Avidity observed between a bivalent inhibitor and an enzyme monomer with a single active site.

Although myriad protein-protein interactions in nature use polyvalent binding, in which multiple ligands on one entity bind to multiple receptors on another, to date an affinity advantage of polyvalent binding has been demonstrated experimentally only in cases where the target receptor molecules are clustered prior to complex formation. Here, we demonstrate cooperativity in binding affinity (i.e., avidity) for a protein complex in which an engineered dimer of the amyloid precursor protein inhibitor (APPI), possessing two fully functional inhibitory loops, interacts with mesotrypsin, a soluble monomeric protein that does not self-associate or cluster spontaneously. We found that each inhibitory loop of the purified APPI homodimer was over three-fold more potent than the corresponding loop in the monovalent APPI inhibitor. This observation is consistent with a suggested mechanism whereby the two APPI loops in the homodimer simultaneously and reversibly bind two corresponding mesotrypsin monomers to mediate mesotrypsin dimerization. We propose a simple model for such dimerization that quantitatively explains the observed cooperativity in binding affinity. Binding cooperativity in this system reveals that the valency of ligands may affect avidity in protein-protein interactions including those of targets that are not surface-anchored and do not self-associate spontaneously. In this scenario, avidity may be explained by the enhanced concentration of ligand binding sites in proximity to the monomeric target, which may favor rebinding of the multiple ligand binding sites with the receptor molecules upon dissociation of the protein complex.

Introduction

Numerous biological activities in nature rely on polyvalent interactions, in which multiple ligands on one entity transiently [1] or irreversibly [2, 3] bind to multiple targets (e.g., receptors) on another [4, 5]. These biological activities include nutrient transport (e.g., hemoglobin), immune recognition (e.g., antibodies), and signal transduction (e.g., receptor tyrosine kinases) [5, 6]. Each non-covalent binding interaction can be characterized by its binding affinity, with the accumulated strength of many individual affinities referred to as functional affinity, or avidity.

The literature classifies polyvalent interactions according to four main groups based on the type of molecular entities that are involved: (i) cooperative interactions following protein aggregation, (ii) intermolecular (allosteric) cooperative interactions, such as binding of hemoglobin to iron atoms, (iii) intramolecular cooperative interactions, such as chelating effects (i.e., in which both the ligand and the receptor are multivalent) and (iv) interannular cooperativity describing the interplay of multiple intramolecular binding interactions [7-10]. An avidity effect, on the other hand, refers to cooperativity that results from chelating effects [7, 11]. Although the majority of polyvalent interactions are collectively much stronger than their corresponding monovalent interactions (i.e., exhibit stronger avidities [5, 9]), there are also examples for negative cooperativity in polyvalent binding due to destabilization of one ligand unit by another [12]. In addition, polyvalency can imbue a ligand with novel properties upon binding to a receptor target, such as the ability to cluster [13, 14] or to disengage from surface-anchored receptors [15]. These properties allow polyvalent ligands to either agonize or antagonize biological interactions that are crucial for intra- and extracellular structural, metabolic, signaling, and regulatory pathways [16].

These agonistic and antagonistic effects have been elucidated from systems in which ligands interact with surface-anchored receptors. Examples include transcription factor binding to multiple DNA regions [17], and influenza virus fusion with the sialic acids found at the host cell surface via the former’s hemagglutinin (HA) glycoproteins and the latter’s cell adhesion mediation properties [18]. Additional examples include conjugating engineered polypeptides that contain multiple integrin-binding RGD motifs spaced by SGSGSGSG linkers to a surface for cell adhesion [19], attachment of immune cells to epithelial cells via glycoproteins to generate an immune response [20], and others (reviewed in [5] and [16]).

Polyvalent interactions may also impact the binding selectivity of a ligand to its target by inducing steric stabilization of specific interactions and/or by enhancing the local concentration of a ligand [21]. The size and distribution of polyvalent ligands in the vicinity of their targets may reduce the interaction of the target with other natural ligands [22]. For example, Lees et al., [23] have shown that a polymer containing multiple sialic acids was able to inhibit the adhesion of influenza virus to erythrocytes by binding to multiple hemagglutinin (HA) proteins on the virus surface. Moreover, the interaction of this multivalent polymer with multiple HA proteins also prevented binding of specific antibodies to HA due to steric hindrance imposed by the multivalency during binding. Polyvalent ligands may also increase the concentration of ligand binding sites in the proximity of their target receptor, such that when the ligand–receptor protein complex dissociates, the receptor target can re-associate with multiple ligand binding sites such that a polyvalent system favors rebinding with the ligand [22, 24].

In theory these advantages may also confer avidity effects between polyvalent ligands and naturally monomeric, soluble receptors which are incapable of self-association except if mediated by the scaffolding of the ligand. Engineering of such polyvalent ligands may provide a novel strategy to enhance both affinity and specificity of protein-protein interactions. However, the affinity implications of polyvalency in such systems has not been explored, possibly because of a lack of suitable and easily accessible model systems [21]. Therefore, we aimed to close this gap by investigating the effect of avidity on a system in which all the binding sites in the polyvalent protein ligand are fully functional (i.e., no destabilization in the polyvalent ligand) and the target protein, in its soluble form, is monomeric and may not self-associate or cluster. The complex formed between the serine protease mesotrypsin and its cognate inhibitor, the human amyloid precursor protein inhibitor (APPI), from the Kunitz domain family, represents an excellent system for that purpose.

As a result of specific evolutionary mutations, mesotrypsin exhibits a distinctive resistance to almost all biological inhibitors including those of the Kunitz domain family [25-29]. Indeed, compared with other trypsin isoforms, the binding affinities of mesotrypsin with human Kunitz domains are 2–4 orders of magnitude weaker [30]. These low affinities (which are expressed as high inhibition constants (K)) render mesotrypsin a good soluble target for exploration of potential avidity effects, since improvements in the relatively weak binding affinities should be easily detectable.

APPI, which is abundant in nature, is composed of 58-amino acids, with a MW of approximately 6 kDa [31]. The canonical loop within the APPI scaffold serves as a recognition site for mesotrypsin [30, 32], to which it binds as a competitive inhibitor with 1:1 stoichiometric ratio [33-35] and inhibition constant of about 133 nM [33, 36]. Here, we envisioned that the APPI Kunitz domain could be arranged in tandem repeats to generate a polyvalent scaffold, inspired by the natural arrangement of tandem Kunitz domains in bikunin, another Kunitz domain family member. In bikunin, the two nonidentical Kunitz domains occur sequentially in a single protein chain, with each subunit possessing a distinct inhibitory spectrum; the N-terminal domain targets elastases, while the C-terminal domain targets trypsin-like serine proteases [37].

Here, we generated a stable homodimeric APPI in which both canonical inhibitory loops, one on each monomer, are correctly folded and fully functional. We show that the inhibitory activity of each loop in polyvalent APPI is over three-fold more potent than that of the corresponding loop in monovalent APPI. Using mesotrypsin, which does not self-associate spontaneously, we probed how each inhibitory loop in the dimer could bind each mesotrypsin monomer and thus provide support for mesotrypsin dimerization upon binding to the bivalent APPI. We also propose a simple kinetic model for mesotrypsin—APPI homodimer binding, quantitatively explaining the experimentally observed cooperativity in binding affinity (i.e., avidity). In so doing, we provide a framework for showing that the valency of ligands may affect avidity in protein–protein interactions that include targets that are not surface-anchored and do not self-associate spontaneously.

Results and discussion

Polyvalent interactions play an important role in many biochemical processes [5]. The conjugation of multiple copies of a ligand to a scaffold facilitates the simultaneous interaction of the latter with multiple target molecules, which strengthens binding affinity through an avidity effect [22, 38, 39]. A key criterion for avidity is prior clustering of the target molecules, such as occurs when receptors are immobilized on a cell surface or solid support antecedent to ligand binding [5, 40]. This effect has been found mostly in antibody–antigen interactions [1] in which the antigen is membrane-anchored. To the best of our knowledge, no attempts have been made to investigate the presence of avidity effects in soluble protein complexes in which a polyvalent ligand interacts with target molecules that are not in close proximity to each other prior to polyvalent protein complex formation. In such instances, it may be less trivial to achieve an avidity effect, as avidity requires that the unanchored, unclustered and freely diffusing monomeric target molecules (which have the potential to interfere with multiple binding to the ligand) exhibit superior binding affinity to polyvalent ligands than to monovalent ligands. The current research was designed to develop and explore avidity under such conditions, that is, when there is no clustering of the target molecules prior to their binding to the polyvalent ligand.

