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Sensitivity analysis of oscillator models in the space of phase response curves: Oscillators as open systems Sacré, Pierre ; Sepulchre, Rodolphe in IEEE Control Systems Magazine (2014), 34(2), 50-74 Detailed reference viewed: 19 (4 ULg)Sensitivity analysis of circadian entrainment in the space of phase response curves Sacré, Pierre ; Sepulchre, Rodolphe in Kulkarni, Vishwesh V.; Stan, Guy-Bart; Raman, Karthik (Eds.) A Systems Theoretic Approach to Systems and Synthetic Biology II: Analysis and Design of Cellular Systems (2014) Sensitivity analysis is a classical and fundamental tool to evaluate the role of a given parameter in a given system characteristic. Because the phase response curve is a fundamental input–output ... [more ▼] Sensitivity analysis is a classical and fundamental tool to evaluate the role of a given parameter in a given system characteristic. Because the phase response curve is a fundamental input–output characteristic of oscillators, we developed a sensitivity analysis for oscillator models in the space of phase response curves. The proposed tool can be applied to high-dimensional oscillator models without facing the curse of dimensionality obstacle associated with numerical exploration of the parameter space. Application of this tool to a state-of-the-art model of circadian rhythms suggests that it can be useful and instrumental to biological investigations. [less ▲] Detailed reference viewed: 13 (1 ULg)Systems analysis of oscillator models in the space of phase response curves Sacré, Pierre Doctoral thesis (2013) Oscillators---whose steady-state behavior is periodic rather than constant---are observed in every field of science. While they have been studied for a long time as closed systems, they are increasingly ... [more ▼] Oscillators---whose steady-state behavior is periodic rather than constant---are observed in every field of science. While they have been studied for a long time as closed systems, they are increasingly regarded as open systems, that is, systems that interact with their environment. Because their functions involve interconnection, the relevance of input--output systems theory to model, analyze, and control oscillators is obvious. Yet, due to the nonlinear nature of oscillators, methodological tools to study their systems properties remain scarce. In particular, few studies focus on the interface between two fundamental descriptions of oscillators, namely the (internal) state-space representation and the (external) circle representation. Starting with the pioneering work of Arthur Winfree, the phase response curve of an oscillator has emerged as the fundamental input--output characteristic linking both descriptions. The present dissertation aims at studying the systems properties of oscillators through the properties of their phase response curve. The main contributions of this dissertation are the following. We distinguish between two fundamental classes of oscillators. These classes differ in the local destabilizing mechanism that transforms the stable equilibrium of a globally dissipative system into a periodic orbit. To address input--output systems questions in the space of response curves, we equip this space with the right metrics and develop a (local) sensitivity analysis of infinitesimal phase response curves. This main contribution of the thesis is completed by the numerical tools required to turn the abstract developments into concrete algorithms. We illustrate how these analysis tools allow to address pertinent systems questions about models of circadian rhythms (robustness analysis and system identification) and of neural oscillators (model classification). These two biological rhythms are exemplative of both main classes of oscillators. We also design elementary control strategies to assign the phase of an oscillator. Motivated by an inherent limitation of infinitesimal methods for relaxation type of oscillators, we develop the novel geometric concept of ``singularly perturbed phase response curve' which exploits the time-scale separation to predict the phase response to finite perturbations. In conclusion, the present dissertation investigates input--output systems analysis of oscillators through their phase response curve at the interface between their external and internal descriptions, developing theoretical and numerical tools to study models arising in the biology of cellular rhythms. [less ▲] Detailed reference viewed: 142 (24 ULg)Singularly perturbed phase response curves Sacré, Pierre ; Franci, Alessio ; Sepulchre, Rodolphe Conference (2013, March 26) Detailed reference viewed: 32 (4 ULg)Kick synchronization versus diffusive synchronization Mauroy, Alexandre ; Sacré, Pierre ; Sepulchre, Rodolphe in Proceedings of the 51st IEEE Conference on Decision and Control (invited tutorial session) (2012, December) The paper provides an introductory discussion about two fundamental models of oscillator synchronization: the (continuous-time) diffusive model, that dominates the mathematical literature on ... [more ▼] The paper provides an introductory discussion about two fundamental models of oscillator synchronization: the (continuous-time) diffusive model, that dominates the mathematical literature on synchronization, and the (hybrid) kick model, that accounts for most popular examples of synchronization, but for which only few theoretical results exist. The paper stresses fundamental differences between the two models, such as the different contraction measures underlying the analysis, as well as important analogies that can be drawn in the limit of weak coupling. [less ▲] Detailed reference viewed: 36 (5 ULg)Metrics for oscillator models: an input-to-phase approach Sacré, Pierre ; Sepulchre, Rodolphe Conference (2012, March) Detailed reference viewed: 90 (26 ULg)Matching an oscillator model to a phase response curve Sacré, Pierre ; Sepulchre, Rodolphe in Proceedings of the Joint 50th IEEE Conference on Decision and Control and European Control Conference (2011, December) The Phase Response Curve (PRC) has proven a useful tool for the reduction of complex