Colocalization and Sequential Enzyme Activity in Aqueous Biphasic Systems: Experiments and Modeling

Abstract

Subcellular compartmentalization of biomolecules and their reactions is common in biology and provides a general strategy for improving and/or controlling kinetics in metabolic pathways that contain multiple sequential enzymes. Enzymes can be colocalized in multiprotein complexes, on scaffolds or inside subcellular organelles. Liquid organelles formed by intracellular phase coexistence could provide an additional means of sequential enzyme colocalization. Here we use experiment and computation to explore the kinetic consequences of sequential enzyme compartmentalization into model liquid organelles in a crowded polymer solution. Two proteins of the de novo purine biosynthesis pathway, ASL (adenylosuccinate lyase, Step 8) and ATIC (5-aminoimidazole-4-carboxamide ribonucleotide transformylase/inosine monophosphate cyclohydrolase, Steps 9 and 10), were studied in a polyethylene glycol/dextran aqueous two-phase system. Dextran-rich phase droplets served as model liquid compartments for enzyme colocalization. In this system, which lacks any specific binding interactions between the phase-forming polymers and the enzymes, we did not observe significant rate enhancements from colocalization for the overall reaction under our experimental conditions. The experimental results were used to adapt a mathematical model to quantitatively describe the kinetics. The mathematical model was then used to explore additional, experimentally inaccessible conditions to predict when increased local concentrations of enzymes and substrates can (or cannot) be expected to yield increased rates of product formation. Our findings indicate that colocalization within these simplified model liquid organelles can lead to enhanced metabolic rates under some conditions, but that very strong partitioning into the phase that serves as the compartment is necessary. In vivo, this could be provided by specific binding affinities between components of the liquid compartment and the molecules to be localized within it.

Introduction

Enzymes of metabolic pathways often exist as multienzyme complexes that are spatially organized within different cellular compartments or organelles (1). Substrate channeling through multienzyme complexes offers many advantages such as the transfer of metabolites from one active site to the next without diffusing throughout the rest of the cell, the sequestration of toxic or labile intermediates, and the reduction of competing reactions from other enzymes (2, 3, 4). Sequential enzymes can colocalize by binding to each other or to a scaffold such as another protein, membrane, or cytoskeletal component (5, 6, 7). The citric acid cycle is a hallmark example of a scaffold-bound multienzyme complex in which all of the enzymes are bound to the inner mitochondrial membrane (8, 9). Recent reports of liquid-like organelles in both cytoplasm and nucleoplasm of eukaryotic cells suggest additional means of colocalization (10, 11, 12). These liquid organelles are thought to be the result of intracellular phase separation, and therefore simple partitioning of enzymes into one of the coexisting phases could offer a means of enzyme colocalization in which enzymes need not be bound to a scaffold. Hence, specific or nonspecific binding interactions with components of the compartment would not be required, but could also be present.

Artificial colocalization of sequential enzymes has been achieved using a variety of scaffolds, such as proteins (13, 14), nanoparticles (15, 16, 17), nanostructured DNA (18), nanostructured RNA (19), and microfluidic channels (20). Many of these approaches have resulted in increased reaction rates and product flux (1, 21, 22) and have provided insight into the design of artificial multienzyme complexes for industrial synthesis of valuable molecules, such as biofuels (23). Colocalization of two enzymes does not always guarantee that a large increase in overall reaction rate will be observed (24, 25). The interenzyme distance, enzyme active site orientation, and relative activities of the enzymes can affect the catalytic efficiency of an artificial multienzyme complex (25). There has been considerably less effort toward the study of in vitro liquid compartments for multiple enzyme colocalization. Freely-diffusing enzymes concentrated together within a micron-scale liquid phase compartment are presumably not as fully colocalized as are enzymes bound to a shared scaffold, and have neither fixed separation nor orientation with respect to each other. Thus, differences in the kinetic consequences of colocalization can be anticipated between these systems.

An aqueous two-phase system (ATPS) where biomolecules concentrate into one phase by partitioning can serve as an in vitro model system for artificial liquid organelles (26, 27, 28). One or both phases in which biochemical reactions can occur is macromolecularly crowded, providing excluded volume and chemical interactions, which is reminiscent of the intracellular milieu. Macromolecular crowding can alter enzyme conformation, substrate binding, etc., and has been reported to increase, decrease, or not change enzyme activity, depending on the system (29, 30, 31, 32, 33). In addition to crowding, enzymes can be concentrated into one phase of the ATPS, resulting in higher local concentration and concomitant rate increases (34, 35). Few examples of sequential enzyme colocalization in ATPS have appeared. Crosby et al. (36) observed an 18-fold increase in product yield when the actinorhodin polyketide synthase complex and its substrate were partitioned in poly(diallyldimethylammonium chloride)/ATP coacervates; the coacervate matrix helped stabilize the complex. When glucose oxidase and horseradish peroxidase were partitioned in a PEG/citrate ATPS, sequential activity was limited due to accumulation of the enzymes in a different phase from the substrate, such that reaction could only occur at the interface (37). In both sequential reaction examples, only one of the phases was macromolecularly crowded, unlike intracellularly where all liquid phases are expected to contain substantial biopolymer concentrations. Here, we used a PEG/dextran ATPS in which both phases are crowded with macromolecules. When mixed, the result is dextran-rich phase droplets dispersed within a continuous PEG-rich phase. The dextran-rich phase droplets serve as model liquid compartments that contain a local high concentration of enzyme because of simple partitioning, rather than any specific biorecognition.

We investigate two sequential enzymes from the de novo purine biosynthetic pathway in the PEG/dextran ATPS. The purine pathway in humans consists of six proteins with 10 enzymatic steps, with the final step being the synthesis of IMP (inosine monophosphate). The enzymes of this pathway have been shown to reversibly colocalize in vivo (38), forming structures termed “purinosomes”. Purinosomes are visualized as cytoplasmic puncta that vary in size and shape (0.2–0.9 μm) (39). Purinosome assembly is thought to be mediated by interactions with microtubules and protein-protein interactions in which several pathway enzymes serve as a scaffold for assembly of the rest (40, 41, 42). These structures have not been considered to be liquid organelles, and indeed some researchers suggest that they could be aggregated protein/stress bodies (43, 44). Purinosomes, nonetheless, were recently shown to share some important features with liquid phase domains in terms of compartment size, absence of a delimiting membrane, and their transient nature (39, 42). Additionally, purinosome formation correlates with pathway activity, indicating a kinetic advantage to enzyme colocalization in these bodies (4, 40, 45). The local concentration increase of these enzymes due to purinosome formation has not been quantified, but published images indicate that while the signal due to labeled enzymes is strongest in the purinosomes, some enzyme remains free in the cytoplasm (38, 42). In addition, unrelated to this pathway, incomplete compartmentalization has been quantified for other proteins, for example for the proteasome subunit Pre9, which partitions between the cytoplasm and membrane of yeast (46). Our model system allows us to investigate the effect of incomplete compartmentalization on sequential enzyme reactions.

