ANRV343-BB37-18 ARI 24 April 2008 15:33

Macromolecular Crowdingand Connement:Biochemical, Biophysical,and Potential PhysiologicalConsequences

Huan-Xiang Zhou,1 German Rivas,2

and Allen P. Minton31Department of Physics and Institute of Molecular Biophysics and School ofComputational Science, Florida State University, Tallahassee, Florida 32306;email: zhou@sb.fsu.edu2Departmento de Ciencia de Proteinas, Centro de Investigaciones Biologicas, CSIC,Madrid 28040, Spain; email: grivas@cib.csic.es3Section on Physical Biochemistry, Laboratory of Biochemistry and Genetics,National Institute of Diabetes and Digestive and Kidney Diseases, National Institutesof Health, U.S. Department of Health and Human Services, Bethesda,Maryland 20892; email: minton@helix.nih.gov

Annu. Rev. Biophys. 2008. 37:37597

The Annual Review of Biophysics is online atbiophys.annualreviews.org

This articles doi:10.1146/annurev.biophys.37.032807.125817

Copyright c 2008 by Annual Reviews.All rights reserved

1936-122X/08/0609-0375$20.00

The U.S. Government has the right to retain anonexclusive, royalty-free license in and to anycopyright covering this paper.

Key Words

excluded volume, congurational entropy, free energy,protein-protein interactions, protein folding, site-binding

AbstractExpected and observed effects of volume exclusion on the free en-ergy of rigid and exible macromolecules in crowded and connedsystems, and consequent effects of crowding and connement onmacromolecular reaction rates and equilibria are summarized. Find-ings from relevant theoretical/simulation and experimental literaturepublished from 2004 onward are reviewed. Additional complexityarising from the heterogeneity of local environments in biologicalmedia, and the presence of nonspecic interactions between macro-molecules over and above steric repulsion, are discussed. Theoreticaland experimental approaches to the characterization of crowding-and connement-induced effects in systems approaching the com-plexity of living organisms are suggested.

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Contents

INTRODUCTION. . . . . . . . . . . . . . . . . 376A COMMON THERMODYNAMIC

FRAMEWORK FOR ANALYSISOF MACROMOLECULARCROWDING ANDCONFINEMENT . . . . . . . . . . . . . . . 377

CROWDING . . . . . . . . . . . . . . . . . . . . . . 378Estimation of FXcrowd . . . . . . . . . . . . 378Association Equilibria . . . . . . . . . . . . 379Association Rates . . . . . . . . . . . . . . . . . 380Site-Binding Equilibria . . . . . . . . . . . 381Two-State Protein Folding

Equilibria . . . . . . . . . . . . . . . . . . . . . 381Two-State Folding Rates . . . . . . . . . . 381

CONFINEMENT . . . . . . . . . . . . . . . . . . 382Estimation of FXconne . . . . . . . . . . . . 382Association Equilibria . . . . . . . . . . . . 382Site-Binding Equilibria . . . . . . . . . . . 382Two-State Protein Folding

Equilibria . . . . . . . . . . . . . . . . . . . . . 382REVIEW OF THEORETICAL/

SIMULATION LITERATURESINCE 2004 . . . . . . . . . . . . . . . . . . . . . 383Effects of Crowding on Protein

Folding . . . . . . . . . . . . . . . . . . . . . . . 383Miscellaneous Crowding Effects . . 384Effects of Connement on

Isomerization and ProteinFolding . . . . . . . . . . . . . . . . . . . . . . . 384

Miscellaneous ConnementEffects . . . . . . . . . . . . . . . . . . . . . . . . 385

REVIEW OF THEEXPERIMENTALLITERATURE SINCE 2004 . . . . . 385

EFFECT OF CROWDING ONTHE COMPETITIONBETWEEN PROTEINFOLDING ANDAGGREGATION . . . . . . . . . . . . . . . 386

A CAUTIONARY NOTEON THE USE OFPOLYETHYLENE GLYCOLAS A CROWDING AGENT. . . . . 387

BEYOND EXCLUDED VOLUME:EFFECTS OF OTHER TYPESOF NONSPECIFICINTERACTIONS . . . . . . . . . . . . . . . 389

INTERPRETATION ANDSIGNIFICANCE OF IN-CELLMEASUREMENTS OFPROTEIN STABILITY ANDASSOCIATION . . . . . . . . . . . . . . . . . 390

NARROWING THE GAPBETWEEN IN VITRO ANDIN VIVO . . . . . . . . . . . . . . . . . . . . . . . . 390

INTRODUCTIONAlmost all proteins and other biologicalmacromolecules in vivo exist, at least tran-siently, as components of structural andfunctional complexes (4). The number ofpublished studies of macromolecular interac-tions has increased almost exponentially forthe past 20 years and amounts to several hun-dred a year at present. However, almost allthese studies are aimed at the characterizationof attractive interactions that result in theformation of protein complexes or complexesof protein and other macromolecules (e.g.,ribonucleoproteins). In contrast, repulsive

interactions between macromolecules, by def-inition, do not lead to the formation of com-plexes and thus may not be observed directly.However, the presence and signicance of re-pulsive interactions in uid media containinga high total concentration of macromoleculesand/or structural obstacles to the free motionof macromolecules may be observed indirectlythrough their effects on a variety of macro-molecular reactions involving association andconformational isomerization (53, 56). Manyof these effects may be predicted qualita-tively (and sometimes quantitatively) usingsimple statistical-thermodynamic models and

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observed experimentally by measurement ofthe dependence of thermodynamically basedsolution properties and reaction kineticsand equilibria on the concentration andcomposition of macromolecular cosolutesthat are nominally inert with respect tothe reaction of interest. The importance ofexcluded-volume interactions lies in theirgenerality. Such interactions are universal andentirely nonspecic and have the potential tosignicantly modulate the kinetics and equi-libria of a large number of macromolecularreactions taking place in physiological uidmedia.

We classify an excluded-volume effect ac-cording to its origin: Macromolecular crowd-ing refers to effects attributed to volumeexcluded by one soluble macromolecule toanother, and macromolecular connementrefers to effects attributed to volume excludedby a xed (or conning) boundary to a solu-ble macromolecule. A number of reviews ofboth crowding and connement effects haveappeared during the past ve years (21, 29,60, 62, 78, 96, 97, 100) and it is not our inten-tion to recapitulate published material. More-over, a separate review of the effect of crowd-ing on macromolecular transport via diffusionappears elsewhere in the present volume (19).However, in the interest of completeness, inthe following section we briey summarizethe various ways that crowding and conne-ment are expected to inuence the equilibriaand kinetics of macromolecular associationsand isomerizations. Next, results of recentlypublished (20042007) theoretical analyses,atomistic simulations, and experiments relat-ing to effects of macromolecular crowdingand connement on a variety of macromolec-ular reactions are summarized. (References towork published prior to 2004 may be found inone or more of the reviews cited above.) Thepresent review concludes with discussions ofseveral topics related to the applicability oftheoretical predictions or the results of exper-iments conducted in vitro to actual macro-molecular processes taking place in livingorganisms.

