Protein Shape Modulates Crowding Effects

Protein shape modulates crowding effects

Alex 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 North Carolina 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 buffered mildly influenced by hard-core repulsions. Berg also predicted solutions with macromolecule concentrations of <10 g/L. In cells, that more-compact dimers are more likely to be stabilized by however, the macromolecule concentration can exceed 300 g/L, hard-core repulsions. Here, we test this idea by changing the resulting in nonspecific interactions between macromolecules. shape of a dimer in a controlled fashion. These interactions can be divided into hard-core steric repulsions Scaled particle theory is based on statistical mechanics. For and “soft” chemical interactions. Here, we test a hypothesis from situations like those investigated here, the theory considers so- scaled particle theory; the influence of hard-core repulsions on a lution nonideality as arising from the presence of cosolutes (13– protein dimer depends on its shape. We tested the idea using a 15). As often applied, the solvent and cosolutes are considered side-by-side dumbbell-shaped dimer and a domain-swapped ellip- hard spheres, which leads to three consequences: Molecules only soidal dimer. Both dimers are variants of the B1 domain of protein interact when they touch, the interaction energy is purely re- G and differ by only three residues. The results from the relatively pulsive, and the energy has a strong distance dependence. The inert synthetic polymer crowding molecules, Ficoll and PEG, sup- inability of billiard balls to interpenetrate is a macroscopic ex- port the hypothesis, indicating that the domain-swapped dimer is ample. Water and cosolute concentration are expressed as vol- stabilized by hard-core repulsions while the side-by-side dimer ume occupancy, Φ, the unitless parameter indicating the fraction shows little to no stabilization. We also show that protein coso- of the volume they occupy. The reversible work (i.e., free energy) lutes, which interact primarily through nonspecific chemical inter- to produce a monomer- and dimer-sized hole in water and in a actions, have the same small effect on both dimers. Our results cosolute-containing solution is calculated, and a thermodynamic suggest that the shape of the protein dimer determines the influ- cycle (16) is used to estimate the change in the free energy ence of hard-core repulsions, providing cells with a mechanism for of dissociation (KD→M) in cosolute solution minus the value − regulating protein protein interactions. in water, i.e., ΔΔG°′D→M, where a positive value indicates stabilization. macromolecular crowding | protein−protein interactions | The theory has several shortcomings, including its spherical scaled particle theory assumptions, neglect of chemical interactions, including solvation, and its extreme sensitivity to sphere size and density (17, rotein−protein interactions are essential for maintaining 18). Nevertheless, it has been successfully applied to assess the Pcellular homeostasis (1). Details of their equilibria under effects of crowding-induced hard-core interactions on protein thermodynamically ideal conditions have provided a trove of stability and protein−protein interactions (18–22). For instance, information. Ideality in this sense refers to dilute solutions, its application to protein stability led to the idea that crowding where each monomer contacts only solvent or another monomer, conditions far removed from those in cells where protein− Significance protein interactions evolved. In the cytoplasm, and other cellular compartments and biological fluids, macromolecules can occupy Macromolecular crowding influences protein−protein interac- up to 30% of the volume, and their concentrations often exceed tions via hard-core repulsions and chemical interactions. Scaled 300 g/L (2). particle theory predicts that the effect of hard-core repulsions Protein molecules take part in more-complex interactions depends on the shape of the protein complex, and simple ideas under nonideal conditions. The surrounding macromolecules about chemical interactions predict a dominant role for the influence proteins in two ways, neither of which is significant in chemical qualities of the protein surface. The theory predicts dilute solution. Hard-core repulsions arise from high volume that a collapsed, ellipsoidal, dimer will be stabilized by hard- occupancy, because two molecules cannot occupy the same space core repulsions, whereas a less collapsed, side-by-side, dimer at the same time. This volume exclusion favors the most compact will not. We applied scaled particle theory to two dimers with state of a protein (3). Chemical interactions comprise transient nearly identical surfaces but different shapes. Our results contacts between protein surfaces arising from the diverse support the predictions; crowders that interact primarily chemical landscapes of proteins (4). When repulsive (i.e., like through hard-core repulsions stabilize the ellipsoidal domain- charges), they favor the state that maximizes the distance be- swapped dimer more than the side-by-side dimer, whereas tween charges, adding to the hard-core repulsions and stabilizing crowders that interact via chemical interactions have the same the native state. Attractive chemical interactions (e.g., opposite effect on both dimers. charges, hydrogen bonds) are destabilizing. We are beginning to understand how hard-core repulsions and chemical interactions Author contributions: A.J.G., G.B.Y., and G.J.P. designed research; A.J.G., G.M.P.G., and affect protein stability (5), but there are few studies about S.L.S. performed research; A.J.G. contributed new reagents/analytic tools; A.J.G., CHEMISTRY crowding effects on protein−protein interactions (6–9). 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. Given the existential roles of both protein−protein interac- wrote the paper. tions and crowding in biology (10), we are undertaking efforts to The authors declare no conflict of interest. determine the effect of crowding on the simplest of protein This article is a PNAS Direct Submission. complexes, homodimers. Our first endeavor, which involved a Published under the PNAS license. side-by-side homodimer, highlighted chemical interactions and 1To whom correspondence should be addressed. Email: [email protected]. showed a small contribution from hard-core repulsions (11, 12). This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.

