The relationship between effective molarity and affinity governs rate enhancements in tethered kinase-substrate reactions

Abstract

Scaffold proteins are thought to accelerate protein phosphorylation reactions by tethering kinases and substrates together, but there is little quantitative data on their functional effects. To assess the contribution of tethering to kinase reactivity, we compared intramolecular and intermolecular kinase reactions in a minimal model system. We find that tethering can enhance reaction rates in a flexible tethered kinase system, and the magnitude of the effect is sensitive to the structure of the tether. The largest effective molarity we obtained was ~0.08 μM, which is much lower than the effects observed in small molecule model systems and other tethered protein reactions. We further demonstrate that the tethered, intramolecular reaction only makes a significant contribution to observed rates when the scaffolded complex assembles at concentrations below the effective molarity. These findings provide a quantitative framework that can be applied to understand endogenous protein scaffolds and to engineer synthetic networks.

Introduction

Scaffold proteins assemble enzymes and their substrates into multiprotein complexes and are ubiquitous in signaling, metabolism, and protein homeostasis networks.^1–3 These proteins are widely assumed to promote reactions by increasing local concentrations, but direct evidence for this model is limited. For example, the prototypical MAP kinase pathway scaffold protein Ste5 was originally identified through genetic screens as a protein essential for signaling in the yeast mating pathway. Although the protein sequence lacked any obvious catalytic domain, the finding that Ste5 binds multiple sequential kinases in the pathway led to the idea that Ste5 acted as a scaffold to promote kinase signaling reactions.⁴ Subsequent work revealed multiple functions beyond simple tethering, including complex allosteric effects on kinase activation.^4–7 Similarly intricate behaviors in other scaffold systems, including 14-3-3 proteins and the mammalian MAP kinase pathway scaffolds KSR and JIP, indicate that many scaffold proteins have multiple functions,^3,8–12 and the contribution to biological function from tethering effects is unclear.

Despite the complexities of natural scaffold protein functions, there is good evidence that tethering can enhance kinase activity and specificity. Both in vitro and in vivo data suggest that AKAP scaffold proteins, which coordinate PKA signaling, use flexible tethers to localize PKA activity and promote reactions with specific substrates.¹³ Biochemical studies on Src family tyrosine kinases suggest that SH2 and SH3 domains tether the kinase to its substrate to enhance multisite phosphorylation reactions, and the effects depend on tether length.^14–16 Similarly, the adapter protein Cks1 binds phosphosites to tether the CDK near additional phosphorylation sites, and in vitro reaction rates depend sharply on the distance between the two sites.¹⁷ Furthermore, synthetic recruitment domains can be used to direct tyrosine kinase signaling to specific substrates in cells.¹⁸ This specificity presumably arises because tethering enhances reaction rates for the recruited substrate. Finally, a general coupling of binding energy to catalysis has been observed in kinase reactions catalyzed by Csk and Sky1p.¹⁹

MAP kinase docking motifs provide another line of evidence supporting the role of tethering in kinase activity and specificity. Docking motifs are modular binding elements that bind a remote site on the kinase surface, and these binding interactions can produce substantial increases in kinase activity, often by decreasing the K_M for the reaction.^20–24 However, docking peptides can also have allosteric effects on kinase activity.^5,25 Some studies suggest that the energetic coupling between docking sites and the active site is small,²⁶ but the possibility for unanticipated complexity in naturally-evolved systems makes it difficult to draw mechanistic conclusions about the contribution from tethering itself in these reactions.

Given the strong evidence from a variety of cellular and biochemical systems supporting a role for tethering effects on kinase activity, there is a compelling need for minimal, simplified biochemical models that can be used to systematically explore the functional properties of tethered kinase systems. Currently, we lack experimental systems to assess how large of a rate effect can be obtained from a scaffold protein, and how varying the structural properties of scaffold proteins affects reaction rates in protein assemblies. There is also substantial interest in engineering scaffold proteins for applications in synthetic biology and bioengineering.^27–31 There have been notable successes in rewiring cell signaling networks with engineered scaffolds,^28–30 but many attempts required screening large numbers of designs, and it is often unclear why plausible designs failed.^{28,29,32–34} Determining the criteria for effective protein scaffolds could enable more predictive rational design of scaffolded interactions.

To test the idea that proximity effects can increase reaction rates in kinase signaling reactions, and to develop a predictive framework for synthetic systems, we have constructed simplified model scaffolds using both covalent and non-covalent tethers that link a kinase to its substrate. We measured phosphorylation rates in both systems and compared them to the corresponding intermolecular, untethered kinase reaction (Figure 1). These comparisons allowed us to define an effective molarity for the intramolecular reaction (the ratio of the intramolecular to intermolecular rate constants), and to assess the effects of systematic variations of tether length on reactivity.

Figure 1. Models for scaffold-mediated kinase reactions.

Natural scaffold proteins recruit kinases and their substrates (shown as blue and purple circles, respectively) to a scaffold (grey) using non-covalent protein interaction domains. To create a simplified scaffold model system, we recruited a kinase to a substrate using covalent and non-covalent tethers and compared them to an intermolecular reaction in the absence of scaffold.

Using this model system, we confirmed that a flexible tether can increase reaction rates, but the effects on kinase reactions are much smaller than expected compared to prior studies with small molecule and tethered protein reaction model systems.^35–37 We also demonstrate that the relationship between the affinity of complex assembly and the effective molarity is a critical parameter that governs rates in scaffolded reactions. When the binding affinity is weaker than the effective molarity, the scaffold complex does not assemble at substrate concentrations where the intramolecular reaction can proceed faster than the intermolecular reaction. These results provide a possible explanation for why simple peptide tethering strategies often fail in synthetic signaling pathways. More broadly, our work provides the foundation for a quantitative framework to evaluate the molecular function of protein scaffolds in natural assemblies and synthetic systems.