Generating the dimer construct gene in a Pichia pastoris expression system

To examine the feasibility of inducing binding avidity in a soluble protein complex comprised of a polyvalent ligand that binds freely diffusing, unclustered, monomeric target molecules, we chose the APPI–mesotrypsin complex, which was first characterized in Salameh et al. [33], as proof of concept. To satisfy the first criterion, namely, that each unit of the polyvalent ligand be fully functional, it was necessary to generate a correctly folded recombinant APPI dimer having two fully functional inhibitory units. Additionally, properties such as ligand density (spacing) and orientation were considered in selecting an appropriate linker. Many studies have suggested that the linker can play a crucial role in facilitating ligand binding and that it can be optimized to allow correct protein folding or to obtain optimal biological activity in fusion proteins [19, 22, 41].

The mesotrypsin-APPI heterodimer is shaped like a mushroom, where mesotrypsin is the mushroom cap and APPI is the elongated mushroom stem [32]. Both the N- and C-termini of APPI are located opposite its inhibitory loop, so that by connecting two APPI molecules in tandem, we connect two mushroom-shaped complexes at the base of their stems via the linker. Even a short linker would allow >50 Å between the two mesotrypsin molecules due to the length of the two stems, resulting in little risk of steric hindrance between mesotrypsin subunits. Our larger concern was thus achieving efficient independent folding and correct disulfide bond configuration within each of the two APPI domains, which we hoped to maximize by selecting a well-characterized flexible linker composed of three repetitions of GlyGlyGlyGlySer (designated GGGGS×3), of ~48 Å in length [41].

The gene construct for dimeric APPI was generated by PCR assembly (S1A Fig in S1 File) and transformed into P. pastoris. We then extracted the genomic DNA and amplified the target genes with AOX primers. The PCR products were separated by electrophoresis on 1% agarose gel and the bands representing the amplified APPI genes were confirmed, as shown in S1B Fig in S1 File. The sequence of the APPI dimer gene construct containing the GGGGS×3 linker was also verified (S1C Fig in S1 File).

Large-scale protein production and purification of APPI variants

The recombinant APPI variants were purified using nickel-affinity chromatography, which is possible because of their C-terminal His tags (Fig 1A and 1B). Size exclusion chromatography (SEC) was then used to eliminate impurities, such as imidazole residuals, from the APPI monomer or dimer (Fig 1C and 1D). Subsequently, we analyzed the purified proteins on 15% SDS-PAGE followed by InstantBlue Coomassie staining to confirm the size of the proteins (Fig 1E and 1F and S1A Raw images).

Fig 1

Purification of APPI variants.

Nickel affinity chromatography (A and B) and size-exclusion chromatography (SEC) (C and D) of recombinant amyloid precursor protein inhibitor (APPI) monomers (A and C) and dimers (B and D). The left peak in (D) is dimeric APPI, whereas the right peak is imidazole, which was used for protein elution in the nickel column. For all chromatograms, the X-axis represents the elution volume and the Y-axis represents absorbance at 280 nm. 15% SDS-PAGE analysis of the SEC-purified APPI variants (E and F).

As expected (given a MW of approximately 9 kDa for the APPI monomer containing a His tag and restriction enzyme site [31]) dimeric APPI showed a predominant band at MW 15 kDa (Fig 1F). However, a significant and unexpected difference was observed between APPI dimer concentrations obtained from analytical and functional assays. Specifically, whole protein concentrations obtained from the absorbance spectrum of the APPI dimer at 280 nm were significantly higher than the inhibitory unit concentrations obtained from its inhibitory activity in the presence of bovine trypsin (i.e., 268 μM and 38 μM from absorbance at 280 nm and active sites titration, respectively). From these observations, we inferred the presence of several recombinant dimeric APPI conformations, of which only some displayed the correctly folded and fully functional canonical loops (i.e., enzyme recognition sites) that serve as inhibitory units in their interaction with trypsins (i.e., bovine trypsin and mesotrypsin). On the basis of the monomeric structure of the APPI Kunitz domain, which contains three intramolecular disulfide bridges, the monomeric units that constitute the APPI dimer may potentially include non-natural, mixed pairs of disulfide bonds that enable only partial protein folding and that are incompatible with correct folding of the inhibitory loop. During protein folding, the correct formation of intramolecular disulfide bonds within each monomeric unit of the APPI dimer is essential for the activity of the inhibitory loop [42]. It is particularly crucial in the context of enzyme–inhibitor complexes, such as trypsin–APPI, in which the inhibitory loop of APPI binds to the active site of mesotrypsin in a site specific manner, as per the lock-and-key interaction model [43].

To generate an APPI dimer in which both the displayed canonical inhibitory loops were fully functional, we applied an additional protein purification step involving affinity chromatography with a bovine trypsin column (Fig 2A) to isolate the fraction of dimeric APPI that is correctly (and fully) folded. Two separate peaks were observed and analyzed by 15% SDS-PAGE (Fig 2B). The protein fraction represented by Peak 2 exhibited superior inhibition of mesotrypsin than the protein fraction represented by Peak 1 (Peak 1 showed a large difference between two concentration values, the first obtained from active sites titration (i.e., 11 μM) and the second that was calculated according to absorbance at 280 nm (i.e., 50 μM). We then compared the dimeric APPI fractions corresponding to affinity chromatography Peaks 1 and 2 with monomeric APPI by means of an additional 15% SDS-PAGE analysis (Fig 2C and S1B Raw images), and these fractions were then used for further functional characterization of the APPI protein dimer. Next, we determined the monomeric and dimeric APPI protein concentrations using absorbance at 280 nm (with extinction coefficients of 13,325 and 22,180 M−1 cm−1, respectively). Approximately 20 mg and 0.4 mg of purified APPI monomer and dimer were produced from a 1 L yeast culture, respectively. Finally, MALDI-TOF spectra confirmed the MW of the purified monomeric and dimeric APPI variants (S2A and S2B Fig in S1 File).

Fig 2

Final purification step to obtain fully functional dimeric APPI.

Using an affinity chromatography approach, dimeric APPI was eluted from a bovine trypsin column using a 0–100 mM HCl gradient (A). The protein fraction eluted in Peak 2 was chosen for further functional (protease inhibition) experiments, because it exhibited greater inhibition potency toward trypsin in comparison with the protein fraction eluted in Peak 1. 15% SDS-PAGE analysis of the purified dimeric APPI fractions (B) and comparison of purified monomeric APPI with dimeric APPI before and after purification (C).

APPI dimer titration analysis is consistent with 1:2 APPI:trypsin binding stoichiometry

Monomeric APPI is a 1:1 tight-binding picomolar inhibitor of trypsin, which can be used as a titrant to determine concentrations of APPI preparations [44]. To determine whether APPI dimer can simultaneously engage two molecules of trypsin, the APPI inhibitory unit concentration (in the APPI monomer and dimer) was determined by trypsin titration analysis and compared with concentrations determined by absorbance (S1 Table in S1 File). To determine concentrations by titration assay (Fig 3), we used a known quantity of bovine trypsin, which has known molecular mass, and our two inhibitors (APPI monomer and dimer), which have known molecular masses. A comparison between (a) the concentration of active inhibitory units determined from the titration (Fig 3) and (b) the inhibitor molecule concentrations measured by absorbance at 280 nm showed that nearly double the amount of trypsin was quenched as could be explained by a 1:1 binding model (S1 Table in S1 File). However, when the concentration of APPI dimer molecules was calculated from the titration results assuming 1:2 APPI:trypsin binding stoichiometry, the concentrations determined by titration and absorbance were highly consistent. These data provide evidence that APPI dimer can bind simultaneously to two molecules of trypsin. Because of the structural similarity of trypsin family members, we anticipate that the APPI dimer is also capable of binding simultaneously to two molecules of mesotrypsin.

Fig 3

Titration of inhibition units.

Bovine trypsin titration curves of monomeric (A) and dimeric (B) APPI. The X-axis represents the APPI volumes added to the reaction and the Y-axis represents the reaction velocity (i.e., velocity of substrate cleavage by bovine trypsin) at several APPI dilutions. The experiment setup is described in the Materials and methods section.

