Compression of random coils due to macromolecular crowding

Molecular Crowding: The History and Development of a Scientific Paradigm

It is now generally accepted that macromolecules do not act in isolation but "live" in a crowded environment, that is, an environment populated by numerous different molecules. The field of molecular crowding has its origins in the far 80s but became accepted only by the end of the 90s. In the present issue, we discuss various aspects that are influenced by crowding and need to consider its effects. This Review is meant as an introduction to the theme and an analysis of the evolution of the crowding concept through time from colloidal and polymer physics to a more biological perspective. We introduce themes that will be more thoroughly treated in other Reviews of the present issue. In our intentions, each Review may stand by itself, but the complete collection has the aspiration to provide different but complementary perspectives to propose a more holistic view of molecular crowding.

Influence of solvent quality on depletion potentials in colloid-polymer mixtures

As first explained by the classic Asakura-Oosawa (AO) model, effective attractive forces between colloidal particles induced by depletion of nonadsorbing polymers can drive demixing of colloid-polymer mixtures into colloid-rich and colloid-poor phases, with practical relevance for purification of water, stability of foods and pharmaceuticals, and macromolecular crowding in biological cells. By idealizing polymer coils as effective penetrable spheres, the AO model qualitatively captures the influence of polymer depletion on thermodynamic phase behavior of colloidal suspensions. In previous work, we extended the AO model to incorporate aspherical polymer conformations and showed that fluctuating shapes of random-walk coils can significantly modify depletion potentials [W. K. Lim and A. R. Denton, Soft Matter 12, 2247 (2016); J. Chem. Phys. 144, 024904 (2016)]. We further demonstrated that the shapes of polymers in crowded environments sensitively depend on solvent quality [W. J. Davis and A. R. Denton, J. Chem. Phys. 149, 124901 (2018)]. Here, we apply Monte Carlo simulation to analyze the influence of solvent quality on depletion potentials in mixtures of hard-sphere colloids and nonadsorbing polymer coils, modeled as ellipsoids whose principal radii fluctuate according to random-walk statistics. We consider both self-avoiding and non-self-avoiding random walks, corresponding to polymers in good and theta solvents, respectively. Our simulation results demonstrate that depletion of polymers of equal molecular weight induces much stronger attraction between colloids in good solvents than in theta solvents and confirm that depletion interactions are significantly influenced by aspherical polymer conformations.

On Protein Folding in Crowded Conditions

The interior of a cell is a highly packed environment that can be occupied up to 40% by different macromolecules. Such crowded media influence different biochemical processes like protein folding, enzymatic activity, and gene regulation. In this work, we use simulations to study protein stability under the presence of crowding agents that interact with the protein by excluded volume interactions. In general, the presence of crowding agents in the solution enhances the stability of the protein's native state. However, we find that the effects of excluded volume depend not only on crowding occupancy but also the crowders' geometry and size. Specifically, we find that polymeric crowders have stronger influence than spherical crowders and that this effect increases with polymer length, while it decreases with increasing size of spherical crowders. These opposing size effects are explained by the interplay of decreasing excluded volume and demixing, which together determine the change in the entropy of the crowders upon folding of the protein.

Quantitative characterization of the concentration-dependent interaction between molecules of Dextran 70 in aqueous solution: Measurement and analysis in the context of thermodynamic and compressible sphere models

The static light scattering and sedimentation equilibrium of solutions of Dextran 70 were measured as functions of concentration up to 100 g/L in pH 7.4 phosphate-buffered saline at temperatures between 5 and 37 °C. The concentration dependence of scattering intensity and the apparent molar mass obtained from sedimentation equilibrium were found to be nearly independent of temperature over this range to within the uncertainty of measurement. Global analysis of the concentration dependence of both properties yielded a reliable estimate of the concentration-dependent thermodynamic activity coefficient, a quantitative measure of the free energy of self-interaction. The self-interaction between Dextran molecules is compared with that of a globular protein (BSA) and a highly crosslinked polymer of similar molar mass (Ficoll 70). The observed concentration dependence of the free energy of Dextran self-interaction may be quantitatively accounted for by a semi-empirical model in which the polymer molecule is represented by a compressible sphere.

