Protein shape modulates crowding effectsAlex J. Gusemana, Gerardo M. Perez Goncalvesa, Shannon L. Speera, Gregory B. Youngb, and Gary J. Pielaka,b,c,d,1

aDepartment of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599; bDepartment of Biochemistry & Biophysics, University of NorthCarolina at Chapel Hill, Chapel Hill, NC 27599; cLineberger Comprehensive Cancer Center, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599;and dIntegrative Program for Biological and Genome Sciences, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599

Edited by Susan Marqusee, University of California, Berkeley, CA, and approved September 12, 2018 (received for review June 18, 2018)

Protein−protein interactions are usually studied in dilute bufferedsolutions with macromolecule concentrations of <10 g/L. In cells,however, the macromolecule concentration can exceed 300 g/L,resulting in nonspecific interactions between macromolecules.These interactions can be divided into hard-core steric repulsionsand “soft” chemical interactions. Here, we test a hypothesis fromscaled particle theory; the influence of hard-core repulsions on aprotein dimer depends on its shape. We tested the idea using aside-by-side dumbbell-shaped dimer and a domain-swapped ellip-soidal dimer. Both dimers are variants of the B1 domain of proteinG and differ by only three residues. The results from the relativelyinert synthetic polymer crowding molecules, Ficoll and PEG, sup-port the hypothesis, indicating that the domain-swapped dimer isstabilized by hard-core repulsions while the side-by-side dimershows little to no stabilization. We also show that protein coso-lutes, which interact primarily through nonspecific chemical inter-actions, have the same small effect on both dimers. Our resultssuggest that the shape of the protein dimer determines the influ-ence of hard-core repulsions, providing cells with a mechanism forregulating protein−protein interactions.

macromolecular crowding | protein−protein interactions |scaled particle theory

Protein−protein interactions are essential for maintainingcellular homeostasis (1). Details of their equilibria under

thermodynamically ideal conditions have provided a trove ofinformation. Ideality in this sense refers to dilute solutions,where each monomer contacts only solvent or another monomer,conditions far removed from those in cells where protein−protein interactions evolved. In the cytoplasm, and other cellularcompartments and biological fluids, macromolecules can occupyup to 30% of the volume, and their concentrations often exceed300 g/L (2).Protein molecules take part in more-complex interactions

under nonideal conditions. The surrounding macromoleculesinfluence proteins in two ways, neither of which is significant indilute solution. Hard-core repulsions arise from high volumeoccupancy, because two molecules cannot occupy the same spaceat the same time. This volume exclusion favors the most compactstate of a protein (3). Chemical interactions comprise transientcontacts between protein surfaces arising from the diversechemical landscapes of proteins (4). When repulsive (i.e., likecharges), they favor the state that maximizes the distance be-tween charges, adding to the hard-core repulsions and stabilizingthe native state. Attractive chemical interactions (e.g., oppositecharges, hydrogen bonds) are destabilizing. We are beginning tounderstand how hard-core repulsions and chemical interactionsaffect protein stability (5), but there are few studies aboutcrowding effects on protein−protein interactions (6–9).Given the existential roles of both protein−protein interac-

tions and crowding in biology (10), we are undertaking efforts todetermine the effect of crowding on the simplest of proteincomplexes, homodimers. Our first endeavor, which involved aside-by-side homodimer, highlighted chemical interactions andshowed a small contribution from hard-core repulsions (11, 12).These results were predicted by Berg (12), who used scaledparticle theory to suggest that side-by-side dimers would be only

mildly influenced by hard-core repulsions. Berg also predictedthat more-compact dimers are more likely to be stabilized byhard-core repulsions. Here, we test this idea by changing theshape of a dimer in a controlled fashion.Scaled particle theory is based on statistical mechanics. For

situations like those investigated here, the theory considers so-lution nonideality as arising from the presence of cosolutes (13–15). As often applied, the solvent and cosolutes are consideredhard spheres, which leads to three consequences: Molecules onlyinteract when they touch, the interaction energy is purely re-pulsive, and the energy has a strong distance dependence. Theinability of billiard balls to interpenetrate is a macroscopic ex-ample. Water and cosolute concentration are expressed as vol-ume occupancy, Φ, the unitless parameter indicating the fractionof the volume they occupy. The reversible work (i.e., free energy)to produce a monomer- and dimer-sized hole in water and in acosolute-containing solution is calculated, and a thermodynamiccycle (16) is used to estimate the change in the free energyof dissociation (KD→M) in cosolute solution minus the valuein water, i.e., ΔΔG°′D→M, where a positive value indicatesstabilization.The theory has several shortcomings, including its spherical

