Free energy of sickle hemoglobin polymerization: a scaled-particle treatment for use with dextran as a crowding agent

The Effect of Attractive Interactions and Macromolecular Crowding on Crystallins Association

In living systems proteins are typically found in crowded environments where their effective interactions strongly depend on the surrounding medium. Yet, their association and dissociation needs to be robustly controlled in order to enable biological function. Uncontrolled protein aggregation often causes disease. For instance, cataract is caused by the clustering of lens proteins, i.e., crystallins, resulting in enhanced light scattering and impaired vision or blindness. To investigate the molecular origins of cataract formation and to design efficient treatments, a better understanding of crystallin association in macromolecular crowded environment is needed. Here we present a theoretical study of simple coarse grained colloidal models to characterize the general features of how the association equilibrium of proteins depends on the magnitude of intermolecular attraction. By comparing the analytic results to the available experimental data on the osmotic pressure in crystallin solutions, we identify the effective parameters regimes applicable to crystallins. Moreover, the combination of two models allows us to predict that the number of binding sites on crystallin is small, i.e. one to three per protein, which is different from previous estimates. We further observe that the crowding factor is sensitive to the size asymmetry between the reactants and crowding agents, the shape of the protein clusters, and to small variations of intermolecular attraction. Our work may provide general guidelines on how to steer the protein interactions in order to control their association.

Wanted: scalable tracers for diffusion measurements

Scalable tracers are potentially a useful tool to examine diffusion mechanisms and to predict diffusion coefficients, particularly for hindered diffusion in complex, heterogeneous, or crowded systems. Scalable tracers are defined as a series of tracers varying in size but with the same shape, structure, surface chemistry, deformability, and diffusion mechanism. Both chemical homology and constant dynamics are required. In particular, branching must not vary with size, and there must be no transition between ordinary diffusion and reptation. Measurements using scalable tracers yield the mean diffusion coefficient as a function of size alone; measurements using nonscalable tracers yield the variation due to differences in the other properties. Candidate scalable tracers are discussed for two-dimensional (2D) diffusion in membranes and three-dimensional diffusion in aqueous solutions. Correlations to predict the mean diffusion coefficient of globular biomolecules from molecular mass are reviewed briefly. Specific suggestions for the 3D case include the use of synthetic dendrimers or random hyperbranched polymers instead of dextran and the use of core-shell quantum dots. Another useful tool would be a series of scalable tracers varying in deformability alone, prepared by varying the density of crosslinking in a polymer to make say "reinforced Ficoll" or "reinforced hyperbranched polyglycerol."

An FFT-based method for modeling protein folding and binding under crowding: benchmarking on ellipsoidal and all-atom crowders

It is now well recognized that macromolecular crowding can exert significant effects on protein folding and binding stability. In order to calculate such effects in direct simulations of proteins mixed with bystander macromolecules, the latter (referred to as crowders) are usually modeled as spheres and the proteins represented at a coarse-grained level. Our recently developed postprocessing approach allows the proteins to be represented at the all-atom level but, for computational efficiency, has only been implemented for spherical crowders. Modeling crowder molecules in cellular environments and in vitro experiments as spheres may distort their effects on protein stability. Here we present a new method that is capable for treating aspherical crowders. The idea, borrowed from protein-protein docking, is to calculate the excess chemical potential of the proteins in crowded solution by fast Fourier transform (FFT). As the first application, we studied the effects of ellipsoidal crowders on the folding and binding free energies of all-atom proteins, and found, in agreement with previous direct simulations with coarse-grained protein models, that the aspherical crowders exert greater stabilization effects than spherical crowders of the same volume. Moreover, as demonstrated here, the FFT-based method has the important property that its computational cost does not increase strongly even when the level of details in representing the crowders is increased all the way to all-atom, thus significantly accelerating realistic modeling of protein folding and binding in cell-like environments.

Contrasting factors on the kinetic path to protein complex formation diminish the effects of crowding agents

The crowded environment of cells poses a challenge for rapid protein-protein association. Yet, it has been established that the rates of association are similar in crowded and in dilute solutions. Here we probe the pathway leading to fast association between TEM1 β-lactamase and its inhibitor protein BLIP in crowded solutions. We show that the affinity of the encounter complex, the rate of final complex formation, and the structure of the transition state are similar in crowded solutions and in buffer. The experimental results were reproduced by calculations based on the transient-complex theory for protein association. Both experiments and calculations suggest that while crowding agents decrease the diffusion constant of the associating proteins, they also induce an effective excluded-volume attraction between them. The combination of the two opposing effects thus results in nearly identical overall association rates in diluted and crowded solutions.