Macromolecular crowding effects in flexible polymer solutions

Biological environments are often “crowded” due to high concentrations (300–400[Formula: see text]g/L) of macromolecules. Computational modeling approaches like Molecular Dynamics (MD), rigid-body Brownian Dynamics and Monte Carlo simulations have recently emerged, which allow to study the effects macromolecular crowding at a microscopic level and to provide complementary information to experiments. Here, we use a recently introduced multiple-conformation Monte Carlo (mcMC) approach in order to study the influence of intermolecular interactions on the structural equilibrium of flexible polyethylene glycol (PEG) polymers under self-crowding conditions. The large conformational space accessible to PEG polymers allows us to evaluate the general applicability of the mcMC approach, which describes the intramolecular degrees of freedom by a finite-size ensemble of discrete conformations. Despite the simplicity of the approach, we show that influences of intermolecular interactions on the intramolecular free energy surface can be described qualitatively using mcMC. By varying the magnitude of distinct terms in the intermolecular potential, we can further study the compensating effects of repulsive and nonspecific attractive intermolecular interactions, which favor compact and extended polymer states, respectively. We use our simulation results to derive an analytical model that describes the effects of intermolecular interactions on the stability of PEG polymer conformations as a function of the radius of gyration and the corresponding solvent accessible surface. We use this model to confirm the role of molecular surfaces for attractive interactions that can counteract excluded volume effects. Extrapolation of the model further allows for the analysis of scenarios that are not easily accessible to direct simulations as described here.

Toward an understanding of biochemical equilibria within living cells

Four types of environmental effects that can affect macromolecular reactions in a living cell are defined: nonspecific intermolecular interactions, side reactions, partitioning between microenvironments, and surface interactions. Methods for investigating these interactions and their influence on target reactions in vitro are reviewed. Methods employed to characterize conformational and association equilibria in vivo are reviewed and difficulties in their interpretation cataloged. It is concluded that, in order to be amenable to unambiguous interpretation, in vivo studies must be complemented by in vitro studies carried out in well-characterized and controllable media designed to contain key elements of selected intracellular microenvironments.

The functional roles of the unstructured N- and C-terminal regions in αB-crystallin and other mammalian small heat-shock proteins

Small heat-shock proteins (sHsps), such as αB-crystallin, are one of the major classes of molecular chaperone proteins. In vivo, under conditions of cellular stress, sHsps are the principal defence proteins that prevent large-scale protein aggregation. Progress in determining the structure of sHsps has been significant recently, particularly in relation to the conserved, central and β-sheet structured α-crystallin domain (ACD). However, an understanding of the structure and functional roles of the N- and C-terminal flanking regions has proved elusive mainly because of their unstructured and dynamic nature. In this paper, we propose functional roles for both flanking regions, based around three properties: (i) they act in a localised crowding manner to regulate interactions with target proteins during chaperone action, (ii) they protect the ACD from deleterious amyloid fibril formation and (iii) the flexibility of these regions, particularly at the extreme C-terminus in mammalian sHsps, provides solubility for sHsps under chaperone and non-chaperone conditions. In the eye lens, these properties are highly relevant as the crystallin proteins, in particular the two sHsps αA- and αB-crystallin, are present at very high concentrations.

Protein Composition Determines the Effect of Crowding on the Properties of Disordered Proteins

Unlike dilute experimental conditions under which biological molecules are typically characterized, the cell interior is crowded by macromolecules, which affects both the thermodynamics and kinetics of in vivo processes. Although the excluded-volume effects of macromolecular crowding are expected to cause compaction of unfolded and disordered proteins, the extent of this effect is uncertain. We use a coarse-grained model to represent proteins with varying sequence content and directly observe changes in chain dimensions in the presence of purely repulsive spherical crowders. We find that the extent of crowding-induced compaction is dependent not only on crowder size and concentration, but also on the properties of the protein itself. In fact, we observe a nonmonotonic trend between the dimensions of the polypeptide chain in bulk and the degree of compaction: the most extended chains experience up to 24% compaction, the most compact chains show virtually no change, and intermediate chains compress by up to 40% in size at a 40% crowder volume fraction. Free-volume theory combined with an impenetrable ellipsoidal representation of the chains predicts the crowding effects only for collapsed protein chains. An additional scaling factor, which can be easily computed from protein-crowder potential of mean force, corrects for the penetrability of extended chains and is sufficient to capture the observed nonmonotonic trend in compaction.