Materials and Methods

Protein expression constructs

All PKA (mouse residues 15-351, Uniprot P05132)³⁸ and SYNZIP-fused substrate constructs were cloned into E. coli expression vectors containing an N-terminal maltose binding protein (MBP) and a C-terminal His₆ tag. SpyCatcher-fused substrate constructs were cloned into E. coli expression vectors containing an N-terminal TEV-cleavable His₆ tag.³⁹ DNA for the SYNZIPs was kindly provided by Amy Keating (MIT) and DNA for SpyCatcher was kindly provided by Lauren Carter (University of Washington). We used a peptide derived from cystic fibrosis transmembrane conductance regulator (residues 693-705, FGEKRKNSILNPI) as a substrate.⁴⁰ All linkers were composed of Gly, Ser, and Thr residues. These linkers are uncharged and predicted to be disordered.³⁷ A complete list of protein expression constructs is provided in Table 1 and protein sequence information is provided in the Supporting Information.

Table 1.

Protein expression plasmids

Plasmid	Vector Backbonea	Expressed Protein
pES263	pMBP-MG	MBP PKA-SpyTag H6
pES367	pBH4	H6 Pep-2x-SpyCatcher
pES368	pBH4	H6 Pep-4x-SpyCatcher
pES264	pBH4	H6 Pep-8x-SpyCatcher
pES343	pBH4	H6 Pep-14x-SpyCatcher
pES340	pBH4	H6 Pep-28x-SpyCatcher
pES341	pBH4	H6 Pep-52x-SpyCatcher
pES339	pBH4	H6 Pep-80x-SpyCatcher
pES265	pBH4	H6 Pep-32x-SpyCatcher
pES266	pBH4	H6 PepΔS-32x-SpyCatcher
pES021	pBH4	H6 DHR10-PKA
pES028	pMBP-MG	MBP Kemptide-SYNZIP2 H6
pES010	pMBP-MG	MBP Kemptide H6
pES011	pMBP-MG	MBP KemptideΔS H6
pES044	pMBP-MG	MBP Pep H6
pES234	pMBP-MG	MBP PKA-SYNZIP6 H6
pES273	pMBP-MG	MBP PKA H6
pES311	pMBP-MG	MBP Pep-SYNZIP5 H6
pES346	pMBP-MG	MBP Pep-SYNZIP5trunc1 H6
pES349	pMBP-MG	MBP Pep-SYNZIP5trunc2 H6

^apMBP-MG is a modified version of pMAL-p2X (New England Biolabs) wit h an N-terminal TEV-cleavable MBP tag and a C-terminal His₆ tag. pBH4 is a modified version of pET15b (Novagen) with an N-terminal TEV-cleavable His₆ tag. pMBP-MG and pBH4 were described previously.⁶ Complete protein sequences are available in the Supporting Information.

Expression and purification of SYNZIP constructs

Proteins were expressed in Rosetta (DE3) pLysS E. coli by inducing with 0.5 mM IPTG overnight at 18 °C. All proteins were purified by Ni-NTA chromatography. Briefly, ~5 mL cell culture pellet was resuspended in 25 mL lysis buffer (25 mM Tris, pH 8.0, 150 mM NaCl, 5 mM Imidazole, 2 mM MgCl₂, 5 mM 2-mercaptoethanol, 5% glycerol, and containing one EDTA-free protease inhibitor tablet) and lysed by sonication. The subsequent lysate was cleared by centrifugation at 32,000xg for 50 minutes. Clarified lysate was incubated with Ni-NTA resin for 1 hour. The resin was washed four times with Buffer A (25 mM Tris, pH 8.0, 150 mM NaCl, 15 mM imidazole, 5% glycerol) and once with Buffer B (25 mM Tris, pH 8.0, 1 M NaCl, 5 mM imidazole, 5% glycerol). Protein was eluted using 25 mM Tris, pH 8.0, 150 mM NaCl, 250 mM imidazole, and 10% glycerol.

All proteins were dialyzed overnight into storage buffer (20 mM Tris, pH 8.0, 150 mM NaCl, 10% glycerol, and 2 mM DTT), aliquoted, and frozen at −80 °C. Protein concentrations were determined using a Bradford assay (Thermo Scientific).

Expression and Purification of SpyTag-SpyCatcher constructs

MBP-SpyTag-H₆ and H₆-SpyCatcher proteins were expressed separately in Rosetta (DE3) pLysS E. coli and purified on Ni-NTA resin as described above. Prior to conjugation, proteins were dialyzed overnight into storage buffer at 4 °C to ensure complete removal of ATP. Subsequently, MBP-SpyTag-H₆ and H₆-SpyCatcher were mixed at a molar ratio of 1:10 in 1xPBS for 16-24 hours and the efficiency of the conjugation reaction was assessed by SDS-PAGE.

To remove excess H₆-SpyCather from the reaction mixture, we further purified the SpyTag-Catcher fusion on amylose resin; the conjugate was applied directly to amylose resin and allowed to bind for at least two hours. The resin was washed five times with amylose wash buffer (20 mM Tris, pH 8.0, 200 mM NaCl, 2 mM 2-mercaptoethanol) and bound protein was eluted using amylose wash buffer that contained 15 mM maltose. Proteins were dialyzed overnight into storage buffer, aliquoted, and frozen at −80 °C.

Kinetic assays

All kinetics measurements were performed in kinase assay buffer (40 mM Tris, pH 7.4, 200 mM NaCl, 10 mM MgCl₂, and 0.05% IGEPAL) at room temperature (21 ± 1 °C). Phosphorylation was initiated by the addition of 100 μM ATP containing 0.02 μCi/μL γ-³²P-ATP. This concentration of ATP is saturating in our system (Figure S1). Approximately 4.5 μL of the reaction was quenched at different time points by spotting onto nitrocellulose membrane and incubating in 0.5% phosphoric acid for at least 10 minutes. To remove excess ATP, the membranes were washed three to four times in 0.5% phosphoric acid, dried, and imaged on a GE Typhoon FLA 9000 imaging scanner. Kinetic parameters were determined using the initial rate method.

