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.     

Effects of Hydrophobic Macromolecular Crowders on Amyloid β (16–22) Aggregation

In Alzheimer’s disease (AD), the amyloid β (Aβ) peptide aggregates in the brain to form progressively larger oligomers, fibrils, and plaques. The aggregation process is strongly influenced by the presence of other macromolecular species, called crowders, that can exert forces on the proteins. One very common attribute of macromolecular crowders is their hydrophobicity. We examined the effect of hydrophobic crowders on protein aggregation by using discontinuous molecular dynamics (DMD) simulations in combination with an intermediate resolution protein model, PRIME20. The systems considered contained 48 Aβ (16–22) peptides and crowders with diameters of 5 Å, 20 Å, and 40 Å, represented by hard spheres or spheres with square-well/square-shoulder interactions, at a crowder volume fraction of ϕ = 0.10. Results show that low levels of crowder hydrophobicity are capable of increasing the fibrillation lag time and high levels of crowder hydrophobicity can fully prevent the formation of fibrils. The types of structures that remain during the final stages of the simulations are summarized in a global phase diagram that shows fibril, disordered oligomer, or β-sheet phases in the space spanned by crowder size and crowder hydrophobicity. In particular, at high levels of hydrophobicity, simulations with 5 Å crowders result in only disordered oligomers and simulations with 40 Å crowders result in only β-sheets. The presence of hydrophobic crowders reduces the antiparallel β-sheet content of fibrils, whereas hard sphere crowders increase it. Finally, strong hydrophobic crowders alter the secondary structure of the Aβ (16–22) monomers, bending them into a shape that is incapable of forming ordered β-sheets or fibrils. These results qualitatively agree with previous theoretical and experimental work.     

Effects of macromolecular crowding on an intrinsically disordered protein characterized by small-angle neutron scattering with contrast matching

Small-angle neutron scattering was used to examine the effects of molecular crowding on an intrinsically disordered protein, the N protein of bacteriophage λ, in the presence of high concentrations of a small globular protein, bovine pancreatic trypsin inhibitor (BPTI). The N protein was labeled with deuterium, and the D₂O concentration of the solvent was adjusted to eliminate the scattering contrast between the solvent and unlabeled BPTI, leaving only the scattering signal from the unfolded protein. The scattering profile observed in the absence of BPTI closely matched that predicted for an ensemble of random conformations. With BPTI added to a concentration of 65 mg/mL, there was a clear change in the scattering profile representing an increase in the mass fractal dimension of the unfolded protein, from 1.7 to 1.9, as expected if crowding favors more compact conformations. The crowding protein also inhibited aggregation of the unfolded protein. At 130 mg/mL BPTI, however, the fractal dimension was not significantly different from that measured at the lower concentration, contrary to the predictions of models that treat the unfolded conformations as convex particles. These results are reminiscent of the behavior of polymers in concentrated melts, suggesting that these synthetic mixtures may provide useful insights into the properties of unfolded proteins under crowding conditions.     

Interplay between Chaperones and Protein Disorder Promotes the Evolution of Protein Networks

Evolution is driven by mutations, which lead to new protein functions but come at a cost to protein stability. Non-conservative substitutions are of interest in this regard because they may most profoundly affect both function and stability. Accordingly, organisms must balance the benefit of accepting advantageous substitutions with the possible cost of deleterious effects on protein folding and stability. We here examine factors that systematically promote non-conservative mutations at the proteome level. Intrinsically disordered regions in proteins play pivotal roles in protein interactions, but many questions regarding their evolution remain unanswered. Similarly, whether and how molecular chaperones, which have been shown to buffer destabilizing mutations in individual proteins, generally provide robustness during proteome evolution remains unclear. To this end, we introduce an evolutionary parameter λ that directly estimates the rate of non-conservative substitutions. Our analysis of λ in Escherichia coli, Saccharomyces cerevisiae, and Homo sapiens sequences reveals how co- and post-translationally acting chaperones differentially promote non-conservative substitutions in their substrates, likely through buffering of their destabilizing effects. We further find that λ serves well to quantify the evolution of intrinsically disordered proteins even though the unstructured, thus generally variable regions in proteins are often flanked by very conserved sequences. Crucially, we show that both intrinsically disordered proteins and highly re-wired proteins in protein interaction networks, which have evolved new interactions and functions, exhibit a higher λ at the expense of enhanced chaperone assistance. Our findings thus highlight an intricate interplay of molecular chaperones and protein disorder in the evolvability of protein networks. Our results illuminate the role of chaperones in enabling protein evolution, and underline the importance of the cellular context and integrated approaches for understanding proteome evolution. We feel that the development of λ may be a valuable addition to the toolbox applied to understand the molecular basis of evolution.     