Two proteins from the pathway, ASL (adenylosuccinate lyase, Step 8) and ATIC (5-aminoimidazole-4-carboxamide ribonucleotide transformylase/inosine monophosphate cyclohydrolase, Steps 9 and 10) are investigated here. ASL and ATIC were chosen for this study because, in addition to partitioning in vivo between the purinosomes and their surroundings (42), both enzymes are relatively stable in buffer solution, and they have been expressed, purified, and characterized previously (47, 48). They are found to be associated with each other (and the rest of the purinosome) (41), and the AICAR substrate is commercially available. The enzymes partition into the dextran-rich phase of a PEG/dextran ATPS. By decreasing the relative volume of the dextran-rich phase to the PEG-rich phase (34), enzymes were increasingly colocalized to that phase. The resulting sequential enzyme activity was similar, regardless of the volume of the dextran-rich phase. Experimental results could be understood in the framework of a mathematical model that also enabled prediction of additional conditions not amenable to experiment.

Materials and Methods

Materials

Human ASL plasmid DNA and human ATIC (AICAR transformylase/IMP cyclohydrolase) plasmid DNA were provided by the Stephen J. Benkovic group at Pennsylvania State University (University Park, PA). Poly(ethylene glycol) 8000 Da, dextran from Leuconostoc mesenteroides 9000–11,000 Da, AICAR (5-aminoimidazole-4-carboxamide ribonucleotide), potassium chloride, glycine, lysozyme, sodium dodecyl sulfate, Coomassie Plus Reagent (Thermo Fisher Scientific, Waltham, MA), DL-dithiothreitol, bromophenol blue, Amicon Ultracel filters (MWCO 10 kDa; EMD Millipore, Billerica, MA), Trizma base, and Trizma hydrochloride were purchased from Sigma-Aldrich (St. Louis, MO). Rosetta 2(DE3)pLysS competent Escherichia coli cells and BL21 (DE3) competent E. coli cells were from Novagen (Madison, WI). Yeast extract, tryptone, agar, PMSF (phenylmethylsulfonyl fluoride), acrylamide/bis-acrylamide 19:1, TLC PEI cellulose F plates, ammonium acetate, ammonium hydroxide, methanol, potassium phosphate monobasic, and potassium phosphate dibasic were acquired from EMD Chemicals (Darmstadt, Germany). Kanamycin sulfate was obtained from Calbiochem (Darmstadt, Germany). Complete EDTA-free protease inhibitor cocktail tablets were purchased from Roche (Indianapolis, IN). Ni-NTA His-Bind resin was obtained from Qiagen (Hilden, Germany). Tetramethylethylenediamine was purchased from IBI Scientific (Peosta, IA). Glacial acetic acid and fumaric acid were acquired from Mallinckrodt Baker (Phillipsburg, NJ). Glycerol and sodium chloride were obtained from BDH Chemicals (West Chester, PA). Slide-A-Lyzer dialysis cassettes (MWCO 10 kDa) and albumin standards were acquired from Thermo Fisher Scientific. Alexa Fluor 488 C₅ maleimide, Alexa Fluor 647 NHS ester labeling kit, and 13 mm Secure-Seal Spacers were purchased from Life Technologies (Carlsbad, CA). mPEG-NH2 MW 5000 was obtained from Shearwater Polymers (Huntsville, AL). Deionized water with a resistivity of 18.2 MΩ-cm from a NANOpure Diamond Water Purification System (Barnstead, Van Nuys, CA) was used for all experiments. Buffers were filtered using 0.45 μm pore size Nalgene filter units (Nalge Nunc, Rochester, NY). All reagents were used as received without further purification.

Expression and purification of enzymes

N-terminal hexahistidine-tagged ASL plasmid DNA in a pET-28 vector was transformed into Rosetta 2(DE3)pLysS competent E. coli cells according to the Novagen protocol and was expressed and purified as reported by Lee and Colman (47) with several adaptations. The cell pellet (∼1 g wet cell pellet per 500 mL cell culture) was dissolved in 50 mL of 50 mM potassium phosphate, pH 8.0, 300 mM potassium chloride, and 10% glycerol lysis buffer. A protease inhibitor cocktail tablet of 10 μg/mL phenylmethylsulfonyl fluoride and 1 mg/mL lysozyme were added and the mixture was stirred for 30 min. The mixture was sonicated on ice using a model No. S-4000 Sonicator (Misonix, Farmingdale, NY). Pulse durations of 15 s at 50% amplitude were followed by a 45 s delay between pulses where the solution was placed in an ice bath, for a total pulse time of 5 min. Cell debris was removed by centrifugation (15,000 × g for 30 min at 4°C). The cell lysate was incubated with Ni(II)-NTA resin and 1% Triton X-100 to inhibit nonspecific protein binding for at least 1 h on an orbital shaker. The cell lysate was transferred to a column and the Ni(II)-NTA resin was washed with one-column volume of lysis buffer and subsequently washed with one-column volume of 20-mM imidazole to remove nonspecific protein binding. A 10-step gradient of lysis buffer to 500 mM imidazole with lysis buffer was used to elute ASL in 10 mL increments and protein purity was determined with sodium dodecyl sulfate polyacrylamide gel electrophoresis. Pure fractions of ASL were concentrated to ∼20% the original volume with centrifugal filter units (MWCO 10 kDa) and dialyzed against a 50 mM potassium phosphate, pH 7.0, 150 mM potassium chloride, 1 mM dithiothreitol, 10% glycerol storage buffer to be stored in small enzyme aliquots at −80°C. Enzyme concentration was determined by the standard Bradford assay utilizing a 1.5 mL Coomassie Plus Reagent (Thermo Fisher Scientific) and 50 μL of sample.