³²P counts were normalized to concentration using an endpoint standard run in parallel to all experiments. Endpoint reactions contained 200 nM PKA, 1 μM MBP-Kemptide, 100 μM ATP containing 0.02 μCi/μL γ-³²P-ATP in endpoint assay buffer (40 mM Tris pH 7.4, 100 μM EGTA, 10 mM MgCl₂, 0.05% IGEPAL). This reaction rapidly proceeds to completion in <1 min (Figure S2, S3D) and time points were taken at 40 minutes.

Unimolecular rate constants (k_intra) for SpyTag-mediated covalently tethered kinase-substrate complexes were measured by varying the covalently-tethered complex concentration over >30-fold range (from 0.005-0.16 μM for complexes containing Pep-SpyCatcher linkers <20 amino acids and 0.0125-0.2 μM for complexes with Pep-SpyCatcher linkers >20 amino acids). At low [substrate], the resulting data (V_obs vs. [Enzyme]) was linear and the slope of this data corresponds to the intramolecular rate constant k_intra (Figure S4). The corresponding intermolecular reaction was measured using a fixed enzyme concentration (2.5 nM) and substrate concentrations that varied >200-fold range (from 0.02-5 μM). Initial rates were quantified as described above and the bimolecular rate constant (k_cat/K_M) was obtained from the slope of a linear fit to a plot of k_obs vs. [substrate]. In separate experiments, we varied the enzyme concentration to confirm that the observed rates for the intermolecular reaction were also first order in enzyme concentration (Figure S5).

To make the tethered PKA-product complex, we allowed the tethered PKA-substrate complex to react to completion. Briefly, we incubated 2.5 μM tethered PKA-substrate complex with 250 μM ATP for two hours at room temperature. To measure reaction rates, the fully phosphorylated complex was diluted to 2.5 nM and mixed with 100 μM cold ATP containing 0.02 μCi/ μL γ-³²P-ATP. The reaction was initiated by the addition of free substrate. Initial rates were quantified as described above and the bimolecular rate constant (k_cat/K_M) was obtained from the slope of a linear fit to a plot of k_obs vs. [substrate].

For the non-covalent reactions, enzyme concentration was held constant at either 1 nM or 2.5 nM and substrate concentrations varied over >20-fold range (from 0.005-0.25 μM for tethered reactions and 0.01-0.25 μM for free reactions). In separate experiments, we varied the concentration of enzyme to verify that initial velocities scaled linearly with enzyme concentration (Figure S6).

Competition Assay

For the competitive reaction with covalently-tethered PKA-substrate complex and free substrate, 0.02 μM covalently-tethered complex was mixed with free substrate that varied over a >200-fold concentration range (from 0.02-5 μM). At a given time point, 9 μL of the reaction was quenched with 6 μL 5xSDS dye. Subsequently, 10 μL of the quenched sample was analyzed by SDS-PAGE. After electrophoresis, gels were washed with 0.5% phosphoric acid twice for five minutes and imaged on a GE Typhoon FLA 9000 gel scanner.

Fluorescence Polarization Binding Assays

Cys-containing proteins were labeled with Bodipy TMR using maleimide chemistry. 100 μM protein was reduced with 1 mM TCEP-HCl and incubated with at least a 10-fold molar excess of dye for 1 hour at room temperature. Free dye was removed by purification on a Ni-NTA column and/or a spin desalting column (Zeba). To determine labeling efficiency, proteins were separated by SDS-PAGE and subsequently imaged on a GE Typhoon FLA 9000 scanner at 532 nm.

1 nM labeled substrate was mixed with >700-fold range of unlabeled protein (from 1 to 700 nM) in binding buffer (20 mM Tris, pH 8.0, 150 mM NaCl, 2 mM TCEP, 2 mM MgCl₂, and 0.05% IGEPAL). Reactions were incubated at room temperature (21 ± 1 °C) for at least one hour in the dark. Polarization was measured in black 96-well plates using an EnVision 2105 multimode plate reader. The polarization of the peptide alone was subtracted from all measurements and the subsequent data was fit to a 1:1 binding model using equation 1:

$$Y=\frac{P_{1}x}{x+P_2}$$ (eq. 1)

where x represents the protein concentration, Y represents the fluorescence polarization, P₁ represents the maximum fluorescence polarization, and P₂ is the dissociation constant.

Competition binding assays were conducted as described above using 1 nM labeled substrate, 30 nM PKA-SYNZIP6, and an unlabeled competing substrate that varied >10,000 fold range (from 1 nM to 13 μM). Background fluorescence polarization from non-specific binding between substrate competitor and labeled substrate was subtracted from each measurement. To determine the IC₅₀, the plot of fluorescence polarization vs. [competitor] was fit to equation 2.

$$Y=\frac{P_1}{1+{10}^{(\mathrm{log }[PepCompetitor]-\log (I{C}_{50}))}}$$ (eq. 2)

Subsequently, the IC₅₀ was related to K_D using equation 3:

$$K_{DPKA-SYNZIP6·PepCompetitor}=\frac{I{C}_{50}}{1+\frac{[labeledsubstrate]}{K_{DPKA-SYNZIP6·labeledsubstrate}}}$$ (eq. 3)

Results and Discussion

We used the catalytic subunit of protein kinase A (PKA) as a model kinase because it has been extensively characterized both structurally and biophysically.^41–43 Furthermore, PKA can be purified in active form from E. coli and can phosphorylate short peptides in vitro.⁴⁴ We chose a natural PKA phosphosite derived from cystic fibrosis transmembrane conductance regulator (CFTR) as a substrate, which has a reported K_M value of 30 μM for PKA.⁴⁰ We tested a smaller minimal peptide (residues 693-705) than was previously described; this peptide is phosphorylated by PKA on Ser700 but does not detectably saturate the kinase active site at concentrations up to 100 μM (Figure S3A–B & Table S1). These data indicate that the reaction between PKA and this peptide substrate is relatively weak and that the observed reaction will be bimolecular in the nM to low μM range, which provides a broad concentration range to assess tethering effects.

