Bovine Pancreatic Trypsin Research Articles

Simple expressions of the nuclear relaxation rate enhancement due to quadrupole nuclei in slowly tumbling molecules.

For slowly tumbling entities or quasi-rigid lattices, we derive very simple analytical expressions of the quadrupole relaxation enhancement (QRE) of the longitudinal relaxation rate R1 of nuclear spins I due to their intramolecular magnetic dipolar coupling with quadrupole nuclei of arbitrary spins S ≥ 1. These expressions are obtained by using the adiabatic approximation for evaluating the time evolution operator of the quantum states of the quadrupole nuclei S. They are valid when the gyromagnetic ratio of the spin S is much smaller than that of the spin I. The theory predicts quadrupole resonant peaks in the dispersion curve of R1 vs magnetic field. The number, positions, relative intensities, Lorentzian shapes, and widths of these peaks are explained in terms of the following properties: the magnitude of the quadrupole Hamiltonian and the asymmetry parameter of the electric field gradient (EFG) acting on the spin S, the S-I inter-spin orientation with respect to the EFG principal axes, the rotational correlation time of the entity carrying the S-I pair, and/or the proper relaxation time of the spin S. The theory is first applied to protein amide protons undergoing dipolar coupling with fast-relaxing quadrupole (14)N nuclei and mediating the QRE to the observed bulk water protons. The theoretical QRE agrees well with its experimental counterpart for various systems such as bovine pancreatic trypsin inhibitor and cartilages. The anomalous behaviour of the relaxation rate of protons in synthetic aluminium silicate imogolite nano-tubes due to the QRE of (27)Al (S = 5/2) nuclei is also explained.

Engineering trypsin for inhibitor resistance

The development of effective protease therapeutics requires that the proteases be more resistant to naturally occurring inhibitors while maintaining catalytic activity. A key step in developing inhibitor resistance is the identification of key residues in protease-inhibitor interaction. Given that majority of the protease therapeutics currently in use are trypsin-fold, trypsin itself serves as an ideal model for studying protease-inhibitor interaction. To test the importance of several trypsin-inhibitor interactions on the prime-side binding interface, we created four trypsin single variants Y39A, Y39F, K60A, and K60V and report biochemical sensitivity against bovine pancreatic trypsin inhibitor (BPTI) and M84R ecotin. All variants retained catalytic activity against small, commercially available peptide substrates [kcat /KM = (1.2 ± 0.3) × 10(7) M(-1) s(-1) . Compared with wild-type, the K60A and K60V variants showed increased sensitivity to BPTI but less sensitivity to ecotin. The Y39A variant was less sensitive to BPTI and ecotin while the Y39F variant was more sensitive to both. The relative binding free energies between BPTI complexes with WT, Y39F, and Y39A were calculated based on 3.5 µs combined explicit solvent molecular dynamics simulations. The BPTI:Y39F complex resulted in the lowest binding energy, while BPTI:Y39A resulted in the highest. Simulations of Y39F revealed increased conformational rearrangement of F39, which allowed formation of a new hydrogen bond between BPTI R17 and H40 of the variant. All together, these data suggest that positions 39 and 60 are key for inhibitor binding to trypsin, and likely more trypsin-fold proteases.

Analysis and Control of Protein Crystallization Using Short Peptide Tags That Change Solubility without Affecting Structure, Thermal Stability, and Function

Short peptide tags attached to recombinant proteins are emerging as an important tool for biochemical research. Here, we report the effects of 10 Solubilization Controlling Peptide (SCP) tags on crystallization behavior of a bovine pancreatic trypsin inhibitor (BPTI) variant. The tags did not affect structure, thermodynamics, and activities of BPTI. Moreover, eight of the tagged variants crystallized under the same condition, and six of them diffracted at high resolution. All variants with long-term solubility (LS) between 1 and 6 mg/mL produced crystals that diffracted well, while variants with LS 6 mg/mL did not crystallize, produced poorly diffracting crystals, or crystallized under a different condition. The only exception was a glutamine tagged variant, which had an LS of 5 mg/mL, but fast aggregation kinetics, and produced mere needles unsuitable for further analysis. Crystal structures indicated that most tags were largely invisible, indicating high flexibility, without having interactions...

