Denesyuk, N. A. ; Thirumalai, D. Crowding promotes the switch from hairpin to pseudoknot conformation in human telomerase RNA. J Am Chem Soc 133, 11858-61.Abstract
Formation of a pseudoknot (PK) in the conserved RNA core domain in the ribonucleoprotein human telomerase is required for function. In vitro experiments show that the PK is in equilibrium with an extended hairpin (HP) structure. We use molecular simulations of a coarse-grained model, which reproduces most of the salient features of the experimental melting profiles of PK and HP, to show that crowding enhances the stability of PK relative to HP in the wild type and in a mutant associated with dyskeratosis congenita. In monodisperse suspensions, small crowding particles increase the stability of compact structures to a greater extent than larger crowders. If the sizes of crowders in a binary mixture are smaller than that of the unfolded RNA, the increase in melting temperature due to the two components is additive. In a ternary mixture of crowders that are larger than the unfolded RNA, which mimics the composition of ribosome, large enzyme complexes and proteins in Escherichia coli , the marginal increase in stability is entirely determined by the smallest component. We predict that crowding can partially restore telomerase activity in mutants with decreased PK stability.
Cho, S. S. ; Reddy, G. ; Straub, J. E. ; Thirumalai, D. Entropic stabilization of proteins by TMAO. J Phys Chem B 115, 13401-7.Abstract
The osmolyte trimethylamine N-oxide (TMAO) accumulates in the cell in response to osmotic stress and increases the thermodynamic stability of folded proteins. To understand the mechanism of TMAO induced stabilization of folded protein states, we systematically investigated the action of TMAO on several model dipeptides (leucine, L(2), serine, S(2), glutamine, Q(2), lysine, K(2), and glycine, G(2)) in order to elucidate the effect of residue-specific TMAO interactions on small fragments of solvent-exposed conformations of the denatured states of proteins. We find that TMAO preferentially hydrogen bonds with the exposed dipeptide backbone but generally not with nonpolar or polar side chains. However, interactions with the positively charged Lys are substantially greater than with the backbone. The dipeptide G(2) is a useful model of the pure amide backbone; interacts with TMAO by forming a hydrogen bond between the amide nitrogen and the oxygen in TMAO. In contrast, TMAO is depleted from the protein backbone in the hexapeptide G(6), which shows that the length of the polypeptide chain is relevant in aqueous TMAO solutions. These simulations lead to the hypothesis that TMAO-induced stabilization of proteins and peptides is a consequence of depletion of the solute from the protein surface provided intramolecular interactions are more favorable than those between TMAO and the backbone. To test our hypothesis, we performed additional simulations of the action of TMAO on an intrinsically disordered Aβ(16-22) (KLVFFAE) monomer. In the absence of TMAO, Aβ(16-22) is a disordered random coil. However, in aqueous TMAO solution, Aβ(16-22) monomer samples compact conformations. A transition from random coil to α-helical secondary structure is observed at high TMAO concentrations. The coil to α-helix transition is highly cooperative especially considering the small number of residues in Aβ(16-22). Our work highlights the potential similarities between the action of TMAO on long polypeptide chains and entropic stabilization of proteins in a crowded environment due to excluded volume interactions. In this sense, the chemical chaperone TMAO is a nanocrowding particle.
O'Brien, E. P. ; Straub, J. E. ; Brooks, B. R. ; Thirumalai, D. Influence of Nanoparticle Size and Shape on Oligomer Formation of an Amyloidogenic Peptide. J Phys Chem Lett 2 1171-1177.Abstract
Understanding the influence of macromolecular crowding and nanoparticles on the formation of in-register β-sheets, the primary structural component of amyloid fibrils, is a first step towards describing in vivo protein aggregation and interactions between synthetic materials and proteins. Using all atom molecular simulations in implicit solvent we illustrate the effects of nanoparticle size, shape, and volume fraction on oligomer formation of an amyloidogenic peptide from the transthyretin protein. Surprisingly, we find that inert spherical crowding particles destabilize in-register β-sheets formed by dimers while stabilizing β-sheets comprised of trimers and tetramers. As the radius of the nanoparticle increases crowding effects decrease, implying smaller crowding particles have the largest influence on the earliest amyloid species. We explain these results using a theory based on the depletion effect. Finally, we show that spherocylindrical crowders destabilize the ordered β-sheet dimer to a greater extent than spherical crowders, which underscores the influence of nanoparticle shape on protein aggregation.