Combining Diffusion NMR and Small-Angle Neutron Scattering Enables Precise Measurements of Polymer Chain Compression in a Crowded Environment

The effect of particles on the behavior of polymers in solution is important in a number of important phenomena such as the effect of "crowding" proteins in cells, colloid-polymer mixtures, and nanoparticle "fillers" in polymer solutions and melts. In this Letter, we study the effect of spherical inert nanoparticles (which we refer to as "crowders") on the diffusion coefficient and radius of gyration of polymers in solution using pulsed-field-gradient NMR and small-angle neutron scattering (SANS), respectively. The diffusion coefficients exhibit a plateau below a characteristic polymer concentration, which we identify as the overlap threshold concentration c^{⋆}. Above c^{⋆}, in a crossover region between the dilute and semidilute regimes, the (long-time) self-diffusion coefficients are found, universally, to decrease exponentially with polymer concentration at all crowder packing fractions, consistent with a structural basis for the long-time dynamics. The radius of gyration obtained from SANS in the crossover regime changes linearly with an increase in polymer concentration, and must be extrapolated to c^{⋆} in order to obtain the radius of gyration of an individual polymer chain. When the polymer radius of gyration and crowder size are comparable, the polymer size is very weakly affected by the presence of crowders, consistent with recent computer simulations. There is significant chain compression, however, when the crowder size is much smaller than the polymer radius gyration.

Tuning knot abundance in semiflexible chains with crowders of different sizes: a Monte Carlo study of DNA chains

We use stochastic simulation techniques to sample the conformational space of linear semiflexible polymers in a crowded medium and study how the knotting properties depend on the crowder size and concentration. The abundance of physical knots in the chains, which for definiteness we model on 10 kb long DNA filaments, is shown to have a non-monotonic, unimodal dependence on the colloid diameter, dc. The maximum incidence of knots occurs when dc is about equal to half of the gyration radius of the isolated chain. The degree of enhancement of knots grows rapidly with the solution density and can be very conspicuous relative to the case of isolated chains with no crowders. For instance, at 30% volume fraction the relative increase is more than fourfold. This dramatic enhancement is shown to originate from the depletion-induced chain compaction over multiple and concurring length scales. The same effect accounts for the variations of the knot length that accompany the changes in knotting probability. The findings suggest that crowded media could be viably used as a passive physical means for controlling and modulating the incidence and length of knots in DNA and other types of semiflexible polymers.

Concentrated Solutions of Single-Chain Nanoparticles: A Simple Model for Intrinsically Disordered Proteins under Crowding Conditions

By means of large-scale computer simulations and small-angle neutron scattering (SANS), we investigate solutions of single-chain nanoparticles (SCNPs), covering the whole concentration range from infinite dilution to melt density. The analysis of the conformational properties of the SCNPs reveals that these synthetic nano-objects share basic ingredients with intrinsically disordered proteins (IDPs), as topological polydispersity, generally sparse conformations, and locally compact domains. We investigate the role of the architecture of the SCNPs in their collapse behavior under macromolecular crowding. Unlike in the case of linear macromolecules, which experience the usual transition from self-avoiding to Gaussian random-walk conformations, crowding leads to collapsed conformations of SCNPs resembling those of crumpled globules. This behavior is already found at volume fractions (about 30%) that are characteristic of crowding in cellular environments. The simulation results are confirmed by the SANS experiments. Our results for SCNPs--a model system free of specific interactions--propose a general scenario for the effect of steric crowding on IDPs: collapse from sparse conformations at high dilution to crumpled globular conformations in cell environments.

Influence of polymer shape on depletion potentials and crowding in colloid-polymer mixtures

Depletion-induced interactions between colloids in colloid-polymer mixtures depend in range and strength on size, shape, and concentration of depletants. Crowding by colloids in turn affects shapes of polymer coils, such as biopolymers in biological cells. By simulating hard-sphere colloids and random-walk polymers, modeled as fluctuating ellipsoids, we compute depletion-induced potentials and polymer shape distributions. Comparing results with exact density-functional theory calculations, molecular simulations, and experiments, we show that polymer shape fluctuations play an important role in depletion and crowding phenomena.