assumptions, neglect of chemical interactions, including solva-tion, and its extreme sensitivity to sphere size and density (17,18). Nevertheless, it has been successfully applied to assess theeffects of crowding-induced hard-core interactions on proteinstability and protein−protein interactions (18–22). For instance,its application to protein stability led to the idea that crowding

Significance

Macromolecular crowding influences protein−protein interac-tions via hard-core repulsions and chemical interactions. Scaledparticle theory predicts that the effect of hard-core repulsionsdepends on the shape of the protein complex, and simple ideasabout chemical interactions predict a dominant role for thechemical qualities of the protein surface. The theory predictsthat a collapsed, ellipsoidal, dimer will be stabilized by hard-core repulsions, whereas a less collapsed, side-by-side, dimerwill not. We applied scaled particle theory to two dimers withnearly identical surfaces but different shapes. Our resultssupport the predictions; crowders that interact primarilythrough hard-core repulsions stabilize the ellipsoidal domain-swapped dimer more than the side-by-side dimer, whereascrowders that interact via chemical interactions have the sameeffect on both dimers.

Author contributions: A.J.G., G.B.Y., and G.J.P. designed research; A.J.G., G.M.P.G., andS.L.S. performed research; A.J.G. contributed new reagents/analytic tools; A.J.G.,G.M.P.G., S.L.S., and G.J.P. analyzed data; and A.J.G., G.M.P.G., S.L.S., G.B.Y., and G.J.P.wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Published under the PNAS license.1To whom correspondence should be addressed. Email: gary_pielak@unc.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1810054115/-/DCSupplemental.

Published online October 9, 2018.

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effects comprise both hard-core repulsions and attractive or re-pulsive chemical interactions (16, 23).We use the implementation of scaled particle theory (13)

described by Berg (12) to assess crowding effects. The monomersare assumed to be spheres. The dimers have twice the volume ofthe monomer, but their shapes, quantified as the eccentricity, L,is varied (Fig. 1). At the compact extreme, L = 0, the dimer is asphere. At the other extreme, L = 1, the dimer comprisestouching monomers (kissing spheres). Berg’s application showsthat shape matters. Treating water as a sphere of radius 1.4 Å,crowding favors more-compact (smaller L) dimers, but the sta-bilization disappears at L = ∼0.9 and then becomes slightlydestabilizing. Using a related form of the theory that treats thesolvent as a continuum also predicts crowding-induced stabili-zation that decreases, but never disappears, with decreasing L(12). The diminution arises because two spherical cavities any-where in the solution are more likely than two cavities next toeach other (12).The system we chose has several favorable attributes for

testing ideas about crowding and dimer formation. The B1 do-main of protein G (GB1; 6.2 kDa, pI 4.5) is a 56-residue modelglobular protein with a thermally stable 4β+α globular fold (24).The Gronenborn laboratory developed two GB1 homodimers ofknown structure (25–27) with 95% sequence identity but differ-ent eccentricities, allowing us to test the effect of hard-core re-pulsions and chemical interactions on dimer shape.

The A34F variant (Fig. 2) forms a dimer reminiscent of kissingspheres (Figs. 1 and 3) that does not require a large conforma-tional change (26, 28). Dimerization occurs because the Phe-34side chain becomes part of the hydrophobic core, displacing theTyr-33 side chain at the surface and causing the C-terminal endof the sole helix to unfold, forming a pocket for the Tyr-33 sidechain of the other monomer. The dimer is also stabilized byhydrogen bonds along the now adjacent β-sheets.The L5V;F30V;Y33F;A34F variant forms a more compact