Macromolecularcrowding: effects ofexcluded volume onthe energetics andtransport propertiesof macromoleculeswithin a solutioncontaining a hightotal volume fractionof macromolecules

Macromolecularconfinement:effects of excludedvolume on the freeenergy and reactivityof a macromoleculesituated in a cavity,bounded byimpenetrable walls,having a smallestinterior dimensiononly slightly largerthan the largestdimension of themacromolecule

A COMMON THERMODYNAMICFRAMEWORK FOR ANALYSISOF MACROMOLECULARCROWDING ANDCONFINEMENT

General features of macromolecular crowdingand connement are qualitatively exhibitedby their effects on three prototypical macro-molecular reactions:

Bimolecular Association

A + B ABAssociation of a Soluble Macromolecular Lig-and with a Specic Surface Binding Site

L + S LSTwo-State Folding of a Protein

U NThese three reactions are characterized, re-spectively, by three standard free energychanges and the corresponding equilibriumconstants:

FAB = RT ln K AB,FLS = RT ln KLS,

andFUN = RT ln KUN,

where R denotes the molar gas constant andT the absolute temperature. The effect of anenvironmental perturbation such as crowdingor connement on the equilibrium state of aparticular chemical reaction may be analyzedby constructing a simple thermodynamic cy-cle as shown in Figure 1ac and Figure 2ac.The value of standard free energy changes andequilibrium constants for a particular reactionin bulk dilute solution is denoted by the super-script 0, e.g., F 0AB , K

0AB . Then the free en-

ergy of hetero-association, site-binding, andunfolding in the bulk and perturbed environ-ments (either crowded or conned) will be re-lated by (62)

FAB FAB F oAB= FCAB FCA FCB , 1.

FLS FLS F oLS = FCLS FCL , 2.

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A B

L

A B+

+

FAB

0

FA

crowdF

B

crowdF

AB

crowd

FAB

FL

crowd

FU

crowdF

N

crowd

F ~0crowd

FLS

0

FUN

0

FUN

FLS

a

b

c

Dilutesolution

Crowdedmedium

Dilutesolution

Crowdedmedium

Dilutesolution

Crowdedmedium

Figure 1Thermodynamic cycles illustrating linkage between free energy oftransfer of reactants and products from dilute solution to crowdedmedium and standard free energy of (a) association in solution,(b) site-binding, and (c) two-state folding of a protein.

and

FUN FUN F oUN= FCN FCU , 3.

where FCX denotes the standard free en-ergy change associated with the transfer of Xfrom bulk solution to the crowded or connedenvironment, as indicated in Figure 1 and

Figure 2.1,2 Free energy changes (on a permole basis) are related to changes in the cor-responding equilibrium constant by

K X = K 0X exp(FX/RT ), 4.where X denotes AB, LS, or UN. The magni-tude of the effect of crowding or connementon a particular reaction equilibrium may thusbe evaluated indirectly by comparing the freeenergies of transfer of reactants and productsfrom bulk solution to the crowded or con-ned medium. Examples of such estimates areprovided below.3 In these examples, we focuson the excluded volume aspect of crowdingand connement, because this effect appearsto be universal. Other nonspecic interactionsof reactants with crowders and conning wallsare discussed below.

CROWDING

Estimation of F crowdXThe colligative properties of concentratedsolutions of globular proteins, under con-ditions such that long-range interactionsbetween protein molecules are damped out,are well described by models in which individ-ual macromolecular species are represented

1Equations 13 apply equally to changes in Helmholtz orGibbs free energies. Simple models used to estimate themagnitude of FCX generally assume constant volume andhence in the strict sense yield estimates of Helmholtz freeenergy changes. However, differences between Helmholtzand Gibbs free energy changes associated with reactions inthe liquid state are not of qualitative signicance.2FCX is formally equivalent to the difference between theequilibrium average free energy of interaction of X with theperturbing cosolutes or boundaries and the equilibrium av-erage free energy of interaction of X with the constituentsof bulk solvent that are replaced by cosolute or boundary.Thus FCX implicitly takes into account any energetic con-sequence of desolvation that may accompany the transfer.3The treatment presented here may be readily extendedto a quasi-equilibrium analysis of the effect of crowdingor connement upon the kinetics of a transition-state lim-ited association or isomerization reaction, in which caseone must additionally estimate the free energy change as-sociated with the transfer of the transition state from bulkto the crowded or conned medium (see for example theAppendix in Reference 59).

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by hard convex particles that resemble themolecules in general size and shape (54, 63),justifying the use of hard-particle models forquantitative estimation of excluded-volumeeffects. The free energy of transfer of a macro-molecule X from a dilute solution to a solutioncontaining an arbitrary concentration of othermacromolecules of the same or other species isthen equivalent to the free energy of creatinga cavity in the solution, free of any part of an-other molecule, that is large enough to accom-modate the newly introduced macromolecule(47). The scaled particle theory (SPT) of hard-particle uids, originally due to Reiss et al.(75), was devised specically to calculate thefree energy of cavity formation and is thusparticularly appropriate for numerical estima-tion of the magnitude of crowding effects. Letus consider as an example a uid contain-ing a volume fraction of inert hard spheri-cal particles with radius rc. According to SPT(15, 77), the free energy or work of placinginto this uid a spherocylinder (sc), that is, aright circular cylinder capped on each end bya hemisphere, with a radius rsc = Rscrc and acylindrical length of 2Lsc rsc, is given by

F crowds c /RT = ln(1 ) + A1 Q + A2 Q2 + A3 Q3, 5.

where

Q = /(1 )

A1 = R3sc + 3R2sc + 3Rsc + 1.5Lsc(R2sc + 2Rsc + 1)

A2 = 1.5(2R3sc + 3R2sc) + 4.5Lsc(R2sc + Rsc)

A3 = 3R3sc + 4.5 Lsc R2sc.

Note that the free energy of transfer of aspherical particle into this uid is just the spe-cial case of Equation 5 with Lsc = 0.