These results were predicted by Berg (12), who used scaled 1073/pnas.1810054115/-/DCSupplemental. BIOPHYSICS AND

particle theory to suggest that side-by-side dimers would be only Published online October 9, 2018. COMPUTATIONAL BIOLOGY

www.pnas.org/cgi/doi/10.1073/pnas.1810054115 PNAS | October 23, 2018 | vol. 115 | no. 43 | 10965–10970 Downloaded by guest on October 9, 2021 The A34F variant (Fig. 2) forms a dimer reminiscent of kissing spheres (Figs. 1 and 3) that does not require a large conformational change (26, 28). Dimerization occurs because the Phe-34 side chain becomes part of the hydrophobic core, displacing the Tyr-33 side chain at the surface and causing the C-terminal end of the sole helix to unfold, forming a pocket for the Tyr-33 side chain of the other monomer. The dimer is also stabilized by hydrogen 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 partially folded, molten-globule-like species (25, 27) (SI Appendix, Fig. S1) that undergoes refolding to form the dimer (Fig. 3). Swapping the turn between β-strand three and β-strand four results in inter- changed secondary structural units with concomitant formation of several interprotein interactions. The volumes, solvent accessible surface 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 ΔΔ o′ Fig. 1. Scaled particle theory-derived values of G D→M as a function of interactions with cosolutes (29–33). An advantageous aspect of eccentricity, L, at 10 values of L (solid symbols) of the indicated radii and the GB1 system is that the interactions are similar for both di- Φ volume occupancies, . As predicted by Berg (12), the more compact mers because their primary structures, and hence their surfaces, spherical, but not the side-by-side, dimer is stabilized. Shaded areas indicate are highly similar (Fig. 3). However, the change in SASA for the the estimated eccentricities of the GB1 dimers. The 4.1-Å species represents sucrose, and the 35-Å species represents BSA. domain-swapped dimer does not reflect its interface area, because the peptide chains penetrate each other. In summary, the GB1 system is well suited for studying crowding effects on pro- effects comprise both hard-core repulsions and attractive or re- tein complex shape, because the monomers are not far removed pulsive chemical interactions (16, 23). from spheres, and the dimers have different shapes but similar We use the implementation of scaled particle theory (13) surfaces. described by Berg (12) to assess crowding effects. The monomers are assumed to be spheres. The dimers have twice the volume of Results the monomer, but their shapes, quantified as the eccentricity, L, Scaled Particle Theory Predictions. Positive values of ΔΔG°′D→M is varied (Fig. 1). At the compact extreme, L = 0, the dimer is a indicate an increase in dimer stability compared with dilute so- sphere. At the other extreme, L = 1, the dimer comprises lution. Scaled particle theory calculations (Table 1) were per- touching monomers (kissing spheres). Berg’s application shows formed as described by Berg (12) using the dimerization reaction that shape matters. Treating water as a sphere of radius 1.4 Å, with a variable cavity shape (Berg’s equations, SI Appendix, Eqs. crowding favors more-compact (smaller L) dimers, but the sta- S1–S8). Cosolutes were assumed to be spheres. Small molecule bilization disappears at L = ∼0.9 and then becomes slightly radii were estimated using molecular volume data from the destabilizing. Using a related form of the theory that treats the ChemAxon chemicalize database (https://chemicalize.com). solvent as a continuum also predicts crowding-induced stabili- Solvation was ignored. Protein radii were estimated from their zation that decreases, but never disappears, with decreasing L surface areas and volumes obtained using Volume Area Dihedral (12). The diminution arises because two spherical cavities any- Angle Reporter (VADAR) and their structures [Protein Data where in the solution are more likely than two cavities next to Bank (PDB) ID code 3V03 for BSA and PDB ID code 1DPX for each other (12). lysozyme] (34). The system we chose has several favorable attributes for To apply Berg’s (12) ideas, we first estimated the dimer ec- testing ideas about crowding and dimer formation. The B1 do- centricities. Distances between the centrally located 5′-proton main of protein G (GB1; 6.2 kDa, pI 4.5) is a 56-residue model on trp43 (35) and the protein surface were measured using a globular protein with a thermally stable 4β+α globular fold (24). Python-based molecular-conversion utility (PyMOL) (36) giving The Gronenborn laboratory developed two GB1 homodimers of a monomer radius of 11.8 Å, and an eccentricity of 0.71 for known structure (25–27) with 95% sequence identity but differ- the side-by-side dimer and 0.56 for the domain-swapped dimer ent eccentricities, allowing us to test the effect of hard-core re- (Fig. 1). We also assessed eccentricity by fitting the solvent- pulsions and chemical interactions on dimer shape. accessible surface areas and volumes to geometric shapes, which

