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Annu Rev Biophys. Author manuscript; available in PMC Feb 22, 2010.
Published in final edited form as:
PMCID: PMC2826134
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Macromolecular crowding and confinement: biochemical, biophysical, and potential physiological consequences*

Abstract

Expected and observed effects of volume exclusion on the free energy of rigid and flexible macromolecules in crowded and confined systems, and consequent effects of crowding and confinement on macromolecular reaction rates and equilibria are summarized. Findings from relevant theoretical/simulation and experimental literature published from 2004 onward are reviewed. Additional complexity arising from the heterogeneity of local environments in biological media, and the presence of nonspecific interactions between macromolecules over and above steric repulsion are discussed. Theoretical and experimental approaches to the characterization of crowding- and confinement-induced effects in systems approaching the complexity of living organisms are suggested.

Keywords: excluded volume, configurational entropy, free energy, protein-protein interactions, macromolecular associations, protein folding, site-binding

Introduction

It is now widely appreciated that almost all proteins and other biological macromolecules in vivo exist, at least transiently, as components of structural and functional complexes (3). The number of published studies of macromolecular interactions has increased almost exponentially for the last 20 years and amounts to several hundred a year at present. However, almost all of these studies are aimed at the characterization of attractive interactions that result in the formation of protein complexes or complexes of protein and other macromolecules (e.g. ribonucleoproteins). In contrast, repulsive interactions between macromolecules, by definition, do not lead to the formation of complexes and thus may not be observed directly. However, the presence and significance of repulsive interactions in fluid media containing a high total concentration of macromolecules and/or structural obstacles to the free motion of macromolecules may be observed indirectly through their effects upon a variety of macromolecular reactions involving association and conformational isomerization (49, 52). Many of these effects may be predicted qualitatively (and sometimes quantitatively) using simple statistical-thermodynamic models, and observed experimentally by measurement of the dependence of thermodynamically-based solution properties and reaction kinetics and equilibria upon the concentration and composition of macromolecular co-solutes that are nominally inert with respect to the reaction of interest. The importance of excluded volume interactions lies in their generality. Such interactions are universal and entirely nonspecific, and have the potential to significantly modulate the kinetics and equilibria of a large number of macromolecular reactions taking place in physiological fluid media.

We shall classify an excluded volume effect according to its origin: macromolecular crowding refers to effects of volume exclusion by one soluble macromolecule to another, and macromolecular confinement refers to effects of volume exclusion by a fixed (or confining) boundary to a soluble macromolecule. A number of reviews of both crowding and confinement effects have appeared during the past five years (19, 27, 55, 57, 71, 89, 92, 93) and it is not our intention to recapitulate published material. Moreover, a separate review of the effect of crowding on macromolecular transport via diffusion appears elsewhere in the present volume. However, in the interest of completeness, in the following section we briefly summarize the various ways that crowding and confinement are expected to influence the equilibria and kinetics of macromolecular associations and isomerizations. Next, results of recently published (2004–2007) theoretical contributions, atomistic simulations, and experiments relating to effects of macromolecular crowding and confinement upon a variety of macromolecular reactions are summarized. (References to work published prior to 2004 may be found in one or more of the reviews cited above.). The present review concludes with discussions of several topics related to the applicability of theoretical predictions or the results of experiments conducted in vitro to actual macromolecular processes taking place in living organisms.

A common thermodynamic framework for analysis of macromolecular crowding and confinement

General features of macromolecular crowding and confinement are qualitatively exhibited by their effects upon three prototypical macromolecular reactions:

Bimolecular association

A+B=AB
(I)

Association of a soluble macromolecular ligand with a specific surface binding site

L+Site=L.Site
(II)

Two-state folding of a protein

U=N
(III)

These three reactions are characterized respectively by three standard free energy changes and the corresponding equilibrium constants:

ΔFAB=RTlnKABΔFLS=RTlnKLSΔFUN=RTlnKUN

where R denotes the molar gas constant and T the absolute temperature. The effect of an environmental perturbation such as crowding or confinement upon the equilibrium state of a particular chemical reaction may be analyzed by constructing a simple thermodynamic cycle as shown in Figures 1A–C and Figures 2A–C. The value of standard free energy changes and equilibrium constants for a particular reaction in bulk dilute solution is denoted by the superscript ‘0’, e.g., ΔFAB0,KAB0. Then the free energy of hetero-association, site binding, and unfolding in the bulk and perturbed environments (either crowded or confined) will be related by (57)

Figure 1Figure 1Figure 1
Thermodynamic cycles illustrating linkage between free energy of transfer of reactants and products from dilute solution to crowded medium and standard free energy of (A) association in solution, (B) site-binding, and (C) two-state folding of a protein. ...
Figure 2Figure 2Figure 2
Thermodynamic cycles illustrating linkage between free energy of transfer of reactants and products from dilute solution to confined volume element and standard free energy of (A) association in solution, (B) site-binding, and (C) two-state folding of ...