Three-dimensional Structure of a Kunitz-type Inhibitor in Complex with an Elastase-like Enzyme

Elastase-like enzymes are involved in important diseases such as acute pancreatitis, chronic inflammatory lung diseases, and cancer. Structural insights into their interaction with specific inhibitors will contribute to the development of novel anti-elastase compounds that resist rapid oxidation and proteolysis. Proteinaceous Kunitz-type inhibitors homologous to the bovine pancreatic trypsin inhibitor (BPTI) provide a suitable scaffold, but the structural aspects of their interaction with elastase-like enzymes have not been elucidated. Here, we increased the selectivity of ShPI-1, a versatile serine protease inhibitor from the sea anemone Stichodactyla helianthus with high biomedical and biotechnological potential, toward elastase-like enzymes by substitution of the P1 residue (Lys(13)) with leucine. The variant (rShPI-1/K13L) exhibits a novel anti-porcine pancreatic elastase (PPE) activity together with a significantly improved inhibition of human neuthrophil elastase and chymotrypsin. The crystal structure of the PPE·rShPI-1/K13L complex determined at 2.0 Å resolution provided the first details of the canonical interaction between a BPTI-Kunitz-type domain and elastase-like enzymes. In addition to the essential impact of the variant P1 residue for complex stability, the interface is improved by increased contributions of the primary and secondary binding loop as compared with similar trypsin and chymotrypsin complexes. A comparison of the interaction network with elastase complexes of canonical inhibitors from the chelonian in family supports a key role of the P3 site in ShPI-1 in directing its selectivity against pancreatic and neutrophil elastases. Our results provide the structural basis for site-specific mutagenesis to further improve the binding affinity and/or direct the selectivity of BPTI-Kunitz-type inhibitors toward elastase-like enzymes.

Conformational change study of dengue virus NS2B-NS3 protease using 19F NMR spectroscopy

The dengue virus NS2B-NS3 protease (NS2B-NS3p), an important antiviral target for drug development, has been reported to adopt an open or closed conformation in crystal structures with different NS2B C-terminus (NS2Bc) positioning. In solution, nevertheless, NS2B-NS3p forms a mixture of open, closed and maybe other intermediate conformations, which is difficult to characterize using conventional biophysical and biochemical techniques. In this study, we developed a new strategy to analyze these conformational changes using 19F NMR spectroscopy. Low pH or bovine pancreatic trypsin inhibitor (BPTI) binding promote the conformation change from open to closed, showing the importance of charge forces in the interaction between NS2Bc and NS3p. The mutation H51A impairs the charge interaction and the pH dependence of the conformational changes. It stabilizes the open conformation, while the addition of BPTI still converts NS2B-NS3p from open to closed conformation.

Independent Metrics for Protein Backbone and Side-Chain Flexibility: Time Scales and Effects of Ligand Binding.

Conformational dynamics are central for understanding biomolecular structure and function, since biological macromolecules are inherently flexible at room temperature and in solution. Computational methods are nowadays capable of providing valuable information on the conformational ensembles of biomolecules. However, analysis tools and intuitive metrics that capture dynamic information from in silico generated structural ensembles are limited. In standard work-flows, flexibility in a conformational ensemble is represented through residue-wise root-mean-square fluctuations or B-factors following a global alignment. Consequently, these approaches relying on global alignments discard valuable information on local dynamics. Results inherently depend on global flexibility, residue size, and connectivity. In this study we present a novel approach for capturing positional fluctuations based on multiple local alignments instead of one single global alignment. The method captures local dynamics within a structural ensemble independent of residue type by splitting individual local and global degrees of freedom of protein backbone and side-chains. Dependence on residue type and size in the side-chains is removed via normalization with the B-factors of the isolated residue. As a test case, we demonstrate its application to a molecular dynamics simulation of bovine pancreatic trypsin inhibitor (BPTI) on the millisecond time scale. This allows for illustrating different time scales of backbone and side-chain flexibility. Additionally, we demonstrate the effects of ligand binding on side-chain flexibility of three serine proteases. We expect our new methodology for quantifying local flexibility to be helpful in unraveling local changes in biomolecular dynamics.