The mesotrypsin affinity of a single inhibitory unit is enhanced in dimeric compared with monomeric APPI

To assess the binding of monomeric and dimeric APPI to mesotrypsin, we carried out enzyme inhibition experiments that monitored cleavage of the chromogenic substrate Z-GPR-pNA by mesotrypsin in the presence of varying APPI concentrations. First, we determined the Michaelis-Menten constant (K) of z-GPR-pNA binding to mesotrypsin. As shown in Fig 4A, the K constant was calculated using nonlinear regression fitting to the Michaelis-Menten equation. The obtained value was 25.1±2.4 μM, consistently with previous studies [36]. Next, we determined the affinity of the inhibitory units in monomeric and dimeric APPI proteins for mesotrypsin using a competitive inhibition model to calculate the inhibition constant, for consistency with prior work [33, 36]. For the dimer, this analysis assumes an absence of cooperativity between the first and second enzyme molecule binding events, and thus yields a single Ki value that applies to each inhibitory unit of the dimer. We observed a classic competition pattern of inhibition for both inhibitors (Fig 4B and 4C). We found that the apparent inhibition constant of a single inhibitory unit in the APPI dimer was K = 36.1±2.2 nM (Fig 4C), which indicates an almost 3.4-fold enhancement of affinity compared with the inhibition constant of the single inhibitory unit of the APPI monomer (K = 122.5±10.0 nM) (Fig 4B), whose K value was consistent with previous studies [33, 36]. This enhancement in affinity may result from the mesotrypsin protein dimerizing upon binding the APPI dimer and the sequential binding of the two mesotrypsin active sites (in the mesotrypsin dimer) to the two APPI canonical binding loops (in the APPI dimer), as discussed in the next section.

Fig 4

Determination of inhibition constants.

Determination of the Michaelis-Menten constant (Km) for binding of the chromogenic substrate Z-GPR-pNA to mesotrypsin (A). Kinetics of mesotrypsin inhibition by the APPI monomer (B) and dimer (C). In all experiments, substrate concentration was 5–250 μM and enzyme concentration was 0.25 nM. The concentration of the APPI inhibitor unit was 0–400 nM for the monomer and 0–96 nM for the dimer (double the concentration of the APPI dimer molecule possessing two inhibitor units). Reactions were followed spectroscopically for 5 min, and initial rates were determined from the increase in absorbance caused by the release of p-nitroaniline (at 410 nm). Data were globally fitted by multiple regression to the classic competitive inhibition equation (Eq 20; see Materials and methods). Raw data can be found in SI.

Kinetic model for APPI homodimer binding to mesotrypsin

To quantitatively understand the observed cooperativity in binding affinity (i.e., avidity) for the APPI homodimer—mesotrypsin complex, we propose a simple kinetic model that goes beyond the standard Michaelis-Menten model for competitive enzyme inhibition (Fig 5). The proposed model assumes that the reaction mechanism consists of two consecutive steps. In the first step one mesotrypsin molecule reversibly binds a single APPI unit of the APPI homodimer. In the second step, the second mesotrypsin molecule reversibly binds the remaining APPI unit of the APPI homodimer. Such model is commonly termed in supramolecular chemistry as ‘The 1:2 system’ (see Ref. [45] for an extensive tutorial review).

Fig 5

Proposed reaction mechanism for the APPI homodimer induced mesotrypsin dimerization.

The mechanism allows two steps. In the first step, one APPI monomer unit reversibly binds one mesotrypsin molecule (and the second APPI unit remains unbound). In the second step, the remaining APPI unit reversibly binds the second mesotrypsin molecule.

The following parallel reactions take place in the system. The enzyme catalyzes its substrate via a standard Michaelis-Menten mechanism:

The reaction equation takes the form: where [E] is the enzyme concentration, [S] is the substrate concentration, and [ES] is the concentration of the enzyme-substrate complex; k and k are the association and dissociation rate constants of the enzyme-substrate binding reaction, respectively, and k is the catalytic rate constant leading to product [P]. In equilibrium this reaction is characterized by the Michaelis-Menten constant KM:

For APPI homodimers interacting with mesotrypsin enzyme molecules, the reaction mechanism allows two steps. In the first step, one APPI monomer unit reversibly binds one mesotrypsin enzyme molecule (and the second APPI unit remains unbound). In the second step, the remaining APPI unit reversibly binds the second mesotrypsin enzyme molecule (Fig 5). The first step of such mechanism is characterized by the reaction: with the following reaction equation: where k1 is the association rate constant of mesotrypsin molecule binding to one unit of APPI homodimer (when the second APPI unit remains unbound), and k-1 is the corresponding dissociation rate constant; [I] is the APPI concentration, [EI] is the concentration of mesotrypsin enzyme molecules bound to a single APPI unit. In equilibrium this reaction is characterized by the equilibrium inhibition constant, KI:

The second step in the APPI homodimer binding to mesotrypsin molecules (Fig 5) is described by the reaction: with the following reaction equation: where k2 is the association rate constant for the binding of the remaining APPI unit of the APPI homodimer to the second mesotrypsin enzyme molecule, and k-2 is the corresponding dissociation rate constant; [(2E)I] is the concentration of mesotrypsin enzyme molecule pairs in complex with APPI homodimers. In equilibrium this reaction is characterized by the equilibrium inhibition constant, K2:

Combining Eqs 6 and 9 we obtain: where we defined a new equilibrium inhibition constant, K2I.

We stress that the consecutive reactions, Eqs 4 and 7, are entirely equivalent to the following elementary reaction: and the corresponding kinetic equation:

Therefore, in equilibrium this equation is characterized by the equilibrium inhibition constant, K, which is identical to Eq 10:

We stress the important fact that unlike the conventional Michaelis-Menten scheme for competitive enzyme inhibition, where the enzyme concentration enters via a linear term, k1[E][I], (Eq 5), here (Eq 12) the enzyme concentration enters via a non-linear term, i.e., quadratic in the mesotrypsin concentration, k2[E]2[I].

Combining the mass conservation equation for mesotrypsin (Etot is the total concentration of mesotrypsin in the system): with the equilibrium equations, Eqs 3, 6 and 10, we obtain the resulting equation for [ES] (see S1 File for a step-by-step derivation): where α is the following:

The solution of this equation: and the resulting reaction velocity: where k is the catalytic rate constant leading to product [P].

Fitting Eq 18 to the experimental data, allows us to obtain the value of K2I (Fig 6). The fits to kinetic measurements performed at different APPI concentrations show an excellent agreement with the data and provide the average value for the equilibrium inhibition constant defined by Eq 10, K2I ≈ 2.1 nM. Intuitively, K represents a measure characterizing the equilibrium balance between two possible types of enzyme-APPI complexes: [EI] (i.e., concentration of mesotrypsin enzyme molecules bound to a single APPI unit), and [(2E)I] (i.e., the concentration of mesotrypsin enzyme molecule pairs in complex with APPI homodimers). We stress the fact that K2I cannot be directly compared to the corresponding equilibrium constant extracted above using a conventional Michaelis-Menten scheme (K = 36.1 nM, Fig 4C), since K2I is obtained using a different kinetic mechanism. Intuitively, the observed cooperativity in binding affinity (i.e., avidity) of the APPI homodimer, as compared to the APPI monomer, stems from the fact that the APPI homodimer—mesotrypsin association rate, k2[E]2[I], scales as a second power of the enzyme concentration, leading to a more efficient inhibition. This is unlike the APPI monomer case, where the APPI—mesotrypsin association rate, k1[E][I], scales linearly with enzyme concentration; here k1 is the association rate constant of the mesotrypsin—monomer APPI binding reaction.

Fig 6

Two-step model (Fig 5) for mesotrypsin inhibition by APPI homodimers provides an excellent fit to experimental data.

Fitting the reaction velocity (Eq 18) measured at different substrate concentration, allows us to extract the equilibrium inhibition constant K2I. Each of the four plots shows the fit corresponding the measurements performed at a given APPI homodimer concentration [I], where [APPI Active Site] = 2[I], stands for the concentration of APPI monomer units. The added mesotrypsin concentration was maintained at [E] = 0.25 nM, and we adopted KI = 122.5 nM, as independently determined from the measurements performed with monomeric APPI (Fig 4B). The fitted values of K2I are presented above each plot. Raw data can be found in SI.