Reaction rates for covalently tethered kinase-substrate complexes

To covalently tether PKA to a peptide substrate, we expressed PKA and its substrate separately and covalently fused them after purification via SpyTag and SpyCatcher proteins, which spontaneously form an irreversible isopeptide bond.³⁹ This approach allowed us to avoid premature phosphorylation of the substrate, which would likely occur with a genetically-fused kinase-substrate complex. We constructed C-terminal fusions of PKA to SpyTag (PKA-SpyTag) via an eight residue Gly/Ser (GS) linker and fused the peptide substrate to SpyCatcher (Pep-SpyCatcher) via a flexible linker (Figure S7). After expression and purification, PKA-SpyTag and Pep-SpyCatcher constructs were mixed to form a covalently tethered kinase-substrate complex (Figure 2).

Figure 2. Reactivity depends on the structural properties of the assembly.

(A) Schematic of the covalently tethered complex. The SpyCatcher-SpyTag complex covalently links the kinase with its substrate. We varied the length of the linker that connects the substrate to SpyCatcher from 2 to 14 residues and measured the unimolecular rate constant (k_intra). (B) Plot of k_intra vs. number of residues. The secondary y-axis shows the effective molarity for each complex, determined using the bimolecular rate constant from the untethered reaction (Figure 3A). Error bars represent the standard error of k_intra obtained from the fit of V_obs vs [tethered complex] as described in Figure S4.

With a covalently tethered complex in hand, we measured phosphorylation over time using γ-³²P-ATP to detect phosphorylation and converted ³²P counts to concentration using an endpoint standard that rapidly proceeds to completion (Figure S2). The plot of [phosphorylation] vs. time reaches an endpoint consistent with a single phosphorylation event per substrate (Figure S8). To ensure that phosphorylation is occurring at the desired CFTR peptide phosphosite and not a different Ser/Thr in a linker or folded protein domain, we performed control reactions with a Ser to Ala phosphosite point mutant (Figure S9A). This mutant is not significantly phosphorylated during the course of the reaction, indicating that the observed reaction represents a single phosphorylation event at the target CFTR peptide substrate (Figure S9B). Finally, to confirm that there were no unanticipated phosphosites in the longer Gly/Ser linkers used in some constructs, we performed additional untethered control reactions between PKA and peptide substrates fused to variable length of Gly/Ser linkers and observed no differences in observed rates (Figure S9C–D). Together, these data indicate that observed rates represent a single phosphorylation event at Ser700 of the CFTR peptide.

Tethered reaction rates are likely to depend on the length of the tether between the kinase and the substrate. Hence, we measured substrate phosphorylation rates for a series of covalently tethered complexes with variable Pep-SpyCatcher linker lengths ranging from 2 to 14 residues. For each complex, we measured initial rates of phosphorylation (V_obs) and calculated the unimolecular rate constant (k_intra) from a plot of V_obs vs. [tethered complex]. These plots are linear at concentrations below 50 nM (Figure S4A), confirming that the observed reaction is intramolecular in this concentration range. However, at concentrations above 50 nM, the observed rates increased non-linearly, likely due to competition from a bimolecular phosphorylation reaction. To extract k_intra, we fit the full dataset to a kinetic model that includes contributions from both the unimolecular and bimolecular reaction (Figure S4B). In parallel, we also fit the linear portion of the dataset at concentrations below 50 nM to a linear model. These fitting methods produce k_intra values that are in close agreement (Figure S10).

As anticipated, we found that reaction rates depended on the structural properties of the tether. The observed values of k_intra vary over a 6-fold range with different Pep-SpyCatcher linker lengths and display a maximum of 0.11 min⁻¹ (1.8 × 10⁻³ s⁻¹) with a 4-residue linker (Figure 2 and Table 2). Thus, the 4-residue linker appears to be sufficient to reach the kinase active site. The distance from the C-terminus of PKA to the C-terminus of a bound peptide is ~23 Å (Figure S7),³⁸ and this distance can plausibly be spanned by the 4-residue linker because the construct also includes an 8-residue PKA-SpyTag linker. Pep-SpyCatcher linkers shorter and longer than 4 residues are suboptimal. The shorter 2-residue Pep-SpyCatcher linker may be unable to reach the active site of the kinase without distorting protein structure, while linkers longer than 4 residues likely result in a larger entropic barrier to finding the kinase active site.

Table 2.

Kinetic parameters for covalently tethered complexes^a

Linker length (AA)	kintra (s−1)a	Effective Molarity (μM)b
2	(6.1 ± 0.3) × 10−4	0.027 ± 0.002
4	(1.8 ± 0.2) × 10−3	0.080 ± 0.007
8	(4.4 ± 0.7) × 10−4	0.020 ± 0.003
14	(2.9 ± 1.0) × 10−4	0.013 ± 0.005
28c	(6.6 ± 0.8) × 10−4	0.030 ± 0.004
52	(2.2 ± 0.4) × 10−3	0.100 ± 0.018
80	(1.9 ± 0.3) × 10−3	0.085 ± 0.013

^aErrors are standard error from the fit to k_intra (Figures 2, S4, & S11).

^bEffective molarity is calculated by dividing k_intra by (2.20 ± 0.03) × 10⁴ M⁻¹ s⁻¹, the value of the corresponding bimolecular rate constant (k_cat/K_M) (Figure 3A). Errors in the effective molarity are propagated from the errors in k_intra and k_cat/K_M.

^cTo obtain the k_intra value for this construct, we fit the V_obs data at low [tethered complex] to a line as described in Figure S4.

To determine how increasingly longer linkers affect reaction rates, we measured k_intra values for a series of covalently-tethered complexes with Pep-SpyCatcher linkers ranging from 16 to 80 residues. We observed an unexpected bimodal behavior with increasing linker length; after the first peak in k_intra at the 4-residue linker, there is a second peak of activity at 52 residues (Figure S11). The structural origins of this bimodal behavior are unknown, but we note that both activity peaks are similar in magnitude (k_intra = ~2 × 10⁻³ s⁻¹), and this value will serve as a key point of comparison between intra-and intermolecular reaction rates.