Xia, F. ; Thirumalai, D. ; Gräter, F. Minimum energy compact structures in force-quench polyubiquitin folding are domain swapped. Proc Natl Acad Sci U S A 108, 6963-8.Abstract
Single molecule experiments that initiate folding using mechanical force are uniquely suited to reveal the nature of populated states in the folding process. Using a strategy proposed on theoretical grounds, which calls for repeated cycling of force from high to low values using force pulses, it was demonstrated in atomic force spectroscopy (AFM) experiments that an ensemble of minimum energy compact structures (MECS) are sampled during the folding of polyubiquitin. The structures in the ensemble are mechanically resistant to a lesser extent than the native state. Remarkably, forced unfolding of the populated intermediates reveals a broad distribution of extensions including steps up to 30 nm and beyond. We show using molecular simulations that favorable interdomain interactions leading to domain swapping between adjacent ubiquitin modules results in the formation of the ensemble of MECS, whose unfolding leads to an unusually broad distribution of steps. We obtained the domain-swapped structures using coarse-grained ubiquitin dimer models by exchanging native interactions between two monomeric ubiquitin molecules. Brownian dynamics force unfolding of the proposed domain-swapped structures, with mechanical stability that is approximately 100-fold lower than the native state, gives rise to a distribution of extensions from 2 to 30 nm. Our results, which are in quantitative agreement with AFM experiments, suggest that domain swapping may be a general mechanism in the assembly of multi-sub-unit proteins.
Straub, J. E. ; Thirumalai, D. Toward a molecular theory of early and late events in monomer to amyloid fibril formation. Annu Rev Phys Chem 62, 437-63.Abstract
Quantitative understanding of the kinetics of fibril formation and the molecular mechanism of transition from monomers to fibrils is needed to obtain insights into the growth of amyloid fibrils and more generally self-assembly multisubunit protein complexes. Significant advances using computations of protein aggregation in a number of systems have established generic and sequence-specific aspects of the early steps in oligomer formation. Theoretical considerations, which view oligomer and fibril growth as diffusion in a complex energy landscape, and computational studies, involving minimal lattice and coarse-grained models, have revealed general principles governing the transition from monomeric protein to ordered fibrillar aggregates. Detailed atomistic calculations have explored the early stages of the protein aggregation pathway for a number of amyloidogenic proteins, most notably amyloid β- (Aβ-) protein and fragments from proteins linked to various diseases. These computational studies have provided insights into the role of sequence, role of water, and specific interatomic interactions underlying the thermodynamics and dynamics of elementary kinetic steps in the aggregation pathway. Novel methods are beginning to illustrate the structural basis for the production of Aβ-peptides through interactions with secretases in the presence of membranes. We show that a variety of theoretical approaches, ranging from scaling arguments to minimal models to atomistic simulations, are needed as a complement to experimental studies probing the principles governing protein aggregation.
