Conformational properties of the unfolded state of Im7 in nondenaturing conditions

The unfolded ensemble in aqueous solution represents the starting point of protein folding. Characterisation of this species is often difficult since the native state is usually predominantly populated at equilibrium. Previous work has shown that the four-helix protein, Im7 (immunity protein 7), folds via an on-pathway intermediate. While the transition states and folding intermediate have been characterised in atomistic detail, knowledge of the unfolded ensemble under the same ambient conditions remained sparse. Here, we introduce destabilising amino acid substitutions into the sequence of Im7, such that the unfolded state becomes predominantly populated at equilibrium in the absence of denaturant. Using far- and near-UV CD, fluorescence, urea titration and heteronuclear NMR experiments, we show that three amino acid substitutions (L18A–L19A–L37A) are sufficient to prevent Im7 folding, such that the unfolded state is predominantly populated at equilibrium. Using measurement of chemical shifts, ¹⁵N transverse relaxation rates and sedimentation coefficients, we show that the unfolded species of L18A–L19A–L37A deviates significantly from random-coil behaviour. Specifically, we demonstrate that this unfolded species is compact (R_h = 25 Å) relative to the urea-denatured state (R_h ≥ 30 Å) and contains local clusters of hydrophobic residues in regions that correspond to the four helices in the native state. Despite these interactions, there is no evidence for long-range stabilising tertiary interactions or persistent helical structure. The results reveal an unfolded ensemble that is conformationally restricted in regions of the polypeptide chain that ultimately form helices I, II and IV in the native state.     

Direct Observation of Downhill Folding of λ-Repressor in a Microfluidic Mixer

The protein λ_6-85 has been implicated in barrierless folding by observations of kinetic relaxation after nanosecond T-jump. In this work we observed folding of this protein after dilution of a high denaturant in an ultrarapid microfluidic mixer at temperatures far below the thermal midpoint. The observations of total intensity and spectral shift of tryptophan fluorescence yielded distinctly different kinetics and activation energies. These results may be explained as diffusion on a low-barrier, one-dimensional, free-energy surface, with different probes having different sensitivities along the reaction coordinate. Additionally, we observed an extremely fast phase within the mixing time that was not observed by T-jump, suggesting that the ensemble of unfolded states populated at high denaturant is distinct from those accessible at high temperature.     

Single-Molecule Studies of the Im7 Folding Landscape

Under appropriate conditions, the four-helical Im7 (immunity protein 7) folds from an ensemble of unfolded conformers to a highly compact native state via an on-pathway intermediate. Here, we investigate the unfolded, intermediate, and native states populated during folding using diffusion single-pair fluorescence resonance energy transfer by measuring the efficiency of energy transfer (or proximity or P ratio) between pairs of fluorophores introduced into the side chains of cysteine residues placed in the center of helices 1 and 4, 1 and 3, or 2 and 4. We show that while the native states of each variant give rise to a single narrow distribution with high P values, the distributions of the intermediates trapped at equilibrium (denoted I^eqm) are fitted by two Gaussian distributions. Modulation of the folding conditions from those that stabilize the intermediate to those that destabilize the intermediate enabled the distribution of lower P value to be assigned to the population of the unfolded ensemble in equilibrium with the intermediate state. The reduced stability of the I^eqm variants allowed analysis of the effect of denaturant concentration on the compaction and breadth of the unfolded state ensemble to be quantified from 0 to 6 M urea. Significant compaction is observed as the concentration of urea is decreased in both the presence and absence of sodium sulfate, as previously reported for a variety of proteins. In the presence of Na₂SO₄ in 0 M urea, the P value of the unfolded state ensemble approaches that of the native state. Concurrent with compaction, the ensemble displays increased peak width of P values, possibly reflecting a reduction in the rate of conformational exchange among iso-energetic unfolded, but compact conformations. The results provide new insights into the initial stages of folding of Im7 and suggest that the unfolded state is highly conformationally constrained at the outset of folding.     