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

10966 | www.pnas.org/cgi/doi/10.1073/pnas.1810054115 Guseman et al. Downloaded by guest on October 9, 2021 denaturant urea at 100 g/L is predicted by scaled particle theory to stabilize the domain-swapped and side-by-side dimers by 0.61 kcal/mol and 0.31 kcal/mol, respectively. We observe destabilizations of 1.31 ± 0.05 kcal/mol and 0.25 ± 0.04 kcal/mol for the domain-swapped and side-by-side dimers, respectively. The predicted and observed results are contradictory in both sign and magnitude. The sign discrepancy highlights a key shortcoming of scaled particle theory: It ignores chemical interactions between the cosolute and the test protein, in this instance the attractive interaction between urea and the protein backbone (44). The magnitude discrepancy means the domain-swapped dimer should be 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 a stable folded protein (26), but, for the domain-swapped dimer, the monomer is a molten globule with an ensemble average of the GB1 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 the predicted stabilization from scaled particle theory. N Fig. 3. The van der Waals volumes, SASAs, measured free energies of dis- Trimethylamine- -oxide (TMAO) at 39 g/L is predicted to sociation, electrostatic surface potentials from PyMOL (36), and geometric stabilize the domain-swapped and side-by-side dimers by representations of the dimers. 0.25 kcal/mol and 0.13 kcal/mol, respectively. We observe stabilizations of 0.16 ± 0.06 and 0.50 ± 0.06 kcal/mol, respectively. The less than expected stabilization of the domain-swapped di- yielded an eccentricity of 0.77 for the side-by-side dimer and 0.53 mer may arise because the monomer is only partially structured for the domain-swapped dimer. The ranges are shaded in the (SI Appendix, Fig. S1) (25–27), and undergoes domain swapping figure. A complete list of input parameters is compiled in SI to form the most thermodynamically favorable state. TMAO, Appendix, Table S1. a known protein stabilizer, compacts proteins (45–47). Such