Based on the determined value of K2I = 2.1 nM, using Eq 10, it is now possible to extract the equilibrium inhibition constant for the second reaction step of mesotrypsin binding to the APPI homodimer, K2: , where we use KI = 122.5 nM is the measured equilibrium inhibition constant for the APPI monomer (Fig 4B). Here we assume that such value of KI measured for the case of monomeric APPI, also represents the equilibrium inhibition constant for the first reaction step (Eq 4) in the case of homodimer APPI. This gives us, K2 = 0.036 nM. Such strikingly low value of K2 as compared to KI (where K2 is nearly four orders of magnitude lower than KI) indicates a high degree of cooperativity (avidity) in the second step of the reaction mechanism, where the second mesotrypsin molecule binds to the remaining unit of APPI homodimer, as compared to the first step, where just a single mesotrypsin molecule binds to a single unit of APPI homodimer (Fig 5). Such low value of K indicates that the equilibrium balance in our system is shifted towards the second reaction step.

The increase in affinity measured here for a dimeric compared with a monomeric inhibitor–enzyme complex is much smaller than that known for polyvalent compared with monovalent antibody–antigen complexes. In our study, avidity occurs in the context of the interaction between a bivalent inhibitor and a monomeric enzyme with a single active site, where the enzyme is in solution and unclustered prior to binding to the bivalent inhibitor.

By contrast, in antibody–antigen complexes, the antigen (or receptor) molecules are anchored to a surface (e.g., to a cell membrane) and thus are clustered in close proximity to each other before they bind the multivalent antibody ligand. Such clustering significantly enhances interaction strength, such that affinity in polyvalent antibody–antigen complexes is 2–3 orders of magnitude stronger than in their monovalent analogues [46, 47]. When monomeric target molecules with a single binding site are in solution, the molecules are separated from each other and have greater mobility than clustered (or surface anchored) target molecules and binding sites. This may make the binding of the monomeric targets to a dimeric ligand more difficult if they follow a ‘lock and key’ mode of molecular recognition. In contrast, during interactions with antibodies, the organization of surface-immobilized targets exhibits a high surface epitope density that allows them to rebind the multivalent ligand much faster and in the correct conformation for optimal binding. This point was recently demonstrated by Hadzhieva et al. [40] in a study that elucidated the correlation between the binding affinities of several IgG antibodies and the density of an antigen attached to a surface. The authors chose several antibodies that bound the HIV envelope glycoprotein 120 (namely gp120) with a wide range of affinities. Using a surface plasmon resonance (SPR) spectroscopy method to evaluate affinity, they controlled the density of antigen immobilized to the surface of a sensor chip and performed avidity measurements. As antigen density increased, enhanced avidity was observed for all the antibodies, as expressed by a systematic decrease in their equilibrium dissociation constants driven largely by reductions in their dissociation rate constants. For example, for the HJ16 antibody, a 60-fold increase in gp120 density led to a 150-fold decrease in the dissociation rate constant that was expressed as a 168-fold increase in binding affinity. One of the proposed explanations for this result was that the high density of gp120 allowed the formation of an IgG hexametric structure, which resulted in enhanced avidity [40]. Taken together, it is plausible that a greater avidity effect is observed in systems that confer both high target density and restricted target movement (as in surface-immobilized antigens or membrane-anchored receptors). This assumption is supported by the fact that proper orientation of free target molecules is a prerequisite for optimal ligand binding. The formation of a soluble complex, such as in interactions between an inhibitor and its target enzyme, requires the specific orientation of the interface residues of both interacting proteins. Obtaining the optimal orientation for binding is much more difficult for soluble complexes because of the dynamic and constant movement of the target molecules in solution, whereas immobilized targets with restricted movements may confer faster association rates and higher affinity in equilibrium.

In other words, the binding epitopes of a surface-anchored protein target may be subject to conformational constraints that may result in lower entropic penalties upon binding to a ligand, which enhances binding affinity [5, 48]. For monomeric protein targets in solution, the structure of the target is flexible, such that there is a large difference in the structural rigidity of the protein target between its unbound state and its state when bound to its polyvalent ligand. In contrast, the structure of the target is more rigid when immobilized to a surface, such that there is little difference in rigidity between its unbound and bound states. This conformational constraint may also be achieved by target dimerization, as observed for mesotrypsin in our system.

The positive cooperativity we observed between APPI units binding to mesotrypsin stands in contrast to the results obtained by Farooq’s group, who characterized ligand binding to the two WW tandem domains of the YAP2 protein, a transcriptional factor that regulates genes related to cell fate [12]. They isolated the WW domains and determined the binding affinity of each WW domain toward each ligand from equilibrium dissociation constants using isothermal titration calorimetry measurements. Next, they compared the constants obtained for a specific ligand with the binding affinity of the same ligand toward the native structure (i.e., to YAP2 containing two WW domains). They found negative cooperativity during ligand binding to tandem WW domains. Specifically, each ligand exhibited higher affinity for the isolated WW domain in comparison with the tandem, fused WW domains of the native YAP2 protein. The researchers explained this negative cooperativity by positing that inter-domain interactions arising from the proximity of the two WW domains to each other impede or sterically hinder ligand binding to each domain.

Bikunin (like APPI) is a member of the Kunitz family, however (unlike APPI) it has two subunits that are linked via a single peptide bond. Similarly to the WW domain in YAP2, bikunin cannot bind two serine protease simultaneously. Ollis’s group postulated that the native structure of bikunin can control the proteolytic activity of enzymes because each domain binds a different protease and so acts as a useful regulatory mechanism, with one Kunitz domain diminishing or abolishing binding at the second domain [37].

These previous studies and our own current study include examples of soluble systems that have two domains within a single protein ligand, with each domain having a single binding site capable of interacting with monomeric protein targets in solution. However, the major difference between our study and the previous studies of bikunin and the WW domains in YAP2 is that their tandem domains, when embedded in the entire protein, do not exhibit enhanced binding affinity, with the lack of enhancement attributed to steric interference. On the other hand, in our system the affinity of the target molecule mesotrypsin to a single binding loop in dimeric APPI was enhanced relative to the binding of mesotrypsin to the same binding loop in monomeric APPI. This was probably because there was negligible steric interference between the single APPI units (and specifically the canonical inhibitory loops) within the dimeric APPI structure. In the absence of steric hindrance, our dimeric APPI could simultaneously bind, via its canonical binding loops, two mesotrypsin units as shown in our APPI dimer titration analysis. In addition, our dimeric APPI protein is a homodimer, whereas the WW domains of the YAP-2 protein and the two Kunitz domains of bikunin differ in their amino acid content (i.e., they are heterodimers) which may also influence their target binding kinetics.

Conclusions

In summary, we have demonstrated the feasibility of enhancing binding affinity through an avidity effect using a complex between mesotrypsin and bivalent APPI, in which the mesotrypsin target protein is monomeric in solution (prior to binding) and has a single binding site. Such enhanced binding affinity (i.e., avidity) stems from statistically enhanced attraction between pairs of mesotrypsin molecules reversibly binding to the homodimer APPI. Isolation of the fully active recombinant dimeric APPI exhibiting correct folding and possessing two fully functional inhibitory loops (one on each monomer) allowed us to achieve accurate results, unaffected by unfolded or partially unfolded protein domains. Within the framework of conventional Michaelis-Menten model for competitive inhibition, the binding affinity, which was measured for a single inhibitory loop, was 3.4-fold stronger for dimeric APPI compared with monomeric APPI. Strikingly, revising such conventional Michaelis-Menten kinetic model, and introducing a non-linear effect induced by the presence of bivalent APPI homodimer, we obtain a nearly four orders of magnitude stronger binding affinity in the second step of the reaction mechanism (two mesotrypsin molecules binding to the APPI homodimer), as compared to the first step (a single mesotrypsin molecule binding to a single APPI unit of the APPI homodimer), Fig 5. This model provides a quantitative explanation for the observed enhanced tendency for mesotrypsin dimerization leading to cooperativity (i.e., avidity) in the binding affinity that cannot be explained by the conventional Michaelis-Menten scheme. Moreover, we validated the ability of dimeric APPI to bind two mesotrypsin units by using binding titration analysis, indicating that the enzyme recognition site on each of the two inhibitory units possesses a canonical loop that is available for simultaneous interaction with trypsins.