ΔΔFABΔFABΔFABo=ΔFABCΔFACΔFBC
(1)

ΔΔFLSΔFLSΔFLSo=ΔFLSCΔFLC
(2)

and

ΔΔFUNΔFUNΔFUNo=ΔFNCΔFUC
(3)

where ΔFXC denotes the standard free energy change associated with the transfer of X from bulk solution to the crowded or confined environment as indicated in Figures 1 and and2.2. [Footnote 1] [Footnote 2] Free energy changes (on a per mole basis) are related to changes in the corresponding equilibrium constant by

KX=KX0exp(ΔΔFX/RT)
(4)

where X denotes AB, LS or UN. The magnitude of the effect of crowding or confinement upon a particular reaction equilibrium may thus be evaluated indirectly by comparing the free energies of transfer of reactants and products from bulk solution to the crowded or confined medium. Examples of such estimates are provided below. [Footnote 3] In these examples, we focus on the excluded volume aspect of crowding and confinement, because this effect appears to be universal. Other nonspecific interactions of reactants with crowders and confining walls will be discussed later.

Crowding

Estimation of ΔFXcrowd

The colligative properties of concentrated solutions of globular proteins, under conditions such that long range interactions between protein molecules are damped out, are well described by models in which individual macromolecular species are represented by hard convex particles that resemble the molecules in general size and shape (50, 58), justifying the use of hard particle models for quantitative estimation of excluded volume effects. The free energy of transfer of a macromolecule X from a dilute solution to a solution containing an arbitrary concentration of other macromolecules of the same or other species is then equivalent to the free energy of creating a cavity in the solution, free of any part of another molecule, that is large enough to accommodates the newly introduced macromolecule (43). The scaled particle theory (SPT) of hard particle fluids, originally due to Reiss et al (68), was devised specifically to calculate the free energy of cavity formation, and is thus particularly appropriate for numerical estimation of the magnitude of crowding effects. Let us consider as an example a fluid containing a volume fraction [var phi] of inert hard spherical particles with radius rc. According to SPT (14, 70) the free energy or work of placing into this fluid a spherocylinder (sc), that is, a right circular cylinder capped on each end by a hemisphere, with a radius rsc = Rscrc and a cylindrical length of 2Lrsc, is given by

ΔFSCcrowd/RT=ln(1φ)+A1Q+A2Q2+A3Q3
(5)

where

Q=φ/(1φ)A1=Rsc3+3Rsc2+3Rsc+1.5L(Rsc2+2Rsc+1)A2=1.5(2Rsc3+3Rsc2)+4.5L(Rsc2+Rsc)A3=3Rsc3+4.5LRsc2

Note that the free energy of transfer of a spherical particle into this fluid is just the special case of equation (5) with L = 0.

Association equilibria (Fig 1A)

Consider a bimolecular association reaction (I) taking place in a solution of spherical crowding molecules. For illustration, let monomeric A and B be represented as identical hard spherical particles with radius equal to that of crowder (i.e., Rsc = R1 = 1, L = L1 = 0). The dimer AB is represented as a spherocylindrical particle with volume equal to twice that of monomer, but with L = L2 and Rsc = R2 simultaneously adjustable to maintain constant volume, to illustrate the effect of different assumed shapes for dimer. Results obtained using equations (1), (4), and (5) are plotted in Figure 3. It is evident that crowding can substantially enhance the equilibrium tendency of A and B to dimerize when AB is compact (L2 ≤ 1), but can also inhibit dimerization when the dimer is so aspherical that it excludes more volume to crowder than two monomers. Many proteins can also form higher order oligomers. The effect of crowding upon the equilibrium constant for concerted association of n monomers to 1 n-mer increases dramatically with the value of n (49).

Figure 3
Effect of volume fraction [var phi] of hard sphere crowders upon equilibrium constant for association of two spherical monomers with R1 = 1 to form a spherocylindrical dimer with twice the volume, and (a) L2 = 0, R2 = 1.26 (spherical dimer); (b) L2 = ...