domain-swapped dimer (Fig. 2) whose monomer is a partiallyfolded, molten-globule-like species (25, 27) (SI Appendix, Fig. S1)that undergoes refolding to form the dimer (Fig. 3). Swapping theturn between β-strand three and β-strand four results in inter-changed secondary structural units with concomitant formation ofseveral interprotein interactions. The volumes, solvent accessiblesurface areas, changes in solvent-accessible surface area (SASA),and measured free energies of dissociation are shown in Fig. 3.The properties of protein surfaces determine the chemical

interactions with cosolutes (29–33). An advantageous aspect ofthe GB1 system is that the interactions are similar for both di-mers because their primary structures, and hence their surfaces,are highly similar (Fig. 3). However, the change in SASA for thedomain-swapped dimer does not reflect its interface area, be-cause the peptide chains penetrate each other. In summary, theGB1 system is well suited for studying crowding effects on pro-tein complex shape, because the monomers are not far removedfrom spheres, and the dimers have different shapes but similarsurfaces.

ResultsScaled Particle Theory Predictions. Positive values of ΔΔG°′D→Mindicate an increase in dimer stability compared with dilute so-lution. Scaled particle theory calculations (Table 1) were per-formed as described by Berg (12) using the dimerization reactionwith a variable cavity shape (Berg’s equations, SI Appendix, Eqs.S1–S8). Cosolutes were assumed to be spheres. Small moleculeradii were estimated using molecular volume data from theChemAxon chemicalize database (https://chemicalize.com).Solvation was ignored. Protein radii were estimated from theirsurface areas and volumes obtained using Volume Area DihedralAngle Reporter (VADAR) and their structures [Protein DataBank (PDB) ID code 3V03 for BSA and PDB ID code 1DPX forlysozyme] (34).To apply Berg’s (12) ideas, we first estimated the dimer ec-

centricities. Distances between the centrally located 5′-protonon trp43 (35) and the protein surface were measured using aPython-based molecular-conversion utility (PyMOL) (36) givinga monomer radius of 11.8 Å, and an eccentricity of 0.71 forthe side-by-side dimer and 0.56 for the domain-swapped dimer(Fig. 1). We also assessed eccentricity by fitting the solvent-accessible surface areas and volumes to geometric shapes, which

Fig. 1. Scaled particle theory-derived values of ΔΔGo′D→M as a function of

eccentricity, L, at 10 values of L (solid symbols) of the indicated radii andvolume occupancies, Φ. As predicted by Berg (12), the more compactspherical, but not the side-by-side, dimer is stabilized. Shaded areas indicatethe estimated eccentricities of the GB1 dimers. The 4.1-Å species representssucrose, and the 35-Å species represents BSA.

Fig. 2. GB1 and its dimers (PDB ID codes 1GB1, 2RMM, and 1Q10).

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yielded an eccentricity of 0.77 for the side-by-side dimer and 0.53for the domain-swapped dimer. The ranges are shaded in thefigure. A complete list of input parameters is compiled in SIAppendix, Table S1.

Observations Using 19F NMR. To test the predictions from scaledparticle theory, we measured ΔΔG°′D→M using the approachdescribed in Materials and Methods and 5-fluorotryptophan-labeled GB1 in buffer (Fig. 4) and in a variety of small andlarge cosolutes at pH 7.5 and 298 K (Table 1). Comparison of15N−1H heteronuclear single quantum coherence (HSQC)data for the domain-swapped dimer (SI Appendix, Fig. S4) andthe side-by-side dimer (37) show that fluorine labeling doesnot significantly affect structure of the proteins.

DiscussionScaled Particle Theory. The predictions for the cosolutes tested(Table 1) agree with Berg’s (12) prediction that the hard-corecomponent of crowding has a larger stabilizing effect on themore compact domain-swapped dimer (38). Our calculationsignore the effect of solvation on size and the fact that thecosolutes, especially urea, are poorly modeled as spheres. Theselimitations do not, however, change the fact that the hard-corecomponent has a larger effect on the domain-swapped dimer.We did not apply the theory to the synthetic polymers, becausethese macromolecules cannot be accurately modeled as spheres,because, at the high concentrations used here (39–41), the in-dividual polymer molecules overlap to form a mesh (42). Thereason is exemplified by the concentration dependence of viscosity.At low concentrations (the so-called dilute regime), there is anapproximately linear relationship between viscosity and concen-tration, as is observed for small molecules. At higher concentra-tions, however, synthetic polymers form a mesh (the semidiluteregime), and there is a much steeper dependence. The intersectionbetween these regimes is called the overlap concentration, c*.Perhaps the best rationale for not treating synthetic polymers asspheres is that polymers form these highly viscous solutions,whereas spheres jam at a volume occupancy of ∼0.6 (43).