Materials and methods

Reagents

Synthetic oligonucleotides were obtained from Integrated DNA Technologies (Coralville, IA, USA). Restriction enzymes, T4 ligase, and Q5 polymerase were purchased from New England Biolabs (Ipswich, MA, USA), and nucleoside triphosphates (dNTPs) from Jena Bioscience (Jena, Germany). The methylotrophic yeast P. pastoris strain GS115 and the Pichia expression vector (pPIC9K) were obtained from Invitrogen (Carlsbad, CA, USA). Bovine trypsin, disuccinimidyl suberate (DSS), and the chromogenic substrates benzyloxycarbonyl-Gly-Pro-Arg-p-nitroanilide (Z-GPR-pNA), 4-nitrophenyl 4-guanidinobenzoate (pNPGB), and benzoyl-L-arginine-p-nitroanilide (L-BAPA) were purchased from Sigma-Aldrich (St. Louis, MO, USA). Rabbit anti-trypsin antibody (Ab-200997) and mouse anti-his tag (Ab-49936) were obtained from Abcam (Cambridge, UK). Affi-gel 10 resin was obtained from Bio-Rad laboratories (Hercules, CA, USA).

Generation of APPI gene constructs in expression vector pPic9k

APPI monomer (PDB:3L33, residues 4–55) was cloned into the plasmid pPic9k as previously described [36] and the gene construct encoding dimeric APPI was generated by a gene assembly method. Briefly, pPic9k plasmid containing the full-length APPI gene was amplified by polymerase chain reaction (PCR) using Q5 DNA polymerase with primers containing appropriate restriction sites for pPic9k plasmid and the addition of GGGGS×3 linker at the C-terminal of APPI unit. The following primers were used to amplify the monomeric APPI: APPI FW: (5’-TGCTACGTATTAATTAACGAAGTTTGTTCTGAACAAGCTG-3’) and APPI RC: (5’-GCAATGGAATTCGGATCCCCCTCCTCCGGATCCTCCCCCTCCGGAACCTCCCCCTCCAATAGCAGAACCACAAACAGC-3’).

Both the amplified PCR fragments and pPick9k plasmid were digested with the SnaBI and EcoRI restriction enzymes to generate an APPI dimer gene construct (S1A Fig in S1 File). The digested fragments were ligated using T4 ligase, transformed into E. coli, and plated on plates with lysogeny broth containing ampicillin (LB-amp). Finally, the dimeric APPI gene construct was sequenced at the DNA Microarray and Sequencing Unit of the National Institute for Biotechnology in the Negev at Ben Gurion University (DMSU, NIBN, BGU). Expression vectors were linearized by SacI digestion and used to transform P. pastoris strain GS115 by electroporation. This resulted in the insertion of the construct at the first alcohol oxidase (AOX1) locus of P. pastoris, thereby generating a His+ Mut+ phenotype. Transformants were selected for the His+ phenotype on 2% agar containing regeneration dextrose biotin (RDB; 18.6% sorbitol, 2% dextrose, 1.34% yeast nitrogen base, 4×10−5% biotin, and 0.005% each of L-glutamic acid, L-methionine, L-lysine, L-leucine, and L-isoleucine) and allowed to grow for 3 days at 30°C. Cells were harvested from the plates and subjected to further selection for high copy number on the basis of their growth on 2% agar containing 1% yeast extract, 2% peptone, 2% dextrose medium, and the antibiotic G418 (Geneticin, 4 mg/mL, Invitrogen). To verify direct insertion of the construct at the AOX1 locus of P. pastoris, the genomic DNA of the highest APPI-expressing colony from each APPI variant was extracted and amplified by PCR with an AOX1 upstream primer, 5´- GACTGGTTCCAATTGACAAGC-3´, and an AOX1 downstream primer, 5´- GCAAATGGCATTCTGACATCC-3´ (S1B Fig in S1 File). The PCR products were separated on 1% agarose gel, purified, and the correct sequence of the APPI dimer was confirmed by DNA sequencing analysis (DMSU, NIBN, BGU) (S1C Fig in S1 File).

Large-scale purification of APPI variants

P. pastoris cultures expressing either monomeric or dimeric APPI were grown in 50 mL of BMGY medium (1% yeast extract, 2% peptone, 0.23% KH2PO4, 1.18% K2HPO4, 1.34% yeast nitrogen base, 4×10−5% biotin, and 1% glycerol) overnight and then in 0.5 L of BMMY medium (similar to BMGY, but with 0.5% methanol instead of 1% glycerol) for 3 days, with 2% methanol being added every 24 h to maintain induction. Following 4 days of induction, the culture was centrifuged at 3800×g for 10 min and the supernatant containing the secreted recombinant inhibitors was prepared for purification by nickel-immobilized metal affinity chromatography (IMAC). The supernatant was adjusted to 10 mM imidazole and 0.5 M NaCl at pH 8.0 and left to stand for 1 h at 4°C. Thereafter, filtration was performed to remove any additional precipitation using a 0.22 μm Steritop bottle-top filter (Millipore, MA, USA). The filtered supernatant was loaded on a HisTrap 5 mL column (GE Healthcare, Piscataway, NJ) at a flow rate of 0.5 mL/min for 24 h, washed with a washing buffer (20 mM sodium phosphate 0.5 M NaCl, and 10 mM imidazole (pH 8.0)), and eluted with an elution buffer (20 mM sodium phosphate, 0.5 M NaCl, and 0.5 M imidazole) in an ÄKTA-Pure instrument (GE Healthcare, Piscataway, NJ). The buffer of the eluted proteins was replaced with a mesotrypsin buffer (100 mM tris(hydroxymethyl)aminomethane (Tris), 1 mM CaCl2 (pH 8.0)) using a 3.5 kDa cutoff dialysis kit (Gene Bio Application, Israel). For all recombinant proteins (both monomeric and dimeric APPI), gel filtration chromatography was performed using a Superdex 75 16/600 column (GE Healthcare, Piscataway, NJ) equilibrated with a mesotrypsin buffer (100 mM Tris, 1mM CaCl2 (pH 8.0)) at a flow rate of 1 mL/min on an ÄKTA-Pure instrument (GE Healthcare, Piscataway, NJ). The purified proteins were analyzed by sodium dodecyl sulphate–polyacrylamide gel electrophoresis (SDS-PAGE) on a 15% polyacrylamide gel under reducing conditions followed by staining with InstantBlue Coomassie Protein Stain (Expedeon, Cambridge, UK). Finally, the correct mass of the proteins was validated using a Matrix-Assisted Laser Desorption/Ionization-Time of Flight (MALDI-TOF) REFLEX-IV (Bruker) mass spectrometer (Ilse Katz Institute for Nanoscale Science & Technology, BGU; S2 Fig in S1 File).

Preparation of the trypsin column

Affi-gel 10 beads (8 mL) were mixed with isopropanol, transferred into a 15 mL falcon tube, and centrifuged at 1000 rpm for 10 min. Then, the isopropanol was discarded, and the beads were washed with cold double-distilled water (DDW; 10 mL) and centrifuged at 2000 rpm for 10 min. This procedure was repeated three times to remove the isopropanol residues for efficient coupling of bovine trypsin to the beads. Thereafter, bovine trypsin powder (29.5 mg) was dissolved in 100 mM HEPES pH 7.5 (3 mL) and added to the falcon tube that contained the resin. The mixture was left rotating overnight at 4°C. The conjugated beads were then packed into a 9 mL glass column (Bio-Rad laboratories, Hercules, CA, USA). The dimeric APPI (15 mL) was loaded onto the column and then eluted with a gradient of 0–100% using 100 mM HCl.

Enzymes and substrates

Recombinant human mesotrypsinogen was expressed in E. coli, extracted from inclusion bodies, refolded, purified, and activated with bovine enteropeptidase, as described previously [49, 50]. The concentrations of mesotrypsin and bovine trypsin were determined by active site titration using p-nitrophenyl 4-guanidinobenzoate hydrochloride (pNPGB) substrate (Sigma-Aldrich, St. Louis, MO, USA), which served as an irreversible inhibitor [51]. For determination of substrate concentration, an aliquot of the chromogenic substrate N-α-benzoyloxycarbonyl-glycylprolylarginine p-nitroanilide (Z-GPR-pNA) dissolved in dimethyl sulfoxide (DMSO) was incubated with an excess of bovine trypsin powder to obtain full substrate cleavage. The substrate concentration was determined from change in absorbance at 410 nm as a result of the release of p-nitroaniline (ε410 = 8480 M-1 cm-1).