Effects of Molecular Crowding on the Dynamics of Intrinsically Disordered Proteins

Inside cells, the concentration of macromolecules can reach up to 400 g/L. In such crowded environments, proteins are expected to behave differently than in vitro. It has been shown that the stability and the folding rate of a globular protein can be altered by the excluded volume effect produced by a high density of macromolecules. However, macromolecular crowding effects on intrinsically disordered proteins (IDPs) are less explored. These proteins can be extremely dynamic and potentially sample a wide ensemble of conformations under non-denaturing conditions. The dynamic properties of IDPs are intimately related to the timescale of conformational exchange within the ensemble, which govern target recognition and how these proteins function. In this work, we investigated the macromolecular crowding effects on the dynamics of several IDPs by measuring the NMR spin relaxation parameters of three disordered proteins (ProTα, TC1, and α-synuclein) with different extents of residual structures. To aid the interpretation of experimental results, we also performed an MD simulation of ProTα. Based on the MD analysis, a simple model to correlate the observed changes in relaxation rates to the alteration in protein motions under crowding conditions was proposed. Our results show that 1) IDPs remain at least partially disordered despite the presence of high concentration of other macromolecules, 2) the crowded environment has differential effects on the conformational propensity of distinct regions of an IDP, which may lead to selective stabilization of certain target-binding motifs, and 3) the segmental motions of IDPs on the nanosecond timescale are retained under crowded conditions. These findings strongly suggest that IDPs function as dynamic structural ensembles in cellular environments.     

Intrinsically Disordered Protein Exhibits Both Compaction and Expansion under Macromolecular Crowding

Conformational malleability allows intrinsically disordered proteins (IDPs) to respond agilely to their environments, such as nonspecifically interacting with in vivo bystander macromolecules (or crowders). Previous studies have emphasized conformational compaction of IDPs due to steric repulsion by macromolecular crowders, but effects of soft attraction are largely unexplored. Here we studied the conformational ensembles of the IDP FlgM in both polymer and protein crowders by small-angle neutron scattering. As crowder concentrations increased, the mean radius of gyration of FlgM first decreased but then exhibited an uptick. Ensemble optimization modeling indicated that FlgM conformations under protein crowding segregated into two distinct populations, one compacted and one extended. Coarse-grained simulations showed that compacted conformers fit into an interstitial void and occasionally bind to a surrounding crowder, whereas extended conformers snake through interstitial crevices and bind multiple crowders simultaneously. Crowder-induced conformational segregation may facilitate various cellular functions of IDPs.     

Measuring how two proteins affect each other's net charge in a crowded environment

Theory predicts that the net charge (Z) of a protein can be altered by the net charge of a neighboring protein as the two approach one another below the Debye length. This type of charge regulation suggests that a protein''s charge and perhaps function might be affected by neighboring proteins without direct binding. Charge regulation during protein crowding has never been directly measured due to analytical challenges. Here, we show that lysine specific protein crosslinkers (NHS ester‐Staudinger pairs) can be used to mimic crowding by linking two non‐interacting proteins at a maximal distance of ~7.9 Å. The net charge of the regioisomeric dimers and preceding monomers can then be determined with lysine‐acyl “protein charge ladders” and capillary electrophoresis. As a proof of concept, we covalently linked myoglobin (Z _monomer = −0.43 ± 0.01) and α‐lactalbumin (Z _monomer = −4.63 ± 0.05). Amide hydrogen/deuterium exchange and circular dichroism spectroscopy demonstrated that crosslinking did not significantly alter the structure of either protein or result in direct binding (thus mimicking crowding). Ultimately, capillary electrophoretic analysis of the dimeric charge ladder detected a change in charge of ΔZ = −0.04 ± 0.09 upon crowding by this pair (Z _dimer = −5.10 ± 0.07). These small values of ΔZ are not necessarily general to protein crowding (qualitatively or quantitatively) but will vary per protein size, charge, and solvent conditions.     