Harnessing selenocysteine reactivity for oxidative protein folding.

Although oxidative folding of disulfide-rich proteins is often sluggish, this process can be significantly enhanced by targeted replacement of cysteines with selenocysteines. In this study, we examined the effects of a selenosulfide and native versus nonnative diselenides on the folding rates and mechanism of bovine pancreatic trypsin inhibitor. Our results show that such sulfur-to-selenium substitutions alter the distribution of key folding intermediates and enhance their rates of interconversion in a context-dependent manner.

Sampling Assessment for Molecular Simulations Using Conformational Entropy Calculations.

The extent and significance of conformational sampling is a major factor determining the reliability of long-scale molecular simulations of large and flexible biomolecules. Although several methods have been proposed to quantify the effective sample size of molecular simulations by transforming root mean squared distances between pairs of configurations into statistical/probabilistic quantities, there is still no standard technique for measuring the size of sampling. In this work, we study conformational entropy (Sconform) as a purely informational and probabilistic measure of sampling that does not require the adoption of any clustering protocol or distance metric between configurations. In addition Sconform, which is calculated from the probability mass functions associated with discretized dihedral angles, offers other potential advantages for sampling assessment (e.g., global character, thermodynamic significance, relationship with internal degrees of freedom, etc.). The utility of Sconform in sampling assessment is illustrated by carrying out test calculations on configurations produced by two extended molecular dynamics simulations, namely, a 2.0 μs trajectory of a highly flexible 17-residue peptide and the trajectory data set of the 1.0 ms bovine pancreatic trypsin inhibitor simulation provided by the D. E. Shaw research group.

Interaction of the BKCa channel gating ring with dendrotoxins

Two classes of small homologous basic proteins, mamba snake dendrotoxins (DTX) and bovine pancreatic trypsin inhibitor (BPTI), block the large conductance Ca2+-activated K+ channel (BKCa, KCa1.1) by production of discrete subconductance events when added to the intracellular side of the membrane. This toxin-channel interaction is unlikely to be pharmacologically relevant to the action of mamba venom, but as a fortuitous ligand-protein interaction, it has certain biophysical implications for the mechanism of BKCa channel gating. In this work we examined the subconductance behavior of 9 natural dendrotoxin homologs and 6 charge neutralization mutants of δ-dendrotoxin in the context of current structural information on the intracellular gating ring domain of the BKCa channel. Calculation of an electrostatic surface map of the BKCa gating ring based on the Poisson-Boltzmann equation reveals a predominantly electronegative surface due to an abundance of solvent-accessible side chains of negatively charged amino acids. Available structure-activity information suggests that cationic DTX/BPTI molecules bind by electrostatic attraction to site(s) on the gating ring located in or near the cytoplasmic side portals where the inactivation ball peptide of the β2 subunit enters to block the channel. Such an interaction may decrease the apparent unitary conductance by altering the dynamic balance of open versus closed states of BKCa channel activation gating.

Weak self-interactions of globular proteins studied by small-angle X-ray scattering and structure-based modeling.

We investigate protein-protein interactions in solution by small-angle X-ray scattering (SAXS) and theoretical modeling. The structure factor for solutions of bovine pancreatic trypsin inhibitor (BPTI), myoglobin (Mb), and intestinal fatty acid-binding protein (IFABP) is determined from SAXS measurements at multiple concentrations, from Monte Carlo simulations with a coarse-grained structure-based interaction model, and from analytic approximate solutions of two idealized colloidal interaction models without adjustable parameters. By combining these approaches, we find that the structure factor is essentially determined by hard-core and screened electrostatic interactions. Other soft short-ranged interactions (van der Waals and solvation-related) are either individually insignificant or tend to cancel out. The structure factor is also not significantly affected by charge fluctuations. For Mb and IFABP, with a small net charge and relatively symmetric charge distribution, the structure factor is well described by a hard-sphere model. For BPTI, with a larger net charge, screened electrostatic repulsion is also important, but the asymmetry of the charge distribution reduces the repulsion from that predicted by a charged hard-sphere model with the same net charge. Such charge asymmetry may also amplify the effect of shape asymmetry on the protein-protein potential of mean force.