The pET-28 N-terminal hexahistidine-tagged ATIC vector was transformed into BL21 (DE3) competent E. coli cells as instructed by Novagen protocol. ATIC was subsequently expressed and purified as indicated by Wolan et al. (48). Cell lysis and enzyme purification was done as described for ASL with lysis buffer (50 mM sodium phosphate, pH 8.0, 300 mM sodium chloride, and 20 mM imidazole). After the pure fractions were concentrated, ATIC was dialyzed against a 20 mM Tris (pH 7.5), 150 mM sodium chloride, and 50 mM potassium chloride buffer. ATIC was quantified by the Bradford assay and was stored in aliquots at 4°C.

SAICAR synthesis

SAICAR was prepared and purified as described by Zikánová et al. (49) with several adaptations. Fumaric acid stock solutions were prepared in the reaction buffer and adjusted to pH 7.0 with sodium hydroxide (50). The 1 mL reaction volume contained 2.6 mM AICAR and 20 mM fumaric acid in a 10 mM Tris, pH 7.5, 10 mM potassium chloride buffer (49). The final concentration of ASL was 0.4 mg/mL and the reactions were allowed to proceed for 5 h at room temperature. Enzyme was removed by centrifugal filter units (MWCO 10 kDa) and the reaction mixture was concentrated to 100 μL via a Savant DNA 120 Speed Vac (Thermo Fisher Scientific) at ambient temperature. Higher temperature settings yielded the pink compound described by van den Bergh (51). Aliquots of 20 μL were spotted on PEI-cellulose TLC plates to provide adequate separation of the concentrated product with 1 M ammonium acetate. Product was eluted with 2 mL of 1 M ammonium hydroxide overnight on an orbital shaker and the supernatant was subsequently evaporated to dryness with a Savant DNA 120 Speed Vac (Thermo Fisher Scientific). SAICAR was resuspended in 33 mM Tris buffer, pH 7.4, 25 mM potassium chloride and the concentration was determined spectrophotometrically at 269 nm using the molar extinction coefficient 13.1 × 10³ M⁻¹ cm⁻¹ (49). Aliquots were stored at −80°C.

10-fTHF synthesis

The cofactor 10-formyltetrahydrofolic acid was prepared as described by Rabinowitz (52) and Rowe (53). After purification, aliquots were stored at −80°C. Concentrations were determined before use by spectrophotometry using the extinction coefficient of 9540 M⁻¹ cm⁻¹ (54).

ATPS preparation

For binodal determination, separate 25% (w/w) PEG 8 kDa and 25% (w/w) dextran 10 kDa stock solutions were prepared with 33 mM Tris, pH 7.4, 25 mM potassium chloride buffer (55) and samples with varying percentages of polymers were prepared near the expected binodal to determine at which concentrations the phase separation occurred. For assays and partitioning experiments, a 10% (w/w) PEG 8 k and 10% (w/w) dextran 10 k in the same buffer was prepared and physically separated. The phases were then recombined at the desired PEG/dextran volume ratios. Samples were subsequently concentrated by a Speed Vac (Thermo Fisher Scientific) so that upon addition of enzymes and/or substrates, the ATPS would be diluted to its original concentration. This ensures the reconstituted volume ratios remain on the same tie line and was done for all described experiments. The viscosity of the phases was measured with an Ostwald viscometer.

Phase composition determination

The polymer composition of each phase was determined using a combination of refractometry and polarimetry (56). Refractive index measurements were done using an Abbe Autorefractometer (Leica Geosystems, Norcross, GA). Polarimetry measurements were done using a model No. 343 Polarimeter (PerkinElmer, Billerica, MA). The concentration of dextran 10 kDa was determined by polarimetry, using a standard curve of known concentrations of dextran. The concentration of PEG was determined using refractometry. Calibration curves of known weight percents of PEG 8 kDa and dextran 10 kDa were prepared, and the refractive index of each of the standards and the PEG-rich and dextran-rich phases was measured. The contribution of the refractive index from dextran was subtracted from the total refractive index and the remaining refractive index was attributed to PEG 8 kDa.

Partitioning coefficients

To determine enzyme partitioning, ASL was labeled at amines using succinimidyl ester functionalized Alexa Fluor 647 (degree of labeling: 4.8 dyes/tetramer), and ATIC was labeled at thiols using C₅-maleimide Alexa Fluor 488 (degree of labeling: 1.1 dyes/dimer). Both enzymes were labeled according to Invitrogen (Carlsbad, CA) protocol, with the exception that enzyme concentration was 5 mg/mL instead of the suggested 2 mg/mL to prevent overlabeling. Upon addition of enzyme to the previously concentrated ATPS samples at a final concentration of 100 nM, samples were allowed to mix on a Tube Rotator Unit (VWR International, Radnor, PA) for 1 h or overnight and were phase-separated by centrifugation. The partitioning coefficient of each of the enzymes was determined within the ATPS at a 1:1 PEG/dextran volume ratio (bulk fluorescence measurements) and a 9:1 PEG/dextran volume ratio (confocal microscopy measurements), using standard curves of each enzyme (ASL and ATIC) in each phase (PEG-rich phase and dextran-rich phase). Bulk fluorescence was measured using a Fluorolog 3-21 fluorimeter with the software FluorEssence (Horiba Jobin Yvon, Edison, NJ). Confocal microscopy images were acquired using a model No. TCS SP5 Laser-Scanning Confocal Inverted Microscope with a 63× oil objective (Leica Microsystems, Buffalo Grove, IL). Samples were vortexed before imaging. Enzyme partitioning was measured individually and with both enzymes together. The predicted concentrations of ASL and ATIC in each phase at each volume ratio were calculated using the measured partitioning coefficients, as described by Strulson et al. (34).

The partitioning of SAICAR, AICAR, 10-fTHF, and IMP was measured individually in a 1:1 PEG/dextran volume ratio at a final concentration of 100 μM. Samples were mixed and phase-separated by centrifugation and the concentration in each phase was determined by high-performance liquid chromatography (HPLC). Before analysis, aliquots from each phase were diluted 2× with 1 M sodium hydroxide.