The denatured state of N-PGK is compact and predominantly disordered

The organisation of the structure present in the chemically denatured N-terminal domain of phosphoglycerate kinase (N-PGK) has been determined by paramagnetic relaxation enhancements (PREs) to define the conformational landscape accessible to the domain. Below 2.0 M guanidine hydrochloride (GuHCl), a species of N-PGK (denoted I_b) is detected, distinct from those previously characterised by kinetic experiments [folded (F), kinetic intermediate (I_k) and denatured (D)]. The transition to I_b is never completed at equilibrium, because F predominates below 1.0 M GuHCl. Therefore, the ability of PREs to report on transient or low population species has been exploited to characterise I_b. Five single cysteine variants of N-PGK were labelled with the nitroxide electron spin-label MTSL [(1-oxyl-2,2,5,5-tetramethyl-3-pyrroline-3-methyl)methanesulfonate] and the denaturant dependences of the relaxation properties of the amide NMR signals between 1.2 and 3.6 M GuHCl were determined. Significant PREs for I_b were obtained, but these were distributed almost uniformly throughout the sequence. Furthermore, the PREs indicate that no specific short tertiary contacts persist. The data indicate a collapsed state with no coherent three-dimensional structure, but with a restricted radius beyond which the protein chain rarely reaches. The NMR characteristics of I_b indicate that it forms from the fully denatured state within 100 μs, and therefore a rapid collapse is the initial stage of folding of N-PGK from its chemically denatured state. By extrapolation, I_b is the predominant form of the denatured state under native conditions, and the non-specifically collapsed structure implies that many non-native contacts and chain reversals form early in protein folding and must be broken prior to attaining the native state topology.     

Propensity to Form Amyloid Fibrils Is Encoded as Excitations in the Free Energy Landscape of Monomeric Proteins

Protein aggregation, linked to many of diseases, is initiated when monomers access rogue conformations that are poised to form amyloid fibrils. We show, using simulations of src SH3 domain, that mechanical force enhances the population of the aggregation-prone (N^?) states, which are rarely populated under force free native conditions but are encoded in the spectrum of native fluctuations. The folding phase diagrams of SH3 as a function of denaturant concentration ([C]), mechanical force (f), and temperature exhibit an apparent two-state behavior, without revealing the presence of the elusive N^? states. Interestingly, the phase boundaries separating the folded and unfolded states at all [C] and f fall on a master curve, which can be quantitatively described using an analogy to superconductors in a magnetic field. The free energy profiles as a function of the molecular extension (R), which are accessible in pulling experiments, (R), reveal the presence of a native-like N^? with a disordered solvent-exposed amino-terminal β-strand. The structure of the N^? state is identical with that found in Fyn SH3 by NMR dispersion experiments. We show that the timescale for fibril formation can be estimated from the population of the N^? state, determined by the free energy gap separating the native structure and the N^? state, a finding that can be used to assess fibril forming tendencies of proteins. The structures of the N^? state are used to show that oligomer formation and likely route to fibrils occur by a domain-swap mechanism in SH3 domain.     

Small-angle X-ray scattering and single-molecule FRET spectroscopy produce highly divergent views of the low-denaturant unfolded state