19 compaction likely favors a monomer conformation similar to that Observations Using F NMR. To test the predictions from scaled of wild-type GB1, which would reduce the tendency to swap particle theory, we measured ΔΔG°′D→M using the approach Materials and Methods domains and dimerize. Molecular dynamics simulations (48) described in and 5-fluorotryptophan- suggest dimerization occurs via a slightly expanded monomer. labeled GB1 in buffer (Fig. 4) and in a variety of small and TMAO would limit the expansion because it stabilizes compact large cosolutes at pH 7.5 and 298 K (Table 1). Comparison of states. 15N−1H heteronuclear single quantum coherence (HSQC) data for the domain-swapped dimer (SI Appendix,Fig.S4)and Synthetic Polymer Cosolutes. These macromolecules are tradi- the side-by-side dimer (37) show that fluorine labeling does tionally used as cosolutes to mimic hard-core repulsions under not significantly affect structure of the proteins. crowded conditions. We tested Ficoll-70, a 70-kDa branched sucrose polymer, at 300 g/L and 8-kDa polyethylene (PEG) at Discussion 200 g/L (Fig. 5A). Scaled Particle Theory. The predictions for the cosolutes tested We first studied their monomers, sucrose and ethylene glycol. (Table 1) agree with Berg’s (12) prediction that the hard-core Sucrose stabilizes the domain-swapped dimer by 0.26 ± 0.06 kcal/mol; component of crowding has a larger stabilizing effect on the more compact domain-swapped dimer (38). Our calculations ignore the effect of solvation on size and the fact that the Table 1. ΔΔG°′D→M values at 298 K predicted by scaled particle cosolutes, especially urea, are poorly modeled as spheres. These theory (SPT) and calculated from NMR data (pH 7.5) for the limitations do not, however, change the fact that the hard-core domain-swapped (L = 0.5) and side-by-side dimer (L = 0.7) component has a larger effect on the domain-swapped dimer. ΔΔG°′D→M, kcal/mol* We did not apply the theory to the synthetic polymers, because these macromolecules cannot be accurately modeled as spheres, Domain-swapped Side-by-side – because, at the high concentrations used here (39 41), the in- † ‡ † ‡,§ dividual polymer molecules overlap to form a mesh (42). The Cosolute g/L SPT NMR SPT NMR reason is exemplified by the concentration dependence of viscosity. Sucrose 300 1.38 0.26 ± 0.06 0.67 0.03 ± 0.04 At low concentrations (the so-called dilute regime), there is an Ethylene glycol 200 1.50 −0.30 ± 0.06 0.76 −0.29 ± 0.05 approximately linear relationship between viscosity and concen- TMAO 38 0.25 0.16 ± 0.06 0.13 0.50 ± 0.06 tration, as is observed for small molecules. At higher concentra- Urea 100 0.61 −1.31 ± 0.05 0.31 −0.25 ± 0.04 tions, however, synthetic polymers form a mesh (the semidilute BSA 100 0.14 0.51 ± 0.05 0.10 0.48 ± 0.06 CHEMISTRY regime), and there is a much steeper dependence. The intersection Lysozyme 50 0.09 −0.12 ± 0.05 0.05 −0.18 ± 0.05 between these regimes is called the overlap concentration, c*. Ficoll-70 300 N/A{ 0.71 ± 0.06 N/A{ 0.15 ± 0.04 Perhaps the best rationale for not treating synthetic polymers as 8-kDa PEG 200 N/A{ 0.39 ± 0.06 N/A{ −0.22 ± 0.03 spheres is that polymers form these highly viscous solutions, *Positive values indicate increased dimer stability. ∼ † whereas spheres jam at a volume occupancy of 0.6 (43). As described by Berg (12) using parameters from SI Appendix, Table S1. ‡ Uncertainties are the SD of the mean from triplicate analysis. Control Small-Molecule Cosolutes. We divided the cosolutes into §From Guseman and Pielak (37). three classes: small-molecule denaturants and stabilizers, syn- {Ficoll and PEG cannot be simulated with scaled particle theory at these BIOPHYSICS AND

thetic polymers and their monomers, and proteins (Fig. 5). The concentrations. COMPUTATIONAL BIOLOGY

Guseman et al. PNAS | October 23, 2018 | vol. 115 | no. 43 | 10967 Downloaded by guest on October 9, 2021 observations on protein folding (54). As discussed above, we cannot make direct comparisons with scaled particle theory, but the Ficoll and PEG results are consistent with Berg’s proposal that the influence of hard-core repulsions on dimer formation depends on the shape of the dimer complex. Specifically, the more compact domain-swapped dimer is stabilized more than the less compact kissing-sphere-shaped side-by-side dimer.