Association rates

The rate constant of association between two molecules can generally be written as (51, 91)

ka=kDkreactkD+kreact
(6)

where kD is the rate constant under diffusion control and kreact is the rate constant under reaction or transition-state control. Crowding affects the rate constant in the two regimes differently. kD is proportional to the relative diffusion constant of the two reactants. Increased crowding is expected to monotonically decrease the diffusion constant and thus acts to decrease kD. At the same time crowding also induces an attractive interaction between the reactants, manifesting itself in the enhanced dimerization noted earlier, which acts to partially compensate for the decrease in kD due to the decrease in diffusion coefficient (88). However, the overall effect is such that generally kD is expected to decrease with increased crowding (51).

In the reaction- or transition-state controlled regime, the rate constant is dictated by the energy barrier arising from conformational changes necessary before forming the transition-state complex. Because the transition state for association in solution is generally nearly as compact as product complex, crowding is expected to effectively lower the energy barrier and thus increase the association rate constant by a factor that is close to the factor for increase of the equilibrium association constant. Correspondingly, a small effect of crowding on the dissociation rate constant is expected (54). Since fast associations are typically under diffusion control and slow associations under reaction control (4), crowding is generally expected to slow fast associations and accelerate slow associations (51).

Site-binding equilibria (Fig 1B)

To illustrate the effect of crowding on a site-binding reaction (II), let the free ligand be represented as a hard spherical particle (L = 0) with radius Rsc times that of a hard spherical crowder. When the bound ligand is buried and thus inaccessible to crowders, crowding affects only the free energy of free ligand (i.e., ΔFLScrowd=0). [Footnote 4]. Results obtained using equations (2), (4), and (5) are plotted in Figure 4, and it is evident that site-binding can be significantly more enhanced by crowding effects than simple bimolecular association in solution. The same approximation may also be used to analyze the effect of crowding on protein solubility, which is modeled by assuming that crowding affects protein in the supernatant solution, but not in the condensed phase (42, 49).

Figure 4
Effect of volume fraction [var phi] of hard sphere crowders upon equilibrium constant for binding of a spherical macromolecular ligand to an immobile surface site. MWligand/MWcrowder = 2 (curve a), 1 (curve b), and 0.5 (curve c).

Two-state protein folding equilibria (Fig 1C)

The presence of crowder will influence equilibria between conformational states of a macromolecule in favor of conformations that exclude less volume to crowder. In the case of protein folding, unfolded conformations are more expanded and thus crowding is expected to favor the native state. However, the use of the hard particle model to estimate ΔFUcrowd is unreliable, as the U state consists of a manifold of conformations instead of a single rigid conformation. Thus the extent to which crowding is predicted to stabilize the native state varies substantially between different models for the unfolded state (see following section for examples).

Two-state folding rates

The rate constant for isomerization can be generally written as

k=k0exp(ΔF/RT)
(7)

where ΔF is the activation free energy (i.e., free energy difference between the transition state and the reactant state) and the pre-factor k0 depends on the dynamics of the isomerization process. Crowding can in principle affect both ΔF and k0. For example, if the transition state is more compact than the reactant state, as in the case of two-state protein folding, then crowding is expected to reduce ΔF. If intra-chain diffusion plays a significant role, crowding may act to reduce the rate of intra-chain diffusion and hence the value of k0 as well (see review of relevant literature below). When the transition state is more expanded than the reactant state, as in the case of protein unfolding, crowding is expected to decrease the rate constant.

Confinement

Estimation of ΔFXconfine

Consider a molecule X within a unit volume of bulk solution, which can exist in a finite number of configurational states, each of which is specified by a set of positional coordinates denoted by r and a set of orientational coordinates denoted by θ. The free energy of transferring the molecule X from this volume to an equal volume of solution that may be bounded by hard walls in one, two, or three dimensions is given by the statistical-thermodynamic expression (23)

ΔFXconfine=RTln(alloweddθdralldθdr)
(8)

Where the multiple integral in the denominator is taken over all configurational states accessible in bulk solution, and the multiple integral in the numerator is taken over all allowed configurational states in the bounded volume, that is, all states in which no part of X intersects any hard wall boundary.

While both confinement and crowding effects result from the reduction in possible configurations available to a macromolecule due to the presence of a high volume fraction of other macromolecules or static barriers to movement, there is one major qualitative difference between the two phenomena. In contrast to the free energy cost of crowding, the free energy cost of confinement is not necessarily minimal for the molecular conformation that is globally the most compact in the sense of having the smallest radius of gyration. Rather, confinement favors conformations having a shape that is complementary to the shape of the confining volume. For example, while a spherical conformation may be favored in a quasi-spherical cavity, the preferred conformation in a cylindrical pore may be rod-like, and the preferred conformation in a planar pore (bounded by two parallel hard walls) may be plate-like. Thus numerical estimates of the magnitude of confinement effects are extremely sensitive to the choice of models for the structure of both confining space and confined macromolecular species (52).

