other experiments [29,30,31]

GdmCl induced unfolding as studied by CD and fluorescence
GdmCl induced unfolding of M-crystallin was characterized by CD and fluorescence emission spectra [32,33,34] as described in Materials and Methods. Figure 2 shows the denaturation curves of M-crystallin as obtained by far-UV CD and fluorescence spectroscopy, wherein the ellipticity at 218 nm ( Figure 2A) and the Trp emission at 331 nm ( Figure 2B) were monitored, respectively. The normalized fluorescence and CD curves (not shown here) show similar trend. Almost no changes were noticed till the GdmCl concentration reached 1.1 M. Between 1.1 and 2.8 M, there was a sudden change, with no change thereafter ( Figure 2B). As it is evident from the Figures 2A and 2B, both the curves depict protein unfolding as a two-state model. Transition mid-point and slope of the transition (m 1 ) thus determined from the fluorescence data were 1.9 M and 2.84 kCal mol 21 M 21 , respectively.

GdmCl dependent [ 15 N-1 H]-HSQC spectra
We used NMR to study the order-disorder transitions in Mcrystallin under various denaturing conditions ranging from 0 to 6 M GdmCl. For this purpose, we recorded a set of [ 15 N-1 H]-HSQC of M-crystallin taken in 0, 0.8, 1.7, 2.0, 3.1, 4.0, 5.2 and 6.0 M GdmCl ( Figure S2). As evident from Figure 1 and Figure  S2, the protein was in a completely folded state at 0 M GdmCl concentration, with a single set of peaks. However, we started observing two sets of peaks as the GdmCl concentration approached 2 M ( Figure S2), one set of peaks corresponding to the folded state (well dispersed peaks; as seen at 0 M) and the other set corresponding to a partially unfolded state (with the 1 H N chemical shifts in a narrow range of chemical shifts; between 7.8-8.8 ppm). This indicated that the protein was not in a completely unfolded state at the above-mentioned denaturant concentration. This observation of protein in its two states, correlates with the biophysical data described above. Further, as the denaturant concentration approached 3 M, the protein showed spectral signatures largely expected from the completely unfolded state of the protein. At this concentration and beyond, only one set of 15 N-1 H N peaks showed-up with the corresponding 1 H N chemical shifts in a narrow range of 7.8-8.8 ppm. This observation is consistent with the fluorescence data discussed above, which indicates loss of the tertiary structure at higher GdmCl concentrations beyond 2.8 M. However, it is worth mentioning here that the protein showed some transient residual structures at denaturant concentrations greater than 3 M, which we probed and characterized, as discussed later.  [35] (shown in Figure 3A) and 3 J( 1 H N -1 Ha) three-bond coupling constants ( Figures S3 and S4). While, the folded protein has a rigid structure, which is predominantly b-sheet in structure, and made up of seven well defined b-strands (Val 6-Glu 10, Ser1 8-Ala 21, Ser 38-Val 41, Thr 45-Tyr 49, Trp 59-Gly 62, Gly 64-Tyr 66 and Ser 81-Gln 84), the protein under denatured condition shows similar secondary structural propensities in these regions. As discussed earlier by several researchers, the denatured state(s) of any given protein may either adopt a completely random coil conformation [36,37,38] or may have regions which adopt preferred conformations or secondary structure propensities for transient structure formations [39,40,41]. The regions, which have certain secondary structural propensities, are termed as folding cores. These folding cores indicate a possible initiation of the folding reaction upon dilution of the denaturant concentrations. Figure 3A suggests that M-crystallin retained its predominantly bsheet conformation during its unfolding pathway. However, three polypeptide stretches (Asp 20-Ala 28, Asp 60-Tyr 66 and Ala 72-Asn 77) did show propensities for helical conformation for the Mcrystallin in 6 M GdmCl.
As mentioned below in Materials and Methods, 3 J( 1 H N -1 Ha) were calculated from GFT (3, 2)D-HNHA spectra. We could measure 3 J( 1 H N - 1 Ha values for 77 out of 80 residues (.95%) in the native state of the protein, while the number of 3 J values were 75 and 68 for the M-crystallin in 4 and 6 M GdmCl ( Figure S4). These 3 J couplings are highly sensitive to the backbone torsion angle Q and carry the information about the conformational preference of individual amino acid residues. The 3 J( 1 H N -Ha) for residues in a-helical segments (a-helix and PP I ) range between 4.0 and 5.5 Hz, while theses values are .8 Hz for residues involved in b-strand structures and 5.5-8.0 Hz for random coil stretches. For the native state of M-crystallin (2k1w), while ,3% residues adopt an a-helical conformation, 42% were in b-sheet and 55% in random coil conformation. In the presence of GdmCl, most of these couplings range between 5.5 and 8.5 Hz, indicating their involvement in an extended structure with some kind of conformational averaging. However, for the polypeptide stretches, Thr22-Gln25, Gly64-Ser68 and Glu70-Ile74, the measured coupling constants were less than 5 Hz indicating a-helical or PP I preferences for these stretches.
(b) Temperature coefficients and residual structure formation. Amide proton ( 1 H N ) exchange rates and their temperature coefficients throw light on hydrogen bonding (if any), both in globular or denatured state of any protein [42]. If an 1 H N is hydrogen bonded, it would have a temperature coefficient more positive than 24.5 ppb/K. Random coiled or non-hydrogen bonded 1 H N tends to have more negative values than 24.5 ppb/ K. In the present study, the 1 H N temperature coefficients were measured by recording a set of HSQC spectra at different temperatures ranging from 15 to 36uC, at an interval of 3uC, for all the three states of the protein ( Figure 3B). As seen from Figure 3B, the protein in its native state (0 M GdmCl) displayed the presence of several continuous polypeptide stretches involved in hydrogen bonding. On the other hand, the protein under denatured conditions (4 M and 6 M GdmCl) exhibits largely extended conformations, with very few signatures of intramolecular hydrogen bonding. The polypeptide stretches that showed signatures of their involvement in hydrogen bonding were Thr22-Asp24, Glu65-Tyr66, and Asn77-Ser78. These polypeptide stretches showed temperature coefficients more positive than 24.0 ppb/K values even in 4 M GdmCl, hinting at their possible involvement in some kind of residual structures even under such denatured conditions.

