Effects of macromolecular crowding on biochemical reaction equilibria: a molecular thermodynamic perspective

A molecular thermodynamic model is developed to investigate the effects of macromolecular crowding on biochemical reactions. Three types of reactions, representing protein folding/conformational isomerization, coagulation/coalescence, and polymerization/association, are considered. The reactants, products, and crowders are modeled as coarse-grained spherical particles or as polymer chains, interacting through hard-sphere interactions with or without nonbonded square-well interactions, and the effects of crowder size and chain length as well as product size are examined. The results predicted by this model are consistent with experimentally observed crowding effects based on preferential binding or preferential exclusion of the crowders. Although simple hard-core excluded-volume arguments do in general predict the qualitative aspects of the crowding effects, the results show that other intermolecular interactions can substantially alter the extent of enhancement or reduction of the equilibrium and can even change the direction of the shift. An advantage of the approach presented here is that competing reactions can be incorporated within the model.     

Excluded volume in solvation: sensitivity of scaled-particle theory to solvent size and density

Changes in solvent environment greatly affect macromolecular structure and stability. To investigate the role of excluded volume in solvation, scaled-particle theory is often used to calculate delta G(tr)(ev), the excluded-volume portion of the solute transfer free energy, delta G(tr). The inputs to SPT are the solvent radii and molarities. Real molecules are not spheres. Hence, molecular radii are not uniquely defined and vary for any given species. Since delta G(tr)(ev) is extremely sensitive to solvent radii, uncertainty in these radii causes a large uncertainty in delta G(tr)(ev)-several kcal/mol for amino acid solutes transferring from water to aqueous mixtures. This uncertainty is larger than the experimental delta G(tr) values. Also, delta G(tr)(ev) can be either positive or negative. Adding neutral crowding molecules may not necessarily reduce solubility. Lastly, delta G(tr)(ev) is very sensitive to solvent density, rho. A few percent error in rho may even cause qualitative deviations in delta G(tr)(ev). For example, if rho is calculated by assuming the hard-sphere pressure to be constant, then delta G(tr)(ev) values and uncertainties are now only tenths of a kcal/mol and are positive. Because delta G(tr)(ev) values calculated by scaled-particle theory are strongly sensitive to solvent radii and densities, determining the excluded-volume contribution to transfer free energies using SPT may be problematic.     

Protein self-association induced by macromolecular crowding: a quantitative analysis by magnetic relaxation dispersion

In the presence of high concentrations of inert macromolecules, the self-association of proteins is strongly enhanced through an entropic, excluded-volume effect variously called macromolecular crowding or depletion attraction. Despite the predicted large magnitude of this universal effect and its far-reaching biological implications, few experimental studies of macromolecular crowding have been reported. Here, we introduce a powerful new technique, fast field-cycling magnetic relaxation dispersion, for investigating crowding effects on protein self-association equilibria. By recording the solvent proton spin relaxation rate over a wide range of magnetic field strengths, we determine the populations of coexisting monomers and decamers of bovine pancreatic trypsin inhibitor in the presence of dextran up to a macromolecular volume fraction of 27%. Already at a dextran volume fraction of 14%, we find a 30-fold increase of the decamer population and 510(5)-fold increase of the association constant. The analysis of these results, in terms of a statistical-mechanical model that incorporates polymer flexibility as well as the excluded volume of the protein, shows that the dramatic enhancement of bovine pancreatic trypsin inhibitor self-association can be quantitatively rationalized in terms of hard repulsive interactions.     

Effects of macromolecular crowding on the structural stability of human α-lactalbumin

The folding of protein, an important process for protein to fulfill normal functions, takes place in crowded physiological environments. α-Lactalbumin, as a model system for protein-folding studies, has been used extensively because it can form stable molten globule states under a range of conditions. Here we report that the crowding agents Ficoll 70, dextran 70, and polyethylene glycol (PEG) 2000 have different effects on the structural stability of human α-lactalbumin (HLA) represented by the transition to a molten globule state: dextran 70 dramatically enhances the thermal stability of Ca(2+)-depleted HLA (apo-HLA) and Ficoll 70 enhances the thermal stability of apo-HLA to some extent, while PEG 2000 significantly decreases the thermal stability of apo-HLA. Ficoll 70 and dextran 70 have no obvious effects on trypsin degradation of apo-HLA but PEG 2000 accelerates apo-HLA degradation by trypsin and destabilizes the native conformation of apo-HLA. Furthermore, no interaction is observed between apo-HLA and Ficoll 70 or dextran 70, but a weak, non-specific interaction between the apo form of the protein and PEG 2000 is detected, and such a weak, non-specific interaction could overcome the excluded-volume effect of PEG 2000. Our data are consistent with the results of protein stability studies in cells and suggest that stabilizing excluded-volume effects of crowding agents can be ameliorated by non-specific interactions between proteins and crowders.     