Conformation of the Poly(ethylene Glycol) Chains in DiPEGylated Hemoglobin Specifically Probed by SANS: Correlation with PEG Length and in Vivo Efficiency

Cell-free hemoglobin (Hb)-based oxygen carriers have long been proposed as blood substitutes but their clinical use remains tricky due to problems of inefficiency and/or toxicity. Conjugation of Hb with the biocompatible polymer poly(ethylene glycol) (PEG) greatly improved their performance. However, physiological data suggested a polymer molecular weight (Mw) threshold of about 10 kDa, beyond which the grafting of two PEG chains no longer improves efficiency and nontoxicity of diPEG/Hb conjugates. We used small-angle neutron scattering and contrast variation, which are the only techniques able to probe separately the conformation of PEG chains and Hb protein within the complex, to investigate the role of PEG chain conformation in diPEGylated Hb conjugates as a function of the polymer Mw. We found out that the structure of Hb tetramer is not modified by the polymer grafting. Similarly, with a constant grafting of two chains per protein, there is no significant change of the Gaussian conformation between free and grafted PEG below ∼10 kDa, the complex being well described by the "dumbbell" model. However, beyond that threshold, the radius of gyration of grafted PEG is significantly smaller than that of the free polymer, showing a compaction of the PEG chains, either in the "dumbbell" model or in the "shroud" one. In the latter model, the polymer may be wrapped on the surface of the protein spreading a protective "shielding" effect over a larger fraction of the protein. Both proposed models are in good agreement with the physiological data reported in the literature.

Excluded-volume effects in living cells

Biomolecules evolve and function in densely crowded and highly heterogeneous cellular environments. Such conditions are often mimicked in the test tube by the addition of artificial macromolecular crowding agents. Still, it is unclear if such cosolutes indeed reflect the physicochemical properties of the cellular environment as the in-cell crowding effect has not yet been quantified. We have developed a macromolecular crowding sensor based on a FRET-labeled polymer to probe the macromolecular crowding effect inside single living cells. Surprisingly, we find that excluded-volume effects, although observed in the presence of artificial crowding agents, do not lead to a compression of the sensor in the cell. The average conformation of the sensor is similar to that in aqueous buffer solution and cell lysate. However, the in-cell crowding effect is distributed heterogeneously and changes significantly upon cell stress. We present a tool to systematically study the in-cell crowding effect as a modulator of biomolecular reactions.

Unusual size-dependence of effective interactions between collapsed polymers in crowded environments

We investigate the influence of macromolecular crowding on interactions between collapsed polymers using computer simulations, to gain insights into biomacromolecular interactions in crowded biological environments. The effective attraction is induced between two collapsed polymers due to the macromolecular crowding, and it is found that the strength of the effective attraction decreases as the crowder size is reduced for a fixed crowder volume fraction, which is sharply contrasted with the conventional viewpoint based on the depletion attraction observed for hard-core spherical colloids. This unusual trend of size-dependence is interpreted by dividing the effective interaction into the polymer-mediated repulsion and crowder-mediated attraction. It is found that the ranges of repulsive and attractive contributions overlap significantly due to the flexible nature of polymer boundaries, resulting in partial cancellation over this range which leads to the observed size-dependence. Thus, this work suggests that the effective interactions between biomacromolecules in crowded environments may be qualitatively different from the depletion interactions predicted for hard-core spherical colloids.

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 (2)H, 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.