HPLC analysis of ATPS

The HPLC system consisted of a 1260 Infinity Quaternary Pump and 1260 Infinity Autosampler coupled to a 1260 Infinity thermostated column compartment (Agilent Technologies, Santa Clara, CA) using a model No. 10-SAX anion-exchange column (0.42 × 22 cm; Partisil, Peterborough, Ontario, Canada) and an anion guard cartridge purchased from Mac-Mod Analytical (Chadds Ford, PA). Absorbance of SAICAR and AICAR were monitored at 267 nm and IMP was monitored at 250 nm with a model No. 1260 diode array detector (Agilent Technologies). The metabolites were eluted with a flow rate of 2.0 mL/min with a 25 min concave gradient (t_G), where n = 7 was used, going from 7.0 mM potassium phosphate, pH 3.0 to 250 mM potassium phosphate, 500 mM KCl, pH 3.8 (Eq. 1) (57) Once the gradient reached 100%, the method was completed with a 5-min flush of the more concentrated eluent before a 5-min ramp to the initial conditions. Concentrations were calculated by measuring the peak area of the samples and standards of known concentration:

$$\%\text{Strong}\text{Eluent}={\left(\frac{t}{t_G}\right)}^n\times 100.$$ (1)

Enzyme assays: Michaelis-Menten kinetics in the individual phases

ASL assays were conducted with adaptations from a previously described method (58) using the difference extinction coefficient of 700 M⁻¹ cm⁻¹ at 267 nm (59) with a model No. 8453 Diode-Array UV-Visible Spectrometer with the software ChemStation (both from Agilent Technologies). SAICAR was varied from 0 to 100 μM and the ASL concentration was 50 nM. Product formation was measured for 5 min and the slope of the linear portion of the curve was used to measure activity. The standard Michaelis-Menten equation (Eq. 2) was used to fit the data in order to determine K_M and V_max using Igor Pro (WaveMetrics, Portland, OR) nonlinear regression analysis. The Michaelis-Menten parameters of the AICAR transformylase activity of ATIC were determined by adaptations from a previous method (54) using a difference extinction coefficient of 19,700 M⁻¹ cm⁻¹ at 298 nm. The final concentration of ATIC was 50 nM. The K_M and V_max of AICAR was determined by varying the AICAR concentration from 0 to 100 μM in the presence of 200 μM 10-fTHF. Absorbance measurements were collected for 5 min and analyzed as described above. The detection of the inosine monophosphate cyclohydrolase activity of ATIC was beyond the sensitivity of a spectrophotometric assay in the presence of AICAR Tfase activity (60). All assays were conducted in triplicate. The V_max of the enzymes needed to be adjusted for the mathematical model because we observed inconsistent activity rates between the activity of the enzyme in these assays and in the ATPS assays described above, most likely due to variabilities in enzyme batch purity and/or activity loss over time. We accounted for this by adjusting the enzyme activity to match the ATPS data described below and measuring the rate of ASL and ATIC at the 100 μM substrate by HPLC, and using that rate for the V_max of the enzymes for the mathematical model, as the 100 μM substrate is well above the K_M of the enzymes:

$$V_0=\frac{V_{\max }\left[S\right]}{K_M+\left[S\right]}.$$ (2)

Enzyme assays: sequential reaction in individual phases and volume ratios

Sequential assays were conducted in the PEG/dextran volume ratios in addition to the individual dextran-rich and PEG-rich phases. Concentrations were 100 nM ASL and ATIC, 100 μM SAICAR, and 400 μM 10-fTHF. Samples were prepared without the initial substrate SAICAR and homogeneously mixed. Upon addition of SAICAR to initiate the reaction, the reaction was mixed on a Tube Rotator Unit (VWR International) and aliquots were taken at time points and diluted 2× with 1 M sodium hydroxide to both quench the reaction and dilute the biphasic system to one phase for HPLC analysis. SAICAR and IMP concentrations were determined by standard curves prepared for each metabolite.

Simulation method

As discussed in the Results and Discussion section, a set of partial differential equations (PDEs) described the system employing the material conservation equations. To simulate the underlying ATPS, we used the software package COMSOL 4.3b (COMSOL, www.comsol.com), which solved the coupled PDEs numerically, using the finite-element method. The minimum and maximum element sizes of the created mesh, and the dimensionless time element in the simulation, were 0.07, 0.5, and 10⁻², respectively. To satisfy the partitioning expressions in Eq. 4 at the interface, we exploited a type of change of variables to define new continuous variables at the interface. By solving the new variables, the local concentration profiles during time were obtained, as discussed in our previous work (37).

Contrary to the ATPS simulation, in PEG-rich or dextran-rich single-phase simulation, due to symmetry, the mathematical model could be simplified. In these cases, at every point, the net rates of diffusion were zero and the concentration of all species was uniform throughout the volume. As a result, the sequential reactions took place uniformly in the domain space, and Eq. 3 became a set of ordinary differential equations. Also, the boundary conditions expressed in Eqs. 4 and 5 were automatically satisfied in these two cases and could be neglected. To solve the ordinary differential equation system for PEG-rich or dextran-rich phase, we used the software package MATLAB 2014a (The MathWorks, Natick, MA), and specifically the fourth-order Runge-Kutta integration method with fifth-order timestep error prediction.

Results and Discussion

Fig. 1 illustrates the sequential reaction investigated here, and the complex reaction medium, in which both enzymes are concentrated within dextran-rich phase droplets of the PEG/dextran ATPS. ASL is a tetramer with four active sites that cleaves SAICAR (5-aminoimidazole-4-(N-succinocarboxamide) ribonucleotide) to form AICAR (5-aminoimidazole-4-carboxamide ribonucleotide) and fumarate (61). ATIC is a bifunctional dimer with single active sites for each enzyme activity (62). The first step uses 10f-THF (10-formyl tetrahydrofolate) as a cofactor and transfers a formyl group to the AICAR amine, forming FAICAR (5-formamidoimidazole-4-carboxamide ribonucleotide) and THF (tetrahydrofolate). The second step catalyzes the internal cyclization of FAICAR to make IMP, and releases a water molecule (63). The AICAR Tfase activity is reversible and the FAICAR to AICAR reaction is 2–3-fold faster, but the IMPCH activity is essentially a forward reaction, which drives the AICAR Tfase reaction toward IMP (63). The bifunctionality may be advantageous in driving the reaction forward. It is also worth noting that there is a lack of substrate channeling between the two active sites (63).

Figure 1.

Reaction schemes. (A) The sequential reaction of purine biosynthesis enzymes ASL and ATIC with the substrate, intermediates, cofactors, and product shown. (B) An illustration of the partitioning of ASL, ATIC, SAICAR, and IMP in the PEG/dextran ATPS from the start of the reaction to near completion.