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.     

The activity coefficient of high density systems with hard-sphere interactions: the application of the IGCMC method

The inverse grand-canonical Monte Carlo (IGCMC) technique is used to calculate the activity coefficients of the following hard-sphere systems: one-component fluid, binary mixture and solvent primitive model (SPM) electrolyte. The calculations for a one-component fluid are performed at different densities. The components of a binary mixture differ in diameters (300 and 500 pm) with the results being presented for different density and composition of a mixture. For the SPM model, simulations are performed for a 1:1 electrolyte at different electrolyte concentrations at the packing fraction equal to 0.3. Ions and solvent molecules of the same or different sizes are considered. The results are compared with those reported by Adams (one-component fluid), with those calculated using the Ebeling and Scherwinski equation (one-component fluid and binary mixture) and with the predictions from the symmetric Poisson–Boltzmann theory and the mean spherical approximation (SPM electrolyte).     

Effects of crowding by mono-, di-, and tetrasaccharides on cytochrome c-cytochrome c peroxidase binding: comparing experiment to theory

In cells, protein-protein interactions occur in an environment that is crowded with other molecules, but in vitro studies are almost exclusively performed in dilute solution. To gain information about the effects of crowding on protein complex formation, we used isothermal titration calorimetry to measure the stoichiometry, the free energy change, and the enthalpy change for the binding of yeast iso-1-ferricytochrome c to yeast ferricytochrome c peroxidase in dilute solution and in solutions crowded with the sugars glucose, sucrose, and stachyose. The stoichiometry is 1:1 under all conditions. The sugars stabilize the complex, but by only 0.1-0.5 kcal.mol(-)(1), and the increased stability is not correlated with the change in enthalpy of complex formation. We then compared the measured stability changes to values obtained from several analyses that are currently used to predict crowding-induced changes in biomolecular equilibria. None of the analyses are completely successful by themselves, and the results suggest that a complete analysis must account for both excluded-volume and chemical interactions.     

Entropic stabilization of the folded states of RNA due to macromolecular crowding

We review the effects of macromolecular crowding on the folding of RNA by considering the simplest scenario when excluded volume interactions between crowding particles and RNA dominate. Using human telomerase enzyme as an example, we discuss how crowding can alter the equilibrium between pseudoknot and hairpin states of the same RNA molecule—a key aspect of crowder–RNA interactions. We summarize data showing that the crowding effect is significant only if the size of the spherical crowding particle is smaller than the radius of gyration of the RNA in the absence of crowding particles. The implication for function of the wild type and mutants of human telomerase is outlined by using a relationship between enzyme activity and its conformational equilibrium. In addition, we discuss the interplay between macromolecular crowding and ionic strength of the RNA buffer. Finally, we briefly review recent experiments which illustrate the connection between excluded volume due to macromolecular crowding and the thermodynamics of RNA folding.     

Noise-reduction through interaction in gene expression and biochemical reaction processes

We demonstrate that interaction in gene expression and biochemical reaction processes has a significant influence on reducing fluctuations. Especially, we have found that the interaction between synthesized proteins and background molecules can reduce the fluctuation level in gene expression, which is a counter example to the intuition that background factors disturb information processing in genetic networks by increasing the noise level. This fact also indicates that the macromolecular crowding observed in actual cells can contribute to reduce the noise level. In addition, the noise-reduction phenomenon is not limited to the interaction between the proteins and background molecules, but can be applied to other reactions such as a dimerization process and the coupling of reactions with large fluctuations by intrinsic noise. Finally, on the basis of these results, we propose a new and plausible method for reducing the fluctuations generated in synthesized genetic networks, and also discuss the applicability of this method to the stabilization of system dynamics by using a toggle switch model.     