Association equilibria (Fig. 2A)

Model calculations of the effect of confinement in differently shaped pores upon the association of two spherical monomers of identical size to form a dimer of twice the volume and varying shapes, suggest that confinement has a small effect on bimolecular association, and is expected to increase the equilibrium constant for bimolecular association by at most a factor of two or three. However, the effect of confinement upon association constants for concerted formation of larger n-mers having a shape compatible with the shape of the confining volume increases strongly as the value of n increases (52).

Site binding equilibria (Fig. 2B)

If the bound ligand is completely immobile, then confinement affects only the free energy of the free ligand (i.e., ΔFLSconfine=0). As a simple example, consider a spherical ligand with radius a confined in a spherical cavity with radius Rcavity. The change in the site binding constant due to ligand confinement may be calculated from equation (2), (4), and (8) to be

KLS/KLS0=(1aRcavity)3
(9)

When a = 0.5Rcavity, the binding constant is increased by a factor of 8.

Two-state protein folding equilibria (Fig 2C)

It is evident upon inspection of Fig 2C that the free energy cost of confining any partially or fully unfolded conformation of a protein will be greater than the cost of confining the native state, and that confinement must stabilize the native state relative to any unfolded state. As pointed out previously when summarizing the effects of crowding on protein folding, numerical estimates of the magnitude of the effect of confinement will be quite sensitive to the nature of approximations made in treating the effect of confinement on the (average) unfolded state. Zhou and Dill (90) presented a simple model in which the unfolded state is modeled as a random walk with a specified radius of gyration. They then estimated the value of ΔFUconfine associated with the placement of U into a variety of confining geometries. Some of their results are plotted in Figure 5. According to this model, confinement is predicted to decrease the value ΔFUN by as much as 20 – 30 RT in very small cavities with a volume only slightly greater than that of the native state. This result makes intuitive sense. In such small cavities it is essentially impossible for proteins to unfold, as there is no space available for proteins to unfold into. By modeling the transition state for protein folding as a sphere with a somewhat larger radius than that of the folded state, a different but conceptually related model (28) has been used to estimate the change in the energy barrier for folding, and calculate the dependence of folding rate on the size of the confining cavity. A maximum acceleration in folding by tuning the cavity size is predicted.

Figure 5
Effect of confinement in a spherical cavity upon the free energy of two-state folding, calculated as a function of cavity radius according to the theory of Zhou and Dill (90), for proteins containing N = 100 residues (a) and 200 residues (b). Vertical ...

In conclusion, it should be noted that enhancement of association and site binding equilibria by confinement only occurs when the confined macromolecules are truly confined, i.e., they cannot equilibrate with bulk solution. When protein can equilibrate between a pore and bulk solution the extent of association resulting in the formation of oligomers in the pore is less than in the bulk, and the extent of site binding in the pore equal to that in the bulk (52).

Review of theoretical/simulation literature since 2004

Most of the effects summarized in the preceding section can be predicted on the basis of simple statistical-thermodynamic models. These models have the advantage that they are focused on specific aspects of crowding and confinement, are intuitive, and their results can often be expressed in the form of reasonably simple analytical expressions.

On the other hand, they do not allow for the exploration of complexities associated with crowding and confinement of real macromolecules by other real macromolecules. A complementary theoretical approach is by atomistic simulations. However, one needs to remain cognizant of the fact that the systems being studied via simulation are still models instead of the “real thing”; not all idiosyncratic details of the model systems are of general value for understanding the real systems. For computational efficiency, in most of the atomistic simulation studies, amino acid residues were modeled by a pseudo-atom representing Cα with or without a second pseudo-atom representing the side-chain, and solvent was not treated explicitly.

Effects of crowding on protein folding

Zhou (94) considered the effect of crowding on the free energy of the unfolded state by treating the unfolded protein as a three-dimensional random walk in the presence of hard spherical obstacles. Calculation of the probability that a random walk consisting of a certain number of steps will not encounter a crowding particle leads to a simple relation:

ΔFUcrowd/RT=ln(1φ)+3φy2(1+2π1/2y1)
(10)

where y is the ratio of the radius of gyration of the unfolded chain in bulk solution to the radius of crowder. Equation (10) takes into account the possibility that an unfolded chain can in principle be accommodated within interstitial voids between spherical crowders that may be too small to accommodate a folded protein modeled as a hard particle. When the folded protein is modeled as a hard sphere, the treatment of Zhou predicts that whereas at low volume fraction of crowder, excluded volume effects stabilize the folded state relative to the unfolded state, at very high volume fractions of crowder, excluded volume stabilizes the unfolded state relative to the folded state. It has also been noted that ΔFUcrowd for a self-avoiding chain can be lower than for an ideal chain with the same radius of gyration (89).