Macromolecular crowding as a suppressor of human IAPP fibril formation and cytotoxicity

The biological cell is known to exhibit a highly crowded milieu, which significantly influences protein aggregation and association processes. As several cell degenerative diseases are related to the self-association and fibrillation of amyloidogenic peptides, understanding of the impact of macromolecular crowding on these processes is of high biomedical importance. It is further of particular relevance as most in vitro studies on amyloid aggregation have been performed in diluted solution which does not reflect the complexity of their cellular surrounding. The study presented here focuses on the self-association of the type-2 diabetes mellitus related human islet amyloid polypeptide (hIAPP) in various crowded environments including network-forming macromolecular crowding reagents and protein crowders. It was possible to identify two competing processes: a crowder concentration and type dependent stabilization of globular off-pathway species and a--consequently--retarded or even inhibited hIAPP fibrillation reaction. The cause of these crowding effects was revealed to be mainly excluded volume in the polymeric crowders, whereas non-specific interactions seem to be most dominant in protein crowded environments. Specific hIAPP cytotoxicity assays on pancreatic β-cells reveal non-toxicity for the stabilized globular species, in contrast to the high cytotoxicity imposed by the normal fibrillation pathway. From these findings it can be concluded that cellular crowding is able to effectively stabilize the monomeric conformation of hIAPP, hence enabling the conduction of its normal physiological function and prevent this highly amyloidogenic peptide from cytotoxic aggregation and fibrillation.

Effect of molecular crowding on the temperature-pressure stability diagram of ribonuclease A

FT-IR spectroscopic and thermodynamic measurements were designed to explore the effect of a macromolecular crowder, dextran, on the temperature and pressure-dependent phase diagram of the protein Ribonuclease A (RNase A), and we compare the experimental data with approximate theoretical predictions based on configuration entropy. Exploring the crowding effect on the pressure-induced unfolding of proteins provides insight in protein stability and folding under cell-like dense conditions, since pressure is a fundamental thermodynamic variable linked to molecular volume. Moreover, these studies are of relevance for understanding protein stability in deep-sea organisms, which have to cope with pressures in the kbar range. We found that not only temperature-induced equilibrium unfolding of RNase A, but also unfolding induced by pressure is markedly prohibited in the crowded dextran solutions, suggesting that crowded environments such as those found intracellularly, will also oppress high-pressure protein unfolding. The FT-IR spectroscopic measurements revealed a marked increase in unfolding pressure of 2 kbar in the presence of 30 wt % dextran. Whereas the structural changes upon thermal unfolding of the protein are not significantly influenced in the presence of the crowding agent, through stabilization by dextran the pressure-unfolded state of the protein retains more ordered secondary structure elements, which seems to be a manifestation of the entropic destabilization of the unfolded state by crowding.

How random are intrinsically disordered proteins? A small angle scattering perspective

While the crucial role of intrinsically disordered proteins (IDPs) in the cell cycle is now recognized, deciphering their molecular mode of action at the structural level still remains highly challenging and requires a combination of many biophysical approaches. Among them, small angle X-ray scattering (SAXS) has been extremely successful in the last decade and has become an indispensable technique for addressing many of the fundamental questions regarding the activities of IDPs. After introducing some experimental issues specific to IDPs and in relation to the latest technical developments, this article presents the interest of the theory of polymer physics to evaluate the flexibility of fully disordered proteins. The different strategies to obtain 3-dimensional models of IDPs, free in solution and associated in a complex, are then reviewed. Indeed, recent computational advances have made it possible to readily extract maximum information from the scattering curve with a special emphasis on highly flexible systems, such as multidomain proteins and IDPs. Furthermore, integrated computational approaches now enable the generation of ensembles of conformers to translate the unique flexible characteristics of IDPs by taking into consideration the constraints of more and more various complementary experiment. In particular, a combination of SAXS with high-resolution techniques, such as x-ray crystallography and NMR, allows us to provide reliable models and to gain unique structural insights about the protein over multiple structural scales. The latest neutron scattering experiments also promise new advances in the study of the conformational changes of macromolecules involving more complex systems.