Association Equilibria

Consider a bimolecular association reactiontaking place in a solution of spherical crowd-ing molecules. Let monomeric A and B berepresented as identical hard spherical parti-

A B A B+

+

FAB

0

FA

confineF

B

confineF

AB

confine

FAB

FL

confine

FU

confineF

N

confine

F =0confine

FLS

0

FUN

0

FUN

FLS

a

b

c

L

Dilutesolution

Confinedvolume

Dilutesolution

Confinedvolume

Dilutesolution

Confinedvolume

Figure 2Thermodynamic cycles illustrating linkage between free energy of transferof reactants and products from dilute solution to conned volume elementand standard free energy of (a) association in solution, (b) site-binding, and(c) two-state folding of a protein.

cles with a radius equal to that of crowder (i.e.,Rsc = R1 = 1, Lsc = L1 = 0). The dimer ABis represented as a spherocylindrical particlewith a volume equal to twice that of monomer,but with Lsc = L2 and Rsc = R2 simultaneouslyadjustable to maintain constant volume, to il-lustrate the effect of different assumed shapes

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-1

0

0 0.1 0.2 0.3 0.4 0.5

1

2

3

R2 2R2L2 a

c

d

e

b

Monomer Dimer

a

e

d

c

b

log

KA

B/K

AB0

R1 = 1

Figure 3Dependence of the equilibrium constant for formation of a spherocylindrical dimer from two sphericalmonomers (R1 = 1) upon the volume fraction of hard-sphere crowders and dimer shape at constantdimer volume. (a) L2 = 0, R2 = 1.26 (spherical dimer); (b) L2 = 2/3, R2 = 1; (c) L2 = 1, R2 = 0.928;(d ) L2 = 1.5, R2 = 0.851; and (e) L2 = 2, R2 = 0.794.

for dimer. Results obtained using Equations 1,4, and 5 are plotted in Figure 3. It is evidentthat crowding can substantially enhance theequilibrium tendency of A and B to dimerizewhen AB is compact (L2 1), but crowdingcan also inhibit dimerization when the dimeris so aspherical that it excludes more volume tocrowder than two monomers. Many proteinscan also form higher-order oligomers. The ef-fect of crowding on the equilibrium constantfor concerted association of n monomers to 1n-mer increases dramatically with the value ofn (53).

Association Rates

The rate constant of association between twomolecules can generally be written as (55,102)

ka = kDkreactkD + kreact , 6.where kD is the rate constant under diffusioncontrol and kreact is the rate constant under re-action or transition-state control. Crowdingaffects the rate constant in the two regimesdifferently. kD is proportional to the relativediffusion constant of the two reactants. In-

creased crowding is expected to monotoni-cally decrease the diffusion constant and thusacts to decrease kD. At the same time crowd-ing also induces an attractive interaction be-tween the reactants, manifesting itself in theenhanced dimerization noted above, whichacts to partially compensate for the decreasein kD owing to the decrease in diffusion coef-cient (98). However, the overall effect is suchthat generally kD is expected to decrease withincreased crowding (55).

In the reaction- or transition-state-controlled regime, the rate constant is dic-tated by the energy barrier arising from con-formational changes necessary before formingthe product. Because the transition state forassociation in solution is generally nearlyas compact as the product complex, crowd-ing is expected to effectively lower the en-ergy barrier and thus increase the associa-tion rate constant by a factor that is closeto the factor for increase of the equilib-rium association constant. Correspondingly,a small effect of crowding on the dissociationrate constant is expected (59). Because fastassociations are typically under diffusion con-trol and slow associations are under reaction

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control (5), crowding is generally expectedto decelerate fast associations and accelerateslow associations (55).

Site-Binding Equilibria

To illustrate the effect of crowding on a site-binding reaction, let the free ligand be repre-sented as a hard spherical particle (Lsc = 0)with radius Rsc times that of a hard spheri-cal crowder. When the bound ligand is buriedand thus inaccessible to crowders, crowdingaffects only the free energy of free ligand (i.e.,F crowdLS = 0).4 Results obtained using Equa-tions 2, 4, and 5 are plotted in Figure 4, andit is evident that the enhancement of associ-ation by crowding can be much more signif-icant for site-binding reactions than for bi-molecular associations in solution. The sameapproximation may also be used to analyze theeffect of crowding on protein solubility, whichis modeled by assuming that crowding affectsprotein in the supernatant solution, but not inthe condensed phase (46, 53).

Two-State Protein Folding Equilibria

The presence of crowder inuences equilib-ria between conformational states of a macro-molecule by favoring conformations that ex-clude less volume to crowder. In the case ofprotein folding, unfolded conformations aremore expanded and thus crowding is expectedto favor the native state. However, the use ofthe hard-particle model to estimate F crowdU isunreliable, as the U state consists of a manifoldof conformations instead of a single rigid con-formation. Thus the extent to which crowd-ing is predicted to stabilize the native statevaries substantially between different models

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

0 0.1 0.2 0.3 0.40

1

2

3

4

5

6

7

log

KLS/K

LS0

b

a

c

Figure 4Dependence of the equilibrium constant for binding of a sphericalmacromolecular ligand to an immobile surface site upon the volumefraction of hard-sphere crowders, with MWligand/MWcrowder =2 (curve a), 1 (curve b), and 0.5 (curve c).

for the unfolded state (see following sectionfor examples).

Two-State Folding Rates

The rate constant for isomerization can begenerally written as

k = k0 exp(F /RT ), 7.

where F is the activation free energy (i.e.,free energy difference between the transitionstate and the reactant state) and the prefactork0 depends on the dynamics of the isomeriza-tion process. Crowding can in principle affectboth F and k0. For example, if the transi-tion state is more compact than the reactantstate, as in the case of a protein folding re-action, then crowding is expected to reduceF . If intrachain diffusion plays a signicantrole, crowding may act to reduce the rate ofintrachain diffusion and hence the value of k0as well (see review of relevant literature be-low). When the transition state is more ex-panded than the reactant state, as in the caseof protein unfolding, crowding is expected todecrease the rate constant.

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CONFINEMENT

Estimation of F conf ineXConsider a molecule X within a unit volumeof bulk solution that can exist in a nite num-ber of congurational states, each of whichis specied by a set of positional coordinatesdenoted by r and a set of orientational coordi-nates denoted by . The free energy of trans-ferring the molecule X from this volume to anequal volume of solution that may be boundedby hard walls in one, two, or three dimensionsis given by the statistical-thermodynamic ex-pression (25)

F conneX = RT ln(

allowed ddrall ddr

), 8.

where the multiple integral in the denomi-nator is taken over all congurational statesaccessible in bulk solution, and the multipleintegral in the numerator is taken over all al-lowed congurational states in the boundedvolume, that is, all states in which no part ofX intersects any hard-wall boundary.