Minton (2005) presented an effective two-state model for protein folding, with the unfolded state modeled as a compressible sphere. Because this model allows for intra-molecular as well as intermolecular excluded volume effects, more compact conformations of the unfolded chain are energetically more costly than in the random walk model, and as a result calculated values of ΔFUcrowd are significantly more positive, and calculated values of ΔΔFUN significantly more negative than in the random walk model. This model also predicts the energetic consequences of neglecting intra-molecular excluded volume, and provides estimates of the extent to which the average radius of gyration of an unfolded polypeptide is reduced by addition of hard particle crowders.

Hu et al. (31) modeled the unfolded state as a chain of small tangent hard spheres. They predicted that smaller crowders stabilize the unfolded state relative to the native state, whereas larger crowders promote the stability of the folded form. This conclusion stands in contradiction to the results of prior theoretical treatments (56, 94), as well as experiment (65).

In a simulation study, Cheung et al (11) found that, at a crowder volume fraction of 0.25, the folding stability of a WW domain was increased by 1.1 kcal/mol. Cheung et al. also found that the folding rate initially increases with crowder concentration but decreases at higher crowder concentrations. The decrease in folding rate was attributed to restriction by crowders of conformational fluctuations necessary for protein folding. A second factor may be an increase in the free energy of the transition state due to the decreased probability of finding voids that can accommodate the protein in an expanded transition state.

Effect of crowding on macromolecular isomerization

Using simple space-filling models for both helix and coil, Snir and Kamien (76) predicted that crowding by hard spheres promotes the formation of helical conformations by random-coil polymers.

Miscellaneous crowding effects

Hall (25, 26) has modeled the folding of a tracer protein in the presence of crowders which themselves can undergo folding/unfolding transitions or can self-associate. As the folded or self-associated crowders present less excluded volume, the model predicts that the stabilization of the native state by crowders will be decreased as the crowders fold or self-associate.

Effects of confinement on isomerization and protein folding

By modeling the unfolded state as a polymer chain and the native and transition states as hard spheres, Hayer-Hartl and Minton (28) obtained simple analytical expressions describing the dependence of the rate of two-state folding within a spherical cavity upon the radius of the cavity and the molecular weight of the confined protein. These expressions predicted that folding rates would be maximized at an intermediate cavity size that increased with the molecular weight of the encapsulated protein. They were able to quantitatively rationalize variations of the rate of refolding of several proteins within the central cavity of different mutants of the chaperonin GroEL/GroES that were specifically designed to change the volume of the cavity.

Maximization of folding rate at an intermediate cavity size has also been observed in atomistic simulations (12, 80, 85). These simulations also indicated that folding rate can be modulated by attractive interactions between the confined protein and the walls of the enclosing cavity. In addition, Cheung and Thirumalai (12) found that the folding yield can be increased by as much as 50% by repeated switching on and switching off of an attractive interaction between cavity wall and the confined protein.

A simulation of Jewett et al (37) suggests that the rate of folding in a confined environment can be increased via an alternative pathway in which a folding intermediate is transiently bound to the cavity wall. In another simulation study, Rathore et al. (66) suggested that although confinement-induced stabilization of the native state is dominated by entropy, stabilizing intra-molecular interactions are not as optimal as in bulk solution. Net stabilization is hence sequence-dependent and not as great as expected on the basis of entropic effects alone.

Ziv et al (97) simulated the helix formation of peptides confined in an infinite cylinder and found that the helical state is stabilized relative to the coil state. They attempted to rationalize their results with a simple statistical-thermodynamic model, in which the coil state is modeled as a polymer chain, and the helix is modeled by a stiffer polymer chain. Helix stabilization is predicted, but the predicted stabilization is independent of peptide length, in contrast to their simulation results.

Pande and co-workers (46, 78) simulated helix formation inside a cylindrical pore and folding of the villin headpiece inside a spherical cavity. Unlike previous simulations, solvent (water) was treated explicitly in these studies. Contrary to the result of Ziv et al (97), confinement in the cylindrical pore was reported to disfavor helix formation. Confinement in the spherical cavity was reported to favor folding of the protein when the solvent was allowed to equilibrate with the bulk, but disfavor folding when solvent was trapped within the cavity.