The results of more than a dozen single-molecule F?rster resonance energy transfer (smFRET) experiments suggest that chemically unfolded polypeptides invariably collapse from an expanded random coil to more compact dimensions as the denaturant concentration is reduced. In sharp contrast, small-angle X-ray scattering (SAXS) studies suggest that, at least for single-domain proteins at non-zero denaturant concentrations, such compaction may be rare. Here, we explore this discrepancy by studying protein L, a protein previously studied by SAXS (at 5?°C), which suggested fixed unfolded-state dimensions from 1.4 to 5?M guanidine hydrochloride (GuHCl), and by smFRET (at 25?°C), which suggested that, in contrast, the chain contracts by 15-30% over this same denaturant range. Repeating the earlier SAXS study under the same conditions employed in the smFRET studies, we observe little, if any, evidence that the unfolded state of protein L contracts as the concentration of GuHCl is reduced. For example, scattering profiles (and thus the shape and dimensions) collected within ～4?ms after dilution to as low as 0.67?M GuHCl are effectively indistinguishable from those observed at equilibrium at higher denaturant. Our results thus argue that the disagreement between SAXS and smFRET is statistically significant and that the experimental evidence in favor of obligate polypeptide collapse at low denaturant cannot be considered conclusive yet.     

Pressure-jump studies of the folding/unfolding of trp repressor.

The dimeric protein, trp apo-repressor of Escherichia coli has been subjected to high hydrostatic pressure under a variety of conditions, and the effects have been monitored by fluorescence spectroscopic and infra-red absorption techniques. Under conditions of micromolar protein concentration and low, non-denaturing concentrations of guanidinium hydrochloride (GuHCl), tryptophan and 8-anilino-1-naphthalene sulfonate (ANS) fluorescence detected high pressure profiles demonstrate that pressures below 3 kbar result in dissociation of the dimer to a monomeric species that presents no hydrophobic binding sites for ANS. The FTIR-detected high pressure profile obtained under significantly different solution conditions (30 mM trp repressor in absence of denaturant) exhibits a much smaller pressure dependence than the fluorescence detected profiles. The pressure-denatured form obtained under the FTIR conditions retains about 50 % alpha-helical structure. From this we conclude that the secondary structure present in the high pressure state achieved under the conditions of the fluorescence experiments is at least as disrupted as that achieved under FTIR conditions. Fluorescence-detected pressure-jump relaxation studies in the presence of non-denaturing concentrations of GuHCl reveal a positive activation volume for the association/folding reaction and a negative activation volume for dissociation/unfolding reaction, implicating dehydration as the rate-limiting step for association/folding and hydration as the rate-limiting step for unfolding. The GuHCl concentration dependence of the kinetic parameters place the transition state at least half-way along the reaction coordinate between the unfolded and folded states. The temperature dependence of the pressure-jump fluorescence-detected dissociation/unfolding reaction in the presence of non-denaturing GuHCl suggests that the curvature in the temperature dependence of the stability arises from non-Arrhenius behavior of the folding rate constant, consistent with a large decrease in heat capacity upon formation of the transition state from the unfolded state. The decrease in the equilibrium volume change for folding with increasing temperature (due to differences in thermal expansivity of the folded and unfolded states) arises from a decrease in the absolute value for the activation volume for unfolding, thus indicating that the thermal expansivity of the transition state is similar to that of the unfolded state.     

A newly synthesized, ribosome-bound polypeptide chain adopts conformations dissimilar from early in vitro refolding intermediates

Little is known about the conformations of newly synthesized polypeptide chains as they emerge from the large ribosomal subunit, or how these conformations compare with those populated immediately after dilution of polypeptide chains out of denaturant in vitro. Both in vivo and in vitro, partially folded intermediates of the tailspike protein from Salmonella typhimurium phage P22 can be trapped in the cold. A subset of monoclonal antibodies raised against tailspike recognize partially folded intermediates, whereas other antibodies recognize only later intermediates and/or the native state. We have used a pair of monoclonal antibodies to probe the conformational features of full-length, newly synthesized tailspike chains recovered on ribosomes from phage-infected cells. The antibody that recognizes early intermediates in vitro also recognizes the ribosome-bound intermediates. Surprisingly, the antibody that did not recognize early in vitro intermediates did recognize ribosome-bound tailspike chains translated in vivo. Thus, the newly synthesized, ribosome-bound tailspike chains display structured epitopes not detected upon dilution of tailspike chains from denaturant. As opposed to the random ensemble first populated when polypeptide chains are diluted out of denaturant, folding in vivo from the ribosome may begin with polypeptide conformations already directed toward the productive folding and assembly pathway.     