Polymersomes in "gelly" polymersomes: toward structural cell mimicry

We demonstrate here the formation of compartmentalized polymersomes with an internal "gelly" cavity using an original and versatile process. Nanosize polymersomes of poly(trimethylene carbonate)-b-poly(L-glutamic acid) (PTMC-b-PGA), formed by a solvent displacement method are encapsulated with a rough "cytoplasm mimic" in giant polymersomes of poly(butadiene)-b-poly(ethylene oxide) PB-b-PEO by emulsion-centrifugation. Such a system constitutes a first step toward the challenge of structural cell mimicry with both "organelles" and "cytoplasm mimics". The structure is demonstrated with fluorescence labeling and confocal microscopy imaging with movies featuring the motion of the inner nanosize polymersomes in larger vesicles. Without "cytoplasm mimic", the motion was confirmed to be Brownian by particle tracking analysis. The inner nanosize polymersomes motion was blocked in the presence of alginate, but only hindered in the presence of dextran. With the use of such high molecular weight and concentrated polysaccharides, the crowded internal volume of cells, responsible for the so-called "macromolecular crowding" effect influencing every intracellular macromolecular association, seems to be efficiently mimicked. This study constitutes major progress in the field of structural biomimicry and will certainly enable the rise of new, highly interesting properties in the field of high-added value soft matter.

Crowding of polymer coils and demixing in nanoparticle-polymer mixtures

The Asakura-Oosawa-Vrij (AOV) model of colloid-polymer mixtures idealises nonadsorbing polymers as effective spheres that are fixed in size and impenetrable to hard particles. Real polymer coils, however, are intrinsically polydisperse in size (radius of gyration) and may be penetrated by smaller particles. Crowding by nanoparticles can affect the size distribution of polymer coils, thereby modifying effective depletion interactions and thermodynamic stability. To analyse the influence of crowding on polymer conformations and demixing phase behaviour, we adapt the AOV model to mixtures of nanoparticles and ideal, penetrable polymer coils that can vary in size. We perform Gibbs ensemble Monte Carlo simulations, including trial nanoparticle-polymer overlaps and variations in the radius of gyration. Results are compared with predictions of free-volume theory. Simulation and theory consistently predict that ideal polymers are compressed by nanoparticles, and that compressibility and penetrability stabilise nanoparticle-polymer mixtures.

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 D(2)O 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.

Molecular crowding stabilizes folded RNA structure by the excluded volume effect

Crowder molecules in solution alter the equilibrium between folded and unfolded states of biological macromolecules. It is therefore critical to account for the influence of these other molecules when describing the folding of RNA inside the cell. Small angle X-ray scattering experiments are reported on a 64 kDa bacterial group I ribozyme in the presence of polyethylene-glycol 1000 (PEG-1000), a molecular crowder with an average molecular weight of 1000 Da. In agreement with expected excluded volume effects, PEG favors more compact RNA structures. First, the transition from the unfolded to the folded (more compact) state occurs at lower MgCl(2) concentrations in PEG. Second, the radius of gyration of the unfolded RNA decreases from 76 to 64 A as the PEG concentration increases from 0 to 20% wt/vol. Changes to water and ion activities were measured experimentally, and theoretical models were used to evaluate the excluded volume. We conclude that the dominant influence of the PEG crowder on the folding process is the excluded volume effect.

Dependence of protein folding stability and dynamics on the density and composition of macromolecular crowders

We investigate the effect of macromolecular crowding on protein folding, using purely repulsive crowding particles and a self-organizing polymer model of protein folding. We find that the variation in folding stability with crowder size for typical alpha-, beta-, and alpha/beta-proteins is well described by an adaptation of the scaled particle theory. The native state, the transition state, and the unfolded protein are treated as effective hard spheres, with the folded and transition state radii independent of the size and concentration of the crowders. Remarkably, we find that, as the effective unfolded state radius is very weakly dependent on the crowder concentration, it can also be approximated by a single size. The same model predicts the effect of crowding on the folding barrier and therefore refolding rates with no adjustable parameters. A simple extension of the scaled-particle theory model, assuming additivity, can also describe the behavior of mixtures of crowding particles.

Compression of random coils due to macromolecular crowding: scaling effects

The addition of a macromolecular crowding agent to a dilute solution of polymer exerts a compressive force that tends to reduce the size of the chain. We study here the effect of changing the size ratio between the random coil and the crowding agent. The compression occurs at lower crowding agent concentration, Φ when polymer molecular weight increases. The Flory exponent ν(Φ) decreases from ν(0)≃0.48 in water down to 0.3 with macromolecular crowding. The effective polymer-polymer interactions change from repulsive to strongly attractive inducing aggregation of the chains. This effect changes drastically for larger polymer sizes, being much more pronounced at high molecular weights.