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Course

BIO-341: Dynamical systems in biology

Lectures in this course (33)

Renku: Collaborative Data Science

Introduces Renku, a platform for collaborative data science enabling reproducibility and promoting code and data reusability.

Dynamic Systems in Biology

Covers dynamic systems in biology, including trajectories, stability, and qualitative analysis.

Limit Cycles and Excitable Systems

Explores limit cycles, excitable systems, positive feedback, and phase locking in human circadian rhythms.

Limit Cycle Oscillators: Stability and Excitability

Explores limit cycle oscillators, stability, excitability, feedbacks, and fixed points in 2D phase portraits.

Entrainment and Synchronization of Oscillators

Explores entrainment and synchronization of oscillators, focusing on the Kuramoto model and resonance phenomena in human circadian rhythms.

Synchronization in Kuramoto Model

Explores the Kuramoto model for synchronization in phase oscillators and discusses stability criteria and critical coupling values.

Kuramoto Model: Generalized Overview

Provides an overview of the generalized Kuramoto model, including natural frequencies, all-to-all coupling, bifurcation diagrams, and diffusion systems.

Diffusion and Logistic Growth

Explores diffusion, logistic growth, genetic circuits, morphogen gradients, and wave propagation in biological systems.

Genetic Circuits and Mechanical Analogies

Explores genetic circuits, negative feedback, and mechanical analogies for spatial problems, including cell coupling and mRNA regulation.

Propagation of Fronts in 1D

Explores the propagation of fronts in 1D systems using a mechanical analogy and bistable systems.

Fixed Points and Stability

Explores fixed points and their stability in dynamic systems, emphasizing linear stability analysis.

Dynamic Systems: Course Review

Covers dynamic systems, trajectories, growth models, stability of fixed points, and linearization of models.

Modeling Gene Expression

Explores modeling gene expression, fixed points analysis, and stability in biological systems.

Nonlinear Systems: Phase Portrait Analysis

Explores nonlinear systems through phase portraits in 2D, focusing on vector fields, isoclines, and trajectories.

Bistability in Cell Cycle

Explores bistability in the cell cycle, emphasizing positive feedback mechanisms and abrupt response transformations.

Phase Portraits and Predator-Prey Models

Explores phase portraits in 2D systems and the dynamics of predator-prey models.

Bistability in Genetic Networks

Explores bistability in genetic networks, analyzing fixed points and stability, phase portraits, and experimental implementation.

Mathematical Analysis of Genetic Circuits

Explores the mathematical analysis of genetic circuits and the implementation of synthetic plasmids in E. coli, focusing on the concept of limit cycle oscillators.

Dynamic Systems: Model Building and Trajectories Representation

Covers model building for switches and trajectory representation in dynamic systems.

Dynamic Systems: Formalism and Bases

Covers the formalism and bases of dynamic systems, including differential equations and non-linear systems.