While both connement and crowding ef-fects result from the reduction in possiblecongurations available to a macromoleculedue to the presence of a high-volume frac-tion of other macromolecules or static barri-ers to movement, there is one major qualita-tive difference between the two phenomena.In contrast to the free energy cost of crowd-ing, the free energy cost of connement is notnecessarily minimal for the molecular confor-mation that is globally the most compact inthe sense of having the smallest radius of gy-ration. Rather, connement favors conforma-tions having a shape that is complementary tothe shape of the conning volume. For exam-ple, although a spherical conformation maybe favored in a quasispherical cavity, the pre-ferred conformation in a cylindrical pore maybe rod-like, and the preferred conformation ina planar pore (bounded by two parallel hardwalls) may be plate-like. Thus numerical esti-mates of the magnitude of connement effectsare sensitive to the choice of models for the

structure of both conning space and connedmacromolecular species (56).

Association Equilibria

Model calculations of the effect of conne-ment in differently shaped pores on the asso-ciation of two spherical monomers of identicalsize to form a dimer of twice the volume andvarying shapes suggest that connement hasa small effect on bimolecular association andis expected to increase the equilibrium con-stant for bimolecular association by at mosta factor of two or three. However, the effectof connement on association constants forconcerted formation of larger n-mers havinga shape compatible with the shape of the con-ning volume increases strongly as the valueof n increases (56).

Site-Binding Equilibria

If the bound ligand is completely immobile,then connement affects only the free energyof the free ligand (i.e., F conneLS = 0). As a sim-ple example, consider a spherical ligand withradius a conned in a spherical cavity withradius Rcavity. The change in the site-bindingconstant due to ligand connement may becalculated from Equations 2, 4, and 8 to be

KLS/K 0LS =(

1 aRcavity

)3. 9.

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

Two-State Protein Folding Equilibria

It is evident upon inspection of Figure 2cthat the free energy cost of conning anypartially or fully unfolded conformation of aprotein is greater than the cost of conningthe native state, and that connement muststabilize the native state relative to any un-folded state. When summarizing the effectsof connement on protein folding, numeri-cal estimates of the magnitude of the effectof connement are sensitive to the nature of

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approximations made in treating the effect ofconnement on the (average) unfolded state.Zhou & Dill (101) presented a simple model inwhich the unfolded state is modeled as a ran-dom walk with a specied radius of gyration.They then estimated the value of F conneU as-sociated with the placement of U into a vari-ety of conning geometries. Some of their re-sults are plotted in Figure 5. According to thismodel, connement is predicted to decreasethe value FUN by as much as 2030 RT invery small cavities, with a volume only slightlygreater than that of the native state. This re-sult makes intuitive sense. In such small cavi-ties it is essentially impossible for proteins tounfold, as there is no space available for pro-teins to unfold into. By modeling the tran-sition state for protein folding as a spherewith a somewhat larger radius than that of thefolded state, a different but conceptually re-lated model (30) has been used to estimate thechange in the energy barrier for folding andto calculate the dependence of folding rate onthe size of the conning cavity. A maximumacceleration in folding by tuning the cavitysize is predicted.

In conclusion, enhancement of associa-tion and site-binding equilibria by conne-ment only occurs when the conned macro-molecules are truly conned, i.e., they cannotequilibrate with bulk solution. When proteincan equilibrate between a pore and bulk solu-tion, the extent of association resulting in theformation of oligomers in the pore is less thanin the bulk, and the extent of site-binding inthe pore is equal to that in the bulk (56).

REVIEW OF THEORETICAL/SIMULATION LITERATURESINCE 2004

Most of the effects summarized in the preced-ing section are predicted on the basis of sim-ple statistical-thermodynamic models. Thesemodels have the advantage that they are fo-cused on specic aspects of crowding andconnement, that they are intuitive, and thattheir results can often be expressed in the

-30

101 102

-20

-10

0

Rcavity

()

F UN/RT

a

b

Figure 5Effect of connement in a spherical cavity on the free energy of two-statefolding, calculated as a function of cavity radius according to the theory ofZhou & Dill (101), for proteins containing (a) N = 100 residues and(b) N = 200 residues. Vertical lines represent the radii of the hard sphericalrepresentation of the folded proteins, calculated according to rN (A) =3.73 N1/3. The radius of gyration of the unfolded protein is calculatedaccording to rg (A) = 3.27 N 1/2.

form of reasonably simple analytical expres-sions. On the other hand, they do not al-low for the exploration of complexities as-sociated with crowding and connement ofreal macromolecules by other real macro-molecules. A complementary theoretical ap-proach is by atomistic simulations. However,one needs to remain cognizant that the sys-tems studied via simulation are still modelsinstead of the real thing; not all idiosyncraticdetails of the model systems are of generalvalue for understanding the real systems. Forcomputational efciency, in most of the atom-istic simulation studies, amino acid residueswere modeled by a pseudoatom representingC with or without a second pseudoatom rep-resenting the side chain, and solvent was nottreated explicitly.

Effects of Crowdingon Protein Folding

Zhou (98) considered the effect of crowd-ing on the free energy of the unfolded stateby treating the unfolded protein as a three-dimensional random walk in the presence ofhard spherical obstacles. Calculation of the

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probability that a random walk consisting of acertain number of steps will not encounter acrowding particle leads to a simple relation:

F crowdU /RT = ln(1 ) + 3y2(1 + 21/2 y1), 10.

where y is the ratio of the radius of gyrationof the unfolded chain in bulk solution to theradius of crowder. Equation 10 takes into ac-count the possibility that an unfolded chaincan in principle be accommodated within in-terstitial voids between spherical crowdersthat may be too small to accommodate afolded protein modeled as a hard particle.When the folded protein is modeled as ahard sphere, the treatment of Zhou (98) pre-dicts that whereas at low-volume fraction ofcrowder, excluded-volume effects stabilize thefolded state relative to the unfolded state, atvery-high-volume fractions of crowder, ex-cluded volume stabilizes the unfolded staterelative to the folded state. F crowdU for a self-avoiding chain can be lower than for an idealchain with the same radius of gyration (100).

Minton (61) presented an effective two-state model for protein folding, with the un-folded state modeled as a compressible sphere.Because this model allows for intramolecu-lar as well as intermolecular excluded-volumeeffects, more compact conformations of theunfolded chain are energetically more costlythan in the random walk model, and as a re-sult calculated values of F crowdU are signi-cantly more positive, and calculated values ofFUN are signicantly more negative thanin the random walk model. This model alsopredicts the energetic consequences of ne-glecting intramolecular excluded volume andprovides estimates of the extent to which theaverage radius of gyration of an unfoldedpolypeptide is reduced by the addition ofhard-particle crowders.