oscillator models. It is also an information often experimentally available to the biologist. This paper introduces a ... [more ▼] The Phase Response Curve (PRC) has proven a useful tool for the reduction of complex oscillator models. It is also an information often experimentally available to the biologist. This paper introduces a numerical tool based on the sensitivity analysis of the PRC to adapt initial model parameters in order to match a particular PRC shape. We illustrate the approach on a simple biochemical model of circadian oscillator. [less ▲] Detailed reference viewed: 72 (19 ULg)Sensitivity analysis of phase response curves Sacré, Pierre ; Sepulchre, Rodolphe Conference (2011, May 23) The Phase Response Curve (PRC) has proven a useful tool for the reduction of complex oscillator models to one-dimensional phase models. We introduce the sensitivity analysis of this important mathematical ... [more ▼] The Phase Response Curve (PRC) has proven a useful tool for the reduction of complex oscillator models to one-dimensional phase models. We introduce the sensitivity analysis of this important mathematical object and its numerical implementation. As an application, we study simple biochemical models of circadian oscillators and discuss how sensitivity analysis helps drawing connections between the state-space model of the oscillator and its phase response curve. [less ▲] Detailed reference viewed: 83 (24 ULg)Sensitivity analysis of phase response curves Sacré, Pierre ; Sepulchre, Rodolphe Conference (2011, March 16) Detailed reference viewed: 38 (17 ULg)Multiple feedback loops in circadian cycles: robustness and entrainment as selection criteria ; Sacré, Pierre ; et al in Proceedings of the Seventh International Workshop on Computational Systems Biology, WCSB 2010 (2010, June) This paper discusses the contribution of an additional feedback loop to the entrainment and the robustness of a circadian system. To quantify robustness, we perform a global analysis of the system's ... [more ▼] This paper discusses the contribution of an additional feedback loop to the entrainment and the robustness of a circadian system. To quantify robustness, we perform a global analysis of the system's parameter space. We quantify the parameter region where the circuit displays an experimentally observed behavior, under entrainment. This global measure is comleted with a classification based on the phase response curve (PRC). For two models of circadian rhythms, we found that the one with two loops is more robust than the one with a single loop: the two-loop model shows better resilience to parameter perturbations and it has also a larger region where the PRC matches experimental PRCs of circadian oscillators. [less ▲] Detailed reference viewed: 127 (39 ULg)Selection of circadian clock models for robust entrainment: an analysis based on the phase response curve Sacré, Pierre ; ; et al Conference (2010, March 30) Detailed reference viewed: 59 (30 ULg)Controlling the phase of an oscillator: a phase response curve approach ; Sacré, Pierre ; Sepulchre, Rodolphe in Proceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (2009, December) The paper discusses elementary control strategies to control the phase of an oscillator. Both feedforward and feedback (P and PI) control laws are designed based on the phase response curve (PRC ... [more ▼] The paper discusses elementary control strategies to control the phase of an oscillator. Both feedforward and feedback (P and PI) control laws are designed based on the phase response curve (PRC) calculated from the linearized model. The performance is evaluated on a popular model of circadian oscillations. [less ▲] Detailed reference viewed: 101 (58 ULg)On the influence of positive and negative feedback loops on the phase response curve of biological oscillators. Sacré, Pierre ; Sepulchre, Rodolphe Conference (2009, March) Detailed reference viewed: 103 (39 ULg)Dynamique non-linéaire de la molécule d’ADN : modélisation de sa dénaturation Sacré, Pierre Master's dissertation (2008) L’ADN est une molécule fabuleuse et essentielle dont la structure et la fonction sont en étroite relation. Elle est un centre d’intérêt important à la fois pour les biologistes, les chimistes et les ... [more ▼] L’ADN est une molécule fabuleuse et essentielle dont la structure et la fonction sont en étroite relation. Elle est un centre d’intérêt important à la fois pour les biologistes, les chimistes et les physiciens. Ce travail s’intéresse à la dynamique non-linéaire de la molécule d’ADN et en particulier à l’étude de sa dénaturation. La modélisation a pour but de compléter les résultats expérimentaux pour mieux comprendre les mécanismes sous-jacents. Après une revue des propriétés biologiques de la molécule et des différents modèles proposés dans la littérature scientifiques, nous présentons le modèle de Peyrard-Bishop-Dauxois qui s’intéresse à la dynamique d’étirement transversal des paires de bases. Ce modèle donne comme solutions des excita- tions non-linéaires localisées, breathers, qui décrivent les ouvertures fluctuantes observées pendant le processus de transcription mais aussi dans l’ADN au repos. Nous nous intéressons à leur propagation et aux mécanismes d’interactions avec des inhomogénéités dans la chaîne à la base de leur croissance. Nous analysons la dénaturation thermique en utilisant des outils de physique statistique standard et des simulations numériques de dynamique moléculaire. Le modèle simple est cependant extrêmement riche du point de vue physique car il exhibe un comportement non-linéaire complexe. Il est également très pertinent pour décrire les mouvements de respiration interne de l’ADN et les mécanismes de leur formation et de leur croissance. L’importance de l’ADN et de ses fonctions demande encore de nombreuses investigations. Les directions les plus prometteuses sont l’étude de modèles non-linéaires inhomogènes et des interactions entre l’ADN et son environnement dans le but de faire un pont entre la physique non-linéaire de l’ADN et la médecine. [less ▲] Detailed reference viewed: 43 (4 ULg) |
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