Structure, function, and folding of phosphoglyceratekinase are strongly perturbed bymacromolecular crowdingApratim Dhara,1, Antonios Samiotakisb,1, Simon Ebbinghausa, Lea Nienhausa, Dirar Homouzb,Martin Gruebelea,c,2, and Margaret S. Cheungb,2

aDepartment of Chemistry, University of Illinois, Urbana, IL 61801; bDepartment of Physics, University of Houston, Houston, TX 77204; andcDepartment of Physics and Center for Biophysics and Computational Biology, University of Illinois, Urbana, IL 61801

Edited by Peter G. Wolynes, University of California, San Diego, La Jolla, CA, and approved August 25, 2010 (received for review May 14, 2010)

We combine experiment and computer simulation to show howmacromolecular crowding dramatically affects the structure, func-tion, and folding landscape of phosphoglycerate kinase (PGK).Fluorescence labeling shows that compact states of yeast PGK arepopulated as the amount of crowding agents (Ficoll 70) increases.Coarse-grained molecular simulations reveal three compact ensem-bles: C (crystal structure), CC (collapsed crystal), and Sph (sphericalcompact). With an adjustment for viscosity, crowdedwild-type PGKand fluorescent PGKareabout 15 timesormore active in 200 mg∕mlFicoll than in aqueous solution. Our results suggest a previouslyundescribed solution to the classic problem of how the ADP anddiphosphoglycerate binding sites of PGK come together to makeATP: Rather thanundergoing ahingemotion, theADPand substratesites are already located in proximity under crowded conditionsthat mimic the in vivo conditions under which the enzyme actuallyoperates. We also examine T-jump unfolding of PGK as a functionof crowding experimentally. We uncover a nonmonotonic foldingrelaxation time vs. Ficoll concentration. Theory and modelingexplain why an optimum concentration exists for fastest folding.Belowtheoptimum, foldingslowsdownbecause theunfoldedstateis stabilized relative to the transition state. Above the optimum,folding slows down because of increased viscosity.

enzymatic activity ∣ FRET ∣ folding kinetics ∣ thermal denaturation ∣protein conformational changes

Phosphoglycerate kinase (PGK) is a 415-residue metabolicenzyme that produces ATP and is composed of two roughly

equally sized subunits connected by a flexible hinge (1). In thecrystal structure, the ADP and diphosphoglycerate binding sites,each located at an N and C subunit, are separated. It has beensuggested that a large-scale conformational change (2) is neces-sary to bring the two subunits together when the phosphorylgroup is catalytically transferred, and a hinge-bending mechanismhas been postulated (3), bringing together both substrates at theinner surfaces of the C and N subdomains (4, 5).

It is still unclear how the conformational and folding dynamicsof PGK is affected by the interior of a cell, which is heavilycrowded by macromolecules (6, 7). Various computational andtheoretical studies have been developed to address the effectof volume exclusion exerted by surrounding macromoleculeson protein activity inside cells, called the “macromolecularcrowding effect” (8). This effect, in addition to weak chemicalinteractions between proteins and crowders (9), can stabilizethe folded states of a protein relative to the unfolded state (10),perturb folding barriers (11, 12), and alter folding rates (13) andfolding routes (14).

Macromolecular crowding could selectively stabilize onefolded protein structure over another (8, 15–17), particularlyfor proteins that are structurally malleable so their domainsaligned in different orientations would have similar free energies(18). Thus, what we regard as the native structural ensemble

depends on whether the protein is in aqueous buffer, in a solutioncrowded by macromolecules, or packed in a crystal.

In our work, structural changes of PGK are revealed byFRET experiments where the N and C termini are labeled withAcGFP1 and mCherry as fluorescent markers (Fig. 1). A crowdedenvironment is achieved by the addition of inert Ficoll 70 carbo-hydrate to the samples. When the crowding content is increased,we observe changes in FRET that point to new compact struc-tures being populated. Our simulations provide a high-resolutioninterpretation of the structural changes induced in PGK bycrowding. Upon crowding, two other compact conformations[collapsed crystal (CC) and spherical (Sph)] exceed the stabilityof the crystal structure.

