Lectures in course BIO-341: Dynamical systems in biology

Dynamic Systems: Model Building and Trajectories Representation

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

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

Dynamic Systems: Formalism and Bases

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

Dynamic Systems in Biology

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

Fixed Points and Stability

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

Qualitative Analysis of Growth Models and Gene Regulation

Explores growth models for populations and gene regulation analysis.

Dynamic Systems: Course Review

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

Bistability in Gene Regulation

Explores bistability in gene regulation, analyzing fixed points, bifurcation diagrams, and hysteresis behavior in gene expression.

Linear Systems in 2D: Stability

Explores stability in linear 2D systems, covering fixed points, vector fields, and phase portraits.

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.

Non-linear Systems in 2D: Predator-Prey Models

Covers non-linear systems in 2D, focusing on predator-prey models and stability analysis of fixed points.

Genetic Toggle Switch: Synthetic Biology Example

Covers the construction of a genetic toggle switch in Escherichia coli, a key example of synthetic biology.

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.

Genetic Toggle Switch: Bistability and Oscillations

Explores the genetic toggle switch, bistability, oscillations, and applications in gene therapy and biotechnology.

Limit Cycles in Biological Systems

Explores the concept of limit cycles in biological systems and their significance in understanding system dynamics.

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.

Circadian Oscillators: Entrainment and Synchronization

Explores the entrainment and synchronization of circadian oscillators, focusing on human circadian rhythms and the impact of external stimuli.