Hu et al. (33) modeled the unfolded stateas a chain of small tangent hard spheres. Theypredicted that smaller crowders stabilize theunfolded state relative to the native state,whereas larger crowders promote the stability

of the folded form. This conclusion stands incontradiction to the results of prior theoreti-cal treatments (61, 98), as well as experiment(72).

In a simulation study, Cheung et al. (12)found that, at a crowder volume fraction of0.25, the folding stability of a WW domainwas increased by 1.1 kcal mol1. Cheunget al. also found that the folding rate ini-tially increases with crowder concentrationbut decreases at higher crowder concentra-tions. The decrease in folding rate was at-tributed to restriction by crowders of con-formational uctuations necessary for proteinfolding. A second factor may be an increase inthe free energy of the transition state due tothe decreased probability of nding voids thatcan accommodate the protein in an expandedtransition state.

Miscellaneous Crowding Effects

Using simple space-lling models for both he-lix and coil, Snir & Kamien (83) predicted thatcrowding by hard spheres promotes the for-mation of helical conformations by random-coil polymers.

Hall and colleagues (27, 28) have modeledthe folding of a tracer protein in the pres-ence of crowders that can undergo folding/unfolding transitions or can self-associate. Asthe folded or self-associated crowders presentless excluded volume, the model predicts thatthe stabilization of the native state by crow-ders will decrease as the crowders fold or self-associate.

Effects of Confinement onIsomerization and Protein Folding

By modeling the unfolded state as a polymerchain and the native and transition statesas hard spheres, Hayer-Hartl & Minton(30) obtained simple analytical expressionsdescribing the dependence of the rate oftwo-state folding within a spherical cavityon the radius of the cavity and the molec-ular weight of the conned protein. Theseexpressions predicted that folding rates would

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be maximized at an intermediate cavity sizethat increases with the molecular weight ofthe encapsulated protein. They quantitativelyrationalized variations of the rate of refold-ing of several proteins within the centralcavity of different mutants of the chaper-onin GroEL/GroES that were specicallydesigned to change the volume of the cavity.

Maximization of folding rate at an inter-mediate cavity size has also been observed inatomistic simulations (13, 88, 93). These sim-ulations also indicated that folding rate canbe modulated by attractive interactions be-tween the conned protein and the walls ofthe enclosing cavity. In addition, Cheung &Thirumalai (13) found that the folding yieldcan be increased by as much as 50% by re-peated switching on and switching off of anattractive interaction between the cavity walland the conned protein.

A simulation by Jewett et al. (39) suggeststhat the rate of folding in a conned environ-ment can be increased via an alternative path-way in which a folding intermediate is tran-siently bound to the cavity wall. In anothersimulation study, Rathore et al. (73) suggestedthat although connement-induced stabiliza-tion of the native state is dominated by en-tropy, stabilizing intramolecular interactionsare not as optimal as in bulk solution. Net sta-bilization is hence sequence dependent andnot as great as expected on the basis of en-tropic effects alone.

Ziv et al. (106) simulated the helix forma-tion of peptides conned in an innite cylin-der and found that the helical state is stabilizedrelative to the coil state. They attempted to ra-tionalize their results with a simple statistical-thermodynamic model, in which the coil stateis modeled as a polymer chain and the helix ismodeled as a stiffer polymer chain. The aver-age helical content is predicted to be increasedby connement, but the increase is indepen-dent of peptide length, in contrast to the re-sults of their simulation. Pande and cowork-ers (50, 85) simulated helix formation inside acylindrical pore and folding of the villin head-piece inside a spherical cavity. Unlike previous

simulations, solvent (water) was treated ex-plicitly in these studies. Connement in thespherical cavity favored helix formation whenthe solvent was allowed to equilibrate withthe bulk, but, disfavored helix formation whensolvent was trapped within the cavity. Zhou(99) has recently proposed that water trappedwithin the cylindrical pore has a higher ther-modynamic activity than bulk water, and thathydrogen bonding between trapped water andthe peptide backbone favors the coil/unfoldedstate.

Miscellaneous Confinement Effects

Elcock (20) simulated the cotranslational fold-ing of three proteins. The proteins were fedoff the peptidyltransferase active site withthe ribosome large subunit, which was repre-sented by atoms and pseudoatoms. No struc-ture formation was observed while the nascentchain was in the ribosome exit tunnel, and thecotranslational folding of two single-domainproteins, CI2 and barnase, followed mecha-nisms identical to those in bulk water. How-ever, for a two-domain protein, Semliki forestvirus protein, cotranslational folding followeda mechanism different from that in bulk water.In the latter environment, the two domainsrst folded independently and then dockedtogether. On the ribosome, the N-terminaldomain folded rst and the structure of the C-terminal domain then gradually accreted ontothe preformed domain.

REVIEW OF THEEXPERIMENTALLITERATURE SINCE 2004

Relevant experimental literature publishedduring the past four years has been clas-sied according to one of six categories:(a) effects of crowding on macromolecu-lar association rates; (b) effects of crowd-ing on macromolecular association equilib-ria; (c) effects of crowding on conformationalisomerization; (d ) effects of crowding onprotein stability with respect to denaturation;

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Table 1 Reported effects of macromolecular crowding on association rates

Addition of proteins, polysaccharides (dextran 138K, Ficoll 70K), and PEG (ranging in molar mass from 0.2K to 3.3K)increases the rate of amyloid fibrillation by -synuclein (66). Approximately 10-fold acceleration in 150 g/L of PEG 3.3Kand approximately threefold acceleration in 150 g/L Ficoll. Approximately ve- to sixfold acceleration in 50 g/L lysozyme orBSA.

Addition of PEG 10K induces the fibrillation of -synuclein in the presence of Zn2+ (94). Both PEG and Zn2+ arerequired for ber formation.

Addition of Ficoll 70K accelerates HIV capsid protein self-assembly (16). The half-time for protein assembly is decreasedapproximately 10-fold in 100 g/L Ficoll.

Addition of PEG 3.3K induces the coassembly of the bacteriophage 29 monomeric capsid protein and dimericscaffolding protein to form bona fide capsid particles (22). In the absence of the scaffolding protein, the capsid proteinforms amorphous polymers in PEG.

Addition of Ficoll 70K and PEG (ranging in molar mass from 0.2K to 8K) reduces the second-order rate constantfor diffusion-limited bimolecular association of beta-lactamase (TEM) and BLIP (4345). At low crowder concentration,rate scales with rotational diffusion. At higher concentrations, rate decreases more strongly with increasing polymerconcentration, possibly due to crowding-induced self-association of reactant species.