Mutational Studies Uncover Non-Native Structure in the Dimeric Kinetic Intermediate of the H2A-H2B Heterodimer

The folding pathway of the histone H2A-H2B heterodimer minimally includes an on-pathway, dimeric, burst-phase intermediate, I₂. The partially folded H2A and H2B monomers populated at equilibrium were characterized as potential monomeric kinetic intermediates. Folding kinetics were compared for initiation from isolated, folded monomers and the heterodimer unfolded in 4 M urea. The observed rates were virtually identical above 0.4 M urea, exhibiting a log-linear relationship on the final denaturant concentration. Below ∼ 0.4 M urea (concentrations inaccessible from the  4-M urea unfolded state), a rollover in the rates was observed; this suggests that a component of the I₂ ensemble contains non-native structure that rearranges/isomerizes to a more native-like species. The contribution of helix propensity to the stability of the I₂ ensemble was assessed with a set of H2A-H2B mutants containing Ala and Gly replacements at nine sites, focusing mainly on the long, central α2 helix. Equilibrium and kinetic folding/unfolding data were collected to determine the effects of the mutations on the stability of I₂ and the transition state between I₂ and N₂. This limited mutational study indicated that residues in the α2 helices of H2A and H2B as well as α1 of H2B and both the C-terminus of α3 and the short αC helix of H2A contribute to the stability of the I₂ burst-phase species. Interestingly, at least eight of the nine targeted residues stabilize I₂ by interactions that are non-native to some extent. Given that destabilizing I₂ and these non-native interactions does not accelerate folding, it is concluded that the native and non-native structures present in the I₂ ensemble enable efficient folding of H2A-H2B.     

Reversible denaturation of the gene V protein of bacteriophage f1

The guanidine hydrochloride (GuHCl)-induced denaturation of the gene V protein of bacteriophage f1 has been studied, using the chemical reactivity of a cysteine residue that is buried in the folded protein and the circular dichroism (CD) at 211 and 229 nm as measures of the fraction of polypeptide chains in the folded form. It is found that this dimeric protein unfolds in a single cooperative transition from a folded dimer to two unfolded monomers. A folded, monomeric form of the gene V protein was not detected at equilibrium. The kinetics of unfolding of the gene V protein in 3 M GuHCl and the refolding in 2 M GuHCl are also consistent with a transition between a folded dimer and two unfolded monomers. The GuHCl concentration dependence of the rates of folding and unfolding suggests that the transition state for folding is near the folded conformation.     

The Origin of Nonmonotonic Complex Behavior and the Effects of Nonnative Interactions on the Diffusive Properties of Protein Folding

We present a method for calculating the configurational-dependent diffusion coefficient of a globular protein as a function of the global folding process. Using a coarse-grained structure-based model, we determined the diffusion coefficient, in reaction coordinate space, as a function of the fraction of native contacts formed Q for the cold shock protein (TmCSP). We find nonmonotonic behavior for the diffusion coefficient, with high values for the folded and unfolded ensembles and a lower range of values in the transition state ensemble. We also characterized the folding landscape associated with an energetically frustrated variant of the model. We find that a low-level of frustration can actually stabilize the native ensemble and increase the associated diffusion coefficient. These findings can be understood from a mechanistic standpoint, in that the transition state ensemble has a more homogeneous structural content when frustration is present. Additionally, these findings are consistent with earlier calculations based on lattice models of protein folding and more recent single-molecule fluorescence measurements.     