Structural and functional characterization of proteinase inhibitors from seeds of Cajanus cajan (cv. ICP 7118)

Proteinase inhibitors (C11PI) from mature dry seeds of Cajanus cajan (cv. ICP 7118) were purified by chromatography which resulted in 87-fold purification and 7.9% yield. SDS-PAGE, matrix assisted laser desorption ionization time-of-flight (MALDI-TOF/TOF) mass spectrum and two-dimensional (2-D) gel electrophoresis together resolved that C11PI possessed molecular mass of 8385.682 Da and existed as isoinhibitors. However, several of these isoinhibitors exhibited self association tendency to form small oligomers. All the isoinhibitors resolved in Native-PAGE and 2-D gel electrophoresis showed inhibitory activity against bovine pancreatic trypsin and chymotrypsin as well as Achaea janata midgut trypsin-like proteases (AjPs), a devastating pest of castor plant. Partial sequences of isoinhibitor (pI 6.0) obtained from MALDI-TOF/TOF analysis and N-terminal sequencing showed 100% homology to Bowman-Birk Inhibitors (BBIs) of leguminous plants. C11PI showed non-competitive inhibition against trypsin and chymotrypsin. A marginal loss (<15%) in C11PI activity against trypsin at 80 °C and basic pH (12.0) was associated with concurrent changes in its far-UV CD spectra. Further, in vitro assays demonstrated that C11PI possessed significant inhibitory potential (IC50 of 78 ng) against AjPs. On the other hand, in vivo leaf coating assays demonstrated that C11PI caused significant mortality rate with concomitant reduction in body weight of both larvae and pupae, prolonged the duration of transition from larva to pupa along with formation of abnormal larval-pupal and pupal-adult intermediates. Being smaller peptides, it is possible to express C11PI in castor to protect them against its devastating pest A. janata.

Tyrosine sulfation of human trypsin steers S2' subsite selectivity towards basic amino acids.

Human cationic and anionic trypsins are sulfated on Tyr154, a residue which helps to shape the prime side substrate-binding subsites. Here, we used phage display technology to assess the significance of tyrosine sulfation for the specificity of human trypsins. The prime side residues P1′–P4′ in the binding loop of bovine pancreatic trypsin inhibitor (BPTI) were fully randomized and tight binding inhibitor phages were selected against non-sulfated and sulfated human cationic trypsin. The selection pattern for the two targets differed mostly at the P2′ position, where variants selected against non-sulfated trypsin contained primarily aliphatic residues (Leu, Ile, Met), while variants selected against sulfated trypsin were enriched also for Arg. BPTI variants carrying Arg, Lys, Ile, Leu or Ala at the P2′ position of the binding loop were purified and equilibrium dissociation constants were determined against non-sulfated and sulfated cationic and anionic human trypsins. BPTI variants harboring apolar residues at P2′ exhibited 3–12-fold lower affinity to sulfated trypsin relative to the non-sulfated enzyme, whereas BPTI variants containing basic residues at P2′ had comparable affinity to both trypsin forms. Taken together, the observations demonstrate that the tyrosyl sulfate in human trypsins interacts with the P2′ position of the substrate-like inhibitor and this modification increases P2′ selectivity towards basic side chains.

In silico concurrent multisite pH titration in proteins.

The concurrent proton binding at multiple sites in macromolecules such as proteins and nucleic acids is an important yet challenging problem in biochemistry. We develop an efficient generalized Hamiltonian approach to attack this issue. Based on the previously developed generalized-ensemble methods, an effective potential energy is constructed which combines the contributions of all (relevant) protonation states of the molecule. The effective potential preserves important phase regions of all states and, thus, allows efficient sampling of these regions in one simulation. The need for intermediate states in alchemical free energy simulations is greatly reduced. Free energy differences between different protonation states can be determined accurately and enable one to construct the grand canonical partition function. Therefore, the complicated concurrent multisite proton titration process of protein molecules can be satisfactorily simulated. Application of this method to the simulation of the pKa of Glu49, Asp50, and C-terminus of bovine pancreatic trypsin inhibitor shows reasonably good agreement with published experimental work. This method provides an unprecedented vivid picture of how different protonation states change their relative population upon pH titration. We believe that the method will be very useful in deciphering the molecular mechanism of pH-dependent biomolecular processes in terms of a detailed atomistic description.

