On the Calculation of SAXS Profiles of Folded and Intrinsically Disordered Proteins from Computer Simulations

Solution techniques such as small-angle X-ray scattering (SAXS) play a central role in structural studies of intrinsically disordered proteins (IDPs); yet, due to low resolution, it is generally necessary to combine SAXS with additional experimental sources of data and to use molecular simulations. Computational methods for the calculation of theoretical SAXS intensity profiles can be separated into two groups, depending on whether the solvent is modeled implicitly as continuous electron density or considered explicitly. The former offers reduced computational cost but requires the definition of a number of free parameters to account for, for example, the excess density of the solvation layer. Overfitting can thus be an issue, particularly when the structural ensemble is unknown. Here, we investigate and show how small variations of the contrast of the hydration shell, δρ, severely affect the outcome, analysis and interpretation of computed SAXS profiles for folded and disordered proteins. For both the folded and disordered proteins studied here, using a default δρ may, in some cases, result in the calculation of non-representative SAXS profiles, leading to an overestimation of their size and a misinterpretation of their structural nature. The solvation layer of the different IDP simulations also impacts their size estimates differently, depending on the protein force field used. The same is not true for the folded protein simulations, suggesting differences in the solvation of the two classes of proteins, and indicating that different force fields optimized for IDPs may cause expansion of the polypeptide chain through different physical mechanisms.     

Denaturation and reassembly of chaperonin GroEL studied by solution X-ray scattering

We measured the denaturation and reassembly of Escherichia coli chaperonin GroEL using small-angle solution X-ray scattering, which is a powerful technique for studying the overall structure and assembly of a protein in solution. The results of the urea-induced unfolding transition show that GroEL partially dissociates in the presence of more than 2 M urea, cooperatively unfolds at around 3 M urea, and is in a monomeric random coil-like unfolded structure at more than 3.2 M urea. Attempted refolding of the unfolded GroEL monomer by a simple dilution procedure is not successful, leading to formation of aggregates. However, the presence of ammonium sulfate and MgADP allows the fully unfolded GroEL to refold into a structure with the same hydrodynamic dimension, within experimental error, as that of the native GroEL. Moreover, the X-ray scattering profiles of the GroEL thus refolded and the native GroEL are coincident with each other, showing that the refolded GroEL has the same structure and the molecular mass as the native GroEL. These results demonstrate that the fully unfolded GroEL monomer can refold and reassemble into the native tetradecameric structure in the presence of ammonium sulfate and MgADP without ATP hydrolysis and preexisting chaperones. Therefore, GroEL can, in principle, fold and assemble into the native structure according to the intrinsic characteristic of its polypeptide chain, although preexisting GroEL would be important when the GroEL folding takes place under in vivo conditions, in order to avoid misfolding and aggregation.     

Unique Features of the Folding Landscape of a Repeat Protein Revealed by Pressure Perturbation

The volumetric properties of proteins yield information about the changes in packing and hydration between various states along the folding reaction coordinate and are also intimately linked to the energetics and dynamics of these conformations. These volumetric characteristics can be accessed via pressure perturbation methods. In this work, we report high-pressure unfolding studies of the ankyrin domain of the Notch receptor (Nank1-7) using fluorescence, small-angle x-ray scattering, and Fourier transform infrared spectroscopy. Both equilibrium and pressure-jump kinetic fluorescence experiments were consistent with a simple two-state folding/unfolding transition under pressure, with a rather small volume change for unfolding compared to proteins of similar molecular weight. High-pressure fluorescence, Fourier transform infrared spectroscopy, and small-angle x-ray scattering measurements revealed that increasing urea over a very small range leads to a more expanded pressure unfolded state with a significant decrease in helical content. These observations underscore the conformational diversity of the unfolded-state basin. The temperature dependence of pressure-jump fluorescence relaxation measurements demonstrated that at low temperatures, the folding transition state ensemble (TSE) lies close in volume to the folded state, consistent with significant dehydration at the barrier. In contrast, the thermal expansivity of the TSE was found to be equivalent to that of the unfolded state, indicating that the interactions that constrain the folded-state thermal expansivity have not been established at the folding barrier. This behavior reveals a high degree of plasticity of the TSE of Nank1-7.     

