| 1 | Introduction: Overview of the course, biology and basic biological processes, and modeling. |
| Modeling of Core Processes |
| 2 | Modeling techniques, chemical reactions and ordinary differentials equations (ODEs), reduced order models for common binding reactions. |
| 3 | Modeling transcription and translation: Chemical reactions and ODEs (full mechanistic models and reduced models). |
| 4 | Modeling transcriptional regulation: Chemical reactions and ODEs (emphasis on reduced models), examples. |
| 5 | Modeling post transcriptional regulation: Allosteric modification, covalent modification, ultrasensitivity, mitogen-activated protein kinases (MAPK) cascades. |
| Analysis Techniques |
| 6 | Dynamic behavior: Stability and analysis near equilibria, nullcline analysis, linearization techniques, frequency response, examples. |
| 7 | Design principles for robustness: Sensitivity analysis to parameter perturbations, examples. |
| 8 | Design principles for robustness: Adaptation and disturbance rejection through integral feedback and feedforward loops, high gain feedback examples. |
| 9 | Design principles for limit cycles: Systems in two dimensions (2D), examples. |
| 10 | Design principles for limit cycles: Systems in nD, examples, bifurcation analysis, examples. |
| 11 | Model reduction through separation of time scales, examples. |
| 12 | Stochastic behavior: Master equation, Stochastic Simulation Algorithm (SSA) by Gillespie, examples. |
| 13 | Stochastic behavior: Langevin equation, examples. |
| Application to Circuit Design |
| 14 | Circuit design: Autorepressed systems, robustness, sensitivity, power spectra, dynamics. |
| 15 | Toggle switches, engineered memory, repressilator and the realization of loop oscillators. |
| 16 | Activator-repressor clock, incoherent feedforward motifs to control plasmid copy number. |
| 17 | Implementation of adaptation through methylation, chemotaxis circuit. |
| 18 | Interconnecting circuits: Retroactivity and examples, transcriptional circuits. |
| 19 | Retroactivity in signal transduction circuits. |
| 20 | Gene circuits: Equivalent input and output retroactivities, Thevenin's theorem. |
| 21 | Insulation devices: Principle of functioning and design based on phosphorylation. |
| 22 | Insulation devices: Designs based on time scale separation and realizations with phosphotransfer cascades. |
| 23 | Insulation devices: Designs based on protease-feedback. |
| 24 | Design examples: Multi-module circuits, input output impedance (retroactivity) matching. |
| 25 | Design tradeoffs: Competition for gene expression machinery and isocosts. |
| 26 | Project presentations. |
