Modeling and synchronization of biological rhythms: from cells to oyster behavior

Hafiz Ahmed 1
1 NON-A - Non-Asymptotic estimation for online systems
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189, Inria Lille - Nord Europe
Abstract : This PhD thesis is dedicated to modeling, analysis and control of oscillations, notably biological rhythms. The thesis is divided into two parts. Part I deals with a real-life application while part II studies more theoretical problems, with potential practical applications. In the first part, motivated by a practical problem of environmental monitoring of coastal environment, this thesis considers the biological rhythms of oysters. It is well known that oysters valve movement activity is heavily influenced by biological rhythms like circadian and circatidal rhythms. Moreover, pollution in the surrounding marine environment can perturb these rhythms, and influence the valve movement activity. Using this information, we propose an indirect environmental monitoring solution using oysters as bio-sensor. The proposed solution works on estimating the perturbation by modeling the biological rhythm of oysters through Van der Pol oscillator model. An inherent limit of this approach is that it works through detecting abnormal behavior only. However abnormal behaviors are not all related to pollution. So, we consider the detection of a particular type of abnormal oscillatory behavior i.e. spawning (behavior during reproduction) which is a natural phenomenon and not related to pollution. The spawning detection algorithm is inspired by the engineering literature of oscillatory fault detection. In the second part, oscillations are studied from a theoretical point of view. Having better understanding of the modeling, analysis and control of oscillations may give rise in the future improved environmental monitoring solutions. The first problem of this part is the robustness of oscillations under cell division. Oscillations persist in genetic oscillators (circadian clocks, synthetic oscillators) after cell division. However, in the literature through stochastic simulation it was found that the phase of the oscillation diverges under high variability of extrinsic noise (variability in the cell division time and in the partition of the molecules into daughter cells, cell–cell variability in kinetic parameters, etc). So, in this thesis, we provide analytical conditions that guarantee phase synchronization after cell division using Phase Response Curve (PRC) formalism. Our results corresponds to the existing stochastic simulation results. Finally we consider the problem of synchronization of multi-stable systems using Input-to-State (ISS) stability tool. Many oscillatory systems are multi-stable. Using a recent generalization of ISS theory for multi-stable systems, we propose sufficient conditions for the synchronization of multi-stable systems. As a side result, this work has been applied for the global synchronization of a recently proposed oscillator model called the Brockett oscillator.
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Hafiz Ahmed. Modeling and synchronization of biological rhythms: from cells to oyster behavior. Systems and Control [cs.SY]. Universite Lille 1, 2016. English. ⟨tel-01439847⟩

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