Large cosolutes, small cosolutes, and dihydrofolate reductase activity

Abstract

Protein enzymes are the main catalysts in the crowded and complex cellular interior, but their activity is almost always studied in dilute buffered solutions. Studies that attempt to recreate the cellular interior in vitro often utilize synthetic polymers as crowding agents. Here, we report the effects of the synthetic polymer cosolutes Ficoll, dextran, and polyvinylpyrrolidone, and their respective monomers, sucrose, glucose, and 1‐ethyl‐2‐pyrrolidone, on the activity of the 18‐kDa monomeric enzyme, Escherichia coli dihydrofolate reductase. At low concentrations, reductase activity increases relative to buffer and monomers, suggesting a macromolecular effect. However, the effect decreases at higher concentrations, approaching, and, in some cases, falling below buffer values. We also assessed activity in terms of volume occupancy, viscosity, and the overlap concentration (where polymers form an interwoven mesh). The trends vary with polymer family, but changes in activity are within threefold of buffer values. We also compiled and analyzed results from previous studies and conclude that alterations of steady‐state enzyme kinetics in solutions crowded with synthetic polymers are idiosyncratic with respect to the crowding agent and enzyme.

Abbreviations

DHF

dihydrofolate

DHFR

dihydrofolate reductase

HLADH

horse liver alcohol dehydrogenase

HRP

horseradish peroxidase

InhA

Mycobacterium tuberculosis 2‐trans‐enoyl‐ACP

LDH

lactate dehydrogenase

MDH

malate dehydrogenase

NADP+

nicotinamide adenine dinucleotide phosphate

NADPH

reduced NADP+, NEP, 1‐ethyl‐2‐pyrrolidone

PEG

polyethylene glycol

PGK

phosphoglycerate kinase

PVP

polyvinylpyrrolidone

THF

tetrahydrofolate

YADH

yeast alcohol dehydrogenase

Introduction

Most enzymes catalyze reactions inside cells, where the concentration of macromolecules is high,1, 2, 3 exceeding 300 g/L in Escherichia coli.4, 5 By contrast, most knowledge about enzyme kinetics comes from studies performed in dilute, buffered solutions. Biochemists have attempted to understand how cell‐like environments modulate steady‐state enzyme kinetics for over 40 years.6 An assumption of many pioneering efforts is that crowding effects arise mainly from hard‐core repulsions between the crowder and the enzyme.7 That is, as the concentration of crowding molecules increases, these repulsions increase the volume excluded to the enzyme, although it was acknowledged that crowding effects can also depend on the size, mechanism, and oligomeric nature of the enzyme.8

Hard‐core repulsions alone, however, cannot fully explain the effects of macromolecular crowding on enzymes. Several studies report excluded volume effects,9, 10, 11, 12 but other effects have been described, including “sieving,” or changes in the effective concentration of enzyme and substrate,6, 13 decreased diffusion of the enzyme, the substrate, or both,9, 10, 13 decreasing diffusion with increased crowder branching,14 crowder–substrate interactions,15 and crowder overlap.16, 17 Of particular interest is the point at which polymer coils begin to intertwine, called the overlap concentration (c*). Below c*, polymers act as individual coils (the dilute regime) while above this concentration, the polymers intertwine to form a semi‐dilute solution.18 Polymers are known to affect differentially protein stability19 and association rates16 above and below the c*.

The effects of crowding on enzyme steady‐state kinetics have proven difficult to predict. Crowding can raise, lower, or have no effect on steady‐state parameters (Table 1). Recent efforts highlight the importance of nonspecific chemical interactions with cellular components and cytoplasm mimetics, which can modulate and even overpower excluded volume effects.20, 21, 22, 23, 24, 25, 26, 27

Table 1.