Determination of the inhibitory unit concentration by trypsin titration

In the canonical APPI monomer, the enzyme recognition site is a single loop, whereas in a fully functional APPI homodimer, enzyme binding should involve two loops. Since APPI inhibits the activity of serine protease mesotrypsin, each APPI loop or binding site may be referred to as an inhibitory unit. To accurately measure the concentration of inhibitory units available to interact with the protease in the APPI monomer and dimer, titration was performed with pre-titrated bovine trypsin and Nα-benzoyl-L-arginine 4-nitroanilide hydrochloride (L-BAPA; Sigma-Aldrich, St. Louis, MO, USA), as described previously [49]. Briefly, an assay cocktail (312 μl; 100 Mm Tris, 5 mM CaCl2 (pH = 8.0)) having a final concentration of 100 μM L-BAPA was added into a 96-well microplate (Greiner, Kremsmünster, Austria). Bovine trypsin enzyme (9 μL, 30 μM) was mixed with each of six dilutions of APPI monomer or dimer to produce six enzyme–inhibitor mixtures (final volume 45 μL). An aliquot (8 μL) of each enzyme–inhibitor mixture was transferred into the wells of a 96-well microplate to initiate the reaction. Reactions were monitored spectroscopically at 410 nm for 5 min at 37°C. The reaction velocity (being the change in absorbance with time during substrate cleavage) was calculated for each inhibitor concentration, and the values were plotted versus the volume of inhibitor (0–30 μL APPI) in the enzyme–inhibitor mixture. From these data, the X-intercept was determined, and the inhibitory unit concentrations were calculated using Eq 19. Reported inhibitory unit concentrations are the average values obtained from two independent experiments, reported as mean±SD. Where [IU] is the inhibitory unit concentration (μM) of the APPI monomer or dimer, DFi is the inhibitor dilution factor (11.5 and 1.7 dilution from the monomeric and dimeric APPI stock solution, respectively), Ve is enzyme volume (i.e., 9 μL bovine trypsin), [E] is enzyme concentration (i.e., 30 μM), and Xint is the value of the x-intercept on a plot of reaction velocity (AU/s) versus inhibitor (APPI) volume (μL).

Inhibition studies

The inhibition constants (K) of monomeric and dimeric APPI in complex with mesotrypsin were determined according to the previously described methodology, with minor changes [49]. Briefly, stock solutions of enzyme, substrate, and APPI monomer (or dimer) were prepared at 40× the desired final concentrations. Assays were performed at 37°C in the presence of different concentrations of Z-GPR-pNA substrate (5–250 μM) and inhibitor (APPI monomer, 0–400 nM; APPI dimer inhibitor units, 0–96 nM (APPI dimer molecule = 0–48 nM to achieve 2× this concentration of inhibitor units) in a Synergy 2 Multi-Detection Microplate Reader (BioTek, VT, USA). Mesotrypsin buffer (296 μL), Z-GPR-pNA (8 μL), and diluted APPI monomer/dimer (8 μL) were mixed and equilibrated in a 96-well microplate (Greiner, Kremsmünster, Austria) prior to the addition of mesotrypsin (8 μL from 10 nM stock). Reactions were followed spectroscopically for 5 min, and initial rates were determined from the increase in absorbance caused by the release of p-nitroaniline. Data were globally fitted by multiple regression to Eq 20, the classic competitive inhibition equation, using Prism (GraphPad Software, San Diego, CA). Where u is the velocity of product formation at the start of the reaction; K (the Michaelis-Menten constant) and k are the kinetic parameters for substrate hydrolysis; [E] and [I] are the total concentrations of enzyme and inhibitor, respectively, and [S] is the initial substrate concentration. The reactions were performed with excess APPI monomer and dimer inhibitor unit concentrations (≥ 20 times the mesotrypsin concentration), and therefore any reduction of inhibitor concentration upon binding was negligible. Reported inhibition constants are average values obtained from three independent experiments, and are expressed as mean±SD.

15% SDS-PAGE analysis of the purified monomeric APPI fraction (A) and comparison of purified monomeric APPI with dimeric APPI before and after purification (B).

This figure shows the original gels presented in Figs 1E and 2C, respectively.

(DOCX)

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(XLSX)

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(DOCX)

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12 Apr 2021

PONE-D-21-08844

Avidity observed between a bivalent inhibitor and an enzyme monomer with a single active site

PLOS ONE

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Reviewer #1: Lacham-Hartman et al. show avidity benefits for a bivalent ligand with a soluble monomeric target, as opposed to the more widely studied systems involving multiple copies of both receptors and ligands. The work is novel, interesting and certainly adds to the knowledge in the field of multivalency.

The manuscript is concisely written and is easy to understand. The authors do a good job at providing enough background of prior work to the reader. The manuscript clearly articulates what the current work adds to the field. Further, the authors also cite and explain other contrasting theories in light of their findings.

Please consider the following minor revisions before publication-

1) In the proposed model in Fig 5, have the authors considered an alternate scenario (or rather a parallelly occuring one) where an APPI dimeric unit inhibits a single mesotrypsin unit – binding to the same mesotrypsin alternating between the two units of the engaged APPI homodimer. This scenario would still offer the proposed benefits of avidity. How does this scenario change the analysis proposed by the authors?

2) Could the authors clarify how they determined 3 repeats of GGGGS to be appropriate for ‘the simultaneous binding to two mesotrypsin units’? (To prevent any antagonistic effects due to steric hindrance, one could rationally determine the length of the spacers: looking at the APPI protein structure, the location of the inhibitory loop, and the terminus chosen to attach the second unit of APPI in tandem. The following review is a good source for fusion protein linkers and estimated lengths for future reference: doi.org/10.1016/j.addr.2012.09.039)

3) In Fig 1D left peak has a little bump which might explain the presence of higher order aggregates.

4) Fig 5 scheme has a typo: “Reversable” -> “Reversible”. Fig 5 caption has a typo: “Ka is the associate rate….” -> “Ka is the association rate…”.

Reviewer #2: The Papo group examines here if a bivalent inhibitor displays avidity towards its monomeric enzyme target. Understanding avidity, or as it is known in chemistry, multivalency, is one of the most important and interesting challenges yet to be fully solved when it comes to understanding intermolecular interactions. It is, as the authors point out, of particular importance when it comes to various biological process as well as in other fields including medical chemistry and nanoscience.

The key claim of this paper seems to be that the authors have uncovered a new insight into avidity through a very simple system; a bivalent inhibitor interacting with its monomer enzyme target.

I am really not certain if this is correct and whether the paper should be published will in my opinion come down to if the authors can make a more convincing case for this claim and make the connections of this work clearer with the current understanding of the field of avidity/multivalency, particularly from within the field of supramolecular chemistry. I will expand on these concerns in more details below:

(see attachment)

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Submitted filename: plosonecomments.pdf

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14 Sep 2021

All page numbers written in the letter refer to the revised (with the track changes) manuscript.

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A1. Done as requested.

Q2. PLOS ONE now requires that authors provide the original uncropped and unadjusted images underlying all blot or gel results reported in a submission’s figures or Supporting Information files. This policy and the journal’s other requirements for blot/gel reporting and figure preparation are described in detail at https://journals.plos.org/plosone/s/figures#loc-blot-and-gel-reporting-requirements and https://journals.plos.org/plosone/s/figures#loc-preparing-figures-from-image-files. When you submit your revised manuscript, please ensure that your figures adhere fully to these guidelines and provide the original underlying images for all blot or gel data reported in your submission. See the following link for instructions on providing the original image data: https://journals.plos.org/plosone/s/figures#loc-original-images-for-blots-and-gels.

In your cover letter, please note whether your blot/gel image data are in Supporting Information or posted at a public data repository, provide the repository URL if relevant, and provide specific details as to which raw blot/gel images, if any, are not available. Email us at plosone@plos.org if you have any questions.

A2. Done as requested. The original gel images of Fig. 1E and 2C are now in Supporting Information section (in Fig. S2). Please note that Figs 1F and 2B were already uncropped in the original figures.

Q3. We note that you have included the phrase “data not shown” in your manuscript. Unfortunately, this does not meet our data sharing requirements. PLOS does not permit references to inaccessible data. We require that authors provide all relevant data within the paper, Supporting Information files, or in an acceptable, public repository. Please add a citation to support this phrase or upload the data that corresponds with these findings to a stable repository (such as Figshare or Dryad) and provide and URLs, DOIs, or accession numbers that may be used to access these data. Or, if the data are not a core part of the research being presented in your study, we ask that you remove the phrase that refers to these data.