Strikingly, these structural changes of PGK upon crowdinghave a major functional consequence. An enzymatic activity assayshows that ATP production is enhanced over 25-fold in thecrowded wild-type enzyme, when taking into account increasedsolvent viscosity. The donor/acceptor labeled PGK also becomesmuch more enzymatically active. We suggest that in vivo, PGK isalready structurally primed to catalyze by forming in a collapsedcompact form (e.g., CC and/or Sph structural ensembles) ratherthan requiring hinge motions.

The effects of crowding on PGK folding kinetics are alsovery pronounced. We measured the folding/unfolding relaxationtime τ near the thermal denaturation midpoint of PGK. A plot ofln τ vs. Ficoll concentration has a “v” or chevron shape, indicatingthat there is an optimal crowder concentration for fastest folding.This observation is in accord with theory and computationalmodels (13). High concentrations of sucrose do not show similarstructural or kinetic effects, so the connectivity of Ficoll andhence crowding are needed to affect the large amplitude motionsof the two-subunit protein PGK, be it functional dynamics invol-ving enzymatic activity (a new compact native state) or foldingdynamics (crowding-viscosity competition).

ResultsProtein Donor–Acceptor Distance Decreases with Increased Crowding.The PGK construct fluorescence signature indicates the presenceof at least two conformational states. The end-to-end size of theAcGFP1-PGK-mCherry construct was monitored as a function of

Author contributions: M.G. and M.S.C. designed research; A.D., A.S., S.E., and L.N.performed research; A.D., A.S., S.E., D.H., M.G., and M.S.C. analyzed data; A.S. contributednew reagents/analytic tools; and A.D., A.S., M.G., and M.S.C. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Freely available online through the PNAS open access option.

See Commentary on page 17457.1A.D. and A.S. contributed equally to this work.2To whom correspondence may be addressed. E-mail: gruebele@scs.uiuc.edu ormscheung@uh.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1006760107/-/DCSupplemental.

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temperature and Ficoll concentration. Monitoring the steady-state donor–acceptor (D/A) ratio of the construct at 22.3�0.5 °C, we observed a small but reproducible lag upon goingfrom 0 mg∕ml Ficoll to 50 mg∕ml Ficoll. As the concentrationof Ficoll was further increased, D/A decreased continuously(Fig. 2A). The highest Ficoll concentration of 300 mg∕ml corre-sponds to an experimental crowder volume fraction of ϕc

E ≈ 20%(see Experimental and Computational Methods for details oncalculation of ϕc

E). At room temperature, crowding conditionsresult in conformational changes of the protein that eventuallydecrease the donor–acceptor distance when more crowderis added.

As a first control, we measured the D/A ratio as a functionof sucrose concentration. We observed that D/A was almost con-stant over the entire range from 0–300 mg∕ml (see SI Appendix),thus showing that Ficoll indeed induces compact states of PGKthrough macromolecular crowding and not through protein–carbohydrate nonspecific interactions. As a second control, wemeasured the intrinsic response of the AcGFP1 and mCherryfluorophores (open triangles in Fig. 2A) as a function of Ficollconcentration. For this purpose, we excited donor (green) fluor-escence of an AcGFP1-PGK construct and acceptor (red) fluor-escence of the AcGFP1-PGK-mCherry construct by excitingmCherry directly. D/A is nearly crowding-independent (Fig. 2A)and cannot account for the compact states of PGK observed athigh crowder concentration.

Protein Stability as a Function of Crowding. Upon Ficoll crowding,the stability of PGK construct increases, in agreement with pre-dictions made previously (13) and also subsequent experimentson other proteins (19). In aqueous buffer, the construct hada melting temperature of Tm ¼ 39 °C (see Experimental and

Computational Methods). Tm increased slightly with crowder con-centration (Fig. 2C). The maximum crowder concentration forthe higher temperature experiments was 200 mg∕ml (ϕc

E ≈ 13%volume fraction) to avoid aggregation of the construct. However,addition of sucrose also results in significant thermodynamicstabilization (see Fig. S1), indicating that thermodynamic stabi-lization caused by macromolecular crowding is modest. Thermaltitrations up to 50 °C were >90% reversible to the room tempera-ture signal in aqueous, sucrose, and Ficoll solutions.