Hydrodynamic radii of native and denatured proteins measured by pulse field gradient NMR techniques

Pulse field gradient NMR methods have been used to determine the effective hydrodynamic radii of a range of native and nonnative protein conformations. From these experimental data, empirical relationships between the measured hydrodynamic radius (R(h)) and the number of residues in the polypeptide chain (N) have been established; for native folded proteins R(h) = 4.75N (0.29)A and for highly denatured states R(h) = 2.21N (0.57)A. Predictions from these equations agree well with experimental data from dynamic light scattering and small-angle X-ray or neutron scattering studies reported in the literature for proteins ranging in size from 58 to 760 amino acid residues. The predicted values of the hydrodynamic radii provide a framework that can be used to analyze the conformational properties of a range of nonnative states of proteins. Several examples are given here to illustrate this approach including data for partially structured molten globule states and for proteins that are unfolded but biologically active under physiological conditions. These reveal evidence for significant coupling between local and global features of the conformational ensembles adopted in such states. In particular, the effective dimensions of the polypeptide chain are found to depend significantly on the level of persistence of regions of secondary structure or features such as hydrophobic clusters within a conformational ensemble.     

Structure and Disorder in an Unfolded State under Nondenaturing Conditions from Ensemble Models Consistent with a Large Number of Experimental Restraints

Obtaining detailed structural models of disordered states of proteins under nondenaturing conditions is important for a better understanding of both functional intrinsically disordered proteins and unfolded states of folded proteins. Extensive experimental characterization of the drk N-terminal SH3 domain unfolded state has shown that, although it appears to be highly disordered, it possesses significant nonrandom secondary and tertiary structure. In our previous attempts to generate structural models of the unfolded state using the program ENSEMBLE, we were limited by insufficient experimental restraints and conformational sampling. In this study, we have vastly expanded our experimental restraint set to include ¹H-¹⁵N residual dipolar couplings, small-angle X-ray scattering measurements, nitroxide paramagnetic relaxation enhancements, O₂-induced ¹³C paramagnetic shifts, hydrogen-exchange protection factors, and ¹⁵N R₂ data, in addition to the previously used nuclear Overhauser effects, amino terminal Cu²⁺-Ni²⁺ binding paramagnetic relaxation enhancements, J-couplings, chemical shifts, hydrodynamic radius, and solvent accessibility restraints. We have also implemented a new ensemble calculation methodology that uses iterative conformational sampling and seeks to calculate the simplest possible ensemble models. As a result, we can now generate ensembles that are consistent with much larger experimental data sets than was previously possible. Although highly heterogeneous and having broad molecular size distributions, the calculated drk N-terminal SH3 domain unfolded-state ensembles have very different properties than expected for random or statistical coils and possess significant nonnative α-helical structure and both native-like and nonnative tertiary structure.     

Toward resolution of ambiguity for the unfolded state

The unfolded states in proteins and nucleic acids remain weakly understood despite their importance in folding processes; misfolding diseases (Parkinson's and Alzheimer's); natively unfolded proteins (as many as 30% of eukaryotic proteins, according to Fink); and the study of ribozymes. Research has been hindered by the inability to quantify the residual (native) structure present in an unfolded protein or nucleic acid. Here, a scaling model is proposed to quantify the molar degree of folding and the unfolded state. The model takes a global view of protein structure and can be applied to a number of analytic methods and to simulations. Three examples are given of application to small-angle scattering from pressure-induced unfolding of SNase, from acid-unfolded cytochrome c, and from folding of Azoarcus ribozyme. These examples quantitatively show three characteristic unfolded states for proteins, the statistical nature of a protein folding pathway, and the relationship between extent of folding and chain size during folding for charge-driven folding in RNA.     

Consistent picture of the reversible thermal unfolding of hen egg-white lysozyme from experiment and molecular dynamics

Synchrotron radiation circular dichroism, Fourier transform infrared, and nuclear magnetic resonance spectroscopies, and small-angle x-ray scattering were used to monitor the reversible thermal unfolding of hen egg white lysozyme. The results were compared with crystal structures and high- and low-temperature structures derived from molecular-dynamics calculations. The results of both experimental and computational methods indicate that the unfolding process starts with the loss of β-structures followed by the reversible loss of helix content from ∼40% at 20°C to 27% at 70°C and ∼20% at 77°C, beyond which unfolding becomes irreversible. Concomitantly there is a reversible increase in the radius of gyration of the protein from 15 Å to 18 Å. The reversible decrease in forward x-ray scattering demonstrates a lack of aggregation upon unfolding, suggesting the change is due to a larger dilation of hydration water than of bulk water. Molecular-dynamics simulations suggest a similar sequence of events and are in good agreement with the ¹H^N chemical shift differences in nuclear magnetic resonance. This study demonstrates the power of complementary methods for elucidating unfolding/refolding processes and the nature of both the unfolded structure, for which there is no crystallographic data, and the partially unfolded forms of the protein that can lead to fibril formation and disease.     