A3. Done as requested. Please see revised parts on pages 7 and 9.

Reviewer #1:

Lacham-Hartman et al. show avidity benefits for a bivalent ligand with a soluble monomeric target, as opposed to the more widely studied systems involving multiple copies of both receptors and ligands. The work is novel, interesting and certainly adds to the knowledge in the field of multivalency.

The manuscript is concisely written and is easy to understand. The authors do a good job at providing enough background of prior work to the reader. The manuscript clearly articulates what the current work adds to the field. Further, the authors also cite and explain other contrasting theories in light of their findings.

Please consider the following minor revisions before publication-

Q1. In the proposed model in Fig 5, have the authors considered an alternate scenario (or rather a parallelly occurring one) where an APPI dimeric unit inhibits a single mesotrypsin unit – binding to the same mesotrypsin alternating between the two units of the engaged APPI homodimer. This scenario would still offer the proposed benefits of avidity. How does this scenario change the analysis proposed by the authors?

A1. We thank Reviewer 1 for her/his important suggestion regarding the model. A similar suggestion was also pointed out by Reviewer 2. As a response to this comment, we revised the model, incorporating a two-step reaction mechanism in section ‘Kinetic model for APPI homodimer binding to mesotrypsin’ (see p. 15-20, the changes tracked, and Conclusions, p. 22). In the framework of the revised model (see new Fig. 5 of the revised manuscript), the reaction mechanism allows two steps. In the first step, one APPI monomer unit reversibly binds one mesotrypsin molecule (and the second APPI unit remains unbound). In the second step, the remaining APPI unit reversibly binds the second mesotrypsin molecule. Introducing two steps in the reaction mechanism, addresses the issue pointed out by Reviewer 1. The revised model leads to qualitatively similar results compared to the original model (new Fig. 6). Quantitatively, introducing the two-step model leads to ~10% increase in the resulting equilibrium constant, ��I (i.e., slightly decreased cooperativity (avidity)), as compared to the original one-step model (Fig. 6). The reason for the observed ~10% decrease in cooperativity stems from the fact that the second step of the two-step reaction mechanism, bringing two mesotrypsin molecules together through binding to APPI homodimer, constitutes the main source for cooperativity (see also the first paragraph on p. 18 of the revised manuscript).

Q2. Could the authors clarify how they determined 3 repeats of GGGGS to be appropriate for ‘the simultaneous binding to two mesotrypsin units’? (To prevent any antagonistic effects due to steric hindrance, one could rationally determine the length of the spacers: looking at the APPI protein structure, the location of the inhibitory loop, and the terminus chosen to attach the second unit of APPI in tandem. The following review is a good source for fusion protein linkers and estimated lengths for future reference: doi.org/10.1016/j.addr.2012.09.039)

A2. We thank the reviewer for the comment. The mesotrypsin-APPI heterodimer is shaped like a mushroom, where mesotrypsin is the mushroom cap (~40 Å in diameter) and APPI is the mushroom stem (~20 Å wide and ~30 Å high). Both the N- and C-termini of APPI are located opposite to its inhibitory loop, at the base of the molecule. By connecting 2 APPI molecules in tandem, we connect two mushroom-shaped complexes at the base of their stems, such that the two APPI subunits themselves can serve as rigid spacer modules of ~25 Å each, connected by the flexible linker hinge. Thus, even a short linker would be expected to allow >50 Å between the two mesotrypsin molecules resulting in little risk of steric hindrance between mesotrypsin subunits. Our larger concern was achieving efficient independent folding and correct disulfide bond configuration within each of the two APPI domains, and toward this end we selected a linker of generous length (i.e., 3 repeats of GGGGS, ~48 Å in length). Additionally, we isolated correctly folded APPI-dimer from misfolded species using affinity chromatography. We have now attempted to better clarify in the manuscript the reasoning behind the linker design (page 6).

Q3. In Fig 1D left peak has a little bump which might explain the presence of higher order aggregates.

A3. We agree with the reviewer and as can be seen in figure 2C (and also in the original gel, new Fig. S2B) upon using a trypsin column, these aggregates were removed.

Q4. Fig 5 scheme has a typo: “Reversable” -> “Reversible”. Fig 5 caption has a typo: “Ka is the associate rate….” -> “Ka is the association rate…”.

A4. Revised as requested.

Reviewer #2:

The Papo group examines here if a bivalent inhibitor displays avidity towards its monomeric enzyme

target. Understanding avidity, or as it is known in chemistry, multivalency, is one of the most

important and interesting challenges yet to be fully solved when it comes to understanding

intermolecular interactions. It is, as the authors point out, of particular importance when it comes to

various biological process as well as in other fields including medical chemistry and nanoscience.

The key claim of this paper seems to be that the authors have uncovered a new insight into avidity

through a very simple system; a bivalent inhibitor interacting with its monomer enzyme target.

I am really not certain if this is correct and whether the paper should be published will in my opinion

come down to if the authors can make a more convincing case for this claim and make the

connections of this work clearer with the current understanding of the field of avidity/multivalency,

particularly from within the field of supramolecular chemistry. I will expand on these concerns in

more details below:

Q1. Part of the problem with this work is that researchers in biology/biophysics and those in

(supramolecular) chemistry use a completely different language about what are essentially the same

things – the (almost) synonyms of avidity and multivalency being a prime example. Usually what

happens then is that researchers will go to extreme lengths to make it appear that there are some

real differences between these terms and again, in the literature there are some very interesting

examples of authors trying to make it so that avidity and multivalency are different things when

there is little substance behind these terms. With this in mind, I would like to start to suggest to the

authors that they have good look at the chemistry literature on multivalency, e.g. from authors such

as Gianfranco Ercolani, George Whitesides, Pall Thordarson and Harry Anderson to mentioned a just

few (see c.f. Angew Chem 1998, 37, 2754, J. Phys. Chem. B, 2007, 111, 12195, Angew. Chem. 2009,

48, 7488, Angew. Chem., 2011, 50, 1762, Chem. Soc. Rev. 2017, 46, 2622, Bioconjugate Chem. 2019,

30, 503). This might obviously have some impact on their introduction to the topic.

A1. We thank the reviewer for this suggestion. Please see our additions (including references) to the Introduction section that better contextualize our current results against the background of the prior chemistry literature and its definitions of avidity and multivalency. In the added text, we identify the differing definitions of these terms in the literature to which the reviewer refers, and more explicitly define what we mean by the terms in our paper.

Questions 2-5 of Reviewer 2 concern the kinetic model that we developed. We are grateful to the Reviewer for pointing out several important issues with this part of our manuscript. In response to these comments, we revised the model, and extended the discussion clarifying all issues raised by Reviewer 2. We also revised Fig. 5 and Fig. 6 of our manuscript. We now give point-by-point response to the comments.

Q2. An often-mentioned topic by the authors/papers mentioned in 1 is that when it comes to

“multivalent” binding, statistical factors need to be taken into account. As discussed also in details in

Chem Soc Rev 2011, 40, 1305, the 2 to 1 interaction is often used as an archetypal example.

Accordingly, care needs to be taken when discussing a 2:1 (or 1:2 – the difference really is only about

which partner in the interaction is defined as the first one) interactions, do the authors mean, e.g.,

the microscopic (Km) or macroscopic (K) binding constants, or do they mean the overall binding

constants (which in chemistry is sometimes shown as β to avoid confusion) in their description of

say, KI in Figure 5/ eq 4 which is shown there in the power of 2: KI2 ? By the looks of it, KI is really the inverse microscopic binding constant (here it does not help that chemist usually use association

constants while biologists prefer dissociation constants which are simply the inverse of the former)

for each stepwise interactions and, additionally, the authors have made the assumptions to use the

language from Chem Soc Rev 2011, 40, 1305 that KI = K1m = K2m, i.e. the stepwise interactions have

no cooperativity. It does not help here that in Eq 2, KI appears to be what in chemistry would be

called the overall binding constant with the units M-2.

Q3. Continuing with the equations: Fig 5 / eq 4 has KI

2 = ki’/ki in which the two rate constants come

from eq 3. But this does not make a lot of sense? This must be a stepwise process (here <->

equilibrium arrows:

E + I <-> EI step 1, rate constants are k1 and k-1

EI + E <-> EI step 2, rate constants are k2 and k-2

Hence Eq 4 seems incorrect. This is also evident if one considers that for Eq 4 to be correct, ki’/ki

must have the units M2.