Partial Specific Volumes (ν₂) and Overlap Concentrations (c*)

Cosolute	ν 2 (mL/g) at 25°C	c* (g/L)
PVP 55	0.8019	350
PVP 40	“	120
PVP 10	“	100
1‐methyl‐2‐pyrrolidoneb	0.9178	NAa
Ficoll 400	0.68	150
Ficoll 70	0.6579	250
sucrose	0.6180	NAa
dextran 20	0.6579	200
glucose	0.6278	NAa

From the literature or measured as described in the Materials and Methods.

^aNot applicable, monomers do not have an overlap concentration.

^bWe used the value for 1‐methyl‐2‐pyrrolidone in lieu of a value for 1‐ethyl‐2‐pyrrolidone.

Synthetic polymers are often used as crowding agents because they are believed to be chemically inert, although some investigators have demonstrated the existence of nonspecific protein–polymer interactions.25, 28, 29 Frequently used polymers include the branched sucrose polymer, Ficoll,9, 30, 31, 32 the glucose polymer, dextran, 9, 10, 11, 12, 13, 33, 34, 35 polyvinylpyrrolidone (PVP)10, 33 and polyethylene glycol (PEG).15, 36, 37, 38 To distinguish between chemical effects and those arising from the macromolecular nature of the polymer, the activity in polymer solutions should be compared to activity in solutions containing monomers: sucrose, glucose, 1‐ethyl‐2‐pyrrolidone (aka N‐ethylpyrrolidone, NEP), and ethylene glycol, respectively.

Here, we assess the effects of synthetic polymers and their respective monomers on the specific activity of E. coli dihydrofolate reductase (DHFR).39 We use the term cosolute to refer to the substance added to influence enzyme activity. We analyzed cosolute effects in terms of mass/volume concentration, volume occupancy, viscosity, and the overlap concentration of the polymers.

DHFR catalyzes the reduction of dihydrofolate (DHF) to tetrahydrofolate (THF) (Scheme 1). The role of DHFR in carbon metabolism makes it a prime drug target; the human isoform is inhibited by methotrexate in the treatment of cancer40 and the E. coli enzyme is the target of the antimicrobial therapeutic trimethoprim.39 DHFR begins its catalytic cycle bound to reduced NADPH. DHF then binds, and the enzyme catalyzes hydride transfer from NADPH to DHF, oxidizing NADPH to NADP+, and reducing DHF to THF. The oxidized cofactor is released, NADPH is rebound, and the THF is released, beginning the next cycle. The rate‐determining step in buffer is the final one, product release,41 which is gated by a flexible active site loop.42

Scheme 1.

DHFR reaction scheme. A hydride is transferred from NADPH to dihydrofolate (DHF), forming the reduced product, tetrahydrofolate (THF), and the oxidized cofactor, NADP⁺.

An advantage of using DHFR as a model enzyme is its monomeric state. Many enzymes examined under crowded conditions are oligomeric. In these instances, it can be difficult to determine if crowding alters activity, oligomerization, or a combination of both.8, 35 Therefore, any crowding effects on DHFR activity arise from protein–cosolute/or substrate‐cosolute—rather than intraprotein—effects.

Results

Polymer and monomer properties

We studied Ficoll 70, Ficoll 400, sucrose, dextran 20, glucose, PVP 10, PVP 40, PVP 55, and NEP. The number after the name of each polymer reflects its approximate molecular mass in kDa, and the small molecules comprise their respective monomers. We compiled or measured the partial specific volumes [(ν ₂), Table 1] and relative viscosities of the polymers as a function of concentration [Fig. 1]. The ν ₂ values were used to calculate fractional volume occupancies.43 The viscosity data were used to estimate the overlap concentrations (Table 1) by fitting the high‐ and low‐concentration regimes to lines and finding the concentration at which they intersected.44, 45

Figure 1.

Relative viscosity (A–C) as a function of concentration. (A) Sucrose, black; Ficoll 70, red; Ficoll 400, blue. (B) Glucose, black; dextran 20, red. (C) NEP, black; PVP 10, red; PVP 40, blue; PVP 55, green. Uncertainties for the viscosity measurements are the standard deviation of the mean from triplicate measurements.