Effective molarity for the covalently-tethered reaction

To identify the conditions in which covalent tethering can increase reaction rates, we compared the intramolecular reaction to an intermolecular reaction containing PKA-SpyTag with a free, untethered substrate. For the free reaction, we measured initial rates over a >200-fold range of substrate concentration (0.02 – 5.1 μM) and a 10-fold range of enzyme concentration (Figure 3A and Figure S5, respectively). In these concentration ranges, observed rates scaled linearly with substrate and enzyme concentration, indicating that the observed reaction is bimolecular. For this reaction, there was no detectable saturation at high substrate concentration, as expected from the K_M >100 μM for PKA and the peptide substrate (Figure S3B).⁴⁰ We therefore fit k_obs (i.e. V_obs/[E]) vs. [substrate] to a linear model, where k_obs = (k_cat/K_M)[S] and obtained a bimolecular rate constant (k_cat/K_M) of 2.2 × 10⁴ M⁻¹ s⁻¹.

Figure 3. Intermolecular reactions readily outcompete the covalently tethered reaction.

(A)Schematic of the tethered (4 aa linker) and free reaction and corresponding plot of k_obs vs. [substrate] for the tethered (red) and free (black) reactions. Inset is marked with light blue rectangle. The observed effective molarity is 0.08 μM.

(B) Schematic of a competitive reaction with both tethered (4 aa linker) and free substrates present, and corresponding plot of k_obs vs. [substrate] for the tethered (red) and free (black) reactions. Inset is marked with light blue rectangle. The observed effective molarity is 0.04 μM.

Each [product] vs time trace was measured from separate reactions in duplicate. For (A) and (B), error bars represent the standard error for k_obs obtained from a linear fit to [product] vs time for both datasets. The error for k_intra is smaller than the thickness of the red line (see Table 2).

The effective molarity is the substrate concentration at which the intermolecular and intramolecular rates are equal and can be obtained by finding the point at which the rate constant k_obs is equal for the two reactions. For the free reaction, k_obs = (k_cat/K_M)[S] and increases linearly with increasing [substrate]. For the tethered reaction, k_obs = k_intra and is constant. Plotting these values together gives a pair of lines that intersect at the effective molarity. For the optimal 4-residue tethered complex, the observed effective molarity is 0.08 μM (Figure 3A). At substrate concentrations <0.08 μM, the intermolecular reaction is slower than the covalently-tethered reaction, while at substrate concentrations >0.08 μM the intermolecular reaction is faster. As with the observed value of k_intra, the effective molarity displays a maximum with a 4-residue Pep-SpyCatcher linker (Figure 2B). Similar effective molarity trends with a maximum at an intermediate linker length have been observed in tethered protein-ligand model systems.¹⁵

To evaluate the significance of an effective molarity of 0.08 μM, we can make comparisons to other systems where these values have been measured. Small molecule reactions have effective molarities that can range above 10⁸ M,^35,45 while tethered protein-ligand interactions have measured and predicted values in the mM range,^36,37,46 and protein kinase docking interactions have estimated effective molarities in the μM to mM range (Table S2).^20,22,26,47 Further, we can obtain a rough estimate of an effective concentration for a tethered substrate by using the covalent tether length to define a spherical volume where the substrate is confined, which gives a value of >4 mM for the 4-residue linker and predicts that effective concentrations should vary >600-fold for the range of linkers lengths used here (Figure S12). Based on these comparisons, the effective molarity of 0.08 μM for our optimal tethered kinase-substrate system is unexpectedly small. We note that this approach to calculate effective concentration is vastly oversimplified, most notably because this model does not account for conformations that are sterically occluded by PKA or the SpyTag domains. These effects could increase rates by confining the substrate to a smaller volume or decrease rates by positioning the substrate in an unfavorable location. More sophisticated polymer models may be necessary to accurately describe the ensembles of conformations available to the system.³⁷ Also, effective molarity is a complex parameter that also depends on orientation effects from rotational and vibrational degrees of freedom.⁴⁵ There is limited data available for effective molarities in tethered enzymatic protein-protein reactions, and it remains to be seen whether there is a general difference in behavior between tethered enzymatic reactions and binding interactions. Larger effective molarities in kinase-substrate reactions could potentially be obtained with a scaffold that precisely constrains the orientation of the substrate relative to the active site.

The covalently-tethered system does not form a stable product-bound complex

One potential tradeoff associated with scaffold-mediated rate enhancements is that, by promoting interactions between a kinase and a substrate, the scaffold may stabilize the product-bound state and inhibit multiple turnovers of the enzyme. To test this possibility, we measured reaction rates in a competitive reaction between free substrate and substrate covalently tethered to enzyme. If product inhibition by the tethered product limits turnover, phosphorylation of the free peptide by the tethered PKA-substrate complex should be slower than the reaction of untethered substrate with free PKA.

To measure rates for a tethered and free substrate in the same reaction, we incubated the covalently tethered PKA-substrate complex with varying concentrations of free substrate and monitored phosphorylation of both substrates simultaneously using SDS-PAGE and autoradiography (Figure S13). We used 20 nM tethered complex, a concentration at which the bimolecular reaction between two tethered complexes is insignificant (Figure S4). From the observed rate of phosphorylation of the free substrate, we obtained a plot of k_obs vs. [substrate] and a bimolecular rate constant (k_cat/K_M) of 3.3 × 10⁴ M⁻¹ s⁻¹ (Figure 3B). In the same reaction, we measured the phosphorylation rate of the tethered substrate and used k_intra = V_obs/[ES]_tethered to obtain a unimolecular rate constant of 1.3 × 10⁻³ s⁻¹. The values of k_cat/K_M and k_intra from this competition experiment are similar to our previous measurements of these values in separate reactions (2.2 × 10⁴ M⁻¹ s⁻¹ and 1.8 × 10⁻³ s⁻¹, respectively) (compare Figure 3A and 3B). In particular, the identical k_intra value indicates the tethered complex is still functional for the intramolecular reaction in these conditions, and the absence of any decrease in k_cat/K_M indicates that the tethered substrate does not stably occupy the active site and inhibit enzyme turnover.