The Conformational Ensembles of α-Synuclein and Tau: Combining Single-Molecule FRET and Simulations

Intrinsically disordered proteins (IDPs) are increasingly recognized for their important roles in a range of biological contexts, both in normal physiological function and in a variety of devastating human diseases. However, their structural characterization by traditional biophysical methods, for the purposes of understanding their function and dysfunction, has proved challenging. Here, we investigate the model IDPs α-Synuclein (αS) and tau, that are involved in major neurodegenerative conditions including Parkinson’s and Alzheimer’s diseases, using excluded volume Monte Carlo simulations constrained by pairwise distance distributions from single-molecule fluorescence measurements. Using this, to our knowledge, novel approach we find that a relatively small number of intermolecular distance constraints are sufficient to accurately determine the dimensions and polymer conformational statistics of αS and tau in solution. Moreover, this method can detect local changes in αS and tau conformations that correlate with enhanced aggregation. Constrained Monte Carlo simulations produce ensembles that are in excellent agreement both with experimental measurements on αS and tau and with all-atom, explicit solvent molecular dynamics simulations of αS, with much lower configurational sampling requirements and computational expense.Abbreviations used: AAMD, all-atom molecular dynamics; ECMC, experimentally constrained Monte Carlo; ET_eff, energy transfer efficiency; (sm)FRET, (single molecule) Förster resonance energy transfer; IDP, intrinsically disordered protein; LJ, Lennard-Jones; MC, Monte Carlo; MD, molecular dynamics; PRE, paramagnetic relaxation enhancement; SAX(N)S, small-angle x-ray (neutron) scattering; UMC, unconstrained Monte Carlo     

Molecular Mechanism of Heat Shock-Provoked Disassembly of the Coliphage λ Replication Complex

We have found previously that, in contrast to the free O initiator protein of λ phage or plasmid rapidly degraded by the Escherichia coli ClpP/ClpX protease, the λO present in the replication complex (RC) is protected from proteolysis. However, in cells growing in a complete medium, a temperature shift from 30 to 43°C resulted in the decay of the λO fraction, which indicated disassembly of RC. This process occurred due to heat shock induction of the groE operon, coding for molecular chaperones of the Hsp60 system. Here we demonstrate that an increase in the cellular concentration of GroEL and GroES proteins is not in itself sufficient to cause RC disassembly. Another requirement is a DNA gyrase-mediated negative resupercoiling of λ plasmid DNA, which counteracts DNA relaxation and starts to dominate 10 min after the temperature upshift. We presume that RC dissociates from λ DNA during the negative resupercoiling, becoming susceptible to the subsequent action of GroEL/S and ClpP/ClpX proteins. In contrast to λcro⁺, in λcro⁻ plasmid-harboring cells, the RC reveals heat shock resistance. After temperature upshift of the λcrots plasmid-harboring cells, a Cro repressor-independent control of λ DNA replication and heat shock resistance of RC are established before the period of DNA gyrase-mediated negative supercoiling. We suggest that the tight binding of RC to λ DNA is due to interaction of RC with other DNA-bound proteins, and is related to the molecular basis of the λcro⁻ plasmid replication control.     

Effects of Macromolecular Crowding on Protein Conformational Changes

Many protein functions can be directly linked to conformational changes. Inside cells, the equilibria and transition rates between different conformations may be affected by macromolecular crowding. We have recently developed a new approach for modeling crowding effects, which enables an atomistic representation of “test” proteins. Here this approach is applied to study how crowding affects the equilibria and transition rates between open and closed conformations of seven proteins: yeast protein disulfide isomerase (yPDI), adenylate kinase (AdK), orotidine phosphate decarboxylase (ODCase), Trp repressor (TrpR), hemoglobin, DNA β-glucosyltransferase, and Ap₄A hydrolase. For each protein, molecular dynamics simulations of the open and closed states are separately run. Representative open and closed conformations are then used to calculate the crowding-induced changes in chemical potential for the two states. The difference in chemical-potential change between the two states finally predicts the effects of crowding on the population ratio of the two states. Crowding is found to reduce the open population to various extents. In the presence of crowders with a 15 Å radius and occupying 35% of volume, the open-to-closed population ratios of yPDI, AdK, ODCase and TrpR are reduced by 79%, 78%, 62% and 55%, respectively. The reductions for the remaining three proteins are 20–44%. As expected, the four proteins experiencing the stronger crowding effects are those with larger conformational changes between open and closed states (e.g., as measured by the change in radius of gyration). Larger proteins also tend to experience stronger crowding effects than smaller ones [e.g., comparing yPDI (480 residues) and TrpR (98 residues)]. The potentials of mean force along the open-closed reaction coordinate of apo and ligand-bound ODCase are altered by crowding, suggesting that transition rates are also affected. These quantitative results and qualitative trends will serve as valuable guides for expected crowding effects on protein conformation changes inside cells.     