DHFR activity

To prevent intermolecular disulfide formation, a double‐cysteine mutant (C85A; C152S) that retains the activity of wild type46 was used. Activity was quantified using Eq. (1),

$$\text{Activity}\left(\frac{\mu \text{mol}/\text{min}}{\text{mg} \text{DHFR}}\right)=\hspace{0.17em}\frac{({(\mathrm{\Delta }{\text{OD}}_{340}/\text{min})}_{\text{sample} }-{(\mathrm{\Delta }{\text{OD}}_{340}/\text{min})}_{\text{blank} }\times \hspace{0.17em}d\hspace{0.17em}(\text{cm})}{12.3 \text{mM} {\text{cm}}^{-1}\hspace{0.17em}\times \hspace{0.17em}V\hspace{0.17em}\times \hspace{0.17em}\frac{g}{L}\text{DHFR}},$$ (1)

where ${(\mathrm{\Delta }{\text{OD}}_{340}/\text{min})}_{\text{sample} }$ is the change in absorbance of the sample at 340 nm, ${(\mathrm{\Delta }{\text{OD}}_{340}/\text{min})}_{\text{blank} }$ is the change in absorbance of the blank, d is the path length, 12.3 mM cm⁻¹ is the extinction coefficient for the DHFR reaction,47 V is the volume of the reaction, and g/L DHFR is the enzyme concentration. Studies of C85A; C152S DHFR activity in 100 mM imidazole, pH 7.0, gave a specific activity of 49 ±2 μmol/min/mg, where the uncertainty is the standard deviation of the mean, in agreement with the reported value of 47 ± 2 μmol/min/mg under the same conditions.48 DHFR activity is sensitive to inorganic cations.48 Therefore, an HEPES/bis Tris propane buffer was used so the pH could be adjusted without adding salt. In 100 mM HEPES/bis‐Tris propane, pH 7.0, the activity of psWT DHFR in 27.9 ± 0.9 μmol/min/mg, where the uncertainty is the standard error of the mean. To mimic the macromolecule concentrations in cells, we assessed DHFR activity at concentrations up to 300 g/L [Fig. 2(A–C)] for many of the cosolutes, but PVPs were studied only up to 200 g/L, because the viscosities of PVP 55 and PVP 40 solutions at higher concentrations made mixing difficult.

Figure 2.

DHFR activity as a function of concentration (A–C), volume occupancy (D–F), and relative viscosity (G–I). (A, D, G) Sucrose, black; Ficoll 70, red; Ficoll 400, blue. (B, E, H): Glucose, black; dextran 20, red. (C, F, I) NEP, black; PVP 10, red; PVP 40, blue; PVP 55, green. Asterisks indicate c*, the polymer overlap concentration. Error bars represent standard deviations of the mean from triplicate experiments.

Discussion

Crowder identity

Classical theory treats crowding agents and test proteins as inert space‐filling molecules that interact solely via steric repulsions.43 Consistent with this idea, some studies find that at similar concentrations, polymers with similar molecular weights have indistinguishable effects on enzyme kinetics, as observed for yeast alcohol dehydrogenase (YADH) in PVP and dextran solutions.10 We observe minor differences in the effects of Ficoll, dextran, and PVP [Fig. 2(A–C)], and the magnitude of the relative activities for DHFR, 0.3–2.0 (Fig. 2) is common for studies in Ficoll and dextran.10, 13, 49 Small differences between Ficoll and dextran effects have been observed, and were ascribed to differences in polymer shape13, 50 and chemical interactions.15, 49 Therefore, we cannot interpret our data in terms of simple theory.

Concentration dependence

Studies of enzyme activity as a function of cosolute concentration also reveal trends that depend on enzyme and crowder. Monotonic decreases in activity and V _max are observed for several enzymes,9, 10, 11, 35, 51 and, in most instances, are attributed to a combination of excluded volume effects and decreased diffusion.

