1. A. Gupta and E. D. Sontag. Cumulative dose responses for adapting biological systems. Royal society Interface, 2024. Note: Submitted. Also preprint in https://doi.org/10.1101/2024.11.22.624851.Keyword(s): dose response, perfect adaptation, systems biology, incoherent feedforward loops, integral feedback, immunology, T cells. Abstract:

   This paper introduces the notion of cumulative dose response (cDR). The cDR is the area under the plot of a response variable, an integral taken over a fixed time interval and seen as a function of an input parameter. This work was motivated by the accumulation of cytokines resulting from T cell stimulation, where a non-monotonic cDR has been observed experimentally. However, the notion is of general applicability. A surprising conclusion is that incoherent feedforward loops studied in the systems biology literature, though capable of non-monotonic dose responses, can be mathematically shown to always result in monotonic cDR.




2. 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: To appear. Note: there is an extended version in arXiv; journal paper in preparation.[PDF] 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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