Effects of macromolecular crowding agents on protein folding in vitro and in silico

Proteins fold and function inside cells which are environments very different from that of dilute buffer solutions most often used in traditional experiments. The crowded milieu results in excluded-volume effects, increased bulk viscosity and amplified chances for inter-molecular interactions. These environmental factors have not been accounted for in most mechanistic studies of protein folding executed during the last decades. The question thus arises as to how these effects—present when polypeptides normally fold in vivo—modulate protein biophysics. To address excluded volume effects, we use synthetic macromolecular crowding agents, which take up significant volume but do not interact with proteins, in combination with strategically selected proteins and a range of equilibrium and time-resolved biophysical (spectroscopic and computational) methods. In this review, we describe key observations on macromolecular crowding effects on protein stability, folding and structure drawn from combined in vitro and in silico studies. As expected based on Minton’s early predictions, many proteins (apoflavodoxin, VlsE, cytochrome c, and S16) became more thermodynamically stable (magnitude depends inversely on protein stability in buffer) and, unexpectedly, for apoflavodoxin and VlsE, the folded states changed both secondary structure content and, for VlsE, overall shape in the presence of macromolecular crowding. For apoflavodoxin and cytochrome c, which have complex kinetic folding mechanisms, excluded volume effects made the folding energy landscapes smoother (i.e., less misfolding and/or kinetic heterogeneity) than in buffer.     

Common Crowding Agents Have Only a Small Effect on Protein-Protein Interactions

Studies of protein-protein interactions, carried out in polymer solutions, are designed to mimic the crowded environment inside living cells. It was shown that crowding enhances oligomerization and polymerization of macromolecules. Conversely, we have shown that crowding has only a small effect on the rate of association of protein complexes. Here, we investigated the equilibrium effects of crowding on protein heterodimerization of TEM1-β-lactamase with β-lactamase inhibitor protein (BLIP) and barnase with barstar. We also contrasted these with the effect of crowding on the weak binding pair CyPet-YPet. We measured the association and dissociation rates as well as the affinities and thermodynamic parameters of these interactions in polyethylene glycol and dextran solutions. For TEM1-BLIP and for barnase-barstar, only a minor reduction in association rate constants compared to that expected based on solution viscosity was found. Dissociation rate constants showed similar levels of reduction. Overall, this resulted in a binding affinity that is quite similar to that in aqueous solutions. On the other hand, for the CyPet-YPet pair, aggregation, and not enhanced dimerization, was detected in polyethylene glycol solutions. The results suggest that typical crowding agents have only a small effect on specific protein-protein dimerization reactions. Although crowding in the cell results from proteins and other macromolecules, one may still speculate that binding in vivo is not very different from that measured in dilute solutions.     

Role of solvent properties of aqueous media in macromolecular crowding effects

Analysis of the macromolecular crowding effects in polymer solutions show that the excluded volume effect is not the only factor affecting the behavior of biomolecules in a crowded environment. The observed inconsistencies are commonly explained by the so-called soft interactions, such as electrostatic, hydrophobic, and van der Waals interactions, between the crowding agent and the protein, in addition to the hard nonspecific steric interactions. We suggest that the changes in the solvent properties of aqueous media induced by the crowding agents may be the root of these “soft” interactions. To check this hypothesis, the solvatochromic comparison method was used to determine the solvent dipolarity/polarizability, hydrogen-bond donor acidity, and hydrogen-bond acceptor basicity of aqueous solutions of different polymers (dextran, poly(ethylene glycol), Ficoll, Ucon, and polyvinylpyrrolidone) with the polymer concentration up to 40% typically used as crowding agents. Polymer-induced changes in these features were found to be polymer type and concentration specific, and, in case of polyethylene glycol (PEG), molecular mass specific. Similarly sized polymers PEG and Ucon producing different changes in the solvent properties of water in their solutions induced morphologically different α-synuclein aggregates. It is shown that the crowding effects of some polymers on protein refolding and stability reported in the literature can be quantitatively described in terms of the established solvent features of the media in these polymers solutions. These results indicate that the crowding agents do induce changes in solvent properties of aqueous media in crowded environment. Therefore, these changes should be taken into account for crowding effect analysis.     