Enzymatic Activity Increases with Crowding. As seen in Table 1,enzymatic activity of wild-type PGK increases about fivefoldwhen the Ficoll concentration is raised to 100 mg∕ml, and evenmore at 200 mg∕ml. Ordinarily, the increased viscosity of theFicoll solution should slow down the catalytic rate. If the viscosityincrease is taken into account (Table 1), the net increase in ac-tivity is over 12-fold at 100 mg∕ml, and even higher at 200 mg∕mlof Ficoll (ϕc

E ≈ 13%).The FRET-labeled PGK yields similar results. Enzymatic

activity is similar compared to the wild type (Table 1) in aqueoussolution. At Ficoll concentrations ≥100 mg∕ml, PGK activity

Excitation Filter

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Fig. 1. Programmable T-jump setup. A computer-controlled diode laserdelivers a shaped heating pulse that induces a sustained step function intemperature for the duration of the measurement. A blue LED excites thedonor label (green barrel on the PGK model). A microscope objective imagesdonor and acceptor (red barrel) fluorescence from the very center of theheated area onto a single CCD camera, which collects successive snapshotsof green and red fluorescence.

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Fig. 2. Conformational, thermal stability and kinetics trends of the PGKconstruct as a function of Ficoll concentration. (A) Donor–acceptor ratio at22.3� 0.5 °C (filled circles). Open triangles show the intrinsic fluorophoreresponse of AcGFP1 and mCherry as a function of Ficoll concentration.(B) “Inverse chevron” plot of the observed T-jump relaxation time. Redsquares show the kinetic trend obtained from simulations in ref. 13 at volumefraction ϕc

0. ϕc0 was computed using the size of the crowding agents equal

to the native state of the protein. The simulations were scaled to match upthe fastest folding rate observed in our experiments. (C) Melting tempera-ture. (D) Cooperativity parameter Δg1 (free energy derivative) from Eq. 1.All error bars are �1 standard deviation.

Table 1. Activity assays of wild-type PGK and the FRET-labeledmutant (PGK–FRET) construct at different crowding concentrations

MutantFicoll 70 concentration

(mg∕ml)Enzyme activity(units∕liter)

Viscosity 20 °CmPas

Wild-type PGK 0 24 ± 1 1.0Wild-type PGK 100 129 ± 33 2.3Wild-type PGK 200 319 ± 199 5.0PGK–FRET 0 18 ± 2 1.0PGK–FRET 100 52 ± 4 2.3PGK–FRET 200 58 ± 6 5.0

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increased about threefold. If one includes the effect of slowersubstrate diffusion in the viscous crowding matrix (Table 1), theactivity increase is actually enhanced over sixfold in 100 mg∕mlFicoll, and over 15-fold in 200 mg∕ml Ficoll. These increases inactivity are much greater than the <2-fold changes usually ob-served upon addition of osmolytes or crowders (20) to enzymesolutions, another indication of a larger structural change.

A control experiment in 100 mg∕ml sucrose simply resultedin a reduction of enzymatic activity (see Fig. S2), as expectedat the higher viscosity. Thus, the enhancement of activity in Ficollgoes hand-in-hand with the more compact structure detected byFRET upon macromolecular crowding, in contrast to sucrose(Fig. S1), and detected by simulations below.

Chevron Plot of Relaxation Time vs. Crowder Concentration. ThePGK relaxation rate is maximized at a well-defined crowderconcentration. The AcGFP1-PGK-mCherry construct was lasertemperature jumped from 39.8� 0.5 to 44.0� 0.5 °C at severalcrowder concentrations. When relaxation is measured by tem-perature jumps to 44 °C, the unfolding rate is weighted slightlymore than the folding rate in the observed relaxation rate becauseTm ranged from 39 to 40.5 °C. The relaxation time vs. crowderconcentration is a “chevron” plot (Fig. 2B). The fastest relaxationis observed at 100 mg∕ml Ficoll concentration. In contrast, therelaxation rate in sucrose decreases monotonically with increas-ing concentration (see SI Appendix). Addition of sucrose onlyresults in increased viscosity, not in any crowding effect.