To independently confirm that tethered product does not inhibit enzyme turnover, we also prepared a fully phosphorylated tethered complex by allowing the covalently tethered PKA-substrate complex to react to completion. When the tethered PKA-product complex is mixed with varying concentrations of free substrate, the observed bimolecular rate constant (k_cat/K_M) is 2.3 × 10⁴ M⁻¹ s⁻¹, indistinguishable from the k_cat/K_M of 2.2 × 10⁴ M⁻¹ s⁻¹ for the free reaction (Figure S14).

Importantly, these results directly demonstrate the conditions in which an untethered reaction outcompetes the tethered reaction. The plot of k_obs vs. [substrate] gives a pair of lines that intersect at an effective molarity of 0.04 μM (Figure 3B), similar to the value of 0.08 μM obtained when the rates are measured in separate reactions (Figure 3A). At concentrations above the effective molarity, even when a substrate is covalently tethered to PKA, the free reaction outcompetes the tethered reaction.

A non-covalent tether can accelerate the kinase reaction at low substrate concentrations

Natural scaffold proteins use non-covalent protein-protein interactions to recruit multiple signaling proteins to the macromolecular complex. To understand how protein-protein interactions affect tethering, we constructed a model system where the substrate can bind non-covalently to a remote binding site on the kinase (Figure 1). For simplicity, the kinase remains covalently fused to the scaffold in our system. This approach allows us to make a direct comparison between the non-covalently tethered reaction and the corresponding free/untethered reaction. It also avoids the complications that arise in a non-covalent three component kinase/substrate/scaffold system where there are additional bound and unbound states to consider (i.e. kinase and substrate segregated on different scaffold proteins).⁴⁸ We expect that the observed effects from this model system should be generalizable to more complex multivalent assemblies.

Based on a minimal kinetic model, we predict that to observe a significant contribution from a tethered reaction, the substrate-scaffold interaction needs to be strong enough to appreciably bind at concentrations below the effective molarity (Scheme 1). In the minimal model, the substrate binds to the scaffold via a remote binding interaction and can then be phosphorylated in an intramolecular reaction. The free substrate can also bind directly to the active site of the kinase and react via an intermolecular reaction without engaging the remote binding site. The kinetic model indicates that the intramolecular, scaffold-mediated reaction (V_intra) is faster than the intermolecular reaction (V_inter) when the effective molarity is greater than K_D + [S], where K_D is the affinity of the substrate for the scaffold (Figure 4). If the affinity of the substrate for the scaffold is weak compared to the effective molarity (i.e. K_D > EM), there is no substrate concentration at which the intramolecular reaction is faster than the intermolecular reaction because the scaffolded complex does not significantly accumulate at concentrations below the effective molarity (Figure 4B). In contrast, if the affinity is strong relative to the effective molarity (i.e. K_D < EM, Figure 4C), then the intramolecular reaction will outcompete the intermolecular reaction at low substrate concentrations (i.e. when [S] < EM - K_D). Even in this scenario, the intermolecular reaction will still outcompete the intramolecular reaction at sufficiently high substrate concentrations. The substrate concentration at which this switch occurs is determined by the effective molarity (Figure 4). Practically, our kinetic model suggests that we will observe the largest effects from tethering with a scaffold that recruits a substrate with a K_D < ~0.08 μM, the effective molarity that we observed in the covalently-tethered kinase-substrate system (Figure 2). A similar conceptual analysis was recently described for tethered protein-ligand interactions.⁴⁹

Scheme 1.

Minimal kinetic scheme for a noncovalent tethered reaction.

The enzyme has a remote tether that can recruit a substrate, which then reacts with the active site through an intramolecular mechanism. Alternatively, the substrate can react with the enzyme through an intermolecular reaction by binding directly to the enzyme active site without engaging the tether. For simplicity, the intermolecular pathway does not include an E-S complex with substrate occupying the active site, because we did not detect saturation in any untethered reaction between PKA and the substrate peptide (Figure 2). We also assumed that the binding step to the tether is fast compared to k_intra. Finally, we assumed that the bimolecular rate constants (k_cat/K_M) for E and E_S are the same. With these simplifying assumptions, the condition for when the intramolecular reaction (V_intra) is faster than the intermolecular reaction (V_inter) is: EM > K_D + [S]. See Supporting Information for a complete derivation.

Figure 4. Predicted rates versus substrate concentration for various tethering strategies.

(A) Observed rates vs. substrate concentration for a bimolecular reaction between kinase and free substrate (solid black line), and a covalently tethered kinase-substrate reaction (solid red line). The effective molarity (EM) is the substrate concentration at which V_inter and V_intra are equal (indicated by grey line).

(B) Observed rates vs. substrate concentration for a model scaffold system where the remote tether binds to the substrate with a K_D > EM. There is no substrate concentration at which the rate of the intramolecular reaction (V_intra, red dotted line) is faster than the intermolecular reaction (V_inter, black dotted line). The observed rate (V_obs, solid red line) will include contributions from both the intramolecular and intermolecular reactions (i.e. V_obs = V_intra+V_inter).

(C) Observed rates vs. substrate concentration for a model scaffold system where the substrate binds to the remote tether with a K_D < EM. At low substrate concentrations (i.e. when [S] < EM - K_D), the intramolecular reaction (V_intra, red dotted line) is faster than the intermolecular reaction (V_inter, black dotted line) because the complex assembles at concentrations below the EM. The total observed rate (V_obs, solid red line) will include contributions from both the intramolecular and intermolecular reactions (i.e. V_obs = V_intra+V_inter).

For all plots the effective molarity is indicated by a vertical grey line and is 0.1 μM. K_D values in B and C are indicated by a vertical red line and are 0.15 μM and 0.01 μM, respectively.