Protein self-association in crowded protein solutions: a time-resolved fluorescence polarization study

The self-association equilibrium of a tracer protein, apomyoglobin (apoMb), in highly concentrated crowded solutions of ribonuclease A (RNase A) and human serum albumin (HSA), has been studied as a model system of protein interactions that occur in crowded macromolecular environments. The rotational diffusion of the tracer protein labeled with two different fluorescent dyes, 8-anilinonaphthalene-1-sulfonate and fluorescein isothiocyanate, was successfully recorded as a function of the two crowder concentrations in the 50-200 mg/mL range, using picosecond-resolved fluorescence anisotropy methods. It was found that apoMb molecules self-associate at high RNase A concentration to yield a flexible dimer. The apparent dimerization constant, which increases with RNase A concentration, could also be estimated from the fractional contribution of monomeric and dimeric species to the total fluorescence anisotropy of the samples. In contrast, an equivalent mass concentration of HSA does not result in tracer dimerization. This different effect of RNase A and HSA is much larger than that predicted from simple models based only on the free volume available to apoMb, indicating that additional, nonspecific interactions between tracer and crowder should come into play. The time-resolved fluorescence polarization methods described here are expected to be of general applicability to the detection and quantification of crowding effects in a variety of macromolecules of biological relevance.     

Comparison of the independent solvent structures of dimeric alpha-chymotrypsin with themselves and with gamma-chymotrypsin

The solvent structure of alpha-chymotrypsin has been determined in the restrained least squares refinement (1.67-A resolution) of the dimeric molecule (Blevins, R. A., and Tulinsky, A. (1985) J. Biol. Chem. 260, 4264-4275). A total of 247 water molecules reduced the R-factor by 0.039 to 0.179. The average occupancy of solvent is 0.77 and the average isotropic thermal parameter is 22 A2. About 80% of the solvent is around the surface, 10% is in the dimer interface, and 10% is interior. There are 49 pairs of water molecules related by 2-fold noncrystallographic symmetry (within 1.0 A) and 199 waters that can potentially hydrogen bond with protein or themselves. The specificity sites contain 5 water molecules, 2 of which are displaced by substrate binding. The remainder probably aid in identifying and positioning the latter for catalysis. Four of these waters also occur in gamma-chymotrypsin. Considering the water structure in the dimer interface region of alpha-chymotrypsin with that of gamma-chymotrypsin reveals that about two-thirds of the solvent in this region is lost on dimerization. Last, 4 of the water molecules of alpha-chymotrypsin have been identified to be sulfate ions from a difference map based on crystals with selenate exchanged mother liquor.     

An effective solvent theory connecting the underlying mechanisms of osmolytes and denaturants for protein stability

An all-atom Gō model of Trp-cage protein is simulated using discontinuous molecular dynamics in an explicit minimal solvent, using a single, contact-based interaction energy between protein and solvent particles. An effective denaturant or osmolyte solution can be constructed by making the interaction energy attractive or repulsive. A statistical mechanical equivalence is demonstrated between this effective solvent model and models in which proteins are immersed in solutions consisting of water and osmolytes or denaturants. Analysis of these studies yields the following conclusions: 1), Osmolytes impart extra stability to the protein by reducing the entropy of the unfolded state. 2), Unfolded states in the presence of osmolyte are more collapsed than in water. 3), The folding transition in osmolyte solutions tends to be less cooperative than in water, as determined by the ratio of van 't Hoff to calorimetric enthalpy changes. The decrease in cooperativity arises from an increase in native structure in the unfolded state, and thus a lower thermodynamic barrier at the transition midpoint. 4), Weak denaturants were observed to destabilize small proteins not by lowering the unfolded enthalpy, but primarily by swelling the unfolded state and raising its entropy. However, adding a strong denaturant destabilizes proteins enthalpically. 5), The folding transition in denaturant-containing solutions is more cooperative than in water. 6), Transfer to a concentrated osmolyte solution with purely hard-sphere steric repulsion significantly stabilizes the protein, due to excluded volume interactions not present in the canonical Tanford transfer model. 7), Although a solution with hard-sphere interactions adds a solvation barrier to native contacts, the folding is nevertheless less cooperative for reasons 1–3 above, because a hard-sphere solvent acts as a protecting osmolyte.     

