A Comprehensive Mathematical Model for Three-Body Binding Equilibria
Open accessAbstract
Three-component systems are often more complex than their two-component counterparts. Although the reversible association of three components in solution is critical for a vast array of chemical and biological processes, no general physical picture of such systems has emerged. Here we have developed a general, comprehensive framework for understanding ternary complex equilibria, which relates directly to familiar concepts such as EC50 and IC50 from simpler (binary complex) equilibria. Importantly, application of our model to data from the published literature has enabled us to achieve new insights into complex systems ranging from coagulation to therapeutic dosing regimens for monoclonal antibodies. We also provide an Excel spreadsheet to assist readers in both conceptualizing and applying our models. Overall, our analysis has the potential to render complex three-component systems--which have previously been characterized as "analytically intractable"--readily comprehensible to theoreticians and experimentalists alike.
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When plotted on a logarithmic scale, the MG dose-response curve has a sigmoid shape, in contrast to the bell-shaped dose-response curve produced by bifunctional proximity inducers.
“When plotted on a logarithmic scale, the MG dose-response curve has a familiar sigmoid shape (Fig. 7c), which is in stark contrast to the bell-shaped dose-response curve produced by the bifunctional proximity inducers36,37.”
From Defining molecular glues with a dual-nanobody cannabidiol sensor (2022) · cites this paper as [36]
In previous studies of bifunctional proximity inducers, a cooperativity term α has been used to characterize the effects of protein-protein interaction in ternary complex formation.
“In previous studies of bifunctional proximity inducers, a cooperativity term (represented by α) has been used to characterize the effects of protein–protein interaction in ternary complex formation36,37.”
From Defining molecular glues with a dual-nanobody cannabidiol sensor (2022) · cites this paper as [36]
The thermodynamic cycle for ternary complex formation mediated by MGs is distinct from that of bifunctional proximity inducers.
“the thermodynamic cycle for ternary complex formation mediated by such compounds is distinct from that of bifunctional proximity inducers, which has been previously described36.”
From Defining molecular glues with a dual-nanobody cannabidiol sensor (2022) · cites this paper as [36]
The U-shaped relationship between degradation metrics and protein expression is consistent with mathematical models of three-body binding equilibria.
“In both cases, a U-shaped relationship was observed between either max FC or degradation frequency and protein expression (Figure 4D), consistent with that expected from mathematical models of three-body binding equilibria (Douglass Jr et al., 2013).”
From Mapping the Degradable Kinome Provides a Resource for Expedited Degrader Development (2020) · cites this paper as Douglass Jr et al., 2013
Saturating doses of free PROTAC molecules can antagonize the binding of binary PROTAC-protein complexes to their ternary partner and abrogate catalytic degradation, a phenomenon known as the hook effect in cell assays.
“Regarding clinical applications, appropriate dosage may be an issue, as saturating doses of free PROTAC molecules can antagonize the binding of binary PROTAC-protein complexes to their ternary partner and abrogate catalytic degradation, a well-documented phenomenon known as the hook effect in cell assays 23,33,34 .”
From Targeted protein degradation: expanding the toolbox (2019) · cites this paper as [33]
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- Authors
- Douglass, E. F., Miller, C. J., Sparer, G., Shapiro, H., & Spiegel, D. A.
- Affiliations
- Yale University (US)
- Pratt Institute (US)
- Courant Institute of Mathematical Sciences (US)
- Corresponding author
- Spiegel, David A.
- Venue
- Journal of the American Chemical Society
- Publisher
- American Chemical Society (ACS)
- Published
- 2013-04-16
- Volume
- 135
- Issue
- 16
- Pages
- 6092-6099
- ISSN
- 0002-7863 (ISSN-L)
- 1520-5126
- PMC
- PMC3717292
- OpenAlex
- W2068455168
- Cited by
- 472
- References
- 44
- Citations by year
- 2026: 64 · 2025: 61 · 2024: 50 · 2023: 64 · 2022: 48 · 2021: 47 · 2020: 51 · 2019: 26 · 2018: 20 · 2017: 20 · 2016: 7 · 2015: 7 · 2014: 3 · 2013: 4
- FWCI
- 3.14
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Journal of the American Chemical Society (publishedVersion)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Institutes of Health (DP2OD002913)
- National Institute of General Medical Sciences (R01GM100283)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Interaction Studies and Fluorescence Analysis
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › thermodynamics and calorimetric analyses
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Keywords
- reversible association, EC50, IC50, coagulation, Excel spreadsheet model
- MeSH terms
- Algorithms, Antibodies, Monoclonal, Antibody-Dependent Cell Cytotoxicity, Anticoagulants, Dose-Response Relationship, Drug, Humans, Kinetics, Male, Prostatic Neoplasms, Protein Binding, Receptors, Fc, Solutions, Models, Statistical, Receptor, EphA2, High-Throughput Screening Assays
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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