To construct a non-covalently tethered kinase substrate system, we used heterodimeric coiled-coil interactions to recruit the substrate to the kinase via a flexible tether (Figure 5A). We used the heterodimeric coiled-coils SYNZIP 5 and SYNZIP 6 because this pair is well-characterized structurally and biophysically and has been used for many applications in synthetic biology and protein design.^50–52 We fused PKA to SYNZIP 6 (PKA-SYNZIP6) and the peptide substrate to SYNZIP5 (Pep-SYNZIP5). We measured a K_D of 0.01 μM for the Pep-SYNZIP5-PKA-SYNZIP6 interaction using fluorescence anisotropy (Figure S15); this binding affinity is consistent with previous measurements for SYNZIP5/6 affinity.⁵¹ Importantly, this affinity is below the predicted effective molarity of 0.08 μM, so we expect to observe a significant contribution from the tethered reaction at substrate concentrations <0.08 μM, but almost no effect on rates at substrate concentrations substantially above the effective molarity.

Figure 5. Non-covalent tethering enhances the rate of phosphorylation and depends on the relationship between effective molarity and K_D.

(A) Schematic of a model scaffold with a non-covalent tether that recruits a substrate to a kinase. The kinase is fused to SYNZIP6 (PKA-SYNZIP6) and the substrate is fused to SYNZIP5, which interact to form the tethered complex. In the corresponding free reaction, we used a kinase without SYNZIP6.

(B) Plot of k_obs vs. [substrate] for the tethered and free reactions for [substrate] < 0.06 μM. At concentrations below the effective molarity, the values of k_obs for the tethered reaction are significantly larger than the untethered reaction. The solid red line is a fit to a kinetic model (Scheme 1 and Supporting Information) that includes a contribution from k_intra, which accurately fits the tethered reaction data. The dotted lines are fits to a model where k_obs = (k_cat/K_M)[S] (this linear fit forces the line through zero). Both fits include data at higher substrate concentrations (full dataset is shown in panel C), and for the tethered reaction this linear model fails to account for the observed rate increase at low substrate concentrations. For the untethered reaction, the data scale linearly with [substrate]. The reaction of PKA-SYNZIP6 is also first order in enzyme concentration (Figure S6).

(C) Plot of k_obs vs. [substrate] over an expanded range of substrate concentrations up to 0.25 μM. The dotted lines are fits to a simple linear model (k_obs = k_cat/K_M [S]), and the solid red line is a fit to the complete model that includes k_intra (Scheme 1 and Supporting Information). For the untethered reaction, the slope corresponds to a bimolecular rate constant (k_cat/K_M) of 4.2 × 10⁴ M⁻¹ s⁻¹. For the tethered reaction, the value of k_cat/K_M obtained from the fit to the complete model (solid red line) is 5.6 × 10⁴ M⁻¹ s⁻¹. This value differs from the untethered reaction by a factor of 1.3, likely due to prep-to-prep variations in the total activity of PKA-SYNZIP6 versus free PKA.

(D) Plot of k_obs vs. [substrate] for the tethered reaction with the SYNZIP 5/6 pair and with two SYNZIP5 truncations that weaken the binding affinity (increasing K_D) (Figure S19). At [substrate] < 0.03 μM, values of k_obs decrease as K_D increases. At [substrate] = 0.25 μM, well above the effective molarity, values of k_obs are indistinguishable for substrates with different SYNZIP interaction affinities. The solid lines represent kinetic models using the values of k_intra and k_cat/K_M from the untruncated pair in Figure 5C, and the corresponding K_D value from each truncated pair. For SYNZIP5trunc2, we used a K_D of 50 μM (using larger K_D values does not change the prediction, see Figure S18B & C). Each [product] vs time trace was measured from separate reactions in duplicate. Error bars in B-D represent the standard error for k_obs obtained from a linear fit to [product] vs time for both datasets.

To test this prediction, we compared phosphorylation rates (k_obs, where k_obs = V_obs/[E]) for the tethered and free reactions over a range of substrate concentrations above and below the anticipated effective molarity (Figure 5). As expected, we observed a significant increase in k_obs for the tethered reaction, particularly at substrate concentrations <0.05 μM (Figure 5B). The observed values of k_obs for the tethered reaction are biphasic with [substrate] and correspond closely to the predictions of the kinetic model that includes contributions from an intramolecular reaction (Scheme 1). At low substrate concentrations, k_obs is dominated by contributions from the intramolecular reaction, while at high substrate concentrations k_obs is dominated by contributions from an intermolecular reaction of the tethered complex with free substrate (Figure 5B & C). For the untethered reaction, k_obs scaled linearly with substrate and enzyme concentrations, consistent with a bimolecular reaction (Figure 5B, 5C, & Figure S6). Thus, tethering can enhance kinase reaction rates at substrate concentrations below the effective molarity.

We performed several controls to confirm that the observed reactions reflect tethered phosphorylation of Ser700 of the CFTR target peptide. First, we did not detect any phosphorylation of off-target sites in the SYNZIP interaction domains or linkers that could potentially confound the assay (Figures S3B, S5, & Table S3). To confirm that product release from the SYNZIP tethering interaction is not limiting the observed rates, we performed control reactions under single turnover conditions and obtained the same value of k_obs as observed in multi-turnover conditions (Figure S16 & S17).

Fitting the data to kinetic models allows us to calculate the effective molarity and define the conditions under which tethering produces significant rate enhancements. For the tethered reaction, the fit provides an intramolecular rate constant (k_intra) of 3.5 × 10⁻³ s⁻¹ for a substrate non-covalently tethered to enzyme (Figure 5B & C), similar to the k_intra value of 1.8 × 10⁻³ s⁻¹ for covalently tethered substrate (Table 2). Using this k_intra value and the k_cat/K_M value of 4.2 × 10⁴ M⁻¹ s⁻¹ derived from the free reaction (Figure 5B & C), we calculated an effective molarity of 0.08 μM for the non-covalently tethered system, identical to the effective molarity obtained for the covalent system (Table 2). At substrate concentrations <0.07 μM (i.e. when [S] < EM - K_D; EM = 0.08 μM and K_D = 0.01 μM), the substrate binds to the scaffold and primarily reacts with the kinase through the intramolecular, tethered reaction. Conversely, at substrate concentrations >0.07 μM (i.e. when [S] > EM - K_D), the substrate predominantly reacts through a bimolecular pathway, even when PKA is fully occupied by a tethered substrate. Hence, we only observe significant effects from tethering with substrate concentrations less than ~70 nM.