Control Small-Molecule Cosolutes. We divided the cosolutes intothree classes: small-molecule denaturants and stabilizers, syn-thetic polymers and their monomers, and proteins (Fig. 5). The

denaturant urea at 100 g/L is predicted by scaled particle theoryto stabilize the domain-swapped and side-by-side dimers by 0.61kcal/mol and 0.31 kcal/mol, respectively. We observe destabili-zations of 1.31 ± 0.05 kcal/mol and 0.25 ± 0.04 kcal/mol for thedomain-swapped and side-by-side dimers, respectively. Thepredicted and observed results are contradictory in both sign andmagnitude. The sign discrepancy highlights a key shortcoming ofscaled particle theory: It ignores chemical interactions betweenthe cosolute and the test protein, in this instance the attractiveinteraction between urea and the protein backbone (44). Themagnitude discrepancy means the domain-swapped dimer shouldbe more stabilized (less destabilized) than the side-by-side dimer.This discrepancy probably arises because the monomers are fun-damentally different. For the side-by-side dimer, the monomer is astable folded protein (26), but, for the domain-swapped dimer, themonomer is a molten globule with an ensemble average of theGB1 fold, but lacking stabilizing hydrogen bonds and salt bridges(SI Appendix, Fig. S1) (25, 27). Urea likely unfolds the globule,resulting in a destabilizing chemical interaction larger than thepredicted stabilization from scaled particle theory.Trimethylamine-N-oxide (TMAO) at 39 g/L is predicted to

stabilize the domain-swapped and side-by-side dimers by0.25 kcal/mol and 0.13 kcal/mol, respectively. We observe sta-bilizations of 0.16 ± 0.06 and 0.50 ± 0.06 kcal/mol, respectively.The less than expected stabilization of the domain-swapped di-mer may arise because the monomer is only partially structured(SI Appendix, Fig. S1) (25–27), and undergoes domain swappingto form the most thermodynamically favorable state. TMAO,a known protein stabilizer, compacts proteins (45–47). Suchcompaction likely favors a monomer conformation similar to thatof wild-type GB1, which would reduce the tendency to swapdomains and dimerize. Molecular dynamics simulations (48)suggest dimerization occurs via a slightly expanded monomer.TMAO would limit the expansion because it stabilizes compactstates.

Synthetic Polymer Cosolutes. These macromolecules are tradi-tionally used as cosolutes to mimic hard-core repulsions undercrowded conditions. We tested Ficoll-70, a 70-kDa branchedsucrose polymer, at 300 g/L and 8-kDa polyethylene (PEG) at200 g/L (Fig. 5A).We first studied their monomers, sucrose and ethylene glycol.

Sucrose stabilizes the domain-swapped dimer by 0.26 ± 0.06 kcal/mol;

Fig. 3. The van der Waals volumes, SASAs, measured free energies of dis-sociation, electrostatic surface potentials from PyMOL (36), and geometricrepresentations of the dimers.

Table 1. ΔΔG°′D→M values at 298 K predicted by scaled particletheory (SPT) and calculated from NMR data (pH 7.5) for thedomain-swapped (L = 0.5) and side-by-side dimer (L = 0.7)

ΔΔG°′D→M, kcal/mol*

Domain-swapped Side-by-side

Cosolute g/L SPT† NMR‡ SPT† NMR‡,§

Sucrose 300 1.38 0.26 ± 0.06 0.67 0.03 ± 0.04Ethylene glycol 200 1.50 −0.30 ± 0.06 0.76 −0.29 ± 0.05TMAO 38 0.25 0.16 ± 0.06 0.13 0.50 ± 0.06Urea 100 0.61 −1.31 ± 0.05 0.31 −0.25 ± 0.04BSA 100 0.14 0.51 ± 0.05 0.10 0.48 ± 0.06Lysozyme 50 0.09 −0.12 ± 0.05 0.05 −0.18 ± 0.05Ficoll-70 300 N/A{ 0.71 ± 0.06 N/A{ 0.15 ± 0.048-kDa PEG 200 N/A{ 0.39 ± 0.06 N/A{ −0.22 ± 0.03

*Positive values indicate increased dimer stability.†As described by Berg (12) using parameters from SI Appendix, Table S1.‡Uncertainties are the SD of the mean from triplicate analysis.§From Guseman and Pielak (37).{Ficoll and PEG cannot be simulated with scaled particle theory at theseconcentrations.