Protein Cosolutes. Unlike synthetic polymers, globular proteins are roughly spherical (55, 56), allowing the application of scaled particle theory. To understand how chemical interactions affect the dimers, we used globular proteins with opposite net charges at pH 7.5, BSA (66 kDa, pI 5) and lysozyme (14 kDa, pI 9), as cosolutes (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 by 0.10 kcal/mol. We observe larger stabilizations, 0.51 ± 0.05 kcal/mol and 0.48 ± 0.06 kcal/mol, respectively. At pH 7.5, BSA is predicted tohaveachargeof−19, while both GB1 dimers are predicted to haveachargeof−4. The more-than-predicted stabilization can be explained by electrostatic repulsions between BSA and acidic patches on the surface of each dimer (29). For lysozyme (50 g/L), scaled particle theory predicts stabilizations of 0.09 kcal/mol and 0.05 kcal/mol for the domain- swapped and side-by-side dimers, respectively, but we observe destabilizations of 0.12 ± 0.05 kcal/mol and 0.18 ± 0.05 kcal/mol, respectively. These results are also explained by charge−charge interactions, because lysozyme has a positive charge of +7at pH 7.5, while the dimers have a charge of −4. In summary, these results show, for both dimers, that chemical interactions can modulate, and even overcome, the effects of hard-core repulsions. The effect of protein cosolutes on ΔG°′D→M is the same for each dimer. This agreement between values supports our hypothesis that similar protein surfaces result in similar chemical interactions. The GB1 dimer system effectively decouples the difference in hard-core repulsions by changing the shape of the protein complex while producing indistinguishable differences in chemical interactions, making it the ideal system to test scaled particle theory predictions. Conclusions 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. We tested Berg’s (12) idea that shape can control the effects of crowding on protein complex stability, by using two nearly identical proteins that form dimers with different shapes but similar this stabilization is predicted by scaled particle theory and surfaces. Scaled particle theory predicts that the more compact likely arises from an increased influence of hard-core repulsions dimer is generally more stabilized by crowding. This observation on the more compact domain-swapped dimer (12, 22). Ethylene suggests that shape dependence may have been used by biology glycol destabilizes the domain-swapped dimer by −0.30 ± to control which proteins interact. That the compact domain- 0.06 kcal/mol. Compared with buffer alone, sucrose at 300 g/L swapped dimer is more influenced by hard-core repulsions from has no effect on ΔG°′D→M of the side-by-side dimer, but ethylene the synthetic polymers than is the side-by-side dimer might be glycol decreases ΔG°′D→M by −0.29 ± 0.05 kcal/mol (37). The important for two reasons. First, it highlights which architecture increased stabilization of the more compact domain-swapped would be favored by the crowded cellular interior, providing a dimer by sucrose is also consistent with theory (12, 22). The means of stabilizing complexes important for metabolism, signal- destabilization of the dimers by ethylene glycol is likely due to ing, and maintaining biological homeostasis. Second, cells could attractive interactions with the test protein; ethylene glycol in- use more self-contained proteins that would form dumbbell- teracts favorably with protein surfaces (49–52). shaped dimers to prevent weak protein−protein interactions Having assessed the monomers, we tested for, and found, a from being stabilized by the crowded interior. We observe these stabilizing macromolecular effect. That is, both polymers are differences in concentrated solutions of the relatively inert syn- more stabilizing than their respective monomers at the same thetic polymers, PEG and Ficoll. However, the predicted differ- mass-per-volume concentration. Ficoll stabilizes the side-by-side ences can be entirely counteracted by electrostatic interactions, as dimer by 0.15 ± 0.04 kcal/mol compared with buffer, and PEG shown by the stabilizing effect of BSA and the destabilizing effect destabilizes this dimer by −0.22 ± 0.03 kcal/mol (37), whereas of lysozyme, and attractive interactions, as shown by ethylene both synthetic polymers stabilize the domain-swapped dimer by glycol. It is important to point out, however, that, unlike the GB1- 0.71 ± 0.06 kcal/mol for Ficoll, and 0.39 ± 0.06 kcal/mol based system, most natural domain-swapped dimers exhibit ex- for PEG. This result is consistent with observations on tremely slow off-rates. We conclude that, to gain biologically other protein−protein interactions (37, 53), but differs from useful knowledge about protein−protein interactions, we must

10968 | www.pnas.org/cgi/doi/10.1073/pnas.1810054115 Guseman et al. Downloaded by guest on October 9, 2021 o′ Fig. 5. ΔΔG D→M at pH 7.5 and 298 K of the domain-swapped dimer and the side-by-side dimer in (A) synthetic polymers and their monomers and (B) urea, TMAO, and globular proteins. Positive values indicate increased dimer stability.