Folding Energy Landscape of PGK in Silico Changes upon Crowding. Inorder to investigate the stability and structure of PGK, we calcu-lated the free energy landscapes of PGK. We identified fourstates: C (crystal structure), CC (collapsed crystal structure),Sph (spherical compact state), and U (thermally denatured state).The structures of these states are discussed in detail in the nextsubsection. In Fig. 3 we plot the ensemble populations as a func-tion of volume fraction of crowders (ϕc ¼ 0–40%) and tempera-ture (0.9 to 1.47kBT∕ε) using structural similarity χ (χ equals 0 for

the crystal structure, 1 for highly dissimilar structures) (21) andradius of gyration Rg as the order parameters characterizing theenergy landscape of PGK.

At low temperature and in the absence of crowders, the C andCC states are populated (Fig. 3A). As ϕc increases, the popula-tion of the C states reduces. At ϕc ¼ 25%, CC and Sph are bothpopulated, while the population of C is significantly destabilizedby approximately 4kBT (Fig. 3D). Finally, at the highest crowding(ϕc ¼ 40%), the Sph structure prevails. (Fig. 3G).

When the temperature is increased from kBT∕ε ¼ 0.9 tokBT∕ε ¼ 1.17 (ε is the solvent-mediated interaction; see SIAppendix for details), the CC and Sph structures becomeextensively populated even in the absence of crowding (Fig. 3B),and the Sph structure dominates under crowded conditions(Fig. 3 E andH). Finally, at the highest temperature, the unfoldedstate dominates under all crowding conditions.

Structural Characteristics of Compact PGK States in Silico. We char-acterized the coarse-grained structural properties of PGK withfour parameters (see Experimental and Computational Methods):structural similarity χ, radius of gyration Rg, asphericity Δ (Δ ¼ 0is sphere, Δ ¼ 1 is rod) and shape parameter S (S ¼ −0.25 isoblate, S ¼ 2 is prolate). The crystal structure ensemble C had0.05 ≤ χ ≤ 0.18 and 22.0 Å ≤ Rg ≤ 24.0 Å. The collapsed crystalstructure CC state had higher χ values but smaller Rg(0.16 ≤ χ ≤ 0.26 and 20.0 Å ≤ Rg ≤ 21.5 Å) than the C state.The calculation of shape and asphericity parameters for theCC structure (S ¼ 0.05 and Δ ¼ 0.1) demonstrated a dramaticshape change to a closed compact state from the open crystalstate (S ¼ 0.26 and Δ ¼ 0.26). Furthermore, at a higher tempera-ture or crowding level the Sph state appears with greater valuesof χ (0.3 ≤ χ ≤ 0.36 and 20.0 Å ≤ Rg ≤ 21.5 Å). The ensemblestructures from the Sph state are characterized by S ¼ 0.01and Δ ¼ 0.02, revealing a spherical nature of this state.

To better illustrate the structural differences among ensembleconformations of PGK in atomistic detail, we reconstructedthe coarse-grained protein models of the C, CC, and Sph statesinto all-atomistic protein models using the reconstruction algo-rithm SCAAL (side chain−Cα to all-atom) (15, 22) (Fig. 4 A–C).In the C state, the two subunits are split wide apart as in an open“pacman” form. In the CC state, the cleft between the two sub-units, a space accommodating the two substrates of PGK, closes,resembling a closed “pacman.” The Sph state is formed by amajor rearrangement of the two subunits over the hinge that in-volves twisting one of the two subunits with respect to the other,leaving at least one of the binding sites exposed to solvent.

In order to investigate the domain rearrangement in the Sphstate in detail, we calculated the orientation between the N and Cdomains of PGK by measuring an angle (θ) formed by tworepresentative vectors. Two vectors were defined, one on eachdomain, that are parallel in the crystal structure, and thesewere used to assess the relative orientation of the two domains(see SI Appendix for details). The calculation reveals that in theensemble of the crystal state (C) θ is 0° (cos θ° ¼ 1 represents thatthe two vectors are in parallel) as shown in Fig. S3 A and C. How-ever, in the ensemble of the Sph state, θ between the two vectorsis centered around 180° (cos θ ¼ −1) as shown in Fig. S3 B andD,representing the alignment of two domains is nearly antiparallel.This result suggests a twist bending motion in the Sph state ofPGK involving a significant rearrangement of the protein’s lobesunder high crowding conditions.

