A Complete Mechanistic Framework for Molecular Glue Characterization

Abstract

The use of molecular glues to modulate protein–protein interactions has emerged as a promising approach to drug previously intractable targets. Despite strong interest in this modality, a comprehensive theoretical framework is lacking. We have established a complete mechanistic analysis which enables the determination of molecular glues’ binding and cooperativity values from a simple biochemical matrix experiment. We validated the model using numerical integration and experimental data from fluorescence resonance energy transfer and fluorescence polarization assays. As the derived models enable the determination of all thermodynamic parameters of any molecular glue, they have significant applications in drug discovery, particularly for molecular glue optimization and characterization of neo-substrates.

Transcription factors and scaffolding proteins represent a wide and untapped pool of potential drug targets. They have proven challenging to drug with traditional small molecule inhibitors as they lack active-site pockets and enzymatic activity. Modulation of protein–protein interactions (PPIs) through induced proximity provides alternative opportunities to drug these targets: , in this approach, a compound (L) induces or enhances an interaction between a target (T) and an effector protein (E), leading to the formation of a ternary complex (Figure ). Depending on the nature of the effector protein that is recruited, degradation, sequestration, or activation of the protein of interest are all possible. −

1.

Different routes to generate ternary complexes. E: Effector Protein, T: Target, L: Ligand (PROTAC or molecular glue). PROTACs predominantly follow obligatory binary complex formation (lower and upper pathways only) prior to forming ternary complexes. Monovalent molecular glues can enhance pre-existing ET interactions (central pathway) and follow either the lower or upper binary complex pathways but usually not both.

The field of induced proximity is most advanced with heterobifunctional molecules, such as PROTACs. Owing to their high molecular weight, the development of PROTACs into drugs requires extensive compound optimization to achieve good levels of cell permeability and oral bioavailability. The emerging field of molecular glues is aiming to circumvent the limitations. Due to their monovalent nature, molecular glues tend to have molecular weights similar to small molecule inhibitors, hence, they pose fewer challenges with optimization of the compounds physicochemical properties.

Modeling ternary complex formation for heterobifunctional molecules and molecular glues is significantly more challenging than modeling binary interactions (Figure ). A comprehensive mathematical model for three-body binding equilibria for heterobifunctional molecules has been described by Douglass et al. In this seminal analysis, exact mathematical models that relate the amount of ternary complex to all possible T, E and L concentrations and cooperativity values were derived. More recently, analytical solutions have been complemented by computational methods. , However, in contrast to heterobifunctional molecules, most molecular glues are monovalent and they can enhance pre-existing interactions, for example, between the β-transducin repeat-containing protein 1 (β-TrCP1) E3 ligase and one of its native protein substrates, β-catenin. Stabilizing existing PPIs may prove to be a broadly applicable mechanism, as more ligandable protein:protein complexes are identified, such as the 14–3–3 protein family and their diverse client proteins. While there is significant overlap between the set of equilibria describing heterobifunctional molecules and molecular glues (Figure ), the differences make the exhaustive work done on three-body systems involving the former not applicable to molecular glues.

Currently, a mechanistic framework and associated mathematical model that relates the amount of ternary complex with the concentrations of proteins and ligand is not available for molecular glues. Such models are needed, particularly in drug discovery, to inform the design of glues based on derived thermodynamic parameters and to correlate results from biochemical assays to those of cellular assays.

Herein, we establish the mechanistic framework necessary to relate the affinity constants of the system and ternary complex concentrations at equilibrium by using analytical and numerical approaches. The model we have developed enables users to derive all the thermodynamic parameters from data generated in a single experiment.

We first solved the system under pseudo-first-order conditions where the glue and one of the proteins are in excess compared to the protein which binds to the glue. For the derivation below, we assume the glue binds to E (Figure A).

2.

Modeling of binary and ternary complexes under pseudo-first-order and non-tight-binding conditions, where glue (L) and target (T) are in excess over the glue binder (E). (A) Thermodynamic equilibria describing a system where the glue binds to E and ET but not to T. (B) Ternary complex modeling with [E]⁰ = 10 nM, K ₁ = 15 μM, K ₂ = 10 μM and α = 0.0333; points represent the results of KinTek modeling, and lines represent the analytical model (eq ). (C) Same as panel B but for the sum [ELT] + [ET] using eq . An increase in EC₅₀ (marked with x) is observed as [T] decreases. (D) Normalized FRET signal generated by performing matrix titrations of NRX-252262 and β-catenin peptide at 1 nM β-TrCP1:Skp1ΔΔ. Data were fitted to eq in GraphPad Prism, giving K ₁ = 810 ± 52 nM, K ₂ = 8900 ± 1300 nM, and α = 0.0008 ± 0.0001 (R² = 0.98).