Abbreviations: BLIP, beta-lactamase inhibitor protein; BSA, bovine serum albumin; K, molar mass in kilograms; PEG, polyethylene glycol.

Table 2 Reported effects of macromolecular crowding on association equilibria

Addition of the unrelated protein RNase A promotes the dimerization of tracer apomyoglobin (107). Signicant effectsare observed at >50 g/L RNase. In contrast, an equivalent mass concentration of HSA did not promote apoMb dimerformation; this differential is much larger than expected from excluded-volume models.

Addition of dextran 10K enhances the formation of a decamer of bovine pancreatic trypsin inhibitor (84). Approximately30-fold increase in decamer fractional abundance and 5 105-fold increase in the association constant at 200 g/Lof dextran.

Addition of BSA or ovalbumin increases the binding affinity of replication protein RepA for specific DNA sequences(18). Approximately 10-fold increase of the equilibrium association constant for RepA-DNA complex formation in150 g/L BSA.

Addition of dextran 70K inhibits the exchange of subunits between aggregates of -crystallin (24). Effect can beattributed to crowding-induced lowering of concentration of monomeric subunit in equilibrium with aggregate.

High area occupancy of an amphiphilic peptide adsorbed onto a phospholipid membrane leads to conversion ofpeptide from an in-plane mode of adsorption to a transverse mode (3). Observed behavior is in qualitative accord withpredictions of earlier theoretical model based upon excluded volume in two dimensions (58).

Abbreviations: BSA, bovine serum albumin; HSA, human serum albumin.

(e) effects of crowding on enzyme activity; and( f ) effects of connement on protein stabil-ity with respect to denaturation. Notewor-thy ndings in the six categories are listed inTables 16.

EFFECT OF CROWDING ONTHE COMPETITION BETWEENPROTEIN FOLDING ANDAGGREGATION

Many partially and fully unfolded proteinsexhibit an increased propensity in vitro to

form insoluble aggregates, leading to irre-versible denaturation (1, 14, 37). Referenceis made to two types of protein stability,namely, stability with respect to unfolding,called thermodynamic stability, and stabilitywith respect to aggregation, called colloidalstability. These two types of stability are or-dinarily interdependent and may be treatedseparately only under special conditions, suchas in the limit of extreme dilution. The closerelationship between the two types of sta-bility is due to the similarity on an atomicscale between the noncovalent interactions

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Table 3 Reported effects of macromolecular crowding on conformational isomerization

Addition of dextran reduces mean distance between residues 169 and 203 in partially unfolded adenylate kinase (36).Inter-residue distance, measured by time-resolved FRET, is reduced from 39 A in 1 M GuHCl to 34 A in 1 M GuHCl +270 g/L dextran. Inter-residue distance in native conformation (no GuHCl) is 29 A.

Addition of Ficoll 70K or PEG 20K shifts near-UV and far-UV CD spectra of RNase A in 2.4 M urea to thatcharacterizing native RNase A (90). Essentially complete transition of spectrum achieved at 35 wt-% added polymer.

Addition of Ficoll 70K or PEG 20K significantly decreases the hydrodynamic radius of partially unfolded RNase A in2.4 M urea but does not affect the hydrodynamic radius of native protein (90). Decrease of 25% in presence of35 wt-% polymer.

Addition of PEG 20K partially restores enzymatic activity of RNase A in 2.4 M urea (90). Enzyme activity increases from8% of native in the absence of polymer to 26% in the presence of 30 wt-% polymer.

High concentrations of macromolecules in vitro and in the periplasm of Escherichia coli stabilize compactconformations of -synuclein relative to expanded conformations (51). Conformational transition from more compact at10C to less compact at 35C in dilute solution is suppressed in 300 g/L BSA or in periplasm of intact E. coli cells.

Pulling force required to unfold ubiquitin increases by 20% in the presence of 300 g/L dextran 40K (71). Observedeffect is 10-fold greater than calculated via excluded-volume model.

Addition of 30 wt-% Ficoll 70K or PEG 6K induces conversion of the unstructured C-terminal domain of histoneH1 to a molten globule (79).

Addition of concentrated Ficoll 70K enhances secondary structure of native apo- and holo-flavodoxin and VlsE (69, 87).

Abbreviations: BSA, bovine serum albumin; FRET, uorescence resonance energy transfer; PEG, polyethylene glycol.

Table 4 Reported effects of macromolecular crowding on protein stability with respect to denaturation

Addition of Ficoll 70K increases the free energy of unfolding of FK506-binding protein (86). GNU increases byapproximately RT upon addition of 160 g/L dextran. Two-state transition veried. Magnitude consistent with predictionof excluded-volume model (98).

Addition of dextran 30K stabilizes the molten globule conformation of apomyoglobin at pH 2 with respect to heat-and cold-induced unfolding (52). T50 for cold denaturation reduced by 13C and Tm for heat denaturation raised by 20Cupon addition of 270 g/L dextran. Results in qualitative agreement with prediction of excluded-volume theory.

Refolding rate of Rd-apocyt b562 increases by 30% at 30C and by 80% at 20C in the presence of 85 g/L PEG 20K(2). Unfolding rate little affected. Measurement via 15N NMR spin-relaxation dispersion.

Addition of PEG 4K increases Tm for thermal denaturation of DNase I (81). Tm increases by more than 15Cin 20 wt-% PEG.

Addition of Ficoll 70K and dextran 70K increases Tm of apo- and holo-flavodoxin (69, 87). Tm increases by 14Cin low-salt buffer and 4C in high-salt buffer upon addition of 300 g/L Ficoll 70K.

Abbreviations: NMR, nuclear magnetic resonance; PEG: polyethylene glycol.

that stabilize the native conformation of aprotein and those that stabilize intermolec-ular noncovalent complexes. The differencein free energy between a natively folded pro-tein and a misfolded and/or aggregated pro-tein may be small, and crowding can shiftthe thermodynamic balance between the twoforms in either direction depending on the de-tails of the folding and aggregation pathways(21, 60).

A CAUTIONARY NOTEON THE USE OFPOLYETHYLENE GLYCOLAS A CROWDING AGENTThe effect of macromolecular crowding ona particular reaction is generally studiedexperimentally by measuring changes inreaction rates or equilibria in the presenceof different concentrations of putatively inertmacromolecular cosolutes. One of the most

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Table 5 Reported effects of macromolecular crowding on enzyme activity

Enzymatic activity increases and then decreases with increasing concentration of protein crowding agents, butdecreases monotonically with increasing concentration of polymeric crowding agents (17). Up to 10-fold increase inspecic activity of urease in 30 wt-% hemoglobin.

Addition of PEG 6K increases enzyme activity of Escherichia coli AspP (65). 50 g/L PEG decreases Km fourfold andincreases Vmax sixfold.