The domain rearrangement can also be demonstrated by thegain or loss of contact formation, in the form of a contact map,in the C, CC, and Sph states characterized from the respectiveensembles in Fig. S4. The formation of new nonnative contacts(in green boxes) and the loss of native contacts (in orange boxes)across subdomains in the CC and Sph states compared to the

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Fig. 3. Two-dimensional folding free energy landscape of PGK in the bulk(A–C) and under the crowded conditions at ϕc ¼ 25% (D–F) and ϕc ¼ 40%

(G–I) as a function of the radius of gyration Rg and the overlap function χat different temperatures (in units of kBT∕ε). The color is scaled by kBT wherekB is the Boltzmann constant and ε is 0.6 kcal∕mol. The crystal structure islabeled C, the collapsed crystal structure CC, the spherical state Sph, andthe unfolded state U.

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crystal state (C) suggest a large-scale structural rearrangementin PGK.

In Silico Investigation of the N–C Termini Distance. The D/A ratiosfrom the FRET-labeled construct correlate with the N–C terminidistribution. The experiments demonstrated a strong decreaseof D/A with increasing Ficoll concentration, indicating theexistence of at least two types of PGK conformations in the pre-sence of crowders. These observations prompted us to computethe distance between the N and C termini (DN-C) for the threepopulated states (C, CC, and Sph) of PGK from computer simu-lations. DN-C is defined as the distance between the Cα beads ofresidues Ser-1 and Lys-415.

Fig. 4D reveals the distinctive profile of the N–C distance(DN-C) distribution for each compact structure taken from thecrowding/temperature ensembles where it dominates. The CCstate has the highest average DN-C, followed by the C and Sphstates. In addition, the DN-C distribution of the CC state is byfar the broadest, ranging from 5 Å to 50 Å. The reason for thiswide distribution profile as well as high average is the greater mo-bility of the N and C termini, which are outwardly protrudedwhen the protein’s hinge is bent. In contrast, in the Sph statein which the two domains are twisted against each other, theN and C termini residues are found in the interior of the protein,thus significantly reducing the distribution and the averageof DN-C.

In Silico Investigation of the Mg-ATP/3PGA Binding Sites. The effectof crowding on the structure of PGK pertinent to its enzymaticactivity can be indicated by the spatial distance Db between theATP and 3PGA binding sites. The two binding sites are locatedseparately at the inner surfaces of the N and C subunits, and it ispostulated that the closure of this cleft, bringing the two sitestogether, is necessary for an active enzymatic reaction (3, 23).Fig. 5 shows the Db distribution of the three ensemble structures,C, CC, and Sph. For the crystal structure ensemble (C), which

dominates the population only in the absence of Ficoll 70(ϕc ¼ 0), Db is centered at 21.5 Å. For the CC state ensemble,which is prominent at ϕc ¼ 25%, the most probable Db is dras-tically reduced to 12.54 Å. Lastly, for the spherical state ensembleSph ϕc ¼ 40%, the Db distribution is centered at 16.41 Å, stillshorter than the most probable Db in the C state.

DiscussionDespite numerous studies of PGK’s folding stability anddynamics (24–26) and the motion of its flexible hinge, by experi-ment (27) as well as by computation (28, 29), it remains an openquestion to what extent the highly crowded environment can af-fect the PGK folding and structure and, ultimately, its enzymaticactivity involving large-scale structural movement inside a cell.Although experimental studies using synthetic crowding agentshave shown that the folding properties and enzymatic activityof simple proteins can be perturbed (30), our study shows thatcrowding leads to major conformational changes of PGK, witha major impact on its enzymatic activity. The tethers labelingPGK are too short to allow the donor–acceptor fluorescenceratio D/A to change by nearly a factor of 2 while PGK remainsopen, and the individual fluorophore controls reveal no intrinsiccrowding dependence of D/A due to changing quantum yields(Fig. 2A). The D/A ratio observed in our experiments decreasesrapidly with increasing Ficoll concentration, showing that the twosubunits of PGK close in on each other upon being placed in acrowded environment. The observed D/A values correspond tothe existence of at least two states of PGK and possibly a thirdstate (resulting in a lag of D/A below 50 mg∕ml).