Biyun, S. ; Cho, S. S. ; Thirumalai, D. Folding of human telomerase RNA pseudoknot using ion-jump and temperature-quench simulations. J Am Chem Soc 133, 20634-43.Abstract
Globally RNA folding occurs in multiple stages involving chain compaction and subsequent rearrangement by a number of parallel routes to the folded state. However, the sequence-dependent details of the folding pathways and the link between collapse and folding are poorly understood. To obtain a comprehensive picture of the thermodynamics and folding kinetics we used molecular simulations of coarse-grained model of a pseudoknot found in the conserved core domain of the human telomerase (hTR) by varying both temperature (T) and ion concentration (C). The phase diagram in the [T,C] plane shows that the boundary separating the folded and unfolded state for the finite 47-nucleotide system is relatively sharp, implying that from a thermodynamic perspective hTR behaves as an apparent two-state system. However, the folding kinetics following single C-jump or T-quench is complicated, involving multiple channels to the native state. Although globally folding kinetics triggered by T-quench and C-jump are similar, the kinetics of chain compaction are vastly different, which reflects the role of initial conditions in directing folding and collapse. Remarkably, even after substantial reduction in the overall size of hTR, the ensemble of compact conformations are far from being nativelike, suggesting that the search for the folded state occurs among the ensemble of low-energy fluidlike globules. The rate of unfolding, which occurs in a single step, is faster upon C-decrease compared to a jump in temperature. To identify "hidden" states that are visited during the folding process we performed simulations by periodically interrupting the approach to the folded state by lowering C. These simulations show that hTR reaches the folded state through a small number of connected clusters that are repeatedly visited during the pulse sequence in which the folding or unfolding is interrupted. The results from interrupted folding simulations, which are in accord with non-equilibrium single-molecule folding of a large ribozyme, show that multiple probes are needed to reveal the invisible states that are sampled by RNA as it folds. Although we have illustrated the complexity of RNA folding using hTR as a case study, general arguments and qualitative comparisons to time-resolved scattering experiments on Azoarcus group I ribozyme and single-molecule non-equilibrium periodic ion-jump experiments establish the generality of our findings.
Thirumalai, D. ; Reddy, G. Protein thermodynamics: Are native proteins metastable?. Nat Chem 3 910-1. protein-thermodynamics-are-native-proteins-metastable.pdf
Chen, W. - T. ; Thirumalai, D. ; Shih, T. T. - F. ; Chen, R. - C. ; Tu, S. - Y. ; Lin, C. - I. ; Yang, P. - C. Dynamic contrast-enhanced folate-receptor-targeted MR imaging using a Gd-loaded PEG-dendrimer-folate conjugate in a mouse xenograft tumor model. Mol Imaging Biol 12, 145-54.Abstract
PURPOSE: The purpose of this study is to validate a folate-receptor (FR)-targeted dendrimer, PEG-G3-(Gd-DTPA)11-(folate)5, for its ability to detect FR-positive tumors, by using dynamic contrast-enhanced MRI. PROCEDURES: KB cells, FR siRNA knockdown KB cells, and FR negative HT-1080 cells, were incubated with fluorescein-labeled dendrimer and their cellular uptake was observed. Dynamic contrast-enhanced MRI was performed on mice-bearing KB and HT-1080 tumors and the enhancement patterns and parameters were analyzed. RESULTS: Green fluorescence was found in the KB cells in the cellular uptake experiment, but was not seen in other settings. In the dynamic contrast-enhanced MRI, the 30-min washout percentage was -4 +/- 18% in the KB tumors and 39 +/- 23% in the HT-1080 tumors. A 17% cut-off point gave a sensitivity of 94.4% and a specificity of 93.8%. CONCLUSIONS: We have demonstrated the targeting ability of PEG-G3-(Gd-DTPA)11-(folate)5 in vitro and in vivo. A 17% cut-off point for a 30-min washout percentage can be a useful parameter for the diagnosis of FR-positive tumors.