Compartmentalization in the ATPS

We used a 10% (w/w) PEG 8 k, 10% (w/w) dextran 10 k ATPS that was prepared in a 33 mM Tris buffer, pH 7.4 and 25 mM potassium chloride. A phase diagram for this system is given in Fig. S1 in the Supporting Material. This composition resulted in a roughly 3:1 volume ratio of PEG-rich phase: dextran-rich phase (abbreviated PEG/dextran going forward) consisting of an upper PEG-rich phase and a lower dextran-rich phase. The physical properties of the phases differed, with the dextran-rich phase being approximately twice as viscous as the PEG-rich phase due to the higher overall polymer concentration of ∼28% (w/w) compared to ∼18% (w/w) (see Table S1 in the Supporting Material). To control the local concentration of enzymes, experiments were performed at specific, nonnative PEG/dextran volume ratios, prepared by mixing desired amounts of each phase from a large volume stock ATPS. Most experimental ATPS used in this work had a smaller volume dextran-rich phase (i.e., PEG-rich/dextran-rich phase volume ratios 9:1, 19:1, and 49:1), such that upon mixing, this phase occurred as droplets surrounded by a continuous PEG-rich phase.

Partitioning was the mechanism used to achieve high local concentration of enzymes in the dextran-rich phase. Enzymes typically partition to the dextran-rich phase of a PEG/dextran ATPS because of their higher affinity for the more hydrophilic dextran-rich phase (64). Many factors influence how a protein will partition in a PEG/dextran ATPS such as protein size, protein shape, surface and overall charge, and weak affinity interactions with the phase-forming components. While correlations have been found (as molecular weight and net positive charge of the protein increases, partitioning increases (65)), partitioning of individual enzymes of interest must be experimentally determined. Partitioning is quantified in terms of the partitioning coefficient, K, where K = C_P/C_D. The value C_P is the concentration in the PEG-rich phase; C_D is the concentration in the dextran-rich phase. We measured the partitioning of the enzymes and substrates at a 1:1 volume ratio (Table 1). The metabolites SAICAR, AICAR, and IMP all partitioned weakly to the dextran-phase. 10f-THF concentration was the same in both phases. The partitioning coefficient of ASL and ATIC was measured individually and in the presence of the other enzyme because any associations between the enzymes could change their partitioning (66, 67). In this case, neither enzyme’s partitioning was significantly affected by the presence of the other. ASL partitioned 8.7× to the dextran-rich phase, while ATIC partitioned much more strongly; it was ∼250× more concentrated in the dextran-rich phase. We also measured the enzyme partitioning after 12 h to determine any changes from being in the ATPS for an extended time; no significant differences were observed. Fig. 2 shows the distribution of fluorescently-labeled ASL and ATIC enzymes in a 9:1 volume ratio ATPS; both enzymes accumulate in the dextran-rich droplet phase and the continuous PEG-rich phase appears dark. Some aggregation can be seen as bright spots in the images for both enzymes, particularly for ASL. Aggregation of ASL has been observed previously using static light scattering in a buffer solution (61).

Table 1.

Partitioning coefficients of enzymes and substrates

Molecule	Partitioning Coefficient
ASLa
Individual	0.115 ± 0.007
With ATIC	0.11 ± 0.01
ATICa
Individual	0.004 ± 0.001
With ASL	0.0056 ± 0.0005
SAICARb	0.318 ± 0.009
AICARb	0.426 ± 0.009
10-fTHFb	1.0 ± 0.3
IMPb	0.43 ± 0.04

^aASL and ATIC partitioning was measured at 100 nM.

^bSmall molecule partitioning measured at 100 μM.

Figure 2.

Confocal fluorescence microscopy of the fluorescently labeled enzymes in the ATPS at a 9:1 volume ratio. Droplets correspond to the dextran-rich phase, surrounded by a continuous PEG-rich phase. (Left) Transmitted light (differential-interference-contrast microscopy), (center) ASL-Alexa Fluor 647, and (right) ATIC-Alexa Fluor 488. Images have been contrast-adjusted and false-colored to aid visualization. To see this figure in color, go online.

Michaelis-Menten enzyme kinetics in the phases

Michaelis-Menten parameters for ASL and AICAR Tfase in the PEG-rich and the dextran-rich phases, as well as noncrowded buffer solutions, are reported in Table 2. ASL activity showed a fivefold difference in K_M and a small increase in k_cat in the dextran-rich phase while the K_M and k_cat AICAR Tfase are within error. Many factors can influence enzyme activity in macromolecularly crowded solutions, both favorably and unfavorably, such as changes in active site of the enzyme, changes in substrate chemical activity, or decreased diffusion in the sample (29, 32). Because there was no difference for K_M of AICAR with respect to ATIC activity and it is similar in size and structure to SACIAR, the most likely explanation is differences in ASL structure in the PEG-rich phase, dextran-rich phase and buffer. Further evidence is the orders-of-magnitude differences in k_cat for ASL in buffers compared to the crowded phases. ASL is sensitive to solution composition, even in two different buffered solutions, which underscores the importance of determining enzyme activity in crowded media. At 100 nM of each enzyme, the activity of ATIC was ∼7× the activity of ASL. This was chosen because enhanced catalysis of a coupled enzyme reaction can only be observed when the rate of the second enzyme is greater than the rate of the first (25).

Table 2.

Michaelis-Menten constants of ASL and ATIC within buffer, PEG-rich phase, and dextran-rich phase

	Reference	KM (μM)	Vmax (μM/min)b	kcat (s−1)
ASL (SAICAR)
40 mM Tris buffer, pH 7.4	(61)	1.8 ± 0.1	—	90.2 ± 1.9
50 mM buffer pH 7.5, 150 mM total ionic strength (NaCl)	(50)	12.8 ± 2	—	259.8 ± 7.8
PEG-rich phase		24 ± 8a	5.4 ± 0.5	0.90 ± 0.08
Dextran-rich phase		5 ± 1a	6.9 ± 0.1	1.15 ± 0.02
AICAR Tfase (AICAR)
66 mM Tris, pH 7.4, 50 mM KCl buffer	(63)	10 ± 1	—	2.9 ± 0.4
33 mM Tris, pH 7.4, 25 mM KCl buffer	(60)	16.8 ± 1.5	different units	—
PEG-rich phase		19 ± 6a	39 ± 3	6.5 ± 0.5
Dextran-rich phase		16 ± 5a	42 ± 3	7.0 ± 0.5

^aK_M measured at 50 nM enzyme.

^bV_max adjusted to match activity at 100 nM enzyme used in the other assays (see Materials and Methods).