Miscellaneous confinement effects

Elcock (18) simulated the co-translational folding of three proteins. The proteins were fed off the peptidyltransferase active site with the ribosome large subunit, which was represented by atoms and pseudo-atoms. No structure formation was observed while the nascent chain was in the ribosome exit tunnel, and the co-translational folding of two single-domain proteins, CI2 and barnase, were found to follow mechanisms identical to those in bulk water. However, for a two-domain protein, Semliki forest virus protein, co-translational folding was found to follow a mechanism different from that in bulk water. In the latter environment, the two domains first folded independently and then docked together. On the ribosome, the N-terminal domain folded first and the structure of the C-terminal domain then gradually accreted onto the pre-formed domain.

Review of the experimental literature since 2004

Relevant experimental literature published during the past four years has been classified according to one of six categories: (1) Effects of crowding on macromolecular association rates; (2) Effects of crowding on macromolecular association equilibria; (3) Effects of crowding on conformational isomerization; (4) Effects of crowding on protein stability with respect to denaturation; (5) Effects of crowding upon enzyme activity; and (6) Effects of confinement on protein stability with respect to denaturation. Noteworthy findings in the six categories are listed in Tables 16.

Table 1
Reported effects of macromolecular crowding on association rates
Table 6
Reported effects of macromolecular confinement on protein stability and conformation

Effect of crowding upon the competition between protein folding and aggregation

It has been known for some time that many partially and fully unfolded proteins exhibit an increased propensity in vitro to form insoluble aggregates, leading to irreversible denaturation (1, 13, 35). Reference is made to two types of protein stability, namely stability with respect to unfolding, referred to as ‘thermodynamic stability’, and stability with respect to aggregation, referred to as ‘colloidal stability’. These two types of stability are in fact ordinarily interdependent and may be treated separately only under special conditions, such as in the limit of extreme dilution. The close relationship between the two types of stability is due to the similarity on an atomic scale between the kinds of non-covalent interactions that stabilize the native conformation of a protein and those that stabilize intermolecular non-covalent complexes. The difference in free energy between a natively folded protein and a misfolded and/or aggregated protein may be quite small and crowding can shift the thermodynamic balance between the two forms in either direction depending upon details of the folding and aggregation pathways (19, 55).

A cautionary note on the use of polyethylene glycol (PEG) as a crowding agent

The effect of macromolecular crowding on a particular reaction is generally studied experimentally by measuring changes in reaction rates or equilibria in the presence of different concentrations of putatively inert macromolecular cosolutes. One of the most popular cosolutes is the highly water-soluble synthetic polymer polyethylene glycol (or polyethylene oxide), which is actually a polyether with monomeric structure (–CH2 – CH2 – O –). It has long been evident that PEG fractions with molecular weights in excess of a few thousand have a large and predominantly repulsive interaction with proteins, and tend to induce macromolecular associations and compaction in qualitative accord with crowding theory (see for example (36, 67) and works cited in Tables 15). However, a number of studies have shown that this interaction cannot be described quantitatively in terms of excluded volume alone, and several independent lines of evidence point to an attractive interaction between PEG and nonpolar or hydrophobic sidechains on the protein surface (5, 6, 50, 83, 84). Thus the repulsive excluded volume contribution to PEG-protein interaction is partially compensated to an unknown extent by an attractive interaction, the strength of which can vary significantly between different proteins of approximately equal size. A variety of other water-soluble polymers and proteins (e.g. Dextrans, Ficoll, hemoglobin, defatted BSA) have been shown to lack such an attractive interaction for other proteins, and their interactions with proteins can be described using pure excluded volume models (42, 50, 69, 70, 73, 84). Since these readily available polysaccharides and proteins have the added advantage of resembling more closely the types of macromolecules encountered in a physiological medium, we recommend them as alternatives to PEG as crowding agents for use in quantitative studies.

Table 5
Reported effects of macromolecular crowding on enzyme activity

From in vitro to in vivo: Addressing additional complications in biological environments

Beyond excluded volume: effects of other types of nonspecific interactions

Theoretical models for estimating the magnitude of crowding and confinement on macromolecular reactions generally assume that these effects are predominantly entropic in origin, i.e., deriving from the relative reduction in configurational entropy of reactants, transition state, and products due to crowding or confinement. Nevertheless, it has been realized from the outset that other nonspecific interactions such as electrostatic repulsion and attraction and hydrophobic attraction are likely to contribute significantly to overall energetics in highly crowded or confined media (50). It has been found that the effects of such interactions upon the colligative and association properties of highly concentrated solutions of a single protein may be satisfactorily accounted for by a simple semi-empirical model in which the protein molecules are treated as effective hard spheres, the apparent size of which reflects short-ranged “soft” attractions or repulsions in addition to steric exclusion (27, 58). However, the “effective hard particle model” cannot be expected to satisfactorily describe a medium containing high concentrations of multiple macromolecular species interacting via qualitatively different potentials, such as a solution containing two concentrated proteins that are oppositely charged at a particular pH (27, 50). At the present time it appears that Monte Carlo and/or Brownian dynamics simulations provide the most promising approach to the theoretical study of crowding effects in such solutions, which should also be accompanied by additional experimental studies.