In Ficoll, dextran, and PVP, DHFR activity slightly increases at low concentrations (or is indistinguishable from buffer values) and then drops below or is equivalent to buffer values at high concentrations [Fig. 2(A–C)]. The Basso group49 observed similar behavior in PEG 6000, with an initial increase in k _cat up to 100 g/L attributed to a shift in the equilibrium toward a more compact isomeric state. At concentrations >200 g/L, k _cat decreased relative to buffer, likely due to a change in the rate‐determining step, a shift to an isoform that more strongly binds the substrate, or the introduction of chemical interactions.49 Plots of activity versus volume occupancy [Fig. 2(D–F)] are like those of activity versus g/L concentration, because the cosolutes have similar partial specific volumes (Table 1). The large uncertainties in activity in these polymers make us wary of over interpreting the data, except to observe that activity generally decreases with both increasing concentrations and increasing volume occupancy for all the cosolutes.

Overlap concentration

Polymers have been shown to affect protein stability and association rates differently above and below the overlap concentration.16, 19 To determine if the differential effects of polymers at high and low concentrations arise from the formation of a polymer mesh, we interpreted the data in the context of the c* and the corresponding dilute and semi‐dilute polymer regimes. Ficoll 70 and 400, Dextran 20, and PVP 55 exhibit a dip in activity between 100 and 200 g/L, a region associated with changes in polymer morphology as reflected by c* [Fig. 2(A–C)].19 In Ficoll 70, Ficoll 400, and PVP 55, there is a dip in activity near c*, however, immediately after the c* in Ficoll 70 and 400, activity values increase. A similar trend is observed for PVP 40, except the dip occurs well above c*. A monotonic decrease is observed in PVP 10, but for this polymer, all the concentrations tested are in the dilute regime. Although polymer overlap may explain the change in activity with concentration, the disparate effects do not coincide with c*, suggesting other factors come into play.

Viscosity

Viscosity increases with weight‐to‐volume concentration, but the effect is more dramatic for polymers [Fig. 2(G–I)].18 Increased viscosity decreases the diffusion of substrates and products,52 and can dampen enzyme motions associated with catalysis. All these outcomes decrease enzymatic rates.10 The general decrease in activity in polymer solutions as a function of viscosity [Fig. 2(G–I)] mirrors the observations for concentration [Fig. 2(A–C)] and volume occupancy [Fig. 2(D–F)], consistent with the idea that increased viscosity affects product release, the rate‐limiting step of the reaction.

Molecular mass

Simple theories predict that polymers of approximately the same size as the enzyme should have the largest effects,7, 53, 54 as observed by the Slade group with malate dehydrogenase (MDH).33 We do not observe a pattern. The Mas group hypothesized that larger enzymes are affected by polymer size but smaller enzymes are not. In agreement with this hypothesis, size‐dependence was observed for LDH (105 kDa)11 and alkaline phosphatase (105 kDa),13 but not for α‐chymotrypsin (25 kDa) and horseradish peroxidase (42 kDa).11, 55 Our observation that the monomeric, 18 kDa enzyme DHFR does not exhibit a size dependence is consistent with this hypothesis. However, neither the relationship observed by the Mas group nor the simple theory holds. For the large enzyme YADH (150 kDa), a size dependence was observed when isopropanol was used as a substrate, but not when ethanol was used,10, 34 and a size‐dependence was not observed for InhA (113 kDa).49, 56 Although the enzymes HLADH (80 kDa) and MDH (70 kDa) exhibited a size dependence, the direction of the change was opposite to that observed for LDH and alkaline phosphatase.10, 33 In summary, we do not observe an appreciable size‐dependence with DHFR, although our analyses of Ficoll and Dextran are complicated by the increased branching that occurs with increasing molecular weight.14 We also do not see an obvious pattern in published data.