Urea-induced conformational changes in cold- and heat-denatured states of a protein, Streptomyces subtilisin inhibitor.

Streptomyces subtilisin inhibitor (SSI) is known to exist in at least two distinct denatured states, cold-denatured (D') and heat-denatured (D) under acidic conditions. In the present work, we investigated the manner how increasing urea concentration from 0 to 8 M changes the polypeptide chain conformation of SSI that exists initially in the D' and D states as well as in the native state (N), in terms of the secondary structure, the tertiary structure, and the chain form, based on the results of the experiments using circular dichroism (CD), small-angle X-ray scattering (SAXS) and 1H-NMR spectroscopy. Our results indicate that the urea-induced conformational transitions of SSI under typical conditions of D' (pH 1.8, 3 degrees C) occur at least in two steps. In the urea concentration range of 0-2 M (step 1), a cooperative destruction of the tertiary structure occurs, resulting in a mildly denatured state (DU), which may still contain a little amount of secondary structures. In the concentration range of 2-4 M urea (step 2), the DU state gradually loses its residual secondary structure, and increases the radius of gyration nearly to a maximum value. At 4 M urea, the polypeptide chain is highly disordered with highly mobile side chains. Increasing the urea concentration up to 8 M probably results in the more highly denatured or alternatively the stiffer chain conformations. The conformational transition starting from the N state proceeds essentially the same way as in the above scheme in which D' is replaced with N. The conformational transition starting from the D state lacks step 1 because the D state contains no tertiary structures and is similar to the DU state. The fact that similar conformations are reached at urea concentrations above 2 M from different conformations of D', D, and N indicates that the effect of urea dominates in determining the polypeptide conformation of SSI in the denatured states rather than the pH and temperature.     

Coulomb forces control the density of the collapsed unfolded state of barstar

Although it has been recently shown that unfolded polypeptide chains undergo a collapse on transfer from denaturing to native conditions, the forces determining the dynamics and the size of the collapsed form have not yet been understood. Here, we use single-molecule fluorescence resonance energy transfer experiments on the small protein barstar to characterize the unfolded chain in guanidinium chloride (GdmCl) and urea. The unfolded protein collapses on decreasing the concentration of denaturants. Below the critical concentration of 3.5 M denaturant, the collapse in GdmCl leads to a more dense state than in urea. Since it is known that GdmCl suppresses electrostatic interactions, we infer that Coulomb forces are the dominant forces acting in the unfolded barstar under native conditions. This hypothesis is clearly buttressed by the finding of a compaction of the unfolded barstar by addition of KCl at low urea concentrations.     

Effects of urea and guanidine · HCl on the folding and unfolding of pancreatic trypsin inhibitor

Concentrated solutions of urea and of guanidine · HCl produced a random spectrum of single-disulphide forms of the polypeptide chain of the pancreatic trypsin inhibitor. Guanidine · HCl also unfolded completely, with accompanying interchange of disulphide bonds, the two-disulphide form of this protein in the native-like conformation; urea produced an equilibrium mixture in which one-quarter of the molecules had the native-like conformation and disulphide bonds. The unfolded forms of the protein in the denaturants were very flexible polypeptide chains. The observations suggest that urea and guanidine · HCl are denaturants because they produce essentially equally favourable solvation of all portions of a polypeptide.The energetics of the conformational transitions involved in folding and unfolding of the inhibitor were determined in urea and compared with those observed in its absence. The denaturant lowers the stability of the native, folded inhibitor relative to that of the reduced, unfolded state by 6.5 kilocalories per mole; the greatest part of this apparent free-energy difference was expressed at the two-disulphide stage of folding. The results are consistent with other indications that most of the favourable interactions stabilizing the native conformation of this protein are not encountered until the final stage of folding, when all may occur simultaneously.The unfolded one- and two-disulphide species produced in guanidine · HCl were trapped, and their rearrangement to the normal intermediates followed after removal of the denaturant. The random single-disulphide species, with one exception, reverted very rapidly to the non-random spectrum of intermediates normally observed during folding; this confirms that these species are normally rapidly interconverted and that normal refolding of the reduced protein is not dependent kinetically upon residual stable conformation in the reduced protein. The unfolded two-disulphide species refolded to the native-like conformation more slowly, but appeared to pass through the same intermediates normally observed during refolding from the fully reduced state.     