A2 and A3. We now respond to comments (2) and (3). The Reviewer was entirely correct in bringing the issue of a two-step reaction mechanism. We thus revised the model, incorporating the two-step mechanism suggested by Reviewer in Q3. This is reflected in our revised manuscript in section ‘Kinetic model for APPI homodimer binding to mesotrypsin’ (see p. 15-20, the changes are marked in red). We also provided the entire derivation of all theoretical results without omitting any steps. We explicitly, carefully defined all parameters that we used, including all equilibrium constants appearing in the model. We believe therefore that we addressed important issues regarding the definition and the clarity of presentation raised by Reviewer in Q2. All issues regarding the definitions of the equilibrium constants were resolved by explicitly defining all these equilibrium constants and all reaction rates for both steps in the reaction mechanism. We also added an extensive discussion about the mechanism of the observed cooperativity (see the discussion on p. 18-19, and Conclusions, p. 22 in the revised manuscript).

Reviewer writes: Hence Eq 4 seems incorrect.

Regarding to Eq. 4 of our original manuscript – we clarified this issue (see the discussion after Eq. 10, Eq. 11, and Eq. 12, p. 16 in the revised manuscript).

Q4. Continuing to Eq 5, I cannot see how it was obtained from Eq 3. Whether my concerns about Eq 3

above are correct or not, the authors need to give more details on this derivation, at least in SI (write

it out in full if necessary).

A4. We clarified this issue including all steps of the derivation (see Eq. 15-20 and related explanation in the text of the revised manuscript).

Q5. Figure 6 – which non-linear models / equations? This is really not clear at all. Again, more details,

and ideally, raw data file etc should be included as SI.

A5. We recomputed Fig. 6 based on the revised model and clarified the caption. The title of Fig. 6 is now ‘Two-step model (Fig. 5) for mesotrypsin inhibition by APPI homodimers provides an excellent fit to experimental data’. In addition, a raw data file is now added as SI.

Q6. Eq 8 on page 22 and related discussion earlier in the paper: Why does the bivalent inhibitor not

bind to two trypsin (but only with mesotrypsin)? Or is this not correctly understood.

A6. We thank the reviewer for this comment. Our data support the model that the dimeric APPI binds simultaneously two units of trypsin during the active site titration experiment (see Table S1). We have attempted to clarify this point through altered presentation of Table S1 and edits to the text (page 11). Because of the structural similarity of trypsin family members, we anticipate that the APPI dimer is also capable of binding simultaneously to two molecules of mesotrypsin.

Q7. Eq 9 seems to be the main method to measure inhibition. But isn’t this very risky? As the

Graphpad manual points out this should not be used for tight binding, rather, using the Morrison

equation:

GraphPad Prism 9 Curve Fitting Guide - Equation: Tight inhibition (Morrison equation)

Now, a companying paper Microsoft PowerPoint - 1305-arqule-002.ppt (biokin.com) explains this

issue in more details.

But on reading about the Morrison Equation, it seems it is a quadratic question that is strongly

related to those used to find free ligand concentration in a typical 1:1 equilibria. If that is so, there

should be a cubic equation equivalent of the Morrison equation that would be related to the cubic

one for 1:2 or 2:1 equilibria in Chem Soc Rev 2011, 40, 1305?

A7. We thank the reviewer for this comment. We used competitive inhibition as our initial approach for data analysis for consistent comparison with prior mesotrypsin-APPI studies. We have substantial experience using this approach and also using the Morrison equation and alternative kinetic treatments appropriate for measuring tight-binding inhibition, in the context of evaluating trypsin and mesotrypsin inhibitors. We have found that the competitive inhibition approach has good sensitivity to discriminate among equilibrium inhibition constants down to the very low nanomolar range, particularly when using an appropriate substrate concentration range sampling concentrations both above and below Ki. Alternative tight-binding approaches are needed for accurate discrimination between Ki values in the sub-nanomolar range. We have found tight-binding and competitive inhibition experimental designs to give similar results for inhibitors with Ki in the 1-5 nM range. As our fits of competitive inhibition studies yielded Ki values in the mid-nanomolar range, and we were able to measure rates accurately when using substrate concentrations well below Ki, we did not use tight-binding models in this case.

Q8. Somewhat related to 7 is that the authors say on page 23 that there is excess of the inhibitor that

argue therefore I think that the “tight binding” models might not be necessary. But based on

experience from supramolecular chemistry, even with such excess this is a dangerous assumption to

make at any point for 1:2 and 2:1 equilibria.

A8. Our enzyme concentration is 0.25 nM in the mesotrypsin assays, and thus inhibitor concentrations are well in excess of enzyme in these experiments. As noted above, we have consistently used this assay and data fitting approach to reproducibly differentiate the equilibrium inhibition constants for inhibitors down to 1-2 nM, more than an order of magnitude below any Ki values measured in the present study.

Q9. And on the topic of concentration – is the concentration of the dimer inhibitor reported in various

plots etc, the concentration of the molecule or the concentration of binding loops? The latter would

be 2x the former. I mentioned this because IF the assumption is made that there is no cooperativity

between the first and second enzyme binding to the inhibitor, then it should be possible to model

the system as a simple 1:1 system provides the 2x inhibitor concentration is used in all the data

analysis.

A9. We thank the reviewer for this comment. We report the concentration of the molecule where we validate of inhibitor integrity/activity by comparing the concentrations determined by absorbance at 280 nm with those determined by bovine trypsin titration using different stoichiometry models. By contrast, in our initial analysis of Ki vs. mesotrypsin, we used the active site concentration, i.e. the concentration of binding loops (2× the concentration of the molecule). In this case, we are using the classic competitive inhibition model for a simple 1:1 system under the assumption that there is no cooperativity between the first and second enzyme binding to the inhibitor, as suggested by the reviewer. We subsequently consider a more complex treatment that does not make this assumption, as described below and in the text. We have edited the text to better clarify these points (page 14).

Q10. It would also help if the authors simply included as much as possible of their raw data and fitting

program(s) as an attached (could be deposited on github or figshare).

A10. As requested by the reviewer, a raw data file is now added as SI. The procedure of fitting the raw data using Eq. (18) is straightforward and it simply requires plotting Eq. (18) at different values of ��I. This was done using a MATLAB script. We specified all the parameters in the caption of Fig. 6.

Q11. In conclusions, this paper appears to be an important contribution to understand avidity /

multivalency / cooperativity better. But a quite a number of issues need to be cleared up first and

the data analysis explained in enough details to make it both reproducible and unambiguous in

terms of links to other related work, particularly in chemistry.

A11. We thank the reviewer for careful reading and many helpful suggestions, and believe that our responsive revisions have greatly improved the manuscript.

Submitted filename: Lacham et al_15.8.21_response to reviewers.docx

Click here for additional data file.

18 Oct 2021

PONE-D-21-08844R1Avidity observed between a bivalent inhibitor and an enzyme monomer with a single active sitePLOS ONE

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Reviewer #2: I thank the authors for the revision of their manuscript and for having by and large addressed all my concerns and questions. I have only one remaining suggestion, and the editor does not need to send the paper back to me should the authors do this:

The derivation of what is equation 15 is still not clear. Yes, it is obtained by combining Eq 3, 6 and 10. But exactly how that leads to 15 is a bit unclear. Perhaps include a more detailed step-by-step derivation in the SI?

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11 Nov 2021

Reviewer #2: I thank the authors for the revision of their manuscript and for having by and large addressed all my concerns and questions. I have only one remaining suggestion, and the editor does not need to send the paper back to me should the authors do this:

The derivation of what is equation 15 is still not clear. Yes, it is obtained by combining Eq 3, 6 and 10. But exactly how that leads to 15 is a bit unclear. Perhaps include a more detailed step-by-step derivation in the SI?

Answer: We thank the reviewer for the comment and added a more detailed step-by-step derivation in the SI section.

Submitted filename: Response to Reviewers.docx

Click here for additional data file.

15 Nov 2021

Avidity observed between a bivalent inhibitor and an enzyme monomer with a single active site

PONE-D-21-08844R2

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16 Nov 2021

PONE-D-21-08844R2

Avidity observed between a bivalent inhibitor and an enzyme monomer with a single active site

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