2.18 | Spring 2015 | Undergraduate

Biomolecular Feedback Systems


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.