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.     

THE EFFECT OF UNILATERAL ULTRAVIOLET LIGHT ON THE DEVELOPMENT OF THE FUCUS EGG

1. When Fucus eggs which have been fertilized for a sufficient length of time are irradiated unilaterally with monochromatic ultraviolet light (λ2804 Å) of adequate dosage, 97–100 per cent form rhizoids on the halves of the eggs away from the source of radiation (see Figs. 1 and 2). 2. The responsiveness of the eggs increases gradually after fertilization and does not reach a maximum until about 7 hours at 15°C. (see Fig. 3). The first rhizoids begin to form in a population at about 12 hours after fertilization. The responsiveness remains maximal until at least 11 hours after fertilization. 3. It is suggested that the low responsiveness of a population of eggs at an earlier period is due to recovery from the effects of irradiation before the rhizoids begin to form. 4. The response of eggs to λ2804 Å is proportional, over a wide range, to the logarithm of the dosage (see Fig. 1). Dosage was regulated by the duration of exposure during the period of maximum response. 5. High dosages of λ2804 Å, of the order of 10,000 ergs per mm.², cause the rhizoids to form fairly precisely away from the source of radiation (see Fig. 2). Twice this dosage inhibits rhizoid formation altogether without causing cytolysis. 6. Other wave-lengths which have also been shown to be effective are: 3660, 3130, 2654, 2537, 2482, and 2345 Å. Only exploratory measurements have been made to test the effectiveness of these wave-lengths, but they show that much greater energy is necessary to obtain a strong response with λ3130 and 3660 Å, especially the latter. The wave-lengths shorter than 2804 Å, on the other hand, show the same order of effectiveness as λ2804 Å. Some may be more effective. 7. A beam of λ2804 Å which is incident on a single layer of Fucus eggs is completely extinguished at 2, 3, 6, or 6½ hours after fertilization. About 85 per cent of a beam of λ3660 Å is extinguished. The wave-length 3660 Å is thus not so completely absorbed as λ2804 Å, but the difference in proportion absorbed by the egg is not nearly so great as the difference in effectiveness.     

Protein Components of Bacteriophages λ and λ Virulent

Parallel studies have been made of the protein coats of the temperate bacteriophage λ and of a deletion mutant, λ virulent. A new method for preparing ghosts of both phages by the action of Cu⁺⁺ is described. Protein ghosts of both phages can be dissolved in citrate at pH values below 3, more rapidly in the presence of 8 m urea. Both phages yielded three apparently identical protein components which can be separated by thin-layer gel filtration and thin-layer gel electrophoresis. The protein of molecular weight 47,000 ± 1,500 represents about 55% of the protein of the ghosts and is therefore likely to be the subunit of the head. The other proteins of molecular weight 30,000 ± 1,500 and 16,000 ± 1,500 represent approximately 25% and 20% of the protein, respectively. Amino acid analyses of the ghosts from the two phages have been carried out and show no significant differences. The buoyant density of phage λ virulent is 0.016 g/ml less than that of λ. Since no differences have been found in the protein components of the two phages, this indicates that the virulent mutant contains approximately 16% less deoxyribonucleic acid than the temperate phage.     