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this stabilization is predicted by scaled particle theory andlikely arises from an increased influence of hard-core repulsionson the more compact domain-swapped dimer (12, 22). Ethyleneglycol destabilizes the domain-swapped dimer by −0.30 ±0.06 kcal/mol. Compared with buffer alone, sucrose at 300 g/Lhas no effect on ΔG°′D→M of the side-by-side dimer, but ethyleneglycol decreases ΔG°′D→M by −0.29 ± 0.05 kcal/mol (37). Theincreased stabilization of the more compact domain-swappeddimer by sucrose is also consistent with theory (12, 22). Thedestabilization of the dimers by ethylene glycol is likely due toattractive interactions with the test protein; ethylene glycol in-teracts favorably with protein surfaces (49–52).Having assessed the monomers, we tested for, and found, a

stabilizing macromolecular effect. That is, both polymers aremore stabilizing than their respective monomers at the samemass-per-volume concentration. Ficoll stabilizes the side-by-sidedimer by 0.15 ± 0.04 kcal/mol compared with buffer, and PEGdestabilizes this dimer by −0.22 ± 0.03 kcal/mol (37), whereasboth synthetic polymers stabilize the domain-swapped dimer by0.71 ± 0.06 kcal/mol for Ficoll, and 0.39 ± 0.06 kcal/molfor PEG. This result is consistent with observations onother protein−protein interactions (37, 53), but differs from

observations on protein folding (54). As discussed above, wecannot make direct comparisons with scaled particle theory, butthe Ficoll and PEG results are consistent with Berg’s proposalthat the influence of hard-core repulsions on dimer formationdepends on the shape of the dimer complex. Specifically, themore compact domain-swapped dimer is stabilized more thanthe less compact kissing-sphere-shaped side-by-side dimer.

Protein Cosolutes. Unlike synthetic polymers, globular proteinsare roughly spherical (55, 56), allowing the application of scaledparticle theory. To understand how chemical interactions affectthe dimers, we used globular proteins with opposite net chargesat pH 7.5, BSA (66 kDa, pI 5) and lysozyme (14 kDa, pI 9), ascosolutes (Fig. 5B).Theory predicts that BSA at 100 g/L stabilizes the domain-

swapped dimer by 0.14 kcal/mol and the side-by-side dimer by0.10 kcal/mol. We observe larger stabilizations, 0.51 ± 0.05 kcal/moland 0.48 ± 0.06 kcal/mol, respectively. At pH 7.5, BSA is predictedto have a charge of −19, while both GB1 dimers are predicted tohave a charge of −4. The more-than-predicted stabilization can beexplained by electrostatic repulsions between BSA and acidicpatches on the surface of each dimer (29).For lysozyme (50 g/L), scaled particle theory predicts stabili-

zations of 0.09 kcal/mol and 0.05 kcal/mol for the domain-swapped and side-by-side dimers, respectively, but we observedestabilizations of 0.12 ± 0.05 kcal/mol and 0.18 ± 0.05 kcal/mol,respectively. These results are also explained by charge−chargeinteractions, because lysozyme has a positive charge of +7 atpH 7.5, while the dimers have a charge of −4. In summary,these results show, for both dimers, that chemical interactionscan modulate, and even overcome, the effects of hard-corerepulsions.The effect of protein cosolutes on ΔG°′D→M is the same for

each dimer. This agreement between values supports our hy-pothesis that similar protein surfaces result in similar chemicalinteractions. The GB1 dimer system effectively decouples thedifference in hard-core repulsions by changing the shape of theprotein complex while producing indistinguishable differences inchemical interactions, making it the ideal system to test scaledparticle theory predictions.