study them, as Anfinsen (57) wrote, in “the environment for which before Fourier transformation. The 5-fluorotryptophan 43 in the domain- they were selected, the so called physiological state.” swapped dimer produces two resonances in slow exchange (37). The downfield resonance at −124.2 ppm corresponds to the monomer. The up- Materials and Methods field resonance at −125.6 ppm corresponds to the dimer (Fig. 4) (shifts for Protein Expression and Purification. The GB1 variants were expressed and the side-by-side dimer are published) (37). Integration of each resonance was purified as described by ref. 37. A detailed description is found in SI Ap- used to obtain their relative populations. The fraction of dimer (Fd)was pendix, Supplemental Materials and Methods. calculated 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 protein Cosolutes. Solutions were prepared to the desired concentration in 20 mM concentration and KD→M is the equilibrium constant for dissociation. Disso- sodium phosphate buffer. The pH was adjusted to 7.5 using concentrated HCl ciation constants were converted to ΔG°′D→M values using the equation

or NaOH. Lyophilized lysozyme and BSA were purchased from Sigma-Aldrich. ΔG°′D→M = −RTln(KD→M), where R is the universal gas constant and T is the Their concentrations were monitored using extinction coefficients at 280 nm absolute temperature. −1 −1 −1 −1 of 6,700 L·mg ·cm and 26,400 L·mg ·cm , respectively (58, 59). qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi + − 2 + 4Pt Kd KD→M *8Pt Kd 19F NMR. Samples were resuspended in buffer containing 10% D O. Experi- F = . [1] 2 d 4P ments were performed at pH 7.5 and 298 K on a Bruker Avance III HD t spectrometer operating at a 19F Larmor frequency of 470 MHz equipped with a cryogenic QCI probe and a tunable H/F channel. Spectra comprising ACKNOWLEDGMENTS. We thank the members of the G.J.P. laboratory for 31,047 points were acquired with a 2-s delay, an acquisition time of 1.4 s, an insightful discussions and Elizabeth Pielak for comments on the manuscript. − offset of 130 ppm, and a sweep width of 22 ppm. Our research is supported by the National Science Foundation (Grants MCB- 1410854 and CHE-1607359) and the National Institutes of Health [Grants F31 Data Analysis. NMR spectra were analyzed using Topspin3.5pl6. A 10-Hz GM126763 (to A.J.G.) and T32 GM008570], and was performed in facilities exponential line-broadening was applied to each free-induction decay supported by National Cancer Institute (Grant P30 CA016086).

1. Sahni N, et al. (2015) Widespread macromolecular interaction perturbations in human 7. Phillip Y, Sherman E, Haran G, Schreiber G (2009) Common crowding agents have only

genetic disorders. Cell 161:647–660. a small effect on protein-protein interactions. Biophys J 97:875–885. CHEMISTRY 2. Zimmerman SB, Trach SO (1991) Estimation of macromolecule concentrations and 8. Kozer N, Kuttner YY, Haran G, Schreiber G (2007) Protein-protein association in excluded volume effects for the cytoplasm of Escherichia coli. J Mol Biol 222: polymer solutions: From dilute to semidilute to concentrated. Biophys J 92:2139–2149. 599–620. 9. Jiao M, Li H-T, Chen J, Minton AP, Liang Y (2010) Attractive protein-polymer inter- 3. Minton AP (1981) Excluded volume as a determinant of macromolecular structure and actions markedly alter the effect of macromolecular crowding on protein association reactivity. Biopolymers 20:2093–2120. equilibria. Biophys J 99:914–923. 4. Cohen RD, Pielak GJ (2017) A cell is more than the sum of its (dilute) parts: A brief 10. Spitzer J, Poolman B (2009) The role of biomacromolecular crowding, ionic strength, history of quinary structure. Protein Sci 26:403–413. and physicochemical gradients in the complexities of life’s emergence. Microbiol Mol 5. Davis CM, Gruebele M, Sukenik S (2018) How does solvation in the cell affect protein Biol Rev 73:371–388. folding and binding? Curr Opin Struct Biol 48:23–29. 11. Zhou H-X, Rivas G, Minton AP (2008) Macromolecular crowding and confinement: 6. Phillip Y, Kiss V, Schreiber G (2012) Protein-binding dynamics imaged in a living cell. Biochemical, biophysical, and potential physiological consequences. Annu Rev BIOPHYSICS AND