Macromolecular effects

Historically, theory emphasized the role of hard‐core repulsions, but recently the importance of chemical interactions between crowders and proteins has been realized.20 A common test for a macromolecular effect is to compare a polymer to its constituent monomer.

Ficoll 70 increases activity relative to its monomer at concentrations <200 g/L, then has a statistically indistinguishable effect, while Ficoll 400 increases activity relative to the monomer at 100 g/L, and decreases relative sucrose at the highest concentrations. One explanation for the increase in activity at low concentrations of Ficoll 70 relative to sucrose could be the relief of nonspecific sucrose–folate interactions. The Howell group demonstrated that osmolytes, including sucrose, compete with DHFR to bind folate,57, 58 which likely lowers activity. Sucrose has been shown to slightly lower the k _cat of another folate‐metabolizing enzyme, E. coli FolM.54 In our experiments, increased activity in Ficoll 70 could arise from the shielding of individual sucrose monomers in the polymer. However, similar trends are observed for PVP, suggesting that a macromolecular effect is present at low concentrations. Additionally, this relief‐of‐sucrose‐substrate‐binding hypothesis is contradicted by both the observation that the rate enhancement in Ficoll 400, which should more effectively shield monomers, is less than the enhancement in Ficoll 70 and the observation that the effect of dextran is indistinguishable from that of glucose (except at 200 g/L). We conclude that there is a macromolecular effect for some polymers at low concentrations that subsides at higher concentrations, but the source of the effect remains unclear.

Cosolute effects are system‐specific

In summary, the effects of crowding on DHFR activity are complex. The origin for the initial increases observed in Ficoll 70 and PVP are unclear, and may arise from a variety of factors, including a decrease in chemical effects due to monomer shielding,59 a caging effect in polymers leading to increased enzyme‐substrate encounters,12 or, in the case of Ficoll, substrate binding by the monomer but not the polymer.57, 58 At higher concentrations, reduction in activity is likely due to a combination of slowed product release arising from dampened conformational fluctuations brought about by increased viscosity or steric‐repulsion induced compaction. The trends, however, differ between polymer families and sizes, suggesting that none of these factors fully explain the observations.

The complicated nature of macromolecular crowding effects on DHFR activity is observed for other enzymes (Table 2 and Supporting Information, Tables SI–SIII). Careful consideration of over 40 years of data reveals that crowding effects on enzyme kinetics are specific to the crowder and enzyme. For example, Ficoll 70 decreases the activity of alkaline phosphatase13 but increases the activity of both PGK60 and Ras.61 Similar mixed effects are observed for Ficoll 70 on k _cat, V _max, and K _m (Supporting Information, Tables SII and SIII).9, 30, 31, 32, 62, 63

Table 2.

Effects of Macromolecular Crowding on Enzyme Kinetics Compiled from 32 Studies (Supporting Information, Tables SI–SIII)

	Number reporting
Parameter	Increase	Decrease	No change
Activity	935, 36, 38, 60, 61, 67, 71, 72, 81	66, 13, 35, 36, 38, 68	613, 35, 36, 38, 67, 68
k cat	69, 31, 49, 57, 65, 69	99, 10, 30, 31, 49, 57, 62, 65, 70	89, 10, 30, 31, 49, 57, 62, 65
V max	815, 32, 33, 34, 37, 38, 63, 71	1210, 11, 12, 15, 33, 34, 36, 38, 55, 63, 66	315, 63, 66
K m	139, 10, 11, 15, 30, 32, 33, 49, 55, 57, 63, 65, 66	1610, 12, 15, 30, 31, 33, 34, 36, 37, 38, 49, 62, 63, 65, 70, 71	119, 10, 12, 15, 30, 31, 33, 34, 49, 57, 62, 63, 65, 69

Even for the same enzyme, crowding effects can depend on the substrate. Notably, the Slade group showed that dextran lowers the V _max of YADH for the forward (ethanol) reaction, while V _max is enhanced for the reverse (isopropanol) reaction (Supporting Information, Table SII). Comparison of reactions with deuterated and nondeuterated substrates reveal that for YADH, crowding effects are linked to the rate‐determining step.34 Substrate‐specific crowding effects are observed for PGK,30 HRP,15 and InhA.49

