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.

SUMMARY Mice deficient in the nuclear hormone receptor RORγt have defective development of thymocytes, lymphoid organs, Th17 cells and type 3 innate lymphoid cells. RORγt binds to oxysterols derived from cholesterol catabolism but it is not clear whether these are its natural ligands. Here, we show that sterol lipids are necessary and sufficient to drive RORγt-dependent transcription. We combined overexpression, RNA interference and genetic deletion of metabolic enzymes to study RORγ-dependent transcription. Our results are consistent with the RORγt ligand(s) being a cholesterol biosynthetic intermediate (CBI) downstream of lanosterol and upstream of zymosterol. Analysis of lipids bound to RORγ identified molecules with molecular weights consistent with CBIs. Furthermore, CBIs stabilized the RORγ ligand-binding domain and induced co-activator recruitment. Genetic deletion of metabolic enzymes upstream of the RORγt-ligand(s) affected the development of lymph nodes and Th17 cells. Our data suggest that CBIs play a role in lymphocyte development potentially through regulation of RORγt.

We and others have shown that transition and maintenance of biological states is controlled by master regulator proteins, which can be inferred by interrogating tissue-specific regulatory models (interactomes) with transcriptional signatures, using the VIPER algorithm. Yet, some tissues may lack molecular profiles necessary for interactome inference (orphan tissues), or, as for single cells isolated from heterogeneous samples, their tissue context may be undetermined. To address this problem, we introduce metaVIPER, an algorithm designed to assess protein activity in tissue-independent fashion by integrative analysis of multiple, non-tissue-matched interactomes. This assumes that transcriptional targets of each protein will be recapitulated by one or more available interactomes. We confirm the algorithm’s value in assessing protein dysregulation induced by somatic mutations, as well as in assessing protein activity in orphan tissues and, most critically, in single cells, thus allowing transformation of noisy and potentially biased RNA-Seq signatures into reproducible protein-activity signatures.

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Methylglyoxal (MGO), a dicarbonyl metabolite produced by all living cells, has been associated with a number of human diseases. However, studies of the role(s) MGO plays biologically have been handicapped by a lack of direct methods for its monitoring and detection. To address this limitation, we have developed a fluorescent sensor (methyl diaminobenzene-BODIPY, or "MBo") that can detect MGO under physiological conditions. We show that MBo is selective for MGO over other biologically relevant dicarbonyls and is suitable for detecting MGO in complex environments, including that of living cells. In addition, we demonstrate MBo's utility in estimating plasma concentrations of MGO. The results reported herein have the potential to advance both clinical and basic science research and practice.