Addition of dextran 70K, Ficoll 70K, or PEG 6K increases enzyme activity of isochorismate synthase (40). At 25 wt-%of additive, Km decreases two- to threefold.

Addition of dextrans (15K to 500K) or Ficoll 70K reduces rate of hydrolysis catalyzed by alkaline phosphatase (32).Larger dextrans have a larger effect per unit w/v concentration; 20 wt-% dextran 500K decreases rate approximately sevenfoldwhile 20 wt-% dextran 15K decreases rate approximately twofold. Effect attributed largely to reduction in rateof enzyme-substrate encounter.

Specific activity of hexokinase reduced in high concentrations of BSA (67). At 250 g/L BSA, kcat decreases33%, Km decreases 25%. Reaction rates measured calorimetrically.

Effects of small osmolytes and high concentrations of BSA on hexokinase activity are additive (68). Consistent withhypothesis that osmolytes (except urea) interact primarily with proteins via volume exclusion.

Addition of PEG 4K to 20K enhances activity of DNase I and S1 nuclease, does not significantly affect activity ofexonuclease III, and decreases activity of exonuclease I (81). Polymer does not affect Km, but increases Vmax ofDNase I 20-fold in 20 wt-% PEG.

Abbreviations: BSA, bovine serum albumin; PEG, polyethylene glycol.

Table 6 Reported effects of macromolecular confinement on protein stability and conformation

Confinement in polyacrylamide gels increases Tm of several proteins (8). Tm increases with increasing polyacrylamideconcentration in gel. 1.5C to 5C increase in 20% gels.

Confinement of glucose isomerase in functionalized mesoporous silica enhances retention of specific activity at highurea concentrations (48). In 300 A pores, enzyme activity in 8 M urea is equal to that in the absence of urea in bulk solution.

Confinement of GFP-mut2 in silica gel increases free energy of unfolding by GuHCl (9). Approximately 3RT increaseat 37C.

Structure of mutationally destabilized protein that is disordered in bulk solution reverts to native state when protein isencapsulated in reverse micelles (70).

Confinement of glucose isomerase in functionalized mesoporous silica and addition of 0.4 M urea increases specificactivity (48) by 50% without covalent cross-linking to silica and by 80% enhancement with covalent cross-linking.

Confinement of several proteins in the cavity of wild-type and mutant forms of GroEL/GroES accelerates ordecelerates rate of refolding in a size-dependent manner (89). Refolding is accelerated in larger cavities and deceleratedin smaller cavities, in qualitative or semiquantitative agreement with predictions of connement simulations and models(30, 41, 88).

popular cosolutes is the highly water-solublesynthetic polymer polyethylene glycol (PEG,or polyethylene oxide), which is actuallya polyether with monomeric structure(CH2CH2O). PEG fractions withmolecular weights in excess of a few thousandhave a large and predominantly repulsiveinteraction with proteins and tend to inducemacromolecular associations and compactionin qualitative accord with crowding theory(see, for example, References 38 and 74and works cited in Tables 15). However,

a number of studies have shown that thisinteraction cannot be described quantita-tively in terms of excluded volume alone, andseveral independent lines of evidence pointto an attractive interaction between PEGand nonpolar or hydrophobic side chains onthe protein surface (6, 7, 54, 91, 92). Thusthe repulsive excluded-volume contributionto the PEG-protein interaction is partiallycompensated to an unknown extent by an at-tractive interaction, the strength of which canvary signicantly between different proteins

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of approximately equal size. A variety of otherwater-soluble polymers and proteins [e.g.,dextrans, Ficoll, hemoglobin, defatted bovineserum albumin (BSA)] lack such an attractiveinteraction for other proteins, and theirinteractions with proteins can be describedusing pure excluded-volume models (46, 54,76, 77, 80, 92). Because these readily availablepolysaccharides and proteins have the addedadvantage of resembling more closely thetypes of macromolecules encountered in aphysiological medium, we recommend themas alternatives to PEG as crowding agents foruse in quantitative studies.

BEYOND EXCLUDED VOLUME:EFFECTS OF OTHER TYPES OFNONSPECIFIC INTERACTIONS

Theoretical models for estimating the magni-tude of crowding and connement on macro-molecular reactions generally assume thatthese effects are predominantly entropic inorigin, i.e., deriving from the relative reduc-tion in congurational entropy of reactants,transition state, and products due to crowdingor connement. Nevertheless, other nonspe-cic interactions such as electrostatic repul-sion and attraction and hydrophobic attrac-tion likely contribute signicantly to overallenergetics in highly crowded or conned me-dia (54). The effects of such interactions onthe colligative and association properties ofhighly concentrated solutions of a single pro-tein may be satisfactorily accounted for by asimple semiempirical model in which the pro-tein molecules are treated as effective hardspheres, the apparent size of which reectsshort-ranged soft attractions or repulsions inaddition to steric exclusion (29, 63, 64). How-ever, the effective hard particle model can-not be expected to satisfactorily describe amedium containing high concentrations ofmultiple macromolecular species interactingvia qualitatively different potentials, such asa solution containing two concentrated pro-teins that are oppositely charged at a particularpH (29, 54). At the present time it appears that

Monte Carlo and/or Brownian dynamics sim-ulations provide the most promising approachto the theoretical study of crowding effects insuch solutions, which should also be accom-panied by additional experimental studies.

The results of experimental studies ofthe effect of high concentrations of a singlespecies of inert macromolecule (crowder) onthe associations of dilute test proteins havebeen interpreted in the context of effectivehard-particle models that take into accountnonspecic repulsive interactions derivingfrom steric exclusion and electrostatic repul-sion as well as attractive interactions leadingto association of the test molecules (76, 77).It is assumed in these models that crowdermolecules interact with each other only viavolume exclusion. One indication that thesituation in physiological media may be morecomplex is provided by a recently publishedreport (95), which showed that concentratedmixtures of protein and polysaccharideexhibit nonadditive effects on the refolding oflysozyme. Moreover, concentrated solutionmixtures of dextran and PEG spontaneouslyseparate into immiscible phases, betweenwhich proteins may partition in accordancewith their relative afnity for each phase(49). The physical bases of these phenomenadeserve closer study, as one would expectthe local environment of most biologicalmacromolecules in vivo to consist of morethan one volume-excluding species.