Kinetics of the sequential reaction

We next measured the sequential reaction kinetics in the individual phases and in the ATPS. We used volume ratios 1:1, 9:1, 19:1, and 49:1 so that as the volume of the dextran-rich phase decreased, the local concentration of enzyme in that phase would increase. This is advantageous because the individual phase composition remained constant, and it allowed us to change the enzyme stoichiometry in each phase without changing to total number of moles of enzymes in the system. SAICAR, AICAR, and IMP have overlapping UV spectra; HPLC was used to distinguish them (Fig. 3). An initial substrate concentration of 100 μM SAICAR was used, as this is an upper estimate of cellular SAICAR concentration (20–100 μM) (68). The final product, IMP, is in approximately the same concentration range (69). Total enzyme concentrations were 100 nM for ASL and ATIC because these concentrations gave reproducible results and provided sufficient IMP formation over the time course of the reaction. Reaction time points were collected by removing aliquots and adding them to an equal volume of 1 M sodium hydroxide solution to stop the reaction and dilute the ATPS to one phase. Metabolite concentrations were quantified at each time point (data points, Fig. 4). For AICAR, we did not observe any appreciable concentration in the HPLC chromatograms, but this was expected given the much higher activity of ATIC compared to ASL. We observed a slight increase in product formation at 20 min for the ATPS samples compared to the individual phases, with the exception that the 49:1 volume ratio was similar to the dextran-rich phase. The concentration of IMP at 20 min in the PEG-rich phase was 78 ± 5 μM, while the dextran-rich phase was 87 ± 2 μM. The ATPS samples were similar: 95 ± 1 μM for 1:1, 99 μM ± 1 μM for 9:1, 98 ± 1 μM for 19:1, and 86 ± 7 μM for 49:1. Overall, there was a modest effect from colocalization in the ATPS compared to the sequential reaction in the individual phases.

Figure 3.

HPLC-UV chromatogram at 267 nm of the purine substrates and products at 100 μM. The peak at 22 min was caused by the salt gradient (see Materials and Methods). To see this figure in color, go online.

Figure 4.

Sequential reaction kinetics in the individual phases and ATPS: (A) PEG-rich phase, (B) dextran-rich phase, and the volume ratios (C) 1:1, (D) 9:1, (E) 19:1, and (F) 49:1. (Red circles) Experimentally determined SAICAR concentrations. (Blue circles) Experimentally determined IMP concentrations. (Solid lines) Model predictions of SAICAR (red), AICAR (green), and IMP (blue); (dashed lines) upper- and lower-limit error of each trace, based on the Michaelis-Menten parameters in Table 2. Initial total reaction concentrations were 100 nM ASL, 100 nM ATIC, 100 μM SAICAR, and 400 μM 10-fTHF; these molecules were distributed throughout the biphasic solutions according to their partitioning (Table 1). To see this figure in color, go online.

Mathematical modeling

Next, we quantitatively described the enzyme kinetics in the individual phases and the ATPS to make predictions about the enzyme activity under other conditions. A mathematical model that we had previously developed for the enzyme kinetics of glucose oxidase and horseradish peroxidase in a PEG/citrate ATPS (37) was adapted to fit this system.

Computational domain

The ATPS reaction medium was modeled as spheres (droplets) of the dextran-rich phase uniformly distributed within a continuous PEG-rich phase. Dextran-rich phase droplet radius for the PEG/dextran volume ratios 1:1, 9:1, 19:1, and 49:1 were measured by microscopy after mixing and determined to be 90 ± 40 μm, 40 ± 20 μm, 18 ± 5 μm, and 7 ± 2 μm, respectively. Also, because the domain space was symmetric, we used a subsection of the domain to simplify the calculations.

Mass conservation

We next described the mass conservation of the system that involved two phenomena: the enzyme reactions and the diffusion of the species. The assumption was that the diffusion coefficient of the components was constant within a phase, and because the average velocity of species was close to zero, the convective forces could be neglected in the simulation volume. The mass conservation of species i was described by the PDE,

$$\frac{\partial c_{i,j}}{\partial t}-D_{i,j}{\nabla }^2{c}_{i,j}=r_{i,j},$$ (3)

where i denoted the substrate species, i.e., i = {s,a,f}, which represented SAICAR, AICAR, and IMP (i.e., f = IMP). The phase j = {P,D} represented the PEG-rich or dextran-rich phase. The concentration and diffusion coefficients of species i in phase j were denoted by c_i,j, and D_i,j, respectively. The values of the diffusion coefficients, D_i,j, were calculated with the Stokes-Einstein equation using the viscosities of the phases listed in Table S1. To further elucidate the role that diffusion played in the specific system, we performed a sensitivity analysis around the calculated values from the Stokes-Einstein equation. We observed no significant difference in the resulting simulations for a one order-of-magnitude perturbation in the diffusion coefficient values (see Fig. S2); this analysis gave us confidence that the simulation predictions would be insensitive to the chosen values of the diffusion coefficients.

The net rates of the reactions that involve species i in phase j were represented by r_i,j. The Laplace operator was denoted by ∇² and described the gradient divergence of the function throughout space. The concentration of each species i in phase j was dependent on the partitioning coefficient, K_i, and provided the following boundary conditions:

$$c_{i,P}\left(r,t\right){|}_{r=R}=K_i{c}_{i,D}\left(r,t\right){|}_{r=R}.$$ (4)

These boundary conditions ensured that the partitioning was maintained if a species were consumed or produced. Because the model was symmetrical, periodic boundary conditions could be applied to opposite faces of the cube,

$$\begin{array}{c}{c_i|}_a={c_i|}_b,\\ {F_{i,j}|}_a=-{F_{i,j}|}_b,\end{array}$$ (5)

where a and b were the two opposite faces of the cube. The inward flux, F, to phase j of the i component at face l was represented by

$$F_{i,j}{|}_l=-D_{i,j}\nabla c_{i,j}{|}_l.$$ (6)

Reaction rate expressions

We modeled ASL and AICAR Tfase using the Michaelis-Menten equation. The IMPCH activity of ATIC was assumed to be instantaneous and equal to the rate of the AICAR Tfase activity. FAICAR could not be detected in our system by HPLC, so we assumed its concentration was low (<3 μM). Additionally, The K_M of FAICAR has been reported to be below 1 μM, and it is beyond the sensitivity of most assays (63). The AICAR Tfase activity required both AICAR and the cofactor 10-fTHF, but we could model with respect to varying AICAR concentration only because 10f-THF was in 4× excess. We anticipated that the concentration of the intermediate, AICAR, would remain relatively low, because it is used by AICAR Tfase faster than it is produced by ASL; hence in practice 10f-THF is always at least ∼50× higher concentration than AICAR and by considering it constant, we introduced negligible absolute errors in the model equations.