The molecular refractive function of lens γ-Crystallins

γ-Crystallins constitute the major protein component in the nucleus of the vertebrate eye lens. Present at very high concentrations, they exhibit extreme solubility and thermodynamic stability to prevent scattering of light and formation of cataracts. However, functions beyond this structural role have remained mostly unclear. Here, we calculate molecular refractive index increments of crystallins. We show that all lens γ-crystallins have evolved a significantly elevated molecular refractive index increment, which is far above those of most proteins, including nonlens members of the βγ-crystallin family from different species. The same trait has evolved in parallel in crystallins of different phyla, including S-crystallins of cephalopods. A high refractive index increment can lower the crystallin concentration required to achieve a suitable refractive power of the lens and thereby reduce their propensity to aggregate and form cataracts. To produce a significant increase in the refractive index increment, a substantial global shift in amino acid composition is required, which can naturally explain the highly unusual amino acid composition of γ-crystallins and their functional homologues. This function provides a new perspective for interpreting their molecular structure.

The role of macromolecular crowding in the evolution of lens crystallins with high molecular refractive index

Crystallins are present in the lens at extremely high concentrations in order to provide transparency and generate a high refractive power of the lens. The crystallin families prevalent in the highest density lens tissues are γ-crystallins in vertebrates and S-crystallins in cephalopods. As shown elsewhere, in parallel evolution, both have evolved molecular refractive index increments 5-10% above those of most proteins. Although this is a small increase, it is statistically very significant and can be achieved only by very unusual amino acid compositions. In contrast, such a molecular adaptation to aid in the refractive function of the lens did not occur in crystallins that are preferentially located in lower density lens tissues, such as vertebrate α-crystallin and taxon-specific crystallins. In the current work, we apply a model of non-interacting hard spheres to examine the thermodynamic contributions of volume exclusion at lenticular protein concentrations. We show that the small concentration decrease afforded by the higher molecular refractive index increment of crystallins can amplify nonlinearly to produce order of magnitude differences in chemical activities, and lead to reduced osmotic pressure and the reduced propensity for protein aggregation. Quantitatively, this amplification sets in only at protein concentrations as high as those found in hard lenses or the nucleus of soft lenses, in good correspondence to the observed crystallin properties in different tissues and different species. This suggests that volume exclusion effects provide the evolutionary driving force for the unusual refractive properties and the unusual amino acid compositions of γ-crystallins and S-crystallins.

Power-law dependence of the melting temperature of ubiquitin on the volume fraction of macromolecular crowders

The dependence of the melting temperature increase (ΔT(m)) of the protein ubiquitin on the volume fraction (ϕ) of several commonly used macromolecular crowding agents (dextran 6, 40, and 70 and ficoll 70) was quantitatively examined and compared to a recently developed theoretical crowding model, i.e., ΔT(m) ∼ (R(g)∕R(c))(α)φ(α∕3). We found that in the current case this model correctly predicts the power-law dependence of ΔT(m) on φ but significantly overestimates the role of the size (i.e., R(c)) of the crowding agent. In addition, we found that for ubiquitin the exponent α is in the range of 4.1-6.5, suggesting that the relation of α=3∕(3ν-1) is a better choice for estimating α based on the Flory coefficient (ν) of the polypeptide chain. Taken together these findings highlight the importance of improving our knowledge and theoretical treatment of the microcompartmentalization of the commonly used model crowding agents.

Nonadditive effects of mixed crowding on protein stability

The crowded environments inside cells can have significant effects on the folding stability and other biophysical properties of proteins. In this study on how macromolecular crowding affects protein folding, we took a significant step toward realistically mimicking intracellular environments by using a mixture of two crowding agents, Ficoll and dextran. We found that the mixed crowding exerts a greater stabilizing effect than the sum of the two individual crowding agents. Therefore, the composition of crowders, not just the total concentration, has a significant influence on the effects of crowding on protein folding. Since the composition of intracellular macromolecules varies within the lifetime of a cell, our finding may provide an explanation for age being an important risk factor for protein aggregation-related diseases such as Alzheimer's disease and Parkinson's disease.