Protein dynamics in the denatured states
The 15 N spin-lattice/spin-spin relaxation times (T 1 /T 2 ), and heteronuclear 1 H-15 N Overhauser effects (NOE) were measured at 25 uC and at two different external magnetic fields (600 and 800 MHz) for the folded protein as well as the protein in the denatured states to throw light on GdmCl induced motional perturbations. We carried out relaxation analysis of 69 and 65 residues of the protein in 4 and 6 M GdmCl, respectively. Relaxation data for the folded protein was taken from our earlier reported work [26]. Three prolines and two N-terminal residues, which do not show their spectral signatures could not be part of  [26]. These residues, belonging to a different Greek keys, are seen to have a higher value of exchange and R 2 value in case of native protein [26].The Nterminal residues and Lys 17, Ala 28, Gly 29, Gly73, and Ile74 residues also show lower R 2 values due to their presence at the edge of structural propensities. This is also supported by the fact that these residues are in the neighborhood of residues Gly, Pro or Ala, which are supposed to create hinges with in a polypeptide stretches and/or act as secondary structure breakers.
The 1 H-15 N steady state nOes have information about high frequency motions As is evident in Figure 4C, three N-terminal residues Asn 3, Ala 4 and Glu 5, and two C-terminal residues Gln 84 and Ile 85 show negative nOes, as a result of their higher order flexibility ( Figure 4C and Figure S5C) in the presence of denaturant (6 and 4 M GdmCl), while the protein in its native state (at 0 M GdmCl) does not show such higher order flexibility at the C-terminal end. All the relevant R 1 , R 2 and nOe data are provided in Table 1.
(b) Spectral densities. 15 N-relaxation data acquired on 600 MHz NMR spectrometer were used to calculate the reduced spectral density functions (J values) at different frequencies (0, 60 and 540 MHz). These J(v H ), J(v N ) and J(0) values were calculated based on Equations 2-5 (see Methods; Figure 4D-F). The J(0) values showed the largest variation across the sequence and are mostly based on R 2 , whereas the J(v H ) values, which are largely determined by nOe data, exhibited a lot of variation in the regions belonging to terminal residues, Asp 20-Ala 28, Gly 44-Ile 52, Asp 60-Tyr 66 and Ala 72-Asn 77. The J(v N ) values, which are largely dependent on R 1 , were found to be constant for most of the residues, except for regions at the N and C-terminals, and the polypeptide stretches Thr 22-Ala 28, and Gly 73-Ser 80. A higher  (Table 2).
(d) Conformational exchanges (R ex ) contribution. The R 2 values are representative of slow time-scale motions including conformational exchanges. They provide evidence for motional restrictions and flexibilities in native as well as in denatured proteins. The R 2 values determined at different denaturing conditions are shown in Figure 6A. As evident in Figure 6A, R 2 values showed finite variations all along the protein primary sequence indicating some degree of restricted motions even under denaturing conditions. Figure 6B shows the changes in the R 2 values for the protein in going from 0 to 4 M, 0 to 6 M and 4 to 6 M of GdmCl concentrations. The negative values in Figure 6B represent increased conformational transitions, while positive deviations indicate decreased conformational transitions. These features were predominantly seen for residues Asp 24 and Glu 50, while going from 4 to 6 M GdmCl concentration. Here, Asp 24 shows decreased conformational transition whereas Glu 50  GdmCl. This could be attributed to the fact that, as the protein attains its native fold, the mechanism for conformational exchange is driven by several factors such as change of viscosity, presence of stable secondary structural elements etc [43,44]. Conformational exchange contributions (R ex ) to the R 2 were calculated based on equation R 2 *R 1 and R 2 /R 1 [45,46]. Higher values of R 2 /R 1 ratio represent the presence of conformational exchange and shed light on motional fluctuations ( Figure 7A