Self-activating G protein α subunits engage seven-transmembrane regulator of G protein signaling (RGS) proteins and a Rho guanine nucleotide exchange factor effector in the amoeba Naegleria fowleri

The free-living amoeba Naegleria fowleri is a causative agent of primary amoebic meningoencephalitis and is highly resistant to current therapies, resulting in mortality rates >97%. As many therapeutics target G protein–centered signal transduction pathways, further understanding the functional significance of G protein signaling within N. fowleri should aid future drug discovery against this pathogen. Here, we report that the N. fowleri genome encodes numerous transcribed G protein signaling components, including G protein–coupled receptors, heterotrimeric G protein subunits, regulator of G protein signaling (RGS) proteins, and candidate Gα effector proteins. We found N. fowleri Gα subunits have diverse nucleotide cycling kinetics; Nf Gα5 and Gα7 exhibit more rapid nucleotide exchange than GTP hydrolysis (i.e., “self-activating” behavior). A crystal structure of Nf Gα7 highlights the stability of its nucleotide-free state, consistent with its rapid nucleotide exchange. Variations in the phosphate binding loop also contribute to nucleotide cycling differences among Gα subunits. Similar to plant G protein signaling pathways, N. fowleri Gα subunits selectively engage members of a large seven-transmembrane RGS protein family, resulting in acceleration of GTP hydrolysis. We show Nf Gα2 and Gα3 directly interact with a candidate Gα effector protein, RGS-RhoGEF, similar to mammalian Gα_12/13 signaling pathways. We demonstrate Nf Gα2 and Gα3 each engage RGS-RhoGEF through a canonical Gα/RGS domain interface, suggesting a shared evolutionary origin with G protein signaling in the enteric pathogen Entamoeba histolytica. These findings further illuminate the evolution of G protein signaling and identify potential targets of pharmacological manipulation in N. fowleri.     

Geometrical Membrane Curvature as an Allosteric Regulator of Membrane Protein Structure and Function

Transmembrane proteins are embedded in cellular membranes of varied lipid composition and geometrical curvature. Here, we studied for the first time the allosteric effect of geometrical membrane curvature on transmembrane protein structure and function. We used single-channel optical analysis of the prototypic transmembrane β-barrel α-hemolysin (α-HL) reconstituted on immobilized single small unilamellar liposomes of different diameter and therefore curvature. Our data demonstrate that physiologically abundant geometrical membrane curvatures can enforce a dramatic allosteric regulation (1000-fold inhibition) of α-HL permeability. High membrane curvatures (1/diameter ∼1/40 nm⁻¹) compressed the effective pore diameter of α-HL from 14.2 ± 0.8 Å to 11.4 ± 0.6 Å. This reduction in effective pore area (∼40%) when combined with the area compressibility of α-HL revealed an effective membrane tension of ∼50 mN/m and a curvature-imposed protein deformation energy of ∼7 k_BT. Such substantial energies have been shown to conformationally activate, or unfold, β-barrel and α-helical transmembrane proteins, suggesting that membrane curvature could likely regulate allosterically the structure and function of transmembrane proteins in general.     

The Reovirus Mutant tsA279 L2 Gene Is Associated with Generation of a Spikeless Core Particle: Implications for Capsid Assembly

Previous studies which used intertypic reassortants of the wild-type reovirus serotype 1 Lang and the temperature-sensitive (ts) serotype 3 mutant clone tsA279 identified two ts lesions; one lesion, in the M2 gene segment, was associated with defective transmembrane transport of restrictively assembled virions (P. R. Hazelton and K. M. Coombs, Virology 207:46–58, 1995). In the present study we show that the second lesion, in the L2 gene segment, which encodes the λ2 protein, is associated with the accumulation of a core-like particle defective for the λ2 pentameric spike. Physicochemical, biochemical, and immunological studies showed that these structures were deficient for genomic double-stranded RNA, the core spike protein λ2, and the minor core protein μ2. Core particles with the λ2 spike structure accumulated after temperature shift-down from a restrictive to a permissive temperature in the presence of cycloheximide. These data suggest the spike-deficient, core-like particle is an assembly intermediate in reovirus morphogenesis. The existence of this naturally occurring primary core structure suggests that the core proteins λ1, λ3, and ς2 interact to initiate the process of virion capsid assembly through a dodecahedral mechanism. The next step in the proposed capsid assembly model would be the association of the minor core protein μ2, either preceding or collateral to the condensation of the λ2 pentameric spike at the apices of the primary core structure. The assembly pathway of the reovirus double capsid is further elaborated when these observations are combined with structures identified in other studies.     