We were able to demonstrate that

$$[\mathit{ELT}]=\frac{{[E]}^0{[L]}^0{[T]}^0}{\alpha K_1{K}_2+\alpha K_2{[T]}^0+\alpha K_1{[L]}^0+{[T]}^0{[L]}^0}$$ 1a

$$[ELT]+[ET]=\frac{{[E]}^0{[T]}^0({[L]}^0+\alpha {\mathrm{K}}_2)}{\alpha K_1{K}_2+\alpha K_2{[T]}^0+\alpha K_1{[L]}^0+{[T]}^0{[L]}^0}$$ 1b

where [E]⁰, [T]⁰ and [L]⁰ are the total amount of E, T and L, respectively, $K_1=\frac{[E][T]}{[ET]}$ , $K_2=\frac{[E][L]}{[EL]}$ and α represents the cooperativity (see Supporting Information for all derivations). In addition to modeling the ternary complex (eq ), we also derived an equation for the sum of [ET] and [ELT] (eq ), as many molecular glue discovery projects are likely to involve systems where a native interaction between E and T already exists. For such cases, the ET complex may also contribute to the signal, depending on the nature of the methodology used e.g. fluorescence resonance energy transfer from donor to acceptor fluorophores on E and T.

Furthermore, in the absence of basal affinity between E and T (ET = 0), the system described in Figure A simplifies to an ordered two step equilibrium and can hence be modeled by eq .

$$[ELT]=\frac{{[E]}^0{[L]}^0{[T]}^0}{\alpha K_1{K}_2+\alpha K_1{[L]}^0+{[T]}^0{[L]}^0}$$ 2

It should be noted that eqs and , perhaps not surprisingly, closely resemble the equations that describe ternary complex formation in rapid equilibrium random and ordered bisubstrate enzyme kinetic mechanisms, respectively.

To further validate our model, we compared its predictions with the values obtained from numerically solving the system in KinTek Explorer (see Supporting Information for simulation methods) and confirmed that the analytical model and the numerical predictions were identical (Figure B,C).

To assess if our model would reflect experimental data, we generated time-resolved fluorescence resonance energy transfer (TR-FRET) data using the well-characterized β-TrCP1:β-catenin peptide system with the molecular glue NRX-252262, which enhances the affinity of the β-TrCP1:β-catenin peptide interaction. We performed a global fit of the data to eq and obtained the thermodynamic parameters: K ₁ = 810 ± 52 nM, K ₂ = 8900 ± 1300 nM, and α = 0.0008 ± 0.0001 (Figure D). The fit was excellent and the fitted values were consistent with those reported previously.

Fits to an equation of the type Y = Y ⁰ + B _max × $\frac{X}{{\mathrm{EC}}_{50}+X}$ may also be carried out on the data for individual values of [L]. Modeling predicts that the EC₅₀ values are expected to decrease as T increases (see the cross symbols in Figure C). To investigate this further, we rearranged eq into

$$[ET]+[ELT]=Y^0+\frac{B_{\max }{[L]}^0}{E{C}_{50}+{[L]}^0}$$ 3

with

$${\mathrm{Y}}^0=\frac{{[E]}^0{[T]}^0}{K_1+{[T]}^0}$$ 3a

$$B_{\max }=\frac{{[E]}^0{[T]}^0{K}_1(1-\alpha )}{(K_1+{[T]}^0)(\alpha K_1+{[T]}^0)}$$ 3b

$$E{C}_{50}=\frac{\alpha (K_1{K}_2+{[T]}^0{K}_2)}{\alpha K_1+{[T]}^0}$$ 3c

The relationship between EC₅₀ and [T]⁰ (eq ) reveals that at low [T], EC₅₀ tends to K ₂ (the affinity between the glue and E), at high [T], EC₅₀ tends toward αK ₂, and there is an inflection point at [T] = αK ₁ where EC₅₀ = $\frac{(\alpha +1)K_2}{2}$ . We replotted the EC₅₀ values obtained from the data in Figure D versus [T]⁰ and observed the expected decreasing relationship (see Figure S1). However, the replot revealed a lack of data at [T] below the inflection point. This is because NRX-252262 is highly cooperative (α ≈ 0.001). For less cooperative glues, however, additional data below the inflection point should be attainable and data fitting to eq should be robust and yield accurate parameters.

In the absence of the model and data analysis presented here, K ₁ and α would be determined using TR-FRET by varying T in absence and presence of glue at saturating concentration, while K ₂ could be estimated from EC₅₀ values. Useful information could also be obtained from the Span of the EC₅₀ curves, as described recently. Using our model, we show that these parameters can be determined from one single dual titration experiment either by fitting the raw data to eq or the derived EC₅₀ values to eq . Biophysical techniques that measure direct binding, such as surface plasmon resonance, are also useful and our model is also applicable to these alternative methodologies