For ASL, the rate of SAICAR consumption was equal to the rate of AICAR production. This rate was solely dependent on ASL and SAICAR concentrations. The rate of IMP production was equal to the rate of AICAR consumption. AICAR, the intermediate of the sequential assay, was first produced by ASL and consumed by ATIC. The Michaelis-Menten reaction rate expressions below described these conditions:

$$r_{s,j}=-\frac{k_{\text{cat},\text{ASL},j}{c}_{\text{ASL},j}{c}_{s,j}}{K_{M,s,j}+c_{s,j}},$$ (7)

$$r_{a,j}=\frac{k_{\text{cat},\text{ASL},j}{c}_{\text{ASL},j}{c}_{s,j}}{K_{M,s,j}+c_{s,j}}-\frac{k_{\text{cat},\text{ATIC},j}{c}_{\text{ATIC},j}{c}_{a,j}}{K_{M,a,j}+c_{a,j}},$$ (8)

$$r_{f,j}=\frac{k_{\text{cat},\text{ATIC},j}{c}_{\text{ATIC},j}{c}_{a,j}}{K_{M,a,j}+c_{a,j}}.$$ (9)

To aid in the simplicity of the simulation, we nondimensionalized the mass conservation equation and the reaction rate expressions. These equations and parameter definitions are given as Eqs. S1–S4 in the Supporting Material and Table S2. The simulation output was the concentration profiles of the reactants and products in time.

Comparison of simulation and experimental results

The simulation concentration profiles are graphed with the experimental data presented earlier in Fig. 4 for comparison. The solid lines are the average Michaelis-Menten parameters, and the dashed lines represent the upper and lower extremes of the standard deviations of the K_M and V_max parameters. The simulations showed that AICAR reached a steady-state concentration between 0 and 3 μM, depending on the case, which is consistent with the lack of detection of AICAR in the sequential assays. Generally, we saw good agreement of the modeling results with most of the experimental results. The four curves with deviations were for the SAICAR curve in the PEG-rich phase, the IMP curve of the dextran-rich phase, and the 19:1 curves, but the simulation still reasonably predicted them. This was significant because the model accurately described the enzyme kinetics in the individual phases and volume ratios.

Effect of compartmentalization on the sequential rate

As the volume ratio increased, the local concentration of enzyme (and degree of compartmentalization) in the dextran-rich phase increased. However, this did not significantly improve the rate of final product formation. The results here are in contrast to the enhanced rates of reaction observed for a single RNA ribozyme (34) and the enzyme urease (70) that were each partitioned to the dextran-rich phase in a PEG/dextran ATPS. The calculated simulation rates for production of IMP for the first 10 min (linear portion of each curve) of each phase and volume ratio are given in Table 3. The model predicted that among the volume ratios, the 1:1 case gave the fastest rate of IMP production. The rate of IMP production decreased as the volume of dextran-rich phase decreased. Analysis of the enzyme distribution in the ATPS as a function of volume ratio, however, explained the result. Table 3 gives the predicted concentrations and number of moles of the enzymes in each phase of the volume ratios. Note that for constant K, although enzyme concentration increased in the dextran-rich phase as the phase volume decreased, the fraction of total enzyme in the dextran-rich phase decreased. At equal volumes of both phases (1:1), the concentration of ASL in the dextran-rich phase was 180 nM, which increased to 782 nM when the relative volume of the dextran-rich phase was reduced to one part in 50 (49:1). At the same time, the total amount of ASL in dextran-rich phase dropped from 90 to 16 pM out of the total 100 pM of ASL present in the reaction. Because ASL is the slower enzyme (has a smaller V_max), its concentration had greater impact on the overall rate of the sequential reaction. This contrasts with prior work in which ribozyme cleavage was enhanced 66-fold by compartmentalization in a 100:1 volume ratio PEG/dextran ATPS, compared to dextran-rich phase alone (34). In the ribozyme experiments, extremely strong partitioning (nearly 3000-fold greater concentration in the dextran-rich phase) meant that nearly all of the total ribozyme remained in the dextran-rich phase even as the volume of this phase became very small.

Table 3.

Predicted rate of IMP formation, concentrations of enzymes, and number of moles of enzymes in the individual phases and volume ratios

		ASL				ATIC
Sample	Rate of IMP Formation (μM/min)a	CP (nM)	CD (nM)	nP (pmol)	nD (pmol)	CP (nM)	CD (nM)	nP (pmol)	nD (pmol)
PEG-rich phase alone	4.0	100	0	100	0	100	0	100	0
Dextran-rich phase alone	6.3	0	100	0	100	0	100	0	100
1:1	6.1	20	180	10	90	1	199	<1	100
9:1	5.2	55	503	50	50	4	965	3	97
19:1	4.8	71	647	68	32	7	1859	7	93
49:1	4.4	86	782	84	16	17	4181	16	84

These rates were calculated based on constant K values for the individual enzymes listed in Table 1, assuming 100 total pM of each enzyme and 1 mL total volume. C_P, concentration in the PEG-rich phase; C_D, concentration in the dextran-rich phase; n_P, number of moles in the PEG-rich phase; n_D, number of moles in the dextran-rich phase.

^aAverage rate from 0 to 10 min, as predicted by the model.

We further explored the sequential activity in each of the phases of the ATPS with the mathematical model in which we decreased the activity in the PEG-rich phase by a factor of 100, essentially turning off the reaction in the PEG-rich phase (Fig. 5). Decreasing the volume of the dextran-rich phase resulted in a decrease in IMP production, which demonstrated that the enzyme in the PEG-rich phase contributed significantly to the amount of IMP produced. We also performed simulations in which we varied the enzyme concentrations (Fig. S3). When both enzymes were at 10 nM, we observed no significant differences between the individual phases and the volume ratios. Simulations at 10 nM ASL and 100 nM ATIC showed similar kinetics to the 10 nM ASL and ATIC case, which was expected because ASL was the slower enzyme. Further simulations of 100 nM ASL and 10 nM ATIC showed that the AICAR intermediate built up to an appreciable extent because the activity of ATIC became the limiting rate.

Figure 5.

Simulated IMP production in the ATPS in which the enzyme activity in the PEG-rich phases is decreased 100×. The traces are 1:1 (black), 9:1 (red), 19:1 (blue), 49:1 (green), and PEG-rich phase (orange). To see this figure in color, go online.