A scaffold-substrate interaction that is weak relative to the EM does not accelerate the reaction

Our model predicts that observed rates from a tethered reaction should depend on the binding affinity between the substrate and the scaffold. If the affinity of the substrate for the scaffold is weak relative to the effective molarity (K_D ≫ EM), then the intermolecular reaction is faster than the intramolecular reaction at all substrate concentrations (Figure 4B). At intermediate binding affinities (K_D ~ EM), we expect to observe detectable rate effects from tethering. These effects will be largest at low substrate concentrations below the effective molarity; at concentrations above the effective molarity, the intermolecular reaction will be faster than the intramolecular reaction regardless of the value of K_D (Figure 4 & S18). To test these predictions, we measured k_obs for PKA-SYNZIP6 and weaker binding variants at substrate concentrations of 0.01 and 0.02 μM, concentrations well below the effective molarity (~0.1 μM), and at 0.25 μM, a concentration well above the effective molarity.

To weaken the binding affinity of the tethering interaction, we made truncations of SYNZIP5. We identified two mutants, SYNZIP5trunc1 and SYNZIP5trunc2, with weaker binding affinities of 0.2 μM and ~50 μM (Figure S19), respectively, compared to 0.01 μM for the cognate pair (Figure S15). As expected, for substrate concentrations below the effective molarity (i.e. 0.01 or 0.02 μM), phosphorylation rates (k_obs) decrease as K_D increases (Figure 5D). At a substrate concentration above the effective molarity (i.e. 0.25 μM), k_obs values are relatively unaffected by binding affinity. These k_obs values are captured by our model using the values of k_intra and k_cat/K_M derived from the cognate SYNZIP5/6 pair in Figure 5C, and the K_D value for each truncated pair. Moreover, this data confirms a key prediction from our model: as K_D increases, there will be less tethered complex assembled and the intramolecular, tethered reaction will therefore make smaller contributions to observed rates. Thus, the relationship between the effective molarity and the K_D is a critical parameter that determines the magnitude of the contribution, if any, from a tethered reaction.

Conclusions

Our results show that tethering a kinase and a substrate together can increase phosphorylation reaction rates. We show experimentally that the affinity for complex assembly plays a central role in the observed rates; if the affinity is weak compared to the effective molarity, a scaffolded complex will not assemble at concentrations where the intramolecular reaction is faster than the intermolecular reaction (Figure 5). This observation follows from a simple, intuitive kinetic model (Figure 4). Somewhat unexpectedly, however, the value of the effective molarity that we observe with a flexible scaffold model, ~0.1 μM, is relatively small compared to effective molarities for small molecule and other tethered protein reactions.^{13,14,20,22,23,26,53} Natural protein-protein affinities span a broad range from low nM to high μM,^29,30 and many scaffold-mediated interactions in signaling networks could be well above a 0.1 μM effective molarity threshold.^29,30 Endogenous scaffold proteins could potentially overcome this problem with multivalent interactions, which would result in tighter affinities and ensure that complexes assemble in a concentration range where scaffold-mediated reactions can make a significant contribution to reaction rates. Alternatively, natural scaffold proteins can have many functions beyond tethering,^1,3,54,55 and it may be that tethering-mediated rate enhancements are simply not the primary function of many scaffold proteins. Additional quantitative biochemical studies with natural scaffold systems will be necessary to explore these possibilities.

Any scaffold-mediated tethering effects that do occur should also depend on cellular concentrations; at substrate concentrations are well above the effective molarity, tethered reaction rates should be small compared to competing untethered reactions (Figure 5). In principle, we could assess whether cellular concentrations of PKA, substrates, and scaffold proteins exist in a range where we would predict significant tethering effects. In practice, however, estimating cellular concentrations for particular cell lines or tissues is challenging. Mass spectrometry data can provide cellular protein abundances, but converting these values to concentration requires knowing how much total protein is free in solution, folded, and active. Defining an appropriate volume is equally challenging, as cells are not well-mixed solutions. Although determining what functional effects are relevant in a given cell is not trivial, we emphasize that the value of in vitro biochemical studies lies more towards allowing us to describe the possible space of functional behaviors that are accessible to biological systems.

While the effective molarities obtained in our minimal model system are small, it is plausible that natural systems could achieve faster tethered reaction rates with different tether designs, or with ordered structures that precisely orient kinase and substrate. Our understanding of scaffold protein structure remains limited, however, and many scaffold proteins are thought to contain intrinsically disordered regions.^13,56,57 Future experiments could test whether larger effective molarities can be obtained in engineered systems with different flexible or well-ordered tether designs. Indeed, a recent paper describes an alternative PKA tethering strategy with different orientations, recruitment domains, and substrates that results in significantly faster tethered reaction rates.⁵⁸ Further studies are needed to determine why conceptually similar design strategies produced distinct behaviors, and to identify the critical structural features responsible for the differing effects. We note that even in a system with different observed rate effects, the relationship between effective molarity and binding affinity that we have described and experimentally characterized here should apply as a useful predictive framework.

While many questions remain open, our work suggests several important conclusions with broad implications. First, many scaffold proteins have been defined by qualitative assays that indicate binding to a kinase and substrate. In the absence of quantitative data for reaction rates and binding constants, however, any inference that the function of these scaffold proteins is to accelerate reaction rates should be viewed with caution. Second, when attempts are made to engineer scaffolds in synthetic networks, careful consideration should be given to both linker structure and interaction affinities. Further studies on both natural and model scaffold proteins will help to expand our understanding of complex signaling networks and improve our ability to engineer effective synthetic systems.