1. E.D. Sontag. Bell-shaped dose response for a system with no IFFLs. bioRxiv, 2020. [PDF] Keyword(s): IFFL, feedforward loops, nonlinear systems, immunology. Abstract:

   It is well known that the presence of an incoherent feedforward loop (IFFL) in a network may give rise to a steady state non-monotonic dose response. This note shows that the converse implication does not hold. It gives an example of a three-dimensional system that has no IFFLs, yet its dose response is bell-shaped. It also studies under what conditions the result is true for two-dimensional systems, in the process recovering, in far more generality, a result given in the T-cell activation literature.

1. P. Yu and E.D. Sontag. A necessary condition for non-monotonic dose response, with an application to a kinetic proofreading model. In Proc. 2024 63rd IEEE Conference on Decision and Control (CDC), 2024. Note: Submitted.Keyword(s): systems biology, IFFL, dose response. Abstract:

   Steady state non-monotonic ("biphasic") dose responses are often observed in experimental biology, which raises the control theoretic question of identifying which possible mechanisms might underlie such behaviors. It is well known that the presence of an incoherent feedforward loop (IFFL) in a network may give rise to a non-monotonic response, and it has been informally conjectured that this condition is also necessary. However, this conjecture has been disproved with an example of a system in which input and output nodes are the same. In this paper, we show that the converse implication does hold when the input and output are distinct. Towards this aim, we give necessary and sufficient conditions for when minors of a symbolic matrix have mixed signs. Finally, we study in full generality when a model of immune T-cell activation could exhibit a steady state non-monotonic dose response.

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