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 Articles in journal or book chapters
1. S. J. Rahi, J. Larsch, K. Pecani, N. Mansouri, A. Y. Katsov, K. Tsaneva-Atanasova, E. D. Sontag, and F. R. Cross. Oscillatory stimuli differentiate adapting circuit topologies. Nature Methods, 14:1010-1016, 2017. [PDF] Keyword(s): biochemical networks, periodic behaviors, monotone systems, entrainment, oscillations, incoherent feedforward loop, feedforward, IFFL.
Abstract:
 Elucidating the structure of biological intracellular networks from experimental data remains a major challenge. This paper studies two types of response signatures'' to identify specific circuit motifs, from the observed response to periodic inputs. In particular, the objective is to distinguish negative feedback loops (NFLs) from incoherent feedforward loops (IFFLs), which are two types of circuits capable of producing exact adaptation. The theory of monotone systems with inputs is used to show that period skipping'' (non-harmonic responses) is ruled out in IFFL's, and a notion called refractory period stabilization'' is also analyzed. The approach is then applied to identify a circuit dominating cell cycle timing in yeast, and to uncover a calcium-mediated NFL circuit in \emph{C.elegans} olfactory sensory neurons.

2. E.D. Sontag. A dynamical model of immune responses to antigen presentation predicts different regions of tumor or pathogen elimination. Cell Systems, 4:231-241, 2017. [PDF] Keyword(s): scale invariance, fold change detection, T cells, incoherent feedforward loops, immunology, cancer, internal model principle, incoherent feedforward loop, feedforward, IFFL.
Abstract:
 Since the early 1990s, many authors have independently suggested that self/nonself recognition by the immune system might be modulated by the rates of change of antigen challenges. This paper introduces an extremely simple and purely conceptual mathematical model that allows dynamic discrimination of immune challenges. The main component of the model is a motif which is ubiquitous in systems biology, the incoherent feedforward loop, which endows the system with the capability to estimate exponential growth exponents, a prediction which is consistent with experimental work showing that exponentially increasing antigen stimulation is a determinant of immune reactivity. Combined with a bistable system and a simple feedback repression mechanism, an interesting phenomenon emerges as a tumor growth rate increases: elimination, tolerance (tumor growth), again elimination, and finally a second zone of tolerance (tumor escape). This prediction from our model is analogous to the two-zone tumor tolerance'' phenomenon experimentally validated since the mid 1970s. Moreover, we provide a plausible biological instantiation of our circuit using combinations of regulatory and effector T cells.

 Conference articles
1. E.D. Sontag. Some remarks on immune control of infections and tumors. In Proc. IEEE Conf. Decision and Control, Dec. 2016, pages 2476-2480, 2016. [PDF] Keyword(s): scale invariance, fold change detection, T cells, incoherent feedforward loops, immunology, cancer.
Abstract:
 This is a conference paper related to the journal paper "A dynamical model of immune responses to antigen presentation predicts different regions of tumor or pathogen elimination". The conference paper includes several theorems for a simplified model which were not included in the journal paper.

 Internal reports
1. E.D. Sontag. A remark on incoherent feedforward circuits as change detectors and feedback controllers. Technical report, arXiv:1602.00162, 2016. [PDF] Keyword(s): scale invariance, fold change detection, T cells, incoherent feedforward loops, immunology, incoherent feedforward loop, feedforward, IFFL.
Abstract:
 This note analyzes incoherent feedforward loops in signal processing and control. It studies the response properties of IFFL's to exponentially growing inputs, both for a standard version of the IFFL and for a variation in which the output variable has a positive self-feedback term. It also considers a negative feedback configuration, using such a device as a controller. It uncovers a somewhat surprising phenomenon in which stabilization is only possible in disconnected regions of parameter space, as the controlled system's growth rate is varied.

2. E.D. Sontag. Two-zone tumor tolerance can arise from a simple immunological feedforward motif that estimates tumor growth rates. Technical report, bioRxiv https://doi.org/10.1101/095455, 2016. [PDF] Keyword(s): scale invariance, fold change detection, T cells, incoherent feedforward loops, immunology, cancer.
Abstract:
 Preprint version of "A dynamical model of immune responses to antigen presentation predicts different regions of tumor or pathogen elimination", appeared in Cell Systems 2017. However, the journal version does not include Section 9 on degradation-based IFFL's from this preprint.

3. E.D. Sontag. Incoherent feedforward motifs as immune change detectors. Technical report, bioRxiv http://dx.doi.org/10.1101/035600, December 2015. [PDF] Keyword(s): scale invariance, fcd, fold change detection, T cells, incoherent feedforward loops, immunology, incoherent feedforward loop, feedforward, IFFL.
Abstract:
 We speculate that incoherent feedforward loops may be phenomenologically involved in self/nonself discrimination in immune-infection and immune-tumor interactions, acting as "change detectors". In turn, this may result in logarithmic sensing (Weber phenomenon) and even scale invariance (fold-change detection).

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