Our experimental interpretation is entirely consistent withthe coarse-grained molecular simulations, which reveal threecompact ensemble structures of PGK below its folding tempera-ture. The lag and decrease of the D/A ratio with increasedcrowding may be explained by a progression of PGK throughC, CC, and Sph states. In Fig. 3 A, D, and G the most probablePGK state is the C state at ϕc ¼ 0, the CC state at ϕc ¼ 25%,and the Sph state at ϕc ¼ 40%. The corresponding average N- toC-terminal distance of the C, CC, and Sph states is DN-C ∼ 19 Å,∼25 Å, and ∼14 Å, respectively. This nonmonotonic trend ofDN-C is in qualitative agreement with the FRET results: a lagphase (or slight increase) of D/A from 0–50 mg∕ml Ficoll, thena strong decrease of D/A.

Crowding dramatically increases PGK activity, as demon-strated by an over 15-fold increase in viscosity-adjusted enzymaticactivity of the construct. The increase is even more dramaticfor wild type yeast PGK (without FRET labels) (Table 1). Com-plementary structural analysis of the compact PGK ensemblesobserved in the computer simulations reveals that the CC andSph states indeed bring the two catalytic sites closer together(Fig. 5). The binding sites of the CC ensemble are intact afterPGK undergoes large structural changes while the binding sitesin the Sph ensemble are rearranged. We suggest that, althoughthe distance between the binding sites is reduced in both CCand Sph states, the CC states whose binding sites are structurallyintact may be the most biochemically active. The additionalactivity of wild-type unlabeled PGK may be due to stabilizationof CC compared to Sph, relative to the fluorescence-labeledtriple mutant.

Our folding kinetics experiments show that domain collapseis not the only large amplitude motion affected by crowding.The measured folding kinetics vary nonmonotonically with crow-der concentration, leading to a chevron-like plot with a maximalfolding rate observed at a Ficoll concentration of 100 mg∕ml(Fig. 2B). Below and above this concentration, the folding/unfolding relaxation time increases. Models of macromolecularcrowding have predicted an initial increase in the relaxation rateas crowder concentration is increased, followed by a decrease ateven higher crowder concentrations. Based on predictions made

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Fig. 4. Structural characteristics of the dominant compact ensemble struc-tures of PGK in cartoon representation. (A) Crystal state C, (B) collapsed crys-tal state CC, and (C) spherical state Sph. The coloring of each protein modelranges from N terminus (red) to C terminus (blue). The N and C termini arerepresented with van der Waals spheres. The schematic representation at thebottom left of each panel is to address a simplistic view of the structural ar-rangement of the N- and C-lobes in each conformation. (D) The probabilitydistribution of the distance between N and C termini (DN-C) of the threedominant structures of PGK under the condition in which each prevails inthe simulations. C state (solid black), CC (dashed red), and Sph (dotted blue).Atomistic structures were reconstructed from coarse-grained protein modelsusing SCAAL.

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by computer simulations on the macromolecular crowding effectsonWW folding (13) (Fig. 2B), we rationalize the observed kineticbehavior as follows: Below the optimal crowder concentration,[Ficoll]*, where the folding rate is maximum (i.e., ½Ficoll�� ¼100 mg∕ml), the unfolded state becomes conformationally morestable, slowing down the refolding rate; above the optimal crow-der concentration, the viscosity increases rapidly, slowing downboth the unfolding and refolding reactions. Chemical and crowd-ing effects can obviously compete with one another, but in the caseof PGK, simple crowding can explain all the observations (31).

In summary, we have shown that macromolecular crowdingprofoundly affects the structure of PGK, resulting in the forma-tion of more compact and enzymatically more active structures.This has far-reaching implications, despite Ficoll 70 still being acytomimetic material and lacking the polydisperse nature of acell (32)—it suggests that in the crowded interior of a living cell,hinge-bending motions may not be necessary for PGK to carryout its function. Instead, the nucleotide and 1,3-DPG bindingdomains may already be in close proximity to each other forefficient catalysis to occur. Finally, we showed that macromo-lecular crowding and viscosity compete with each other, result-ing in a uniquely defined concentration at which PGK folding isfastest. A speedup of folding upon crowding was also observedfor lysozyme’s “prompt” folding phase (33) (the one relevanthere because PGK has no disulfide bridges).