Reddy, G. ; Straub, J. E. ; Thirumalai, D. Dry amyloid fibril assembly in a yeast prion peptide is mediated by long-lived structures containing water wires. Proc Natl Acad Sci U S A 107, 21459-64.Abstract
Amyloid-like fibrils from a number of small peptides that are unrelated by sequence adopt a cross-β-spine in which the two sheets fully interdigitate to create a dry interface. Formation of such a dry interface is usually associated with self-assembly of extended hydrophobic surfaces. Here we investigate how a dry interface is created in the process of protofilament formation in vastly different sequences using two amyloidogenic peptides, one a polar sequence from the N terminus of the yeast prion Sup35 and the other a predominantly hydrophobic sequence from the C terminus of Aβ-peptide. Using molecular dynamics simulations with three force fields we show that spontaneous formation of two ordered one-dimensional water wires in the pore between the two sheets of the Sup35 protofilaments results in long-lived structures, which are stabilized by a network of hydrogen bonds between the water molecules in the wires and the polar side chains in the β-sheet. Upon decreasing the stability of the metastable structures, water molecules are expelled resulting in a helically twisted protofilament in which side chains from a pair of β-strands in each sheet pack perfectly resulting in a dry interface. Although drying in hydrophobically dominated interfaces is abrupt, resembling a liquid to vapor transition, we find that discrete transitions between the liquid to one-dimensional ordered water in the nanopore enclosed by the two β-sheets to dry interface formation characterizes protofilament assembly in the yeast prions. Indeed, as the two sheets of the hydrophobic Aβ-sequence approach each other, fibril formation and expulsion of water molecules occur rapidly and nearly simultaneously.
Thirumalai, D. ; Zhang, Z. Myosin VI: how do charged tails exert control?. Structure 18, 1393-4.Abstract
Molecular dynamics simulations and single molecule experiments are used to suggest that charged helices in the medial tail domain participate in myosin VI dimerization (Kim et al., 2010), which reinforces the mechanism that unfolding of the three helix bundle in the proximal tail serves as a lever arm extension.
Straub, J. E. ; Thirumalai, D. Principles governing oligomer formation in amyloidogenic peptides. Curr Opin Struct Biol 20, 187-95.Abstract
Identifying the principles that describe the formation of protein oligomers and fibrils with distinct morphologies is a daunting problem. Here we summarize general principles of oligomer formation gleaned from molecular dynamics simulations of Abeta-peptides. The spectra of high free energy structures sampled by the monomer provide insights into the plausible fibril structures, providing a rationale for the 'strain phenomenon.' Heterogeneous growth dynamics of small oligomers of Abeta(16-22), whose lowest free energy structures are like nematic droplets, can be broadly described using a two-stage dock-lock mechanism. In the growth process, water is found to play various roles depending on the oligomer size, and peptide length, and sequence. Water may be an explicit element of fibril structure linked to various fibril morphologies.
Chen, J. ; Darst, S. A. ; Thirumalai, D. Promoter melting triggered by bacterial RNA polymerase occurs in three steps. Proc Natl Acad Sci U S A 107, 12523-8.Abstract
RNA synthesis, carried out by DNA-dependent RNA polymerase (RNAP) in a process called transcription, involves several stages. In bacteria, transcription initiation starts with promoter recognition and binding of RNAP holoenzyme, resulting in the formation of the closed (R.P(c)) RNAP-promoter DNA complex. Subsequently, a transition to the open R.P(o) complex occurs, characterized by separation of the promoter DNA strands in an approximately 12 base-pair region to form the transcription bubble. Using coarse-grained self-organized polymer models of Thermus aquatics RNAP holoenzyme and promoter DNA complexes, we performed Brownian dynamics simulations of the R.P(c) --> R.P(o) transition. In the fast trajectories, unwinding of the promoter DNA begins by local melting around the -10 element, which is followed by sequential unzipping of DNA till the +2 site. The R.P(c) --> R.P(o) transition occurs in three steps. In step I, dsDNA melts and the nontemplate strand makes stable interactions with RNAP. In step II, DNA scrunches into RNA polymerase and the downstream base pairs sequentially open to form the transcription bubble, which results in strain build up. Subsequently, downstream dsDNA bending relieves the strain as R.P(o) forms. Entry of the dsDNA into the active-site channel of RNAP requires widening of the channel, which occurs by a swing mechanism involving transient movements of a subdomain of the beta subunit caused by steric repulsion with the DNA template strand. If premature local melting away from the -10 element occurs first then the transcription bubble formation is slow involving reformation of the opened base pairs and subsequent sequential unzipping as in the fast trajectories.