The results of experimental studies of the effect of high concentrations of a single species of inert macromolecule (‘crowder’) upon the associations of dilute test proteins have been interpreted in the context of effective hard particle models that take into account nonspecific repulsive interactions deriving from steric exclusion and electrostatic repulsion in as well as attractive interactions leading to association of the test molecules (69, 70). It is assumed in these models that crowder molecules interact with each other only via volume exclusion. One indication that the situation in physiological media may be more complex is provided by a recently published report (87), where concentrated mixtures of protein and polysaccharide were shown to exhibit non-additive effects upon the refolding of lysozyme. Moreover, concentrated solution mixtures of dextran and polyethylene glycol have been found to spontaneously separate into immiscible phases, between which proteins may partition in accordance with their relative affinity for each phase (45). The physical bases of these phenomena deserve closer study, as one would expect the local environment of most biological macromolecules in vivo to consist of more than one volume-excluding species.

We cannot yet adequately assess functional consequences of the nearly ubiquitous proximity of soluble proteins to the surfaces of biological structures (e.g., phospholipid membranes and protein fibers). However some directions for future research have been suggested by relevant in vitro studies. A variety of proteins have been shown to associate weakly with actin fibers, microtubules, DNA, and phospholipid membranes in a non site-specific fashion (see (10)for references to specific studies). Proteins are localized at the surfaces of these structures by attractive electrostatic and/or hydrophobic interactions in addition to repulsive volume-exclusion (hard wall) interactions. The reduction in configurational entropy of the protein resulting from this dual mode of localization is greater than that achieved by hard wall confinement alone, and in fact magnifies significantly the consequences of confinement. Simple theoretical models (53) predict that adsorbed macromolecules, like hard-wall confined macromolecules, have a stronger tendency to self- or hetero-associate than they do in bulk solution, and that the tendency to associate increases substantially with the strength of attraction between the soluble macromolecule and the surface. Adsorption may also increase the rate of macromolecular binding to specific surface sites (95). A number of macromolecular associations have been reported to proceed more rapidly or to a greater extent on surfaces than in bulk solution (e.g. (29, 40, 75, 95)), suggesting that the consequences of localization via adsorption may be quite general and of potential importance in heterogeneous physiological media.

Interpretation and significance of in-cell measurements of protein stability and association

Experimental techniques have been developed recently that provide information about either the stability and conformation or the association properties of specific labeled proteins within living cells (reviewed in (24)). The use of some of these techniques to study diffusional transport of labeled macromolecules in cytoplasm and tissue is reviewed elsewhere in this volume. In these studies a labeled protein (or pair of labeled proteins) is introduced into a cell via expression of recombinant proteins or microinjection. Then, a signal that reflects conformation or association of labeled protein, or co-localization (hetero-association) of two labeled proteins is monitored. In certain experiments, the intracellular environment is globally perturbed via addition of denaturant, temperature change, or application of hyper- or hypo-osmotic stress (21, 32, 33, 47). The monitored response of the labeled protein(s) within the cell to the applied perturbation is compared to that of the same protein(s) in dilute solution, and conclusions are drawn regarding the effect of the environment in vivo upon the stability of the labeled protein(s).

While each of these techniques does indeed provide information about aspects of the behavior of tracer proteins within a cell, one must be very careful about the interpretation of the results of such experiments. The potential impact of labeling procedures upon the spatial distribution of the tracer species, possible induction of artificial associations, and/or disruption of specific interactions of interest must be assessed. A number of additional questions must be answered: 1) How is the test protein distributed among the different local microenvironments within an intact cell? If it is found in multiple environments, how does one interpret the overall average signal? 2) If a tracer protein that is not native to a host organism such as E. coli is highly over-expressed within that organism, how likely is it that the protein is situated within a microenvironment that closely resembles its native milieu? 3) How does the living cell respond to applied stress? Does this response alter the distribution of the test protein, the composition of the microenvironment(s) of the test protein, and the interactions between the test protein and its surroundings within each microenvironment? 4) Since a living cell is a homeostatic system, within which one cannot vary the composition of individual microenvironments in a systematic and quantifiable fashion, how can one determine the extent to which a particular tracer protein in a particular intracellular microenvironment is either confined or crowded?