Residual structural preferences in the unfolded states
The presence of hydrophobic clustering has been quite often reported to be the prime reason for the formation of residual structural element(s) in unfolded state of proteins [38,47,48,49]. The hydrophobic clustering in M-crystallin (if any) was quantified using the per-residue average area buried upon folding AABUF [50], which is defined as the ''change in average area of each amino acid residue upon unfolding''. AABUF is well correlated in several unfolding studies [51,52,53] and is used as a measure for the identification of folding sites in proteins. The correlation of J(0) values and AABUF with the protein primary sequence is shown in Figure 8A. As is evident from this figure, the AABUF values were relatively higher in the polypeptide stretches Val 6-Phe 14, Lys 42-Gly 62, and Ser 78-Phe 82. Interestingly, J(0) and the AABUF showed a similar trend in these regions only under denaturing conditions of 4 and 6 M GdmCl. These regions with reduced flexibilities identified from J(0) analysis were found to correlate well with increased AABUF values (increased hydrophobic content). This correlation suggests the presence of local hydrophobic clustering in these regions under denaturing conditions. A further analysis of HSQC peaks with lower intensities or absence of HSQC peaks in these regions led to our conclusion of occurrence of possible transient hydrophobic clustering under denaturing conditions mentioned above ( Figure 8B). It is also interesting to note that region Asn 77-Arg 83 shows variation in J(v H ) and J(v N ) values in its native state (0 M GdmCl). Incidentally, the three polypeptide stretches Val 6-Phe14, Lys 42-Gly 62, and Ser 78-Phe 82 discussed above comprise four b-strands, namely b1, b4, b5 and b7, in the native state protein structure ( Figure 8A). Thus, it is obvious that local interactions in these regions resulted in restricted

Sequence-structure-function paradigm and folding mechanism
The primary sequence, structure and dynamics reflect the design of function of any protein. Structural Biology is guided by this motivation. Solution structures are ideally suited for unrav-eling such functional states. It is widely accepted that residual structures under denaturing conditions are indicative of structural nucleation for proper folding of the protein [41]. For M-crystallin under different denaturing conditions, many segments followed the b-strand structural preferences, with few polypeptide stretches showing a-helical propencities, Based on the temperature coefficients, dynamics study and nOe information, we propose a model for the folding of M-crystallin. The protein starts from the natively folded state when the M-crystallin is in 0 M GdmCl [25]. Subsequently, protein undergoes transition and starts showing two distinct sets of peaks when it is in the 2 M GdmCl ( Figure S2). Thereafter, when the protein is in 4 M GdmCl, it starts showing secondary structural elements and finally adopts an unfolded state under 6 M GdmCl.

Unfolding Study of M-crystallin and its biological relevance
The unfolding study of M-crystallin under different GdmCl concentrations provided residue level insights into the intrinsic conformational preferences of different polypeptide stretches in the protein. The backbone dynamics, NOESY data and biophysical data of the protein under different GdmCl concentrations taken together suggest that the protein adopts few aand b-type structural preferences under different denaturing conditions. In conclusion, these fluctuating structural preferences and the possible intermolecular interaction/association, as predicted based on the spectral density data, might be a leading cause for aggregation of crystallins resulting in cataract.

