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כיוונים חדשים בתורת המערכות והבקרה עם יישומים בביולוגיה מערכתית
New directions in systems and control theory inspired by systems biology |
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2 נ.ז.
דרישת קדם: מבוא לתורת הבקרה
הקורס יעסוק בכלים מתקדמים מתורת המערכות והבקרה שמשמשים במידול וניתוח מודלים מביולוגיה מערכתית. אלה כוללים: התיאוריה של מערכות מונוטוניות, contraction theory , compartmental models, נעילת פאזה לעירור מחזורי, ועוד. היישומים לביולוגיה מערכתית כוללים ביטוי גנים ובפרט תרגום של mRNA, מודלים של התפשטות מחלות, תחרות על משאבים מוגבלים בתוך התא ועוד.
ציון: 30% תרגילי בית, 70% מבחן סופי.
This course covers advanced tools from systems and control theory that have proved useful in the analysis of models from systems biology. These include: the theory of monotone dynamical systems, contraction theory, compartmental models, entrainment and phase locking, retroactivity and insulation, and more. Applications to systems biology will include topics from: gene expression and in particular mRNA translation, models in epidemiology, competition for limited biological resources, and more.
This course will cover modern and advanced tools in systems and control theory that are not covered in any other course in the faculty (and in TAU in general), as well as demonstrating their applications to interesting models from systems biology.
A unifying thread is the study of an important model for the dynamics of mRNA translation, called the ribosome flow model, using the set of tools covered in the course.
Grading: homework exercises 30%, final exam 70%.
הנדסה | ביה"ס להנדסת חשמל
0510-7325-01 כיוונים חדשים בתורת המערכות והבקרה עם יישומים בביולוגיה מערכתית
New directions in systems and control theory inspired by systems biology
שנה"ל תשע"ז | סמ' א' | פרופ מרגליות מיכאל
Detailed course plan:
Week 1: Introduction: what is systems biology; what is the role and potential of systems and control theory in systems biology and related fields such as synthetic biology and biotechnology.
Week 2: Introduction to gene expression.
Week 3: Modeling mRNA translation-the totally asymmetric simplex exclusion process and the ribosome flow model (RFM).
Week 4: A review of ordinary differential equations; existence and uniqueness of solutions; Lyapunov stability.
Week 5, 6: Contraction theory; induced matrix measures and sufficient conditions for contraction; contraction in networks.
Week 7, 8: The theory of monotone dynamical systems; monotone systems with a first integral; Smillie’s stability theorem; applications to the RFM.
Week 9: Entrainment to periodic excitations; the importance of entrainment in biological systems and processes: synchrony in fireflies and the solar day; sufficient conditions for entrainment in linear and nonlinear dynamical systems. Applications to the RFM.
Week 10, 11: Convex analysis; optimization problems; an application: maximizing protein production rate in mRNA translation.
Week 12: Competition for limited resources; retroactivity and insulation.
Week 13: Epidemics and the SIRS model.