Solvent denaturation and stabilization of globular proteins

Statistical thermodynamic theory has recently been developed to account for the stabilities of globular proteins. Here we extend that work to predict the effects of solvents on protein stability. Folding is assumed to be driven by solvophobic interactions and opposed by conformational entropy. The solvent dependence of the solvophobic interactions is taken from transfer experiments of Nozaki and Tanford on amino acids into aqueous solutions of urea or guanidine hydrochloride (GuHCl). On the basis of the assumption of two pathways involving collapse and formation of a core, the theory predicts that increasing denaturant should lead to a two-state denaturation transition (i.e., there is a stable state along each path separated by a free energy barrier). The denaturation midpoint is predicted to occur at higher concentrations of urea than of GuHCl. At neutral pH, the radius of the solvent-denatured state should be much smaller than for a random-flight chain and increase with either denaturant concentration or number of polar residues in the chain. A question of interest is whether free energies of folding should depend linearly on denaturant, as is often assumed. The free energy is predicted to be linear for urea but to have some small curvature for GuHCl. Predicted slopes and exposed areas of the unfolded states are found to be in generally good agreement with experiments. We also discuss stabilizing solvents and compare thermal with solvent denaturation.     

Time-resolved small-angle X-ray scattering study of the folding dynamics of barnase

Structural changes of barnase during folding were investigated using time-resolved small-angle X-ray scattering (SAXS). The folding of barnase involves a burst-phase intermediate, sometimes designated as the denatured state under physiological conditions, D_phys, and a second hidden intermediate. Equilibrium SAXS measurements showed that the radius of gyration (R_g) of the guanidine unfolded state (U) is 26.9 ± 0.7 Å, which remains largely constant over a wide denaturant concentration range. Time-resolved SAXS measurements showed that the R_g value extrapolated from kinetic R_g data to time zero, R_g,0, is 24.3 ± 0.1 Å, which is smaller than that of U but which is expanded from that of folding intermediates of other proteins with similar chain lengths (19 Å). After the burst-phase change, a single-exponential reduction in R_g² was observed, which corresponds to the formation of the native state for the major component containing the native trans proline isomer. We estimated R_g of the minor component of D_phys containing the non-native cis proline isomer (D_phys,cis) to be 25.7 ± 0.6 Å. Moreover, R_g of the major component of D_phys containing the native proline isomer (D_phys,tra) was estimated as 23.9 ± 0.2 Å based on R_g,0. Consequently, both components of the burst-phase intermediate of barnase (D_phys,tra and D_phys,cis) are still largely expanded. It was inferred that D_phys possesses the N-terminal helix and the center of the β-sheet formed independently and that the formation of the remainder of the protein occurs in the slower phase.     

Rapid collapse and slow structural reorganisation during the refolding of bovine alpha-lactalbumin.

The refolding of bovine alpha-lactalbumin (BLA) from its chemically denatured state in 6 M GuHCl has been investigated by a variety of complementary biophysical approaches. CD experiments indicate that the species formed in the early stages of refolding of the apo-protein have at least 85 % of the alpha-helical content of the native state, and kinetic NMR experiments show that they possess near-native compactness. Hydrogen exchange measurements using mass spectrometry and NMR indicate that persistent structure in these transient species is located predominantly in the alpha-domain of the native protein and is similar to that present in the partially folded A-state formed by the protein at low pH. The extent of the exchange protection is, however, small, and there is no evidence for the existence of well-defined discrete kinetic intermediates of the type populated in the refolding of the structurally homologous c-type lysozymes. Rather, both mass spectrometric and NMR data indicate that the rate-determining transition from the compact partially structured (molten globule) species to the native state is highly cooperative. The data show that folding in the presence of Ca2+ is similar to that in its absence, although the rate is increased by more than two orders of magnitude. Sequential mixing experiments monitored by fluorescence spectroscopy indicate that this slower folding is not the result of the accumulation of kinetically trapped species. Rather, the data are consistent with a model in which binding of Ca2+ stabilizes native-like contacts in the partially folded species and reduces the barriers for the conversion of the protein to its native state. Taken together the results indicate that folding of BLA, in the presence of its four disulphide bonds, corresponds to one of the limiting cases of protein folding in which rapid collapse to a globule with a native-like fold is followed by a search for native-like side-chain contacts that enable efficient conversion to the close packed native structure.     