Our combined experimental and computational effort high-lights the importance of in vivo studies (34) in addition to crystal-lographic structure-function relationships and in vitro studies.The states in which PGK protein exists under crowding condi-tions have structural and kinetic characteristics very differentfrom the state in dilute aqueous buffer (35) or in the crystal.This could turn out to be a general phenomenon for multisubunit(36–38) or partly unstructured proteins: the structural character-istics of the so-called “native state(s)” and how rapidly they foldor unfold will depend sensitively on the nature of their surround-ing crowding conditions.

Experimental and Computational MethodsProtein Design and Expression. We designed a fusion proteinconsisting of a low-melting mutant (Y122W/W308F/W333F) of

phosphoglycerate kinase (PGK) (24), fused between a GreenFluorescent Protein (AcGFP1) donor (D) and an mCherry accep-tor (A). AcGFP1 and mCherry are connected to the N and Ctermini by amino acid linkers consisting of two amino acids each.Unfolding of this protein leads to an increase in the N–C terminaldistance, resulting in an increase in donor to acceptor fluores-cence ratio (D/A) due to decrease in energy transfer by Försterresonance energy transfer. We expressed the fusion protein inE. coli and purified the construct on a Ni-NTA column as de-scribed previously (35). A fusion protein consisting of AcGFP1tagged to the N terminus of PGK was expressed and purifiedas described above.

Stability and Kinetics of Crowded Phosphoglycerate Kinase. For boththermodynamic and kinetic measurements, the protein solutionwas sandwiched between a cover slip and microscope slideby a 100 μm spacer, resulting in a column density of about1;000 proteins∕μm2. This low density avoids protein–proteininteractions while providing sufficient fluorescence for gooddetection sensitivity with a N/A 0.65 objective in an invertedfluorescence microscope.

Equilibrium titrations were performed by resistive heating ofthe microscope stage. Temperature was detected by mCherryfluorescence excited at 532 nm, which decreases as temperatureincreases, and independently calibrated by thermocouples belowand above the sample slide. Measuring the equilibrium D/Aratio as a function of temperature yielded protein unfoldingcurves that were fitted to a sigmoidal model with a linear tem-perature dependence:

Keff ¼ e−ΔG∕RT; ΔG ¼ Δg1ðT − TmÞ [1]

The equilibrium constant is an effective equilibrium constantbecause PGK is known not to be a two-state folder. We analyzedthe melting temperature Tm and the cooperativity parameterΔg1 (negentropy, or first derivative of the free energy at Tm)of the unfolding transition in aqueous solution up to Ficollconcentrations of 200 mg∕ml. Δg1 from Eq. 1 was fitted to1.07� 0.16 kJ∕mole∕°C. The measurement uncertainty was toolarge to discern a trend (Fig. 2D). The AcGFP1 and mCherrymelting points exceed 70 °C, so the observed transition corre-sponds to melting of the PGK within the construct. Concentra-tions greater than 200 mg∕ml resulted in PGK aggregation atthe higher temperatures. 200 mg∕ml corresponds to a volumefraction of approximately ϕc

E ≈ 13%. Thermodynamic measure-ments in sucrose (Fisher Scientific) were possible up to a concen-tration of 150 mg∕ml; at higher concentrations, the proteinstarted aggregating before yielding a denatured baseline, thusprecluding determination of the melting temperature and effec-tive cooperativity.

Experimental volume fractions of Ficoll 70 (ϕcE) were calcu-

lated using the partial specific volume of Ficoll, which is0.67 ml∕g (39). We used Ficoll with an average molecular massof 70 kDa from Sigma-Aldrich. The highest volume fractionachievable in our experiments was ϕc

E ≈ 20%, while the simula-tions (see below) were carried out at ϕc ¼ 0%, 25%, and 40%,thus allowing us to qualitatively compare the experimental resultswith the computer simulations.

