1. M. Skataric, E.V. Nikolaev, and E.D. Sontag. A fundamental limitation to fold-change detection by biological systems with multiple time scales. IET Systems Biology, 9:1-15, 2015. [PDF] Keyword(s): adaptation, biological adaptation, perfect adaptation, singular perturbations, scale invariance, systems biology, transient behavior, symmetries, fcd, fold-change detection, incoherent feedforward loop, feedforward, IFFL. Abstract:

   The phenomenon of fold-change detection, or scale invariance, is exhibited by a variety of sensory systems, in both bacterial and eukaryotic signaling pathways. It has been often remarked in the systems biology literature that certain systems whose output variables respond at a faster time scale than internal components give rise to an approximate scale-invariant behavior, allowing approximate fold-change detection in stimuli. This paper establishes a fundamental limitation of such a mechanism, showing that there is a minimal fold-change detection error that cannot be overcome, no matter how large the separation of time scales is. To illustrate this theoretically predicted limitation, we discuss two common biomolecular network motifs, an incoherent feedforward loop and a feedback system, as well as a published model of the chemotaxis signaling pathway of Dictyostelium discoideum.




2. M. Skataric and E.D. Sontag. A characterization of scale invariant responses in enzymatic networks. PLoS Computational Biology, 8:e1002748, 2012. [PDF] Keyword(s): adaptation, biological adaptation, perfect adaptation, scale invariance, systems biology, transient behavior, symmetries, fcd, fold-change detection. Abstract:

   This paper studies a recently discovered remarkable feature that was shown in many adapting systems: scale invariance, which means that the initial, transient behavior stays approximately the same when the background signal level is scaled. Not every adapting system is scale-invariant: we investigate under which conditions a broadly used model of biochemical enzymatic networks will show scale invariant behavior. For all 3-node enzymatic networks, we performed a wide computational study to find candidates for scale invariance, among 16,038 possible topologies. This effort led us to discover a new necessary and sufficient mechanism that explains the behavior of all 3-node enzyme networks that have this property, which we call``uniform linearizations with fast output''. We also apply our theoretical results to a concrete biological example of order six, a model of the response of the chemotaxis signaling pathway of Dictyostelium discoideum to changes in chemoeffector cyclic adenosine monophosphate (cAMP).

1. M. Skataric, E.V. Nikolaev, and E.D. Sontag. Scale-invariance in singularly perturbed systems. In Proc. IEEE Conf. Decision and Control, Los Angeles, Dec. 2014, pages 3035-3040, 2014. [PDF] Keyword(s): adaptation, biological adaptation, perfect adaptation, singular perturbations, scale invariance, systems biology, transient behavior, symmetries, fcd, fold-change detection, incoherent feedforward loop, feedforward, IFFL. Abstract:

   This conference paper (a) summarizes material from "A fundamental limitation to fold-change detection by biological systems with multiple time scales" (IET Systems Biology 2014) and presents additional remarks regarding (b) expansion techniques to compute FCD error and (c) stochastic adaptation and FCD




2. M. Skataric and E.D. Sontag. Remarks on model-based estimation of nonhomogeneous Poisson processes and applications to biological systems. In Proc. European Control Conference, Strasbourg, France, June 2014, pages 2052-2057, 2014. [PDF] Keyword(s): systems biology, random dynamical systems. Abstract:

   This paper studies model-based estimation methods of a rate of a nonhomogeneous Poisson processes that describes events arising from modeling biological phenomena in which discrete events are measured. We describe an approach based on observers and Kalman filters as well as preliminary simulation results, and compare these to other methods (not model-based) in the literature. The problem is motivated by the question of identification of internal states from neural spikes and bacterial tumbling behavior.




3. M. Skataric and E.D. Sontag. Exploring the scale invariance property in enzymatic networks. 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, enzymatic networks. Abstract:

   This is a conference version of ``A characterization of scale invariant responses in enzymatic networks.

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