Proc Natl Acad Sci USA 109:1461–1466. Biophys 37:375–397. COMPUTATIONAL BIOLOGY

Guseman et al. PNAS | October 23, 2018 | vol. 115 | no. 43 | 10969 Downloaded by guest on October 9, 2021 12. Berg OG (1990) The influence of macromolecular crowding on thermodynamic ac- 37. Guseman AJ, Pielak GJ (2017) Cosolute and crowding effects on a side-by-side protein tivity: Solubility and dimerization constants for spherical and dumbbell-shaped mol- dimer. Biochemistry 56:971–976. ecules in a hard-sphere mixture. Biopolymers 30:1027–1037. 38. Christiansen A, Wittung-Stafshede P (2013) Quantification of excluded volume effects 13. Lebowitz JL, Helfand E, Praestgaard E (1965) Scaled particle theory of fluid mixtures. on the folding landscape of Pseudomonas aeruginosa apoazurin in vitro. Biophys J J Chem Phys 43:774–779. 105:1689–1699. 14. Reiss H (2007) Scaled particle methods in the statistical thermodynamics of fluids. Adv 39. Fissell WH, et al. (2007) Ficoll is not a rigid sphere. Am J Physiol Renal Physiol 293: Chem Phys 9:1–84. F1209–F1213. 15. Gibbons RM (1969) The scaled particle theory for particles of arbitrary shape. Mol 40. Acosta LC, Perez Goncalves GM, Pielak GJ, Gorensek-Benitez AH (2017) Large coso- Phys 17:81–86. lutes, small cosolutes, and dihydrofolate reductase activity. Protein Sci 26:2417–2425. 16. Saunders AJ, Davis-Searles PR, Allen DL, Pielak GJ, Erie DA (2000) Osmolyte-induced 41. Lee H, Venable RM, Mackerell AD, Jr, Pastor RW (2008) Molecular dynamics studies of changes in protein conformational equilibria. Biopolymers 53:293–307. polyethylene oxide and polyethylene glycol: Hydrodynamic radius and shape an- 17. Tang KES, Bloomfield VA (2000) Excluded volume in solvation: Sensitivity of scaled- isotropy. Biophys J 95:1590–1599. – particle theory to solvent size and density. Biophys J 79:2222 2234. 42. Rubinstein M, Colby RH (2003) Polymer Physics (Oxford Univ Press, Oxford). 18. Davis-Searles PR, Saunders AJ, Erie DA, Winzor DJ, Pielak GJ (2001) Interpreting the 43. Song C, Wang P, Makse HA (2008) A phase diagram for jammed matter. Nature 453: effects of small uncharged solutes on protein-folding equilibria. Annu Rev Biophys 629–632. – Biomol Struct 30:271 306. 44. Guinn EJ, Pegram LM, Capp MW, Pollock MN, Record MT, Jr (2011) Quantifying why 19. Christiansen A, Wang Q, Samiotakis A, Cheung MS, Wittung-Stafshede P (2010) Fac- urea is a protein denaturant, whereas glycine betaine is a protein stabilizer. Proc Natl tors defining effects of macromolecular crowding on protein stability: An in vitro/in Acad Sci USA 108:16932–16937. – silico case study using cytochrome c. Biochemistry 49:6519 6530. 45. Su Z, Mahmoudinobar F, Dias CL (2017) Effects of trimethylamine-N-oxide on the 20. Chalikian TV (2016) Excluded volume contribution to cosolvent-mediated modulation conformation of peptides and its implications for proteins. Phys Rev Lett 119:108102. – of macromolecular folding and binding reactions. Biophys Chem 209:1 8. 46. Auton M, Bolen DW (2004) Additive transfer free energies of the peptide backbone 21. Rivas G, Minton AP (2016) Macromolecular crowding in vitro, in vivo, and in between. unit that are independent of the model compound and the choice of concentration Trends Biochem Sci 41:970–981. scale. Biochemistry 43:1329–1342. 22. Sharp KA (2015) Analysis of the size dependence of macromolecular crowding shows 47. Auton M, Rösgen J, Sinev M, Holthauzen LMF, Bolen DW (2011) Osmolyte effects on that smaller is better. Proc Natl Acad Sci USA 112:7990–7995. protein stability and solubility: A balancing act between backbone and side-chains. 23. Schellman JA (2003) Protein stability in mixed solvents: A balance of contact in- Biophys Chem 159:90–99. teraction and excluded volume. Biophys J 85:108–125. 