The dengue virus NS2B-NS3 protease retains the closed conformation in the complex with BPTI.

The C-terminal β-hairpin of NS2B (NS2Bc) in the dengue virus NS2B-NS3 protease is required for full enzymatic activity. In crystal structures without inhibitor and in the complex with bovine pancreatic trypsin inhibitor (BPTI), NS2Bc is displaced from the active site. In contrast, nuclear magnetic resonance (NMR) studies in solution only ever showed NS2Bc in the enzymatically active closed conformation. Here we demonstrate by pseudocontact shifts from a lanthanide tag that NS2Bc remains in the closed conformation also in the complex with BPTI. Therefore, the closed conformation is the best template for drug discovery.

Bovine pancreatic trypsin inhibitor is a new antifungal peptide that inhibits cellular magnesium uptake.

Antimicrobial peptides (AMPs) are promising agents for control of bacterial and fungal infections. Traditionally, AMPs were thought to act through membrane disruption but recent experiments have revealed a diversity of mechanisms. Here we describe a novel antifungal activity for bovine pancreatic trypsin inhibitor (BPTI). BPTI has several features in common with a subset of antimicrobial proteins in that it is small, cationic and stabilized by disulphide bonds. BPTI inhibits growth of Saccharomyces cerevisiae and the human pathogen Candida albicans. Screening of the yeast heterozygous essential deletion collection identified the magnesium transporter Alr1p as a potential BPTI target. BPTI treatment of wild type cells resulted in a lowering of cellular Mg(2+) levels. Populations treated with BPTI had fewer cells in S-phase of the cell cycle and a corresponding increase of cells in G(0)/G(1) and G(2) phases. The same patterns of cell cycle arrest obtained with BPTI were also obtained with the magnesium channel inhibitor hexamine(III)cobalt chloride. Analysis of the growth inhibition of C. albicans revealed that BPTI is inhibiting growth via the same mechanism in the two yeast species. Inhibition of magnesium uptake by BPTI represents a novel mechanism of action for AMPs.

Correlation as a Determinant of Configurational Entropy in Supramolecular and Protein Systems

For biomolecules in solution, changes in configurational entropy are thought to contribute substantially to the free energies of processes like binding and conformational change. In principle, the configurational entropy can be strongly affected by pairwise and higher-order correlations among conformational degrees of freedom. However, the literature offers mixed perspectives regarding the contributions that changes in correlations make to changes in configurational entropy for such processes. Here we take advantage of powerful techniques for simulation and entropy analysis to carry out rigorous in silico studies of correlation in binding and conformational changes. In particular, we apply information-theoretic expansions of the configurational entropy to well-sampled molecular dynamics simulations of a model host–guest system and the protein bovine pancreatic trypsin inhibitor. The results bear on the interpretation of NMR data, as they indicate that changes in correlation are important determinants of entropy changes for biologically relevant processes and that changes in correlation may either balance or reinforce changes in first-order entropy. The results also highlight the importance of main-chain torsions as contributors to changes in protein configurational entropy. As simulation techniques grow in power, the mathematical techniques used here will offer new opportunities to answer challenging questions about complex molecular systems.