Effect of solvent conditions upon refolding pathways and intermediates for a simple lattice protein

Folding pathways and intermediates for a two-dimensional lattice protein have been investigated via computer simulation at various denaturant concentrations. The protein is represented as a chain of 8 hydrophobic (H) and 12 polar (P) beads on a square lattice sequenced in such a way that the native state is a compact hydrophobic core surrounded by a shell of polar beads. Two nonbonded H beads are said to attract each other with a potential of mean force of strength ϵ. Increasing |ϵ/kT| mimics decreasing the denaturant concentration in the solution. Dynamic Monte Carlo simulations have been performed in order to investigate the folding transition and the folding pathways. Sharp folding—unfolding transitions are observed and the folding process proceeds along well-defined pathways that are populated by partially folded intermediates. The folding pathways as well as the populations of the intermediates are strongly dependent upon the denaturant concentration. Generally, intermediates containing long open stretches of H beads are more populated at high denaturant concentration, whereas compact intermediates containing a substantial number of hydrophobic contacts are more populated at low denaturant concentrations. The folding process is also observed to be cooperative in nature in that the chain does not start folding until a key fold in the middle section of the chain is formed correctly. © 1997 John Wiley & Sons, Inc. Biopoly 42: 399–409, 1997     

Microsecond Barrier-Limited Chain Collapse Observed by Time-Resolved FRET and SAXS

It is generally held that random-coil polypeptide chains undergo a barrier-less continuous collapse when the solvent conditions are changed to favor the fully folded native conformation. We test this hypothesis by probing intramolecular distance distributions during folding in one of the paradigms of folding reactions, that of cytochrome c. The Trp59-to-heme distance was probed by time-resolved Förster resonance energy transfer in the microsecond time range of refolding. Contrary to expectation, a state with a Trp59–heme distance close to that of the guanidinium hydrochloride (GdnHCl) denatured state is present after ~ 27 μs of folding. A concomitant decrease in the population of this state and an increase in the population of a compact high-FRET (Förster resonance energy transfer) state (efficiency > 90%) show that the collapse is barrier limited. Small-angle X-ray scattering (SAXS) measurements over a similar time range show that the radius of gyration under native favoring conditions is comparable to that of the GdnHCl denatured unfolded state. An independent comprehensive global thermodynamic analysis reveals that marginally stable partially folded structures are also present in the nominally unfolded GdnHCl denatured state. These observations suggest that specifically collapsed intermediate structures with low stability in rapid equilibrium with the unfolded state may contribute to the apparent chain contraction observed in previous fluorescence studies using steady-state detection. In the absence of significant dynamic averaging of marginally stable partially folded states and with the use of probes sensitive to distance distributions, barrier-limited chain contraction is observed upon transfer of the GdnHCl denatured state ensemble to native-like conditions.     

Alternatively folded states of an immunoglobulin

Well-defined, non-native protein structures of low stability have been increasingly observed as intermediates in protein folding or as equilibrium structures populated under specific solvent conditions. These intermediate structures, frequently referred to as molten globule states, are characterized by the presence of secondary structure, a lack of significant tertiary contacts, increased hydrophobicity and partial specific volume as compared to native structures, and low cooperativity in thermal unfolding. The present study demonstrates that under acidic conditions (pH less than 3) the antibody MAK33 can assume a folded stable conformation. This A-state is characterized by a high degree of secondary structure, increased hydrophobicity, a native-like maximum wavelength of fluorescence emission, and a tendency toward slow aggregation. A prominent feature of this low-pH conformation is the stability against denaturant and thermal unfolding that is manifested in highly cooperative reversible phase transitions indicative of the existence of well-defined tertiary contacts. These thermodynamic results are corroborated by the kinetics of folding from the completely unfolded chain to the alternatively folded state at pH 2. The given data suggest that MAK33 at pH 2 adopts a cooperative structure that differs from the native immunoglobulin fold at pH 7. This alternatively folded state exhibits certain characteristics of the molten globule but differs distinctly from it by its extraordinary structural stability that is characteristic for native protein structures.     