We cannot yet adequately assess func-tional consequences of the nearly ubiqui-tous proximity of soluble proteins to thesurfaces of biological structures (e.g., phos-pholipid membranes and protein bers).However, some directions for future re-search have been suggested by relevant invitro studies. A variety of proteins asso-ciate weakly with actin bers, microtubules,DNA, and phospholipid membranes in anon-site-specic fashion (see Reference 11and references therein). Proteins are lo-calized at the surfaces of these structuresby attractive electrostatic and/or hydropho-bic interactions in addition to repulsive

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volume-exclusion (hard-wall) interactions.The reduction in congurational entropy ofthe protein resulting from this dual modeof localization is greater than that achievedby hard-wall connement alone and, in fact,magnies signicantly the consequences ofconnement. Simple theoretical models (57)predict that adsorbed macromolecules, likehard-wall-conned macromolecules, have astronger tendency to self- or hetero-associatethan they do in bulk solution, and that the ten-dency to associate increases substantially withthe strength of attraction between the solublemacromolecule and the surface. Adsorptionmay also increase the rate of macromolecularbinding to specic surface sites (103). A num-ber of macromolecular associations proceedmore rapidly or to a greater extent on sur-faces than in bulk solution (31, 42, 82, 104),suggesting that the consequences of localiza-tion via adsorption may be general and of po-tential importance in heterogeneous physio-logical media.

INTERPRETATION ANDSIGNIFICANCE OF IN-CELLMEASUREMENTS OF PROTEINSTABILITY AND ASSOCIATION

Experimental techniques have been devel-oped recently that provide information abouteither the stability and conformation or theassociation properties of specic labeledproteins within living cells (26). The use ofsome of these techniques to study diffusionaltransport of labeled macromolecules incytoplasm and tissue is reviewed in Reference19. In live-cell studies a labeled protein (orpair of labeled proteins) is introduced into acell via expression of recombinant proteinsor microinjection. Then, a signal that reectsconformation or association of labeled pro-tein, or colocalization (hetero-association) oftwo labeled proteins, is monitored. In certainexperiments, the intracellular environment isglobally perturbed via addition of denaturant,temperature change, or application of hyper-or hypo-osmotic stress (23, 34, 35, 51). The

monitored response of the labeled protein(s)within the cell to the applied perturbationis compared with that of the same protein(s)in dilute solution, and conclusions are drawnregarding the effect of the environment invivo on the stability of the labeled protein(s).

Although each of these techniques does in-deed provide information about aspects of thebehavior of tracer proteins within a cell, onemust be careful about the interpretation ofthe results of such experiments. The poten-tial impact of labeling procedures on the spa-tial distribution of the tracer species, possi-ble induction of articial associations, and/ordisruption of specic interactions of inter-est must be assessed. A number of additionalquestions must be answered: (a) How is thetest protein distributed among the differentlocal microenvironments within an intact cell?If it is found in multiple environments, howdoes one interpret the overall average signal?(b) If a tracer protein that is not native to a hostorganism such as Escherichia coli is highly over-expressed within that organism, how likely is itthat the protein is situated within a microenvi-ronment that closely resembles its native mi-lieu? (c) How does the living cell respond toapplied stress? Does this response alter thedistribution of the test protein, the compo-sition of the microenvironment(s) of the testprotein, and the interactions between the testprotein and its surroundings within each mi-croenvironment? (d ) Because a living cell is ahomeostatic system, within which one cannotvary the composition of individual microen-vironments in a systematic and quantiablefashion, how can one determine the extent towhich a particular tracer protein in a partic-ular intracellular microenvironment is eitherconned or crowded?

NARROWING THE GAPBETWEEN IN VITRO ANDIN VIVO

We suggest that the inuence of crowd-ing and connement on macromolecular re-activity in vivo may be best explored by

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means of a bottom-up approach, according towhich the behavior of test proteins is studiedquantitatively within a series of media inwhich features thought to be essential to a par-ticular microenvironment are incorporated ina systematic fashion, from the most simple tothe most complex (105). Such a bottom-up ap-proach would ultimately lead to constructionof a cytomimetic medium incorporating allthe major elements thought to be present inthe selected microenvironment. The ability tocontrol and independently manipulate tem-perature, pH, salt, and osmolyte concentra-tion; the types and concentrations of solu-ble bystander macromolecules; and the typesand abundances of structural elements suchas membranes and cytoskeletal laments (if

appropriate) in this model system provide arigorous approach to the characterization ofnonspecic interactions inuencing the be-havior of proteins and other macromoleculeswithin a native-like environment. This is nosimple task, but we believe that if our goal isto understand in quantitative terms the roleof nonspecic interactions in biologya rolewe believe is absolutely essential to the mech-anism of lifewe cannot avoid paying atten-tion to the details of these inherently complexsystems.5

5It may not be a dream to imagine that, using reconstitutedsystems of increasing complexity, the coordinated motilityof an articial cell will eventually be mimicked. . . . How-ever, in many instances the analysis of molecular eventsusing classical biochemical and structural approaches re-mains the limiting factor for future progress (10).

SUMMARY POINTS

1. Macromolecular crowding nonspecically enhances reactions, leading to the reduc-tion of total excluded volume. In general these reactions include the formation ofmacromolecular complexes in solution, binding of macromolecules to surface sites,formation of insoluble aggregates, and compaction or folding of proteins. The ex-pected magnitude of the effect is strongly dependent on the relative sizes and shapes ofconcentrated crowding species and on 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-limitedassociation reactions.

3. Simple statistical-thermodynamic theories based on coarse-grained structural modelsusually provide reliable predictions of qualitative effects and, in favorable circum-stances, can provide reasonably good semiquantitative predictions of the magnitudeof an expected effect.

4. Biological uids are more complex than systems studied theoretically or experimen-tally in vitro because of increased heterogeneity and the probable presence of non-specic attractive and repulsive intermolecular interactions in addition to volumeexclusion. Theoretical and experimental explorations of model systems containingwell-dened elements of added complexity are strongly encouraged.

DISCLOSURE STATEMENT

The authors are not aware of any biases that might be perceived as affecting the objectivity ofthis review.

ACKNOWLEDGMENTS

Research of HXZ is supported by NIH grant GM058187. Research of GR is supported bygrants BFU2005-04807-C02-01 from the Spanish Ministry of Education and S-BIO-0260/

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2006 from the Madrid Government. Research of APM is supported by the Intramural ResearchProgram, National Institute of Diabetes and Digestive and Kidney Diseases, NIH. This reviewis dedicated to Steven B. Zimmerman, pioneering investigator of excluded-volume effects inbiological systems, with emphasis on the inuence of macromolecular crowding on the structureand function of DNA.

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AR343-FM ARI 10 April 2008 7:2

Annual Review ofBiophysics

Volume 37, 2008

Contents

FrontispieceRobert L. Baldwin xiv

The Search for Folding Intermediates and the Mechanismof Protein FoldingRobert L. Baldwin