Validating Solution Ensembles from Molecular Dynamics Simulation by Wide-Angle X-ray Scattering Data

Wide-angle x-ray scattering (WAXS) experiments of biomolecules in solution have become increasingly popular because of technical advances in light sources and detectors. However, the structural interpretation of WAXS profiles is problematic, partly because accurate calculations of WAXS profiles from structural models have remained challenging. In this work, we present the calculation of WAXS profiles from explicit-solvent molecular dynamics (MD) simulations of five different proteins. Using only a single fitting parameter that accounts for experimental uncertainties because of the buffer subtraction and dark currents, we find excellent agreement to experimental profiles both at small and wide angles. Because explicit solvation eliminates free parameters associated with the solvation layer or the excluded solvent, which would require fitting to experimental data, we minimize the risk of overfitting. We further find that the influence from water models and protein force fields on calculated profiles are insignificant up to q ≈ 15 nm^?1. Using a series of simulations that allow increasing flexibility of the proteins, we show that incorporating thermal fluctuations into the calculations significantly improves agreement with experimental data, demonstrating the importance of protein dynamics in the interpretation of WAXS profiles. In addition, free MD simulations up to one microsecond suggest that the calculated profiles are highly sensitive with respect to minor conformational rearrangements of proteins, such as an increased flexibility of a loop or an increase of the radius of gyration by  <  1%. The present study suggests that quantitative comparison between MD simulations and experimental WAXS profiles emerges as an accurate tool to validate solution ensembles of biomolecules.     

Self Crowding of Globular Proteins Studied by Small-Angle X-Ray Scattering

Small-angle x-ray scattering (SAXS) was used to study the behavior of equine metmyoglobin (Mb) and bovine pancreatic trypsin inhibitor (BPTI) at concentrations up to 0.4 and 0.15 g/mL, respectively, in solutions also containing 50% D₂O and 1 M urea. For both proteins, significant effects because of interference between x-rays scattered by different molecules (interparticle interference) were observed, indicating nonideal behavior at high concentrations. The experimental data were analyzed by comparison of the observed scattering profiles with those predicted by crystal structures of the proteins and a hard-sphere fluid model used to represent steric exclusion effects. The Mb scattering data were well fit by the hard-sphere model using a sphere radius of 18 Å, only slightly smaller than that estimated from the three-dimensional structure (20 Å). In contrast, the scattering profiles for BPTI in phosphate buffer displayed substantially less pronounced interparticle interference than predicted by the hard-sphere model and the radius estimated from the known structure of the protein (15 Å). Replacing the phosphate buffer with 3-(N-morpolino)propane sulfonic acid (MOPS) led to increased interparticle interference, consistent with a larger effective radius and suggesting that phosphate ions may mediate attractive intermolecular interactions, as observed in some BPTI crystal structures, without the formation of stable oligomers. The scattering data were also used to estimate second virial coefficients for the two proteins: 2.0 ×10^-4 cm³mol/g² for Mb in phosphate buffer, 1.6 ×10^-4 cm³mol/g² for BPTI in phosphate buffer and 9.2 ×10^-4 cm³mol/g² for BPTI in MOPS. The results indicate that the behavior of Mb, which is nearly isoelectric under the conditions used, is well described by the hard-sphere model, but that of BPTI is considerably more complex and is likely influenced by both repulsive and attractive electrostatic interactions. The hard-sphere model may be a generally useful tool for the analysis of small-angle scattering data from concentrated macromolecular solutions.     

Minimal Effects of Macromolecular Crowding on an Intrinsically Disordered Protein: A Small-Angle Neutron Scattering Study

Small-angle neutron scattering was used to study the effects of macromolecular crowding by two globular proteins, i.e., bovine pancreatic trypsin inhibitor and equine metmyoglobin, on the conformational ensemble of an intrinsically disordered protein, the N protein of bacteriophage λ. The λ N protein was uniformly labeled with ²H, and the concentrations of D₂O in the samples were adjusted to match the neutron scattering contrast of the unlabeled crowding proteins, thereby masking their contribution to the scattering profiles. Scattering from the deuterated λ N was recorded for samples containing up to 0.12 g/mL bovine pancreatic trypsin inhibitor or 0.2 g/mL metmyoglobin. The radius of gyration of the uncrowded protein was estimated to be 30 Å and was found to be remarkably insensitive to the presence of crowders, varying by <2 Å for the highest crowder concentrations. The scattering profiles were also used to estimate the fractal dimension of λ N, which was found to be ∼1.8 in the absence or presence of crowders, indicative of a well-solvated and expanded random coil under all of the conditions examined. These results are contrary to the predictions of theoretical treatments and previous experimental studies demonstrating compaction of unfolded proteins by crowding with polymers such as dextran and Ficoll. A computational simulation suggests that some previous treatments may have overestimated the effective volumes of disordered proteins and the variation of these volumes within an ensemble. The apparent insensitivity of λ N to crowding may also be due in part to weak attractive interactions with the crowding proteins, which may compensate for the effects of steric exclusion.     

