1. E. D. Sontag. Dynamics and dose response in scaffold ligand binding. 2026. Note: Submitted. Preprint in arXiv:2508.06599.Keyword(s): bispecific antibodies, synthetic biology, immunology, dCAs9, CRISPR, CRN, chemical reaction networks, complex balanced, detail balanced. Abstract:

   This paper considers systems in which two or more ligands bind independently to distinct sites in a common scaffold. Such systems arise in a range of applications, including immunotherapy and synthetic biology. We show that each stoichiometric compatibility class contains a unique steady state, and that this steady state is asymptotically stable. The main result gives a rigorous proof that the steady-state concentration of the fully bound complex, viewed as a function of the total scaffold concentration, has a unique maximum. This biphasic dose response behavior is a characteristic feature of scaffolding systems and, in the special case of two ligands, plays an important role in the design and analysis of bispecific antibody drugs.




2. E. D. Sontag. Dynamics of binding three independent ligands to a single scaffold. arXiv, pp 2508.06599, 2025. [WWW] Keyword(s): bispecific antibodies, synthetic biology, immunology, dCAs9, CRISPR, CRN, chemical reaction networks, complex balanced, detail balanced. Abstract:

   This note considers a system in which three ligands can independently bind to a scaffold. Such systems arise in diverse applications, including immunotherapy and synthetic biology. It is shown that there are unique steady states in each conservation class, and these are asymptotically stable. The dependency of the steady-state amount of fully bound complex, as a function of total scaffold, is analyzed as well.




3. S. Barish, M.F. Ochs, E.D. Sontag, and J.L. Gevertz. Evaluating optimal therapy robustness by virtual expansion of a sample population, with a case study in cancer immunotherapy. Proc Natl Acad Sci USA, 114:E6277-E6286, 2017. [WWW] [PDF] [doi:10.1073/pnas.1703355114] Keyword(s): cancer, oncolytic therapy, immunotherapy, optimal therapy, identifiability, systems biology. Abstract:

   This paper proposes a technique that combines experimental data, mathematical modeling, and statistical analyses for identifying optimal treatment protocols that are robust with respect to individual variability. Experimental data from a small sample population is amplified using bootstrapping to obtain a large number of virtual populations that statistically match the expected heterogeneity. Alternative therapies chosen from among a set of clinically-realizable protocols are then compared and scored according to coverage. As proof of concept, the method is used to evaluate a treatment with oncolytic viruses and dendritic cell vaccines in a mouse model of melanoma. The analysis shows that while every scheduling variant of an experimentally-utilized treatment protocol is fragile (non-robust), there is an alternative region of dosing space (lower oncolytic virus dose, higher dendritic cell dose) for which a robust optimal protocol exists.

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