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. J. K. Kim and E.D. Sontag. Reduction of multiscale stochastic biochemical reaction networks using exact moment derivation. PLoS Computational Biology, 13:13(6): e1005571, 2017. [PDF] Keyword(s): systems biology, reaction networks, stochastic systems, chemical master equation, reaction networks, reaction networks, moments, molecular networks, complex-balanced networks. Abstract:

   Biochemical reaction networks in cells frequently consist of reactions with disparate timescales. Stochastic simulations of such multiscale BRNs are prohibitively slow due to the high computational cost incurred in the simulations of fast reactions. One way to resolve this problem is to replace fast species by their stationary conditional expectation values conditioned on slow species. While various approximations schemes for this quasi-steady state approximation have been developed, they often lead to considerable errors. This paper considers two classes of multiscale BRNs which can be reduced by through an exact QSS rather than approximations. Specifically, we assume that fast species constitute either a feedforward network or a complex balanced network. Exact reductions for various examples are derived, and the computational advantages of this approach are illustrated through simulations.

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