Tehver, R. ; Thirumalai, D. Rigor to post-rigor transition in myosin V: link between the dynamics and the supporting architecture. Structure 18, 471-81.Abstract
The detachment kinetics from actin upon ATP binding is a key step in the reaction cycle of myosin V. We show that a network of residues, constituting the allostery wiring diagram (AWD), that trigger the rigor (R) to post-rigor (PR) transition, span key structural elements from the ATP and actin-binding regions. Several of the residues are in the 33 residue helix (H18), P loop, and switch I. Brownian dynamics simulations show that a hierarchy of kinetically controlled local structural changes leads to the opening of the "cleft" region, resulting in the detachment of the motor domain from actin. Movements in switch I and P loop facilitate changes in the rest of the motor domain, in particular the rotation of H18, whose stiffness within the motor domain is crucial in the R --> PR transition. The finding that residues in the AWD also drive the kinetics of the R --> PR transition shows how the myosin architecture regulates the allosteric movements during the reaction cycle.
Thirumalai, D. ; O'Brien, E. P. ; Morrison, G. ; Hyeon, C. Theoretical perspectives on protein folding. Annu Rev Biophys 39, 159-83.Abstract
Understanding how monomeric proteins fold under in vitro conditions is crucial to describing their functions in the cellular context. Significant advances in theory and experiments have resulted in a conceptual framework for describing the folding mechanisms of globular proteins. The sizes of proteins in the denatured and folded states, cooperativity of the folding transition, dispersions in the melting temperatures at the residue level, and timescales of folding are, to a large extent, determined by N, the number of residues. The intricate details of folding as a function of denaturant concentration can be predicted by using a novel coarse-grained molecular transfer model. By watching one molecule fold at a time, using single-molecule methods, investigators have established the validity of the theoretically anticipated heterogeneity in the folding routes and the N-dependent timescales for the three stages in the approach to the native state. Despite the successes of theory, of which only a few examples are documented here, we conclude that much remains to be done to solve the protein folding problem in the broadest sense.
Li, M. S. ; Co, N. T. ; Reddy, G. ; Hu, C. - K. ; Straub, J. E. ; Thirumalai, D. Factors governing fibrillogenesis of polypeptide chains revealed by lattice models. Phys Rev Lett 105, 218101.Abstract
Using lattice models we explore the factors that determine the tendencies of polypeptide chains to aggregate by exhaustively sampling the sequence and conformational space. The morphologies of the fibril-like structures and the time scales (τ(fib)) for their formation depend on a balance between hydrophobic and Coulomb interactions. The extent of population of an ensemble of N* structures, which are fibril-prone structures in the spectrum of conformations of an isolated protein, is the major determinant of τ(fib). This observation is used to determine the aggregating sequences by exhaustively exploring the sequence space, thus providing a basis for genome wide search of fragments that are aggregation prone.