Conclusions

DHFR activity decreases slightly with increasing crowder concentration, volume occupancy, and viscosity. Comparisons to monomer data reveal a macromolecular effect at lower concentrations that decreases with increasing concentration. Examination of the data as a function of polymer size, however, did not yield a clear‐cut size dependence. Similarly, regions in the dilute and semi‐dilute polymer regimes do not coincide with changes in DHFR behavior. These observations indicate that polymer overlap is not the primary cause of the concentration, viscosity, and volume occupancy dependencies. Considering DHFR activity as a function of all these factors suggests that changes in DHFR activity with added cosolutes arise from a complex combination of polymer concentration, viscosity, volume occupancy, and overlap effects; no single aspect completely explains the trends. Ultimately, the changes in DHFR activity are small, in line with recent work on the enzyme InhA.49

In summary, a great deal of effort has been expended in attempts to understand how and why macromolecular crowding affects enzyme kinetics.6, 9, 10, 11, 12, 13, 15, 30, 31, 32, 33, 34, 35, 36, 37, 38, 55, 57, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72 However, a trend has not emerged, suggesting that steady‐state enzyme kinetics alone is not the best system for understanding the effects of macromolecular crowding and that more insight might be gained from combining studies on activity with studies of protein stability, folding, and diffusion.

Materials and Methods

Cosolutes

Dextran from Leuconostoc mesenteroides (∼20 kDa) was purchased from Alfa Aesar. Its monomer, glucose, was purchased from Fisher Scientific. Ficolls were purchased from Sigma Aldrich. Its monomer, sucrose, was acquired from Fisher Scientific. PVPs (∼10, 40, and 55 kDa) and NEP were purchased from Sigma Aldrich. The pH of all cosolute solutions was adjusted to pH 7.0 ± 0.1.

Protein preparation and purification

Site‐directed mutagenesis was performed using the Phusion^® High Fidelity polymerase (New England Biolabs) as specified in the Phusion^® manual on the pET‐22b plasmid containing the gene for E. coli DHFR to create the C85A;C152S variant. The forward primer to produce the C85A change comprised 5′‐GGC GGC CGG TGA CGT ACC AGA AAT CAT G‐3′. The reverse primer comprised 5′‐CAC CGG CCG CCG CGA TGG CTT CGT C‐3′. The forward primer to produce the C152S change comprised 5′‐GCT ATA GCT TCG AAA TCC TCG AGC GTC G‐3′. The reverse primer comprised 5′‐ CGA AGC TAT AGC TAT GCG AGT TCT GCG C‐3′. Plasmids harboring the gene were transformed into BL21 (DE3) Gold cells (Agilent). A single colony was picked to inoculate 50 mL of Lenox broth (LB, 10 g/L tryptone, 5 g/L yeast extract, 5 g/L NaCl). The culture as incubated at 37°C with shaking for 16 h. This culture was added to 950 mL of LB, and the culture was shaken at 37°C. When the optical density at 600 nm reached 0.6, isopropyl β‐d‐1‐thiogalactopyranoside (1 mM final concentration) was added. Expression was allowed to proceed for 1 h with shaking at 37°C. Cells were pelleted at 3,000g, resuspended in 50 mM Tris, 1 mM EDTA (pH 7.5) and frozen at −80°C.

Cells were thawed at room temperature and lysed by sonication (Fisher Scientific Sonic Dismembrator Model 500, 15% amplitude, 15 min, 67% duty cycle) in an ice bath. Cell debris was removed by centrifugation at 16,000g for 30 min at 10°C, and the supernatant was passed through a 0.45 μm filter.