Effect of macromolecular crowding on protein binding stability: modest stabilization and significant biological consequences

Macromolecular crowding has long been known to significantly affect protein oligomerization, and yet no direct quantitative measurements appear to have been made of its effects on the binding free energy of the elemental step of adding a single subunit. Here, we report the effects of two crowding agents on the binding free energy of two subunits in the Escherichia coli polymerase III holoenzyme. The crowding agents are found, paradoxically, to have only a modest stabilizing effect, of the order of 1 kcal/mol, on the binding of the two subunits. Systematic variations in the level of stabilization with crowder size are nevertheless observed. The data are consistent with theoretical predictions based on atomistic modeling of excluded-volume interactions with crowders. We reconcile the apparent paradox presented by our data by noting that the modest effects of crowding on elemental binding steps are cumulative, and thus lead to substantial stabilization of higher oligomers. Correspondingly, the effects of small variations in the level of crowding during the lifetime of a cell may be magnified, suggesting that crowding may play a role in increased susceptibility to protein aggregation-related diseases with aging.

Crowding effects of membrane proteins

In cell membranes, membrane proteins occupy approximately 30% of the total surface area. Crowding effects similar to those in the solution phase are thus to be expected. In addition, there are crowding effects unique to proteins bound to the two-dimensional membranes, such as those exerted on the equilibration of a protein between two membrane orientations and on the redistribution of proteins between different locations in a cell membrane. This article aims to present a theoretical framework for understanding the various crowding effects within membranes. For illustration, the theory is used to analyze previously published experimental and simulation data. It is hoped that the article will encourage quantitative analyses in future experiments and spur systematic investigation of membrane crowding effects.

Macromolecular crowding improves polymer encapsulation within giant lipid vesicles

We report the effect of macromolecular crowding on encapsulation efficiency of fluorescently labeled poly(ethylene glycol) (PEG) and dextran polymers within individual giant lipid vesicles (GVs). Low concentrations of the fluorescently labeled polymers (82 nM to 186 pM) were mixed with varying concentrations of nonfluorescent polymers that served as crowding agents during vesicle formation by gentle hydration. Encapsulation efficiency of the fluorescently labeled polymers in individual GVs (EEind) was determined via confocal fluorescence microscopy. EEind for high molecular weight polymers (e.g., fluorescein isothiocyanate (FITC)-dextran 500 and 2000 kDa) increased substantially in the presence of several weight percent unlabeled PEG or dextran. For example, when 0.24 microM FITC dextran 500 kDa was encapsulated, addition of 3% PEG 8 kDa improved the mean concentration in the GVs from 0.14 microM (+/-50%) to 0.24 microM (+/-12%). Light scattering data indicate reduced hydrodynamic radii for polymers as a function of increasing polymer concentration, suggesting that the improvements in EEind result from polymer condensation due to macromolecular crowding. Polymeric cosolutes did not significantly impact EEind for lower molecular weight polymers (e.g., Alexa Fluor 488-PEG 20 kDa), which already encapsulated efficiently (EEind to approximately 1). However, for both the higher and lower molecular weight labeled polymers, cosolutes led to improved uniformity in EEind for vesicles within a batch. Methods for improving the value and homogeneity of EEind for polymeric solutes in lipid vesicles are important in a variety of applications, including the use of vesicles as microreactors and as vehicles for drug delivery.

The effects of macromolecular crowding on the mechanical stability of protein molecules

Macromolecular crowding, a common phenomenon in the cellular environments, can significantly affect the thermodynamic and kinetic properties of proteins. A single-molecule method based on atomic force microscopy (AFM) was used to investigate the effects of macromolecular crowding on the forces required to unfold individual protein molecules. It was found that the mechanical stability of ubiquitin molecules was enhanced by macromolecular crowding from added dextran molecules. The average unfolding force increased from 210 pN in the absence of dextran to 234 pN in the presence of 300 g/L dextran at a pulling speed of 0.25 microm/sec. A theoretical model, accounting for the effects of macromolecular crowding on the native and transition states of the protein molecule by applying the scaled-particle theory, was used to quantitatively explain the crowding-induced increase in the unfolding force. The experimental results and interpretation presented could have wide implications for the many proteins that experience mechanical stresses and perform mechanical functions in the crowded environment of the cell.