ConclusionsWe tested Berg’s (12) idea that shape can control the effects ofcrowding on protein complex stability, by using two nearly iden-tical proteins that form dimers with different shapes but similarsurfaces. Scaled particle theory predicts that the more compactdimer is generally more stabilized by crowding. This observationsuggests that shape dependence may have been used by biologyto control which proteins interact. That the compact domain-swapped dimer is more influenced by hard-core repulsions fromthe synthetic polymers than is the side-by-side dimer might beimportant for two reasons. First, it highlights which architecturewould be favored by the crowded cellular interior, providing ameans of stabilizing complexes important for metabolism, signal-ing, and maintaining biological homeostasis. Second, cells coulduse more self-contained proteins that would form dumbbell-shaped dimers to prevent weak protein−protein interactionsfrom being stabilized by the crowded interior. We observe thesedifferences in concentrated solutions of the relatively inert syn-thetic polymers, PEG and Ficoll. However, the predicted differ-ences can be entirely counteracted by electrostatic interactions, asshown by the stabilizing effect of BSA and the destabilizing effectof lysozyme, and attractive interactions, as shown by ethyleneglycol. It is important to point out, however, that, unlike the GB1-based system, most natural domain-swapped dimers exhibit ex-tremely slow off-rates. We conclude that, to gain biologicallyuseful knowledge about protein−protein interactions, we must

Fig. 4. The 19F NMR spectra of 5-fluorotryptophan-43−labeled domain-swapped dimer at pH 7.5 and 298 K at the indicated protein concentrations.

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study them, as Anfinsen (57) wrote, in “the environment for whichthey were selected, the so called physiological state.”

Materials and MethodsProtein Expression and Purification. The GB1 variants were expressed andpurified as described by ref. 37. A detailed description is found in SI Ap-pendix, Supplemental Materials and Methods.

Cosolutes. Solutions were prepared to the desired concentration in 20 mMsodium phosphate buffer. The pH was adjusted to 7.5 using concentrated HClor NaOH. Lyophilized lysozyme and BSA were purchased from Sigma-Aldrich.Their concentrations were monitored using extinction coefficients at 280 nmof 6,700 L·mg−1·cm−1 and 26,400 L·mg−1·cm−1, respectively (58, 59).

19F NMR. Samples were resuspended in buffer containing 10% D2O. Experi-ments were performed at pH 7.5 and 298 K on a Bruker Avance III HDspectrometer operating at a 19F Larmor frequency of 470 MHz equippedwith a cryogenic QCI probe and a tunable H/F channel. Spectra comprising31,047 points were acquired with a 2-s delay, an acquisition time of 1.4 s, anoffset of −130 ppm, and a sweep width of 22 ppm.

Data Analysis. NMR spectra were analyzed using Topspin3.5pl6. A 10-Hzexponential line-broadening was applied to each free-induction decay

before Fourier transformation. The 5-fluorotryptophan 43 in the domain-swapped dimer produces two resonances in slow exchange (37). Thedownfield resonance at −124.2 ppm corresponds to the monomer. The up-field resonance at −125.6 ppm corresponds to the dimer (Fig. 4) (shifts forthe side-by-side dimer are published) (37). Integration of each resonance wasused to obtain their relative populations. The fraction of dimer (Fd) wascalculated by dividing the area of the dimer peak by the sum of the areas.Data were fit to Eq. 1 using MATLAB (R2017A), where Pt is the total proteinconcentration and KD→M is the equilibrium constant for dissociation. Disso-ciation constants were converted to ΔG°′D→M values using the equationΔG°′D→M = −RTln(KD→M), where R is the universal gas constant and T is theabsolute temperature.

Fd =4Pt +Kd −

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiK2D→M + *8PtKd

q

4Pt. [1]

ACKNOWLEDGMENTS. We thank the members of the G.J.P. laboratory forinsightful discussions and Elizabeth Pielak for comments on the manuscript.Our research is supported by the National Science Foundation (Grants MCB-1410854 and CHE-1607359) and the National Institutes of Health [Grants F31GM126763 (to A.J.G.) and T32 GM008570], and was performed in facilitiessupported by National Cancer Institute (Grant P30 CA016086).

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