The DHFR purification involved two chromatography steps using a GE AKTA FPLC. The first step was anion exchange chromatography (GE Q anion exchange column, 0–50% gradient, 50 mM Tris, 1 mM EDTA wash/50 mM Tris, 2 M NaCl, 1 mM EDTA eluent, pH 7.5). The second step was size exclusion chromatography (GE Superdex 75 column, eluted with 50 mM potassium phosphate, 150 mM KCl, 1mM EDTA, pH 6.8). Purified psWT DHFR was dialyzed into 10 mM HEPES/bis‐Tris propane, pH 7.0 at room temperature for 6 h. Buffer was refreshed after 3 h. The sample was flash frozen in an ethanol/CO₂(s) bath and lyophilized for 12 h (Labconco FreeZone) after dialysis and filtration through a 0.22 μm filter.

Enzyme activity

The buffer comprised 100 mM HEPES/bis‐Tris propane, pH 7.0 ± 0.1. Cosolute‐containing buffers were prepared by weight using an Ohaus PA64 balance. Purified lyophilized DHFR, dihydrofolic acid (DHF, Sigma Aldrich), and NADPH (Sigma Aldrich) were dissolved and stored in buffer without crowder. To prevent light‐induced degradation, NADPH and DHF were stored in foil‐covered amber tubes and stored on ice during activity assays. Stock solutions of DHF were stored at −20°C for no more than one week and NADPH for no more than one month.

Reaction mixtures were prepared in 10‐mm path length plastic cuvettes. psWT DHFR was added to the reaction mixture to a final concentration of 80 nM, and NADPH was diluted to 100 μM. The solution was mixed by inversion, and preincubated in the spectrophotometer (Cary 100, Agilent) at 25°C for 2 min to prevent hysteresis.73 After preincubation, DHF was added to a final concentration of 100 μM. After a 20 s dead time, arising from manual mixing, reaction progress was monitored by measuring the absorbance at 340 nm every 10 s for 2 min. The data were linear for the first 60 s. The absolute value of the slope from the no‐enzyme control was then subtracted, and the resulting value used to calculate the specific activity using Eq. (1).

For each series, samples were assayed in random order and interleaved with a buffer control. At each concentration, the specific activity for each triplicated sample was calculated using Eq. (1), and the resulting activities were averaged. Measures were performed in triplicate except for Ficoll 400 at 100, 200, and 300 g/L and PVP‐55 at 200 g/L, where 5 measurements were averaged, and 0 g/L dextran where two measurements were averaged. Activity values were rejected for 250 and 300 g/L PVPs and NEP, due to high background. Uncertainties represent the standard deviation of the mean. To account for day‐to‐day variation, specific activities in cosolutes were divided by the activity in buffer alone. Error propagation for division was performed using the square root of the sum of the squares.74

Polymer properties

The overlap concentration (c*)18 was calculated by plotting the viscosity as a function of polymer concentration.44, 45 Two distinct sections of the curve, representing the dilute and semi‐dilute regimes, were fit to lines.18 The polymer concentration at their intersection is c*. Viscosities and partial specific volumes were determined in water. For viscosity measurements, samples were prepared in increments of 10 g/L (PVP‐40 and 55), 25 g/L (Ficoll 70 and 400 and Dextran 20), or 50 g/L (PVP‐10), and the viscosities were measured in triplicate using a Viscolite 700 viscometer (Hydramotion Ltd., England). Viscosities were also measured for the monomers sucrose, glucose, and NEP. Viscosities were normalized to that of water at 298 K. Temperature was maintained using a Fischer Scientific Isotemp 210 water bath.

Volume occupancies were calculated for Ficoll 70 and Dextran 20,75 PVP‐10, 40, and 55,19 and sucrose and glucose76 by multiplying their partial specific volumes by the g/L concentration.43 We determined the partial specific volume of Ficoll 400 by measuring solution densities using a vibrating tube densitometer (DMA 5000, Anton Paar) and employing the linear relationship between density and mass fraction.77

Supporting information

Supporting Information