Relaxation kinetics were induced by temperature jumps andmonitored with 17 ms time-resolution for 15 s. A tailored mid-IRpulse (λ ¼ 2;200 nm) emitted by a diode laser jumped up thetemperature of the protein solution from 39 °C to 43 °C, acrossthe thermal unfolding transition. The key advantage of using aprogrammable diode laser is that the temperature profile can beadjusted to a step function, so the temperature after the jump isconstant to within �0.25 °C. No sample recooling and backwardrelaxation occurs. The kinetics were described by a stretched-exponential signal of the form SðtÞ ∼ e−ðt∕τÞβ , which has been usedpreviously to describe folding kinetics of several PGK mutants

Pro

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Fig. 5. The probability distribution of the distance between the centersof mass of the Mg-ATP and 3PG binding sites ðDbÞ calculated for the threedominant structures of PGK under the condition in which each prevails inthe simulations. ðDbÞ of C state (solid black), CC (dotted red), and Sph (dottedblue) ensembles are plotted. The purple solid line represents the convolutionof the two profiles from CC and Sph states. The three characteristic structuresare illustrated in cartoon representation. The coloring of each protein modelranges from N terminus (red) to C terminus (blue). The Mg-ATP and 3PGbinding sites are colored in yellow and green representations of van derWaals spheres, respectively. Atomistic structures were reconstructed fromcoarse-grained protein models using SCAAL.

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(24, 40). The hierarchical stretched-exponential description or“strange kinetics” provides a convenient way of summarizingthe intermediate stages of folding with a single parameter β.The precision of the stretched-exponential fits for the timeconstant τ was �0.01 s, while the error bar in Fig. 2B showsthe accuracy of our kinetics measurements based on repeatedmeasurement.

PGK Activity Assay. We measured PGK activity using the coupledreaction with glyceraldehyde-3-phosphate dehydrogenase fromthe previous step of the glycolytic pathway, as described in detailearlier. NADH consumption was monitored as a function oftime by following the absorbance at 340 nm. The rate of NADHconsumption was measured at various concentrations of thesubstrate 3-phosphoglycerate and plotted as a function of sub-strate concentration to extract the enzyme activity. For purposesof comparison, we assayed the activity of wild-type PGK withoutany labels. Wild-type PGK and all chemicals required for theassay were purchased from Sigma-Aldrich.

Simulation Details.The coarse-grained models of PGK proteins, aswell as the simulation methods, are provided in the SI Appendix.The thermodynamic properties of PGK were studied at thevolume fractions of crowder Ficoll 70 ϕc ¼ 0%, ϕc ¼ 25%, andϕc ¼ 40% by coarse-grained molecular simulation (by conven-tion, the volume fraction of crowders is presented as a percentageof total volume; i.e., ϕc ¼ 25% corresponds to 0.25 of the totalvolume). Several represented coarse-grained structures were

reconstructed to all-atomistic protein models for illustration byusing SCAAL (15, 22).

Structural Characterization of PGK. To analyze the structural char-acteristics of PGK, we used four parameters: (i) Overlap functionχ is to measure the structural similarity to the crystal structure(21). χ equals 0 for the crystal structure, 1 for highly dissimilarstructures. (ii) The radius of gyration Rg is to measure the sizeof PGK. (iii) Asphericity S and (iv) shape parameters Δ are cal-culated from the inertia tensor (15). S lies between −0.25 (oblateellipsoid) and 2 (prolate ellipsoid). Δ lies between 0 (sphere) and1 (rod). For a sphere, S and Δ are equal to zero.

Binding Sites Distance Calculation. To calculate the distance be-tween the Mg-ATP and 3PGA binding sites in the characteristicstructures of PGK we defined Db to be the distance between thecenters of mass of the amino acid residues involved in the twosubstrate binding sites. The selection of Mg-ATP binding siteresidues were obtained from ref. 1), while the residues that bind3PGA were taken from ref. 23).

ACKNOWLEDGMENTS. We thank Tripta Mishra for assistance with proteingrowth and purification. This work was supported by National ScienceFoundation grants MCB 1019958 (M.G.) and MCB 0919974 (M.S.C.). M.S.C.thanks the computational sources from the Texas Learning and ComputationCenter and the University of Houston. S.E. was the recipient of a vonHumboldt Fellowship. A.D. and S.E. were supported by the NSF Center forthe Physics of Living Cells.

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