48. Malevanets A, Sirota FL, Wodak SJ (2008) Mechanism and energy landscape of do- 24. Gronenborn AM, et al. (1991) A novel, highly stable fold of the immunoglobulin main swapping in the B1 domain of protein G. J Mol Biol 382:223–235. binding domain of streptococcal protein G. Science 253:657–661. 49. Knowles DB, et al. (2015) Chemical interactions of polyethylene glycols (PEGs) and 25. Byeon I-JL, Louis JM, Gronenborn AM (2003) A protein contortionist: Core mutations glycerol with protein functional groups: Applications to effects of PEG and glycerol of GB1 that induce dimerization and domain swapping. J Mol Biol 333:141–152. on protein processes. Biochemistry 54:3528–3542. 26. Jee J, Byeon I-JL, Louis JM, Gronenborn AM (2008) The point mutation A34F causes 50. Shkel IA, Knowles DB, Record MT, Jr (2015) Separating chemical and excluded volume dimerization of GB1. Proteins 71:1420–1431. interactions of polyethylene glycols with native proteins: Comparison with PEG ef- 27. Byeon I-JL, Louis JM, Gronenborn AM (2004) A captured folding intermediate in- – volved in dimerization and domain-swapping of GB1. J Mol Biol 340:615–625. fects on DNA helix formation. Biopolymers 103:517 527. λ – 28. Jee J, Ishima R, Gronenborn AM (2008) Characterization of specific protein association 51. Chao S-H, Schäfer J, Gruebele M (2017) The surface of protein 6 85 can act as a – by 15N CPMG relaxation dispersion NMR: The GB1(A34F) monomer-dimer equilibrium. template for recurring poly(ethylene glycol) structure. Biochemistry 56:5671 5678. J Phys Chem B 112:6008–6012. 52. Crowley PB, Brett K, Muldoon J (2008) NMR spectroscopy reveals cytochrome – 29. Guseman AJ, Speer SL, Perez Goncalves GM, Pielak GJ (2018) Surface charge modulates c-poly(ethylene glycol) interactions. ChemBioChem 9:685 688. protein–protein interactions in physiologically relevant environments. Biochemistry 57: 53. Munari F, et al. (2017) Identification of primary and secondary UBA footprints on the – 1681–1684. surface of ubiquitin in cell-mimicking crowded solution. FEBS Lett 591:979 990. 30. Sarkar M, Li C, Pielak GJ (2013) Soft interactions and crowding. Biophys Rev 5: 54. Smith AE, Zhou LZ, Gorensek AH, Senske M, Pielak GJ (2016) In-cell thermodynamics – 187–194. and a new role for protein surfaces. Proc Natl Acad Sci USA 113:1725 1730. 31. Miklos AC, Sarkar M, Wang Y, Pielak GJ (2011) Protein crowding tunes protein sta- 55. Majorek KA, et al. (2012) Structural and immunologic characterization of bovine, bility. J Am Chem Soc 133:7116–7120. horse, and rabbit serum albumins. Mol Immunol 52:174–182. 32. Sarkar M, Lu J, Pielak GJ (2014) Protein crowder charge and protein stability. 56. Weiss MS, Palm GJ, Hilgenfeld R (2000) Crystallization, structure solution and re- Biochemistry 53:1601–1606. finement of hen egg-white lysozyme at pH 8.0 in the presence of MPD. Acta 33. Kyne C, Crowley PB (2017) Short arginine motifs drive protein stickiness in the Escherichia Crystallogr D Biol Crystallogr 56:952–958. coli cytoplasm. Biochemistry 56:5026–5032. 57. Anfinsen CB (1973) Principles that govern the folding of protein chains. Science 181: 34. Willard L, et al. (2003) VADAR: A web server for quantitative evaluation of protein 223–230. structure quality. Nucleic Acids Res 31:3316–3319. 58. Putnam F (1984) Progress in plasma proteins. The Plasma Proteins, ed Putnam F 35. Campos-Olivas R, Aziz R, Helms GL, Evans JNS, Gronenborn AM (2002) Placement of (Academic, New York), 2nd Ed, pp 1–44. 19F into the center of GB1: Effects on structure and stability. FEBS Lett 517:55–60. 59. Aune KC, Tanford C (1969) Thermodynamics of the denaturation of lysozyme by 36. Schrödinger LCC (2015) The PyMOL Molecular Graphics System, Version 2.0. Available guanidine hydrochloride. I. Depdendence on pH at 25 degrees. Biochemistry 8: at https://pymol.org/2/. Accessed September 30, 2018. 4579–4585.

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