Having verified that the analytical derivation, the numerical modeling, and experimental data for the model presented above were all in agreement, we proceeded to consider additional cases that one is likely to encounter. There may be occasions where it may be not possible to carry out experiments under pseudo-first-order conditions e.g. if the proteins of interest are unstable at low nanomolar concentrations, and experiments may hence be restricted to relatively high protein concentrations; or if the assay relies on fluorescence polarization (FP). Under these conditions, it may be necessary to vary the concentration of the protein the glue binds to, which may lead to glue depletion and the assumptions underlying eqs and not being satisfied. For those situations, we derived eqs and :

$$[ELT]=\frac{{[T]}^0({[E]}^0+{[L]}^0+K_2-\sqrt{\mathrm{\Delta }})}{2\alpha K_1+{[E]}^0(\alpha +1)+({[L]}^0+K_2-\sqrt{\mathrm{\Delta }})(1-\alpha )}$$ 4a

$$[ELT]+[ET]=\frac{{[T]}^0{([\mathrm{E}]}^0(\alpha +1)+({[L]}^0+K_2-\sqrt{\mathrm{\Delta }})(1-\alpha ))}{2\alpha K_1+{[E]}^0(\alpha +1)+({[L]}^0+K_2-\sqrt{\mathrm{\Delta }})(1-\alpha )}$$ 4b

with Δ = ([E]⁰ + [L]⁰ + K ₂)² – 4­[E]⁰[L]⁰.

As before, we showed that numerical modeling with KinTek Explorer gave the same results as the analytical model (Figure A,B). We used the same β-TrCP1:β‑catenin and NRX-262262 system as the experimental test case. We selected the plate-based, high-throughput methodology FP. The labeled β-catenin peptide was fixed at a low concentration (2 nM), and, in this instance, we varied the concentration of the glue at multiple fixed levels of β-TrCP1­(Figure C). We fitted the data to eq , and the resulting derived parameters were in agreement with the expected values (K ₁ = 620 ± 34 nM, K ₂ = 9000 ± 1530 nM and α = 0.0011 ± 0.0002).

3.

Modeling of protein complex levels when glue (L) and glue binder (E) are in excess to the target (T). (A) Ternary complex modeling with [T]⁰ = 10 nM, K ₁ = 15 μM, K ₂ = 10 μM and α 0.0333;points represent the results of KinTek modeling, and lines represent the analytical model (eq ). (B) Same as panel A for [ELT]+[ET] with eq . (C) FP signal generated by performing matrix titrations of β-TrCP:Skp1ΔΔ and NRX-252262 at 2 nM β-catenin peptide. Data were fitted to eq , giving K ₁ = 620 ± 34 nM, K ₂ = 9000 ± 1530 nM and α = 0.0011 ± 0.0002 (R² = 0.98).

The presence of the √Δ term in eqs and prevents its rearrangement to the same form as eq . Furthermore, fitting concentration–response data under tight-binding conditions would not yield true EC₅₀ values.

While our focus has been to derive equations to fit equilibrium data under non-tight-binding and tight-binding conditions, considering kinetics would enrich the understanding of the system. We modeled cases of covalent and slow binding reversible molecular glues using KinTek Explorer, selecting values of key rate constants to allow formation of ternary complexes to be observed on the minute to hour time scale (Figures S2 and S3). Analogous to enzyme inhibitors, in both situations, the EC₅₀ decreases as a function of time. For covalent glues, the EC₅₀ asymptotically approaches half the glue binding partner concentration as would be expected, while for the slow-binding reversible glue case, the final EC₅₀ is affinity driven and is hence predicted by eq c.

In conclusion, we have derived a series of analytical solutions for molecular glue-induced ternary complexes covering the most common biochemical settings. We supported our analysis with numerical resolutions of the system and experimental data. Our models can be used to experimentally determine all the thermodynamic parameters of glue-induced ternary complex formation: the “basal” affinity between the proteins of interest (K ₁), the affinity of the glue for its binding partner (K ₂) and the glue-induced cooperativity (α). It hence completes the theoretical framework for the dual optimization of glue affinity and induced K _D shift. In addition, there have been many reports of molecular glues inducing interaction between proteins without any detectable affinity (e.g., CRBN and most IMiDs neo substrates). By enabling scientists to determine this basal affinity from measurable ternary complex data, we believe the methods presented here fill an important gap in molecular glue discovery and will be extremely valuable to study and compare various neo-substrate systems. Our work provides the scientific community with the essential tools to study existing molecular glue systems and can be very impactful in current and future molecular glue drug discovery projects.

Glossary

Abbreviations

FP

fluorescence polarization

TR-FRET

time-resolved fluorescence resonance energy transfer

IMiDs

immunomodulatory drugs

PROTAC

proteolysis targeting chimera

PPI

protein–protein interaction

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.5c09166.

• All derivations and experimental procedures (protein generation, biochemical assays) (PDF)

‡.

M.C. and R.G. contributed equally to this work.

This work was solely funded by AstraZeneca.

The authors declare the following competing financial interest(s): All authors are employees of AstraZeneca and have stock ownership and/or stock options or interests in the company.