Materials and Methods
Protein sample preparation 13 C-or/and 15 N-labelled M-crystallin were over-expressed and purified as mentioned elsewhere [16] [54]. The purity of samples was checked using SDS-PAGE and mass spectroscopy (MALDI-TOF). The protein samples denatured in the presence of varying concentrations of guanidine-HCl (GdmCl; in 0-6 M range at an interval of 0.2-0.3 M) were prepared in milliQ H 2 O solution (10 mM Tris, 50 mM KCl, 5-10 mM CaCl 2 , pH 5.5) for various purposes as discussed above.
For NMR measurements, the protein samples were concentrated to 1.2 mM and exchanged with the proper buffer containing GdmCl at concentrations 0, 1, 2, 4, and 6 M. NMR experiments were recorded after equilibrating the samples in GdmCl for 6-8 hrs. The data acquired with the protein samples in 4 and 6 M GdmCl concentrations is discussed in the results and discussion.

Denaturation studies in guanidine-HCl
The denaturation profile of M-crystallin was studied by optical (circular dichroism (CD) and fluorescence) and NMR spectroscopy. The GdmCl concentrations were determined using a refractometer. For optical measurements, the protein samples of 45 mM concentration with different concentrations of GdmCl were prepared and equilibrated for at least a period of 5-8 hrs.
Far-UV CD spectra were recorded at 25uC on a JASCO J-810 spectropolarimeter (JASCO, Europe) and corrected for buffer baseline. Each scan ranged from 200 to 260 nm with a scan speed of 20 nm/min with a quartz cell having a path length of 0.1 cm. The CD spectra below 200 nm were saturated due to high salt (particularly in the presence of 6 M GdmCl) and hence were not included in the data analysis. Each spectrum was an average of 4 scans (Figure 2A). Fluorescence spectroscopy experiments were performed on a Hitachi F-4500 spectrofluorimeter with a protein concentrations of 45 mM, as mentioned above ( Figure 2B). The Trp emission spectra were recorded by exciting the protein samples at 295 nm. The intensity maxima, wavelength maxima, and intensity value at 331 nm were plotted as a function of GdmCl concentration to determine the fractions unfolded. The data were fitted to a twostate denaturation model, and parameters were determined by a non-linear curve fitting to the following equation [55]: where, Y is the observed spectroscopic signal; s n and s d represent the spectroscopic signals of folded and denatured proteins, respectively; g 1 and m 1 represent the free-energy change and slope of the transition, respectively; D is the denaturant concentration; T is the temperature (in K), and R is the universal gas constant (1.987 cal K 21 mol 21 ).

NMR spectroscopy
NMR experiments were performed either on a Bruker Avance spectrometer with a 1 H frequency of 800.12 MHz, or on a Varian Inova spectrometer with 1 H frequency of 600.51 MHz at 25uC. Both the spectrometers were equipped with cryogenically cooled probes. Sensitivity-enhanced 2D [ 15 N-1 H]-HSQC was recorded for each NMR sample, with 256 and 1024 complex data points along the 15 N and 1 H dimensions, respectively. The spectral widths along 1 H and 15 N dimensions were 12 and 30 ppm, respectively. No changes in HSQC spectra were noticed during the data acquisition, indicating a stable equilibrium under all the experimental conditions. The data were apodized using a sinesquared bell window functions along both the dimensions, zero filled to yield a final resolution of 0.9 and 2.5 Hz/pt along v 1 and v 2 dimensions, respectively, and followed by Fourier transformation. A suite of 3D experiments (CBCACONH, CBCANH, HNCO) and 15 N-edited TOCSY-HSQC with a mixing time of 80 ms were recorded for complete resonance assignments [27,28]. 15  dimensions, respectively. 100-128 complex increments were used along the indirect 1 H dimension.
Amide proton temperature coefficients were measured by recording a suite of sensitivity-enhanced 2D [ 15 N-1 H]-HSQC at different temperatures ranging from 15 to 36uC, at an interval of 3uC, with 256 t 1 increments along the 15 N dimension. Number of scans was 16, and the spectral widths were 12 and 30 ppm along the 1 H and 15 N dimensions, respectively. The protein was stable over the entire temperature and pH (5.5 and 7.5) ranges. 3 J( 1 H N -1 Ha) coupling constants were measured from (3, 2) HNHA [31]. All the experiments were processed using Felix (Accelrys Software Inc., San Diego, CA), NMRPipe [58] and analyzed using Felix (http://www.felixnmr.com) and CARA (http://cara.nmr. ch). The (3, 2)D HNHA, (3, 2)D HNHB, (3, 2)D CB(CA-CO)NHN, (3, 2)D CT-HCCH-COSY spectral data were processed and used as mentioned elsewhere [31]. Sensitivityenhanced 2D [ 15 N-1 H]-HSQC were recorded at the beginning and end of all the 3D experiments and compared to make sure the stability of the protein. No observable changes were seen in the HSQC indicating high stability of the protein during the entire collection of the NMR Data. All the data were apodized with a sine-bell window function, shifted by 56u along both the dimensions of 2D data, and by 60u along all the three dimensions of 3D data, followed by zero-filling and Fourier transformation. The final processed data matrices had 2048*1024 and 1024*128*256 complex data points in all 2D and 3D spectra, respectively.
In the temperature coefficient measurement study, the chemical shift information derived from individual HSQC was tabulated and fitted to a straight line and the corresponding temperature coefficients (dd/dT) were determined from its slope. The digital resolutions in these HSQC spectra were 2.0 and 0.5 Hz/pt along v 1 and v 2 dimensions, respectively.
In relaxation data measurements, peak heights with their respective errors were measured. The peak-heights thus derived were fitted to a single exponential decay function, to derive the individual R 1 and R 2 values, where I(t) is the intensity at delay t (ms) used in the measurement of R 1 and R 2 . A+B is the intensity at initial time t = 0, and A is the steady-state intensity at t = '.
The 1 H-15 N heteronuclear nOe was calculated from the following equation, nOe~I sat I eq where, I sat and I eq are the intensities of individual peaks in the spectra recorded with and without proton saturation. The errors in the nOes were obtained using the root-mean-square value of the background noise as described by Farrow et al. [59,60]. Proton chemical shifts were referenced using DSS at 0.00 ppm in H 2 O/ 2 H 2 O solution at 25uC (6 M GdmCl, pH 5), whereas 15 N and 13 C were referenced indirectly as described elsewhere [61].