Toward a narrowing of the gap between “in vitro” and “in vivo”

We suggest that the influence of crowding and confinement upon macromolecular reactivity in vivo may be best explored by means of a “bottom-up” approach, according to which the behavior of test proteins is studied quantitatively within a series of media in which features thought to be essential to a particular microenvironment are incorporated in a systematic fashion, from the most simple to the most complex (see for example (96)). Such a bottom-up approach would ultimately lead to construction of a cytomimetic medium incorporating all of the major elements thought to be present in the selected microenvironment. The ability to control and independently manipulate temperature, pH, salt and osmolyte concentration, the types and concentrations of soluble bystander macromolecules and the types and abundances of structural elements such as membranes and cytoskeletal filaments (if appropriate) in this model system provides a rigorous approach to the characterization of nonspecific interactions influencing the behavior of proteins and other macromolecules within a native-like environment. Clearly this is no simple task, but we believe that if our goal is to understand in quantitative terms the role of nonspecific interactions in biology – a role we believe is absolutely essential to the mechanism of life – we cannot avoid paying attention to the details of these inherently complex systems [Footnote 5].

Summary points

  1. Macromolecular crowding nonspecifically enhances reactions leading to the reduction of total excluded volume. In general these include the formation of macromolecular complexes in solution, binding of macromolecules to surface sites, formation of insoluble aggregates, and compaction or folding of proteins. The expected magnitude of the effect is strongly dependent upon the relative sizes and shapes of concentrated crowding species and dilute macromolecular reactants and products.
  2. Macromolecular crowding is generally expected to increase the rate of slow, transition-state limited association reactions and to decrease the rate of fast, diffusion-limited association reactions.
  3. Simple statistical-thermodynamic theories based upon coarse-grained structural models usually provide reliable predictions of qualitative effects, and in favorable circumstances can provide reasonably good semi-quantitative predictions of the magnitude of an expected effect.
  4. Biological fluids are more complex than systems studied theoretically or experimentally in vitro due to increased heterogeneity and the probable presence of nonspecific attractive and repulsive intermolecular interactions in addition to volume exclusion. Theoretical and experimental exploration of model systems containing well-defined elements of added complexity are strongly encouraged.
Table 2
Reported effects of macromolecular crowding on association equilibria
Table 3
Reported effects of macromolecular crowding on conformational isomerization
Table 4
Reported effects of macromolecular crowding on protein stability with respect to denaturation

Acknowledgments

Research of HXZ is supported by NIH Grant GM058187. Research of GR is supported by Grants BFU2005-04807-C02-01 from the Spanish Ministry of Education and S-BIO-0260/2006 from the Madrid Government. Research of APM is supported by the Intramural Research Program, National Institute of Diabetes and Digestive and Kidney Diseases, NIH.

Terms/definitions

Macromolecular crowding
a term used to connote the influence of mutual volume exclusion upon the energetics and transport properties of macromolecules within a solution containing a high total volume fraction of macromolecules
Macromolecular confinement
a term used to connote the influence of excluded volume upon the free energy and reactivity of a macromolecule situated in a cavity, bounded by impenetrable walls, having a smallest interior dimension only slightly larger than the largest dimension of the macromolecule

Footnotes

*Dedicated to Steven B. Zimmerman, pioneering investigator of excluded volume effects in biological systems, with emphasis on the influence of macromolecular crowding on the structure and function of DNA

1Equations (13) apply equally to changes in Helmholtz or Gibbs free energies.

Simple models used to estimate the magnitude of ΔFXC generally assume constant volume and hence in the strict sense yield estimates of Helmholtz free energy changes. However, differences between Helmholtz and Gibbs free energy changes associated with reactions in the liquid state are not of qualitative significance.

2 ΔFXC is formally equivalent to the difference between the equilibrium average free energy of interaction of X with the perturbing co-solutes or boundaries and the equilibrium average free energy of interaction of X with the constituents of bulk solvent that are replaced by co-solute or boundary. Thus ΔFXC implicitly takes into account any energetic consequence of de-solvation that may accompany the transfer.

3The treatment presented here may be readily extended to a quasi-equilibrium analysis of the effect of crowding or confinement upon the kinetics of a transition-state limited association or isomerization reaction, in which case one must additionally estimate the free energy change associated with the transfer of the transition state from bulk to the crowded or confined medium (see for example the Appendix of (54)).

4The assumption that bound ligand excludes no volume to crowder provides an upper bound estimate of the effect of crowding, which may be less to the extent that bound ligand retains mobility and/or solvent exposure.

5“It may not be a dream to imagine that, using reconstituted systems of increasing complexity, the coordinated motility of an artificial cell will eventually be mimicked…. However, in many instances the analysis of molecular events using classical biochemical and structural approaches remains the limiting factor for future progress” (9).

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