Pincus, D. L. ; Thirumalai, D. Crowding effects on the mechanical stability and unfolding pathways of ubiquitin. J Phys Chem B 113, 359-68.Abstract
The interiors of cells are crowded, thus making it important to assess the effects of macromolecules on the folding of proteins. Using the self-organized polymer (SOP) model, which is a coarse-grained representation of polypeptide chains, we probe the mechanical stability of ubiquitin (Ub) monomers and trimers ((Ub)(3)) in the presence of monodisperse spherical crowding agents. Crowding increases the volume fraction (Phi(c))-dependent average force (f(u)(Phi(c))), relative to the value at Phi(c) = 0, needed to unfold Ub and the polyprotein. For a given Phi(c), the values of f(u)(Phi(c)) increase as the diameter (sigma(c)) of the crowding particles decreases. The average unfolding force f(u)(Phi(c)) depends on the ratio D/R(g), where D approximately sigma(c)(pi/6Phi(c))(1/3), with R(g) being the radius of gyration of Ub (or (Ub)(3)) in the unfolded state. Examination of the unfolding pathways shows that, relative to Phi(c) = 0, crowding promotes reassociation of ruptured secondary structural elements. Both the nature of the unfolding pathways and f(u)(Phi(c)) for (Ub)(3) are altered in the presence of crowding particles, with the effect being most dramatic for the subunit that unfolds last. We predict, based on SOP simulations and theoretical arguments, that f(u)(Phi(c)) approximately Phi(c)(1/3nu), where nu is the Flory exponent that describes the unfolded (random coil) state of the protein.
Tehver, R. ; Chen, J. ; Thirumalai, D. Allostery wiring diagrams in the transitions that drive the GroEL reaction cycle. J Mol Biol 387, 390-406.Abstract
Determining the network of residues that transmit allosteric signals is crucial to understanding the function of biological nanomachines. During the course of a reaction cycle, biological machines in general, and Escherichia coli chaperonin GroEL in particular, undergo large-scale conformational changes in response to ligand binding. Normal mode analyses, based on structure-based coarse-grained models where each residue is represented by an alpha carbon atom, have been widely used to describe the motions encoded in the structures of proteins. Here, we propose a new Calpha-side chain elastic network model of proteins that includes information about the physical identity of each residue and accurately accounts for the side-chain topology and packing within the structure. Using the Calpha-side chain elastic network model and the structural perturbation method, which probes the response of a local perturbation at a given site at all other sites in the structure, we determine the network of key residues (allostery wiring diagram) responsible for the T-->R and R''-->T transitions in GroEL. A number of residues, both within a subunit and at the interface of two adjacent subunits, are found to be at the origin of the positive cooperativity in the ATP-driven T-->R transition. Of particular note are residues G244, R58, D83, E209, and K327. Of these, R38, D83, and K327 are highly conserved. G244 is located in the apical domain at the interface between two subunits; E209 and K327 are located in the apical domain, toward the center of a subunit; R58 and D83 are equatorial domain residues. The allostery wiring diagram shows that the network of residues are interspersed throughout the structure. Residues D83, V174, E191, and D359 play a critical role in the R''-->T transition, which implies that mutations of these residues would compromise the ATPase activity. D83 and E191 are also highly conserved; D359 is moderately conserved. The negative cooperativity between the rings in the R''-->T transition is orchestrated through several interface residues within a single ring, including N10, E434, D435, and E451. Signal from the trans ring that is transmitted across the interface between the equatorial domains is responsible for the R''-->T transition. The cochaperonin GroES plays a passive role in the R''-->T transition. Remarkably, the binding affinity of GroES for GroEL is allosterically linked to GroEL residues 350-365 that span helices K and L. The movements of helices K and L alter the polarity of the cavity throughout the GroEL functional cycle and undergo large-scale motions that are anticorrelated with the other apical domain residues. The allostery wiring diagrams for the T-->R and R''-->T transitions of GroEL provide a microscopic foundation for the cooperativity (anticooperativity) within (between) the ring (rings). Using statistical coupling analysis, we extract evolutionarily linked clusters of residues in GroEL and GroES. We find that several substrate protein binding residues as well as sites related to ATPase activity belong to a single functional network in GroEL. For GroES, the mobile loop residues and GroES/GroES interface residues are linked.