Spectral density functions and correlation times
The spectral density functions J(0), J(v N ), and J(v H ) were calculated as described by Wagner et al. [59,60] and Lefevre et al. [62] According to these approaches, J(0), J(v N ), and J(v H ) terms can be expressed in terms of 15 N spin-lattice (R1) and spin-spin (R2) relaxation rates and heteronuclear [ 1 H-15 N] NOEs as follows: where, The constant d 2 is approximately equal to 1.35610 9 (rad/s) 2 , whereas the constant c 2 is approximately 1.25610 9 (rad/s) 2 and 2.25610 9 (rad/s) 2 at 600 and 800 MHz, respectively. Errors in the individual spectral density functions were calculated from the error in the related parameters and by solving above equations [63]. After calculating J(0), J(v N ), and J(v H ), the linear correlation between J(0) and J(v N ), and J(0) and J(v H ) was examined ( Figure 4). Only few residues showed distinctly higher values of J(0), indicating that chemical exchange motions have significant contributions to the mobility of their NH vectors. A linear correlation between J(v N,H ) and corresponding J(0) values using the equation J(v N,H ) = a J(0)+b, has been proposed for the calculation of t m [60,62]. The values of a and b derived from the plot of J(v N ) versus J(0) were found to be 0.14 and 0.30 ns/ rad, respectively, for 4 M GdmCl case, whereas 0.11 and 0.31 ns/ rad, respectively, for 6 M case. These values were then used to calculate the overall correlation time (t m ) using the following equation [60,62]: The solution of the above cubic equation yields three values of t m ( Table 2). The values in milli-seconds to micro-seconds, subnano-seconds and pico-seconds represent the chemical exchange, overall rotational correlation time and internal motions, respectively, depending on their amplitudes.

Average area buried upon folding
The per-residue average area buried upon folding (AABUF) was calculated using the method of Rose et al. [50]. A nine-residue moving-average window was used in the AABUF calculations. Figure S1 Sequence alighment of M-crystallin with other known lens crystallins, bB2-crystallin, cB-crystallin, ciona-crystallin and DdCAD, Trp corner and Tyr corner, special features of crystallins are shown with black arrow. Higher sequence similarity in the alignment chart is highlighted with red color. (TIF) Figure S2 Sensitivity-enhanced 2D [ 15 N-1 H]-HSQC of [Ca 2+ ] 2 -M-crystallin in the presence of 0 (A), 2 (B), 4 (C) and 6 M (D) GdmCl (pH 5.5 and temperature 298 K). These spectra were recorded on a Bruker Avance 800 MHz spectrometer with 128 and 1024 points along t 1 and t 2 dimensions, respectively. Individual peak assignments are shown by the corresponding single-letter code of the amino acid residue and its sequence number along the primary sequence. (TIF) Figure S3 15 N] NOE enhancements derived from I sat /I eq ratio, where I sat and I eq are the intensities of peaks in the 2D spectra recorded with and without proton saturation, respectively. Error bars in the T 1 and T 2 data denote curve-fitting uncertainties: errors in the [ 1 H- 15