Molecular Dynamics Simulations of Bromodomains Reveal Binding‐Site Flexibility and Multiple Binding Modes of the Natural Ligand Acetyl‐Lysine

AbstractExperimental protein structures provide spatial information at the atomic level. A further dimension, time, is supplemented by molecular dynamics. Since the pioneering work on the 58‐residue inhibitor of bovine pancreatic trypsin in the group of Martin Karplus in the seventies, molecular dynamics simulations have shown that the intrinsic flexibility of proteins is essential for their function. Here, we review simulation studies of bromodomains. These protein modules are involved in the recognition of acetylated lysine side chains, a post‐translational modification frequently observed in histone tails. The molecular dynamics simulations have unmasked: (i) the large plasticity of the loops lining the acetyl‐lysine binding site (coupled to its self‐occlusion), and (ii) multiple binding modes of acetyl‐lysine. These simulation results suggest that recognition of histone tails by bromodomains is modulated by their intrinsic flexibility, and further corroborate the utility of molecular dynamics in understanding (macro)molecular recognition.

Off-resonance rotating-frame relaxation dispersion experiment for 13C in aromatic side chains using L-optimized TROSY-selection

Protein dynamics on the microsecond–millisecond time scales often play a critical role in biological function. NMR relaxation dispersion experiments are powerful approaches for investigating biologically relevant dynamics with site-specific resolution, as shown by a growing number of publications on enzyme catalysis, protein folding, ligand binding, and allostery. To date, the majority of studies has probed the backbone amides or side-chain methyl groups, while experiments targeting other sites have been used more sparingly. Aromatic side chains are useful probes of protein dynamics, because they are over-represented in protein binding interfaces, have important catalytic roles in enzymes, and form a sizable part of the protein interior. Here we present an off-resonance R 1ρ experiment for measuring microsecond to millisecond conformational exchange of aromatic side chains in selectively 13C labeled proteins by means of longitudinal- and transverse-relaxation optimization. Using selective excitation and inversion of the narrow component of the 13C doublet, the experiment achieves significant sensitivity enhancement in terms of both signal intensity and the fractional contribution from exchange to transverse relaxation; additional signal enhancement is achieved by optimizing the longitudinal relaxation recovery of the covalently attached 1H spins. We validated the L-TROSY-selected R 1ρ experiment by measuring exchange parameters for Y23 in bovine pancreatic trypsin inhibitor at a temperature of 328 K, where the ring flip is in the fast exchange regime with a mean waiting time between flips of 320 μs. The determined chemical shift difference matches perfectly with that measured from the NMR spectrum at lower temperatures, where separate peaks are observed for the two sites. We further show that potentially complicating effects of strong scalar coupling between protons (Weininger et al. in J Phys Chem B 117: 9241–9247, 2013b) can be accounted for using a simple expression, and provide recommendations for data acquisition when the studied system exhibits this behavior. The present method extends the repertoire of relaxation methods tailored for aromatic side chains by enabling studies of faster processes and improved control over artifacts due to strong coupling.

Determining the role(s) of prime‐side residues in macromolecular inhibition of trypsin‐fold serine proteases (933.2)

Trypsin‐fold serine proteases are among the most abundant of proteases. By identifying residues that are important for enzyme‐inhibitor interactions in trypsin, we may advance the development of protease‐based therapies in general. Lysine‐60 (K60) is a highly conserved prime‐side residue in trypsin‐fold serine proteases. In trypsin‐inhibitor co‐crystals, K60 hydrogen bonds to tyrosine‐39 (Y39) and is positioned to restrict conformational mobility of phenylalanine‐41 (F41), possibly optimizing the observed hydrogen bond interactions between inhibitors, Y39 and F41. Substitution of K60 with other residues may disrupt these interactions and provide insight to their significance with respect to inhibitor binding. To test this hypothesis, we created trypsin variants K60G, K60A, K60V, K60I, K60M, K60R, Y39S, and Y39F and characterized them with respect to their activities and sensitivities to macromolecular inhibitors soybean trypsin inhibitor (SBTI), bovine pancreatic trypsin inhibitor (BPTI) and ecotin, an inhibitor expressed in E. coli. Our initial results show that, compared to wild‐type trypsin, all variants maintain similar catalytic activity, but‐K60A, K60V, K60I, K60M, and Y39F are more sensitive to inhibition while variants K60R and Y39S are less sensitive to inhibition. Collectively, these results suggest that K60 and Y39 do indeed play significant roles in inhibitor binding.Grant Funding Source: This work was supported by NSF

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.