Ziv, G. ; Thirumalai, D. ; Haran, G. Collapse transition in proteins. Phys Chem Chem Phys 11, 83-93.Abstract
The coil-globule transition, a tenet of the physics of polymers, has been identified in recent years as an important unresolved aspect of the initial stages of the folding of proteins. We describe the basics of the collapse transition, starting with homopolymers and continuing with proteins. Studies of denatured-state collapse under equilibrium are then presented. An emphasis is placed on single-molecule fluorescence experiments, which are particularly useful for measuring properties of the denatured state even under conditions of coexistence with the folded state. Attempts to understand the dynamics of collapse, both theoretically and experimentally, are then described. Only an upper limit for the rate of collapse has been obtained so far. Improvements in experimental and theoretical methodology are likely to continue to push our understanding of the importance of the denatured-state thermodynamics and dynamics for protein folding in the coming years.
Zheng, W. ; Thirumalai, D. Coupling between normal modes drives protein conformational dynamics: illustrations using allosteric transitions in myosin II. Biophys J 96, 2128-37.Abstract
Structure-based elastic network models (ENMs) have been remarkably successful in describing conformational transitions in a variety of biological systems. Low-frequency normal modes are usually calculated from the ENM that characterizes elastic interactions between residues in contact in a given protein structure with a uniform force constant. To explore the dynamical effects of nonuniform elastic interactions, we calculate the robustness and coupling of the low-frequency modes in the presence of nonuniform variations in the ENM force constant. The variations in the elastic interactions, approximated here by Gaussian noise, approximately account for perturbation effects of heterogeneous residue-residue interactions or evolutionary sequence changes within a protein family. First-order perturbation theory provides an efficient and qualitatively correct estimate of the mode robustness and mode coupling for finite perturbations to the ENM force constant. The mode coupling analysis and the mode robustness analysis identify groups of strongly coupled modes that encode for protein functional motions. We illustrate the new concepts using myosin II motor protein as an example. The biological implications of mode coupling in tuning the allosteric couplings among the actin-binding site, the nucleotide-binding site, and the force-generating converter and lever arm in myosin isoforms are discussed. We evaluate the robustness of the correlation functions that quantify the allosteric couplings among these three key structural motifs.
O'Brien, E. P. ; Morrison, G. ; Brooks, B. R. ; Thirumalai, D. How accurate are polymer models in the analysis of Förster resonance energy transfer experiments on proteins?. J Chem Phys 130, 124903.Abstract
Single molecule Förster resonance energy transfer (FRET) experiments are used to infer the properties of the denatured state ensemble (DSE) of proteins. From the measured average FRET efficiency, , the distance distribution P(R) is inferred by assuming that the DSE can be described as a polymer. The single parameter in the appropriate polymer model (Gaussian chain, wormlike chain, or self-avoiding walk) for P(R) is determined by equating the calculated and measured . In order to assess the accuracy of this "standard procedure," we consider the generalized Rouse model (GRM), whose properties [ and P(R)] can be analytically computed, and the Molecular Transfer Model for protein L for which accurate simulations can be carried out as a function of guanadinium hydrochloride (GdmCl) concentration. Using the precisely computed for the GRM and protein L, we infer P(R) using the standard procedure. We find that the mean end-to-end distance can be accurately inferred (less than 10% relative error) using and polymer models for P(R). However, the value extracted for the radius of gyration (R(g)) and the persistence length (l(p)) are less accurate. For protein L, the errors in the inferred properties increase as the GdmCl concentration increases for all polymer models. The relative error in the inferred R(g) and l(p), with respect to the exact values, can be as large as 25% at the highest GdmCl concentration. We propose a self-consistency test, requiring measurements of by attaching dyes to different residues in the protein, to assess the validity of describing DSE using the Gaussian model. Application of the self-consistency test to the GRM shows that even for this simple model, which exhibits an order-->disorder transition, the Gaussian P(R) is inadequate. Analysis of experimental data of FRET efficiencies with dyes at several locations for the cold shock protein, and simulations results for protein L, for which accurate FRET efficiencies between various locations were computed, shows that at high GdmCl concentrations there are significant deviations in the DSE P(R) from the Gaussian model.