1. M.A. Al-Radhawi, D. Del Vecchio, and E.D. Sontag. Identifying competition phenotypes in synthetic biochemical circuits. IEEE Control Systems Letters, 7:211-216, 2023. Note: (Online published in 2022; in print 2023.). [PDF] Keyword(s): Resource competition, model discrimination, synthetic biology, system identification. Abstract:

   Synthetic gene circuits require cellular resources, which are often limited. This leads to competition for resources by different genes, which alter a synthetic genetic circuit's behavior. However, the manner in which competition impacts behavior depends on the identity of the "bottleneck" resource which might be difficult to discern from input-output data. In this paper, we aim at classifying the mathematical structures of resource competition in biochemical circuits. We find that some competition structures can be distinguished by their response to different competitors or resource levels. Specifically, we show that some response curves are always linear, convex, or concave. Furthermore, high levels of certain resources protect the behavior from low competition, while others do not. We also show that competition phenotypes respond differently to various interventions. Such differences can be used to eliminate candidate competition mechanisms when constructing models based on given data. On the other hand, we show that different networks can display mathematically equivalent competition phenotypes.




2. A.O. Hamadeh, B.P. Ingalls, and E.D. Sontag. Transient dynamic phenotypes as criteria for model discrimination: fold-change detection in Rhodobacter sphaeroides chemotaxis. Proc. Royal Society Interface, 10:20120935, 2013. [PDF] Keyword(s): adaptation, biological adaptation, perfect adaptation, scale invariance, systems biology, transient behavior, symmetries, fcd, fold-change detection, chemotaxis. Abstract:

   The chemotaxis pathway of the bacterium Rhodobacter sphaeroides has many similarities to that of Escherichia coli. It exhibits robust adaptation and has several homologues of the latter's chemotaxis proteins. Recent theoretical results have correctly predicted that, in response to a scaling of its ligand input signal, Escherichia coli exhibits the same output behavior, a property known as fold-change detection (FCD). In light of recent experimental results suggesting that R. sphaeroides may also show FCD, we present theoretical assumptions on the R. sphaeroides chemosensory dynamics that can be shown to yield FCD behavior. Furthermore, it is shown that these assumptions make FCD a property of this system that is robust to structural and parametric variations in the chemotaxis pathway, in agreement with experimental results. We construct and examine models of the full chemotaxis pathway that satisfy these assumptions and reproduce experimental time-series data from earlier studies. We then propose experiments in which models satisfying our theoretical assumptions predict robust FCD behavior where earlier models do not. In this way, we illustrate how transient dynamic phenotypes such as FCD can be used for the purposes of discriminating between models that reproduce the same experimental time-series data.

1. A.O. Hamadeh, B.P. Ingalls, and E.D. Sontag. Fold-Change Detection As a Chemotaxis Model Discrimination Tool. In Proc. IEEE Conf. Decision and Control, Maui, Dec. 2012, 2012. Note: Paper WeC09.2.Keyword(s): adaptation, biological adaptation, perfect adaptation, scale invariance, systems biology, transient behavior, symmetries, fcd, fold-change detection, chemotaxis.

1. Eduardo D. Sontag. Dynamic response phenotypes and model discrimination in systems and synthetic biology, 2025. [WWW] Keyword(s): transient behavior, cumulative dose response, dose respose, monotone systems, fold-change detection, scale invariance, reverse engineering, gene networks, cell signaling. Abstract:

   Biological systems encode function not primarily in steady states, but in the structure of transient responses elicited by time-varying stimuli. Overshoots, biphasic dynamics, adaptation kinetics, fold-change detection, entrainment, and cumulative exposure effects often determine phenotypic outcomes, yet are poorly captured by classical steady-state or dose-response analyses. This paper develops an input-output perspective on such "dynamic phenotypes," emphasizing how qualitative features of transient behavior constrain underlying network architectures independently of detailed parameter values. A central theme is the role of sign structure and interconnection logic, particularly the contrast between monotone systems and architectures containing antagonistic pathways. We show how incoherent feedforward (IFF) motifs provide a simple and recurrent mechanism for generating non-monotonic and adaptive responses across multiple levels of biological organization, from molecular signaling to immune regulation and population dynamics. Conversely, monotonicity imposes sharp impossibility results that can be used to falsify entire classes of models from transient data alone. Beyond step inputs, we highlight how periodic forcing, ramps, and integral-type readouts such as cumulative dose responses offer powerful experimental probes that reveal otherwise hidden structure, separate competing motifs, and expose invariances such as fold-change detection. Throughout, we illustrate how control-theoretic concepts, including monotonicity, equivariance, and input-output analysis, can be used not as engineering metaphors, but as precise mathematical tools for biological model discrimination. Thus we argue for a shift in emphasis from asymptotic behavior to transient and input-driven dynamics as a primary lens for understanding, testing, and reverse-engineering biological networks.

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