Atomistic Modeling of Macromolecular Crowding Predicts Modest Increases in Protein Folding and Binding Stability

Theoretical models predict that macromolecular crowding can increase protein folding stability, but depending on details of the models (e.g., how the denatured state is represented), the level of stabilization predicted can be very different. In this study, we represented the native and denatured states atomistically, with conformations sampled from explicit-solvent molecular dynamics simulations at room temperature and high temperature, respectively. We then designed an efficient algorithm to calculate the allowed fraction, f, when the protein molecule is placed inside a box of crowders. That a fraction of placements of the protein molecule is disallowed because of volume exclusion by the crowders leads to an increase in chemical potential, given by Δμ = −k_BT lnf. The difference in Δμ between the native and denatured states predicts the effect of crowding on the folding free energy. Even when the crowders occupied 35% of the solution volume, the stabilization reached only 1.5 kcal/mol for cytochrome b₅₆₂. The modest stabilization predicted is consistent with experimental studies. Interestingly, a mixture of different sized crowders was found to exert a greater effect than the sum of the individual species of crowders. The stabilization of crowding on the binding stability of barnase and barstar, based on atomistic modeling of the proteins, was similarly modest. These findings have profound implications for macromolecular crowding inside cells.     

Simple Uniaxial and Uniform Biaxial Deformation of Nearly Isotropic Incompressible Tissues

A method is developed for analyzing in a unified manner both uniaxial and uniform biaxial strain data obtained from nearly isotropic tissues. The formulation is a direct application of nonlinear elasticity theory pertaining to large deformations. The general relation between Eulerian stress (σ) and extension ratio (λ) in soft isotropic elastic bodies undergoing uniform deformation takes the simple form: σ = ((λ³ - 1)/λ) f(λ), where f(λ) must be determined for each material. The extension ratio may be either greater than 1.0 (uniaxial elongation), or lie between zero and 1.0 (uniform biaxial extension). Simple analytical functions for f(λ) are most readily found for each tissue by plotting all data as (λ³ - 1)/λσ vs. λ. Of those tissues investigated in this way (dog pericardium and pleura, and cat mesentery and dura), all but pleura could be adequately described by a parabola: 1/f(λ) = 1/k{[(λ_M - λ)(λ - λ_m)]/[λ_M - λ_m}. In these instances, three material constants per tissue (K, λ_M, λ_m) served to predict approximately the stresses attained during both small and large deformations, in strips and sheets alike. It was further found that the uniaxial strain asymptote (λ_M) was linearly related to the biaxial strain asymptote (Λ_M), thus effectively reducing the number of constants by one.     

Probing the Average Local Structure of Biomolecules Using Small-Angle Scattering and Scaling Laws

Small-angle neutron and x-ray scattering have become invaluable tools for probing the nanostructure of molecules in solution. It was recently shown that the definite integral of the scattering profile exhibits a scaling (power-law) behavior with respect to molecular mass. We derive the origin of this relationship, and discuss how the integrated scattering profile can be used to identify differing levels of disorder over local ≲30 Å length scales. We apply our analysis to globular and intrinsically disordered proteins.     

RNA-binding specificity of E. coli NusA

The RNA sequences boxA, boxB and boxC constitute the nut regions of phage λ. They nucleate the formation of a termination-resistant RNA polymerase complex on the λ chromosome. The complex includes E. coli proteins NusA, NusB, NusG and NusE, and the λ N protein. A complex that includes the Nus proteins and other factors forms at the rrn leader. Whereas RNA-binding by NusB and NusE has been described in quantitative terms, the interaction of NusA with these RNA sequences is less defined. Isotropic as well as anisotropic fluorescence equilibrium titrations show that NusA binds only the nut spacer sequence between boxA and boxB. Thus, nutR boxA5-spacer, nutR boxA16-spacer and nutR boxA69-spacer retain NusA binding, whereas a spacer mutation eliminates complex formation. The affinity of NusA for nutL is 50% higher than for nutR. In contrast, rrn boxA, which includes an additional U residue, binds NusA in the absence of spacer. The K_d values obtained for rrn boxA and rrn boxA-spacer are 19-fold and 8-fold lower, respectively, than those for nutR boxA-spacer. These differences may explain why λ requires an additional protein, λ N, to suppress termination. Knowledge of the different affinities now describes the assembly of the anti-termination complex in quantitative terms.