Relationship between the native-state hydrogen exchange and folding pathways of a four-helix bundle protein

The hydrogen exchange behavior of a four-helix bundle protein in low concentrations of denaturant reveals some partially unfolded forms that are significantly more stable than the fully unfolded state. Kinetic folding of the protein, however, is apparently two-state in the absence of the accumulation of early folding intermediates. The partially unfolded forms are either as folded as or more folded than the rate-limiting transition state and appear to represent the major intermediates in a folding and unfolding reaction. These results are consistent with the suggestion that partially unfolded intermediates may form after the rate-limiting step for small proteins with apparent two-state folding kinetics.     

Residual structure and dynamics in DMSO-d6 denatured dynein light chain protein

Structural and motional features in the denatured state of a protein dictate the early folding events starting from that state and these features vary depending upon the nature of the denaturant used. Here, we have attempted to decipher the early events in the folding of Dynein Light Chain protein (DLC8), starting from DMSO-d6 denatured state. Multinuclear NMR experiments were used to obtain the full spectral assignment. The HSQC spectrum shows the presence of two sets of peaks for the residues Met 1, Ser 2, Arg 4, Ala 11, Met 17, Thr 26, Lys 44, Tyr 50, Asn 51, Trp 54, His 55, Val 58, Gly 59, Ser 64, Tyr 65, His 68, Phe 86, Lys 87 indicating the presence of slow conformational transition in the heterogeneous ensemble. Analysis of residual structural propensities with secondary ¹³C chemical shifts, ³J(H^N₋H^α) coupling constants and ¹H-¹H NOE revealed the presence of local preferences which encompass both native and non-native like structures. The spectral density calculations, as obtained from measured R₁, R₂ and ¹H-¹⁵N steady state NOE values provide insights into the backbone dynamics on the milli to picosecond timescale. The segment Ser 14 - His 55 exhibits slow motions on the milli- to microsecond timescale arising from conformational exchange. The presence of native like structural preference, as well as conformational exchange classifies the above segment as the nucleation site of folding. Based on the observations, we propose here, the probable hierarchy of folding of DLC8 on dilution of denaturant: the two helices are formed first followed by the formation of β2 and β5.     

An Extended Guinier Analysis for Intrinsically Disordered Proteins

Guinier analysis allows model-free determination of the radius of gyration (R_g) of a biomolecule from X-ray or neutron scattering data, in the limit of very small scattering angles. Its range of validity is well understood for globular proteins, but is known to be more restricted for unfolded or intrinsically disordered proteins (IDPs). We have used ensembles of disordered structures from molecular dynamics simulations to investigate which structural properties cause deviations from the Guinier approximation at small scattering angles. We find that the deviation from the Guinier approximation is correlated with the polymer scaling exponent ν describing the unfolded ensemble. We therefore introduce an empirical, ν-dependent, higher-order correction term, to augment the standard Guinier analysis. We test the new fitting scheme using all-atom simulation data for several IDPs and experimental data for both an IDP and a destabilized mutant of a folded protein. In all cases tested, we achieve an accuracy of the inferred R_g within ～ 3% of the true R_g. The method is straightforward to implement and extends the range of validity to a maximum qR_g of ～ 2 versus ～ 1.1 for Guinier analysis. Compared with the Guinier or Debye approaches, our method allows data from wider angles with lower noise to be used to analyze scattering data accurately. In addition to R_g, our fitting scheme also yields estimates of the scaling exponent ν in excellent agreement with the reference ν determined from the underlying molecular ensemble.