Probing changes in enzyme and substrate partitioning with the mathematical model

Next, we used the mathematical model to explore how changes in enzyme partitioning would affect the reaction rate. In this experimental system, the enzymes partition because of nonspecific interactions with the phase-forming components. In the cell, however, enzyme localization is controlled through a number of different means, such as weak and strong binding interactions, phosphorylation states of enzymes, and conformational changes. We investigated IMP formation by simulating changes in the partitioning of both ASL and ATIC using the mathematical model. Fig. 6 shows the effect on IMP formation from varying the enzymes from equal concentration in both phases (K = 1) to 1000× more concentrated in the dextran-rich phase (K = 0.001). At each volume ratio, as the partitioning of the enzymes increased, the rate of IMP formation increased. No further enhancement was observed by simulating the partitioning beyond K = 0.001. While the enhancements here were rather small, increased local concentrations under these conditions led to increased product formation. Recently, it was reported that purinosome-containing cells had increased purine biosynthesis compared to cells without purinosomes; a nearly threefold increase in IMP cellular concentration was observed (4, 40, 45). These results and our modeling results are consistent with the hypothesis that increased local concentration of the sequential enzymes leads to an increase in final product formation.

Figure 6.

Effect of simulated changes in enzyme partitioning at each of the volume ratios. (A) 1:1, (B) 9:1, (C) 19:1, and (D) 49:1. (Bottom to top: black traces, K = 1; red traces, K = 0.1; blue traces, K = 0.01; and green traces, K = 0.001.) As the partitioning is increased to the dextran-rich phase, the IMP production is increased for each volume ratio. To see this figure in color, go online.

We explored the effect of changes in both substrate partitioning and enzyme concentration. We increased the partitioning of the small molecules (SAICAR, AICAR, 10f-THF, and IMP) to the dextran-rich phase, using K = 0.1 and K = 0.01, and the experimental enzyme partitioning coefficients (Fig. 7, A and B). We observed a trend as we have with the previous conditions in Fig. 4, in that the rate of IMP decreased as the volume ratio increased. IMP formation was decreased in the K = 0.01 condition compared to K = 0.1 because there was less substrate available to the active enzyme in the PEG-rich phase. These results indicated that because functional enzymes are present in both phases, there was not a large advantage to substrate localization in this PEG/dextran model system with ASL and ATIC at the experimental partitioning coefficients. Next, we simulated changes in which both the enzymes and substrates partitioned strongly to the dextran-rich phase and the enzyme concentrations were varied. We held each enzyme partitioning at K = 0.001 and used partitioning of the substrates K = 0.01. We used enzyme concentrations of 100 nM (experimental concentration) and 10 nM. At 100 nM enzyme concentration, increasing the substrate partitioning did not increase the overall rate to an appreciable extent in the volume ratios (Figs. 7 C and S4). At 10 nM enzyme concentration, the concentration of intermediate AICAR was decreased and the concentration of final product IMP was increased for the 49:1 case compared to the individual phases; SAICAR concentration was similar for the dextran-rich phase and the volume ratios (Fig. S5). There was a kinetic advantage to localizing ATIC at this concentration.

Figure 7.

The effect of changes in substrate partitioning. (A) K = 0.1 for all small molecules (SAICAR, AICAR, 10-fTHF, IMP) and (B) is K = 0.01. The activity decreased as the volume ratio is increased (from top to bottom): 1:1 (black), 9:1 (red), 19:1 (blue), and 49:1 (green). (C) K = 0.001 for both enzymes with experimental K (black) and K = 0.01 (red) for the small molecules. To see this figure in color, go online

Here, substrate location and enzyme concentration had an impact on the sequential rate. Enzyme and small molecule localization is important in vivo in the form of substrate channeling (21, 71). Substrate channeling has been observed under other experimental model conditions (1, 14, 18), but we did not believe that was happening to an appreciable extent here because the enzymes were free to diffuse independently from each other in the compartment. Cluster-mediated channeling has also been proposed (4). Enzymes and metabolites are not likely to be found distributed evenly throughout an entire cell because of specific interactions with other biomolecules, and they are involved with metabolic processes that only occur in specific areas (2).

Conclusions

The presence of liquid-like compartments in cytoplasm and nucleoplasm of biological cells suggests new ways to compartmentalize and potentially control metabolic pathways. These liquid organelles are an attractive possibility for transient multienzyme assembly because they allow for reversible localization of the enzymes based on formation/dissolution of the liquid compartment. Our experimental and computational model for compartmentalization of the purine enzymes to a liquid compartment did not result in a large increased flux of the sequential reaction. Instead, an increase in the number of total moles of ASL in the PEG-rich phase compared to the dextran-rich phase caused a decrease in rate of the final product, IMP, as the volume ratio was increased. Our computational model allowed us to consider systems beyond those readily accessible to experiment, including conditions more closely relevant to the purine de novo pathway and other multienzyme pathways in vivo. Significantly increased reaction rates could only be realized if essentially all active copies of the enzyme were localized exclusively to compartments. For the PEG/dextran ATPS used here, which intentionally lacked any affinity interactions with the enzymes (although ASL partitioning led to 8.7-fold higher local concentration), this compartmentalization was not strong enough to result in overall rate increases. Recent work by Levy et al. (46) has shown that enzymes partition between the cytoplasm and the membrane of yeast cells. They showed that the protein there was an ∼9.5-fold difference in concentration of proteasome subunit Pre9 between the cytoplasm and the membrane. In total, 566 other proteins had at least a fourfold difference in concentration between the two locations. In principle, selective biorecognition partners present within an intracellular liquid organelle could provide the necessary local concentration to increase flux for the sequential reaction in vivo. For the purinosomes, interactions with other purine biosynthetic enzymes and unidentified factors are thought to be important in localization (41). More generally, intracellular liquid phases are rich in both nucleic acids and proteins that could provide ample opportunity for strong affinity partitioning. Additionally, the cell could modulate an enzyme’s activity depending on its cellular location. Future work in this area could explore using phase-forming components (such as proteins and nucleic acids) that have stronger interactions with the enzymes, which would have the potential to change enzyme activity and local enzyme concentration. In the specific case of the de novo purine pathway, we note that only the last two proteins were included in this study. Greater kinetic advantages may be expected for the full pathway, particularly if it assembles onto a scaffold such as the cytoskeleton, as has been proposed (4, 40).

Author Contributions

B.W.D., W.M.A., and C.D.K. designed experiments; N.H. and A.A. designed simulations; S.A. contributed new reagents/analytic tools; B.W.D. and W.M.A. performed the experiments; N.H. performed the simulations; B.W.D., W.M.A., N.H., A.A., and C.D.K. analyzed the results; and all authors contributed to writing the article.

Editor: Alexander Berezhkovskii.