Dissection of the ATP-Dependent Conformational Change Cycle of a Group II Chaperonin

Group II chaperonin captures an unfolded protein while in its open conformation and then mediates the folding of the protein during ATP-driven conformational change cycle. In this study, we performed kinetic analyses of the group II chaperonin from a hyperthermophilic archaeon, Thermococcus sp. KS-1 (TKS1-Cpn), by stopped-flow fluorometry and stopped-flow small-angle X-ray scattering to reveal the reaction cycle. Two TKS1-Cpn variants containing a Trp residue at position 265 or position 56 exhibit nearly the same fluorescence kinetics induced by rapid mixing with ATP. Fluorescence started to increase immediately after the start of mixing and reached a maximum at 1–2 s after mixing. Only in the presence of K⁺ that a gradual decrease in fluorescence was observed after the initial peak. Similar results were obtained by stopped-flow small-angle X-ray scattering. A rapid fluorescence increase, which reflects nucleotide binding, was observed for the mutant containing a Trp residue near the ATP binding site (K485W), irrespective of the presence or absence of K⁺. Without K⁺, a small, rapid fluorescence decrease followed the initial increase, and then a gradual decrease was observed. In contrast, with K⁺, a large, rapid fluorescence decrease occurred just after the initial increase, and then the fluorescence gradually increased. Finally, we observed ATP binding signal and also subtle conformational change in an ATPase-deficient mutant with K485W mutation. Based on these results, we propose a reaction cycle model for group II chaperonins.     

Fibril growth kinetics reveal a region of beta2-microglobulin important for nucleation and elongation of aggregation

Amyloid is a highly ordered form of aggregate comprising long, straight and unbranched proteinaceous fibrils that are formed with characteristic nucleation-dependent kinetics in vitro. Currently, the structural molecular mechanism of fibril nucleation and elongation is poorly understood. Here, we investigate the role of the sequence and structure of the initial monomeric precursor in determining the rates of nucleation and elongation of human β₂-microglobulin (β₂m). We describe the kinetics of seeded and spontaneous (unseeded) fibril growth of wild-type β₂m and 12 variants at pH 2.5, targeting specifically an aromatic-rich region of the polypeptide chain (residues 62-70) that has been predicted to be highly amyloidogenic. The results reveal the importance of aromatic residues in this part of the β₂m sequence in fibril formation under the conditions explored and show that this region of the polypeptide chain is involved in both the nucleation and the elongation phases of fibril formation. Structural analysis of the conformational properties of the unfolded monomer for each variant using NMR relaxation methods revealed that all variants contain significant non-random structure involving two hydrophobic clusters comprising regions 29-51 and 58-79, the extent of which is critically dependent on the sequence. No direct correlation was observed, however, between the extent of non-random structure in the unfolded state and the rates of fibril nucleation and elongation, suggesting that the early stages of aggregation involve significant conformational changes from the initial unfolded state. Together, the data suggest a model for β₂m amyloid formation in which structurally specific interactions involving the highly hydrophobic and aromatic-rich region comprising residues 62-70 provide a complementary interface that is key to the generation of amyloid fibrils for this protein at acidic pH.     

Structural characteristics of thermostable immunogenic outer membrane protein from Salmonella enterica serovar Typhi