Coarse-grained molecular simulation of diffusion and reaction kinetics in a crowded virtual cytoplasm

We present a general-purpose model for biomolecular simulations at the molecular level that incorporates stochasticity, spatial dependence, and volume exclusion, using diffusing and reacting particles with physical dimensions. To validate the model, we first established the formal relationship between the microscopic model parameters (timestep, move length, and reaction probabilities) and the macroscopic coefficients for diffusion and reaction rate. We then compared simulation results with Smoluchowski theory for diffusion-limited irreversible reactions and the best available approximation for diffusion-influenced reversible reactions. To simulate the volumetric effects of a crowded intracellular environment, we created a virtual cytoplasm composed of a heterogeneous population of particles diffusing at rates appropriate to their size. The particle-size distribution was estimated from the relative abundance, mass, and stoichiometries of protein complexes using an experimentally derived proteome catalog from Escherichia coli K12. Simulated diffusion constants exhibited anomalous behavior as a function of time and crowding. Although significant, the volumetric impact of crowding on diffusion cannot fully account for retarded protein mobility in vivo, suggesting that other biophysical factors are at play. The simulated effect of crowding on barnase-barstar dimerization, an experimentally characterized example of a bimolecular association reaction, reveals a biphasic time course, indicating that crowding exerts different effects over different timescales. These observations illustrate that quantitative realism in biosimulation will depend to some extent on mesoscale phenomena that are not currently well understood.     

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.     

Solute excluded-volume effects on the stability of globular proteins: A statistical thermodynamic theory

A statistical thermodynamic theory is developed to investigate the effects of solute excluded volume on the stability of globular proteins. Proteins are modeled as two states in chemical equilibrium: the denatured state is modeled as a flexible chain of tangent hard spheres (pearl-necklace chain) while the native state is modeled as a single hard sphere. Study of model proteins bovine pancreatic trypsin inhibitor and lysozyme in a McMillan-Mayer model solution of hard spheres indicates that the excluded volume of solutes has three distinct types of effects on protein stability: (1) small-size solutes strongly denature proteins, (2) medium-size solutes stabilize proteins at low solute concentrations and destabilize them at high concentrations, and (3) large-size solutes stabilize native-state proteins across the whole liquid region. The study also finds that increasing the chain length of hard-chain polymer solutes has an effect on protein stability that is similar to increasing the diameter of spherical solutes. This work qualitatively explains why stabilizers tend to be large size molecules such as sugars, polymers, polynols, nonionic, and anionic surfactants while denaturants tend to be small size molecules such as alcohols, glycols, amides, formamides, ureas, and guanidium salts. Quantitative comparison between theoretical predictions and experimental results for folding free energy changes shows that the excluded-volume effect is at least as important as the binding and/or electrostatic effects on solute-assisted protein-denaturation processes. Our theory may also be able to explain the effect of excluded volume on the Φ condensation of DNA. © 1996 John Wiley & Sons, Inc.     

Protein folding by the effects of macromolecular crowding

Unfolded states of ribonuclease A were used to investigate the effects of macromolecular crowding on macromolecular compactness and protein folding. The extent of protein folding and compactness were measured by circular dichroism spectroscopy, fluorescence correlation spectroscopy, and NMR spectroscopy in the presence of polyethylene glycol (PEG) or Ficoll as the crowding agent. The unfolded state of RNase A in a 2.4 M urea solution at pH 3.0 became native in conformation and compactness by the addition of 35% PEG 20000 or Ficoll 70. In addition, the effects of macromolecular crowding on inert macromolecule compactness were investigated by fluorescence correlation spectroscopy using Fluorescence-labeled PEG as a test macromolecule. The size of Fluorescence-labeled PEG decreased remarkably with an increase in the concentration of PEG 20000 or Ficoll 70. These results show that macromolecules are favored compact conformations in the presence of a high concentration of macromolecules and indicate the importance of a crowded environment for the folding and stabilization of globular proteins. Furthermore, the magnitude of the effects on macromolecular crowding by the different sizes of background molecules was investigated. RNase A and Fluorescence-labeled PEG did not become compact, and had folded conformation by the addition of PEG 200. The effect of the chemical potential on the compaction of a test molecule in relation to the relative sizes of the test and background molecules is also discussed.