In this work, we explored the acid-induced unfolding pathway of non-porin outer membrane protein (OMP), an immunogenic protein from Salmonella Typhi, by monitoring the conformational changes over a pH range of 1.0–7.0 by circular dichroism, intrinsic fluorescence, ANS binding, acrylamide quenching, and dynamic light scattering. The spectroscopic measurements showed that OMP in its native state at pH 7.0 exists in more stable and compact conformation. In contrast, at pH 2.0, OMP retains substantial amount of secondary structure, disrupted side chain interactions, increased hydrodynamic radii, and nearly four-fold increase in ANS fluorescence with respect to the native state, indicating that MG state exists at pH 2.0. Quenching of tryptophan fluorescence by acrylamide further confirmed the accumulation of a partially unfolded state between native and unfolded state. The effect of pH on the conformation and thermostability of OMP points towards its heat resistance at neutral pH (T _m?~?69 °C at pH 7.0, monitored by change in MRE_{222 nm}). Acid unfolded state was also characterized by the lack of a cooperative thermal transition. All these results suggested that acid-induced unfolded state of OMP at pH 2.0 represented the molten globule state. The chemical denaturation studies with GuHCl and urea as denaturants showed dissimilar results. The chemical unfolding experiments showed that in both far-UV CD and fluorescence measurements, GuHCl is more efficient than urea. GuHCl is characterized by low C _m (~1 M), while urea is characterized by high C _m (~3 M). The fully unfolded states were reached at 2 M GuHCl and 4 M urea concentration, respectively. This study adds to several key considerations of importance in the development of therapeutic agents against typhoid fever for clinical purposes.     

Self Crowding of Globular Proteins Studied by Small-Angle X-Ray Scattering

Small-angle x-ray scattering (SAXS) was used to study the behavior of equine metmyoglobin (Mb) and bovine pancreatic trypsin inhibitor (BPTI) at concentrations up to 0.4 and 0.15 g/mL, respectively, in solutions also containing 50% D₂O and 1 M urea. For both proteins, significant effects because of interference between x-rays scattered by different molecules (interparticle interference) were observed, indicating nonideal behavior at high concentrations. The experimental data were analyzed by comparison of the observed scattering profiles with those predicted by crystal structures of the proteins and a hard-sphere fluid model used to represent steric exclusion effects. The Mb scattering data were well fit by the hard-sphere model using a sphere radius of 18 Å, only slightly smaller than that estimated from the three-dimensional structure (20 Å). In contrast, the scattering profiles for BPTI in phosphate buffer displayed substantially less pronounced interparticle interference than predicted by the hard-sphere model and the radius estimated from the known structure of the protein (15 Å). Replacing the phosphate buffer with 3-(N-morpolino)propane sulfonic acid (MOPS) led to increased interparticle interference, consistent with a larger effective radius and suggesting that phosphate ions may mediate attractive intermolecular interactions, as observed in some BPTI crystal structures, without the formation of stable oligomers. The scattering data were also used to estimate second virial coefficients for the two proteins: 2.0 ×10^-4 cm³mol/g² for Mb in phosphate buffer, 1.6 ×10^-4 cm³mol/g² for BPTI in phosphate buffer and 9.2 ×10^-4 cm³mol/g² for BPTI in MOPS. The results indicate that the behavior of Mb, which is nearly isoelectric under the conditions used, is well described by the hard-sphere model, but that of BPTI is considerably more complex and is likely influenced by both repulsive and attractive electrostatic interactions. The hard-sphere model may be a generally useful tool for the analysis of small-angle scattering data from concentrated macromolecular solutions.     

Minimal Effects of Macromolecular Crowding on an Intrinsically Disordered Protein: A Small-Angle Neutron Scattering Study

Small-angle neutron scattering was used to study the effects of macromolecular crowding by two globular proteins, i.e., bovine pancreatic trypsin inhibitor and equine metmyoglobin, on the conformational ensemble of an intrinsically disordered protein, the N protein of bacteriophage λ. The λ N protein was uniformly labeled with ²H, and the concentrations of D₂O in the samples were adjusted to match the neutron scattering contrast of the unlabeled crowding proteins, thereby masking their contribution to the scattering profiles. Scattering from the deuterated λ N was recorded for samples containing up to 0.12 g/mL bovine pancreatic trypsin inhibitor or 0.2 g/mL metmyoglobin. The radius of gyration of the uncrowded protein was estimated to be 30 Å and was found to be remarkably insensitive to the presence of crowders, varying by <2 Å for the highest crowder concentrations. The scattering profiles were also used to estimate the fractal dimension of λ N, which was found to be ∼1.8 in the absence or presence of crowders, indicative of a well-solvated and expanded random coil under all of the conditions examined. These results are contrary to the predictions of theoretical treatments and previous experimental studies demonstrating compaction of unfolded proteins by crowding with polymers such as dextran and Ficoll. A computational simulation suggests that some previous treatments may have overestimated the effective volumes of disordered proteins and the variation of these volumes within an ensemble. The apparent insensitivity of λ N to crowding may also be due in part to weak attractive interactions with the crowding proteins, which may compensate for the effects of steric exclusion.