ECEA 5936: Abstraction Methods
3rd course in the Engineering Genetic Circuits Specialization
Instructor: Chris Myers,ÌýPh.D., Professor
This course introduces how to perform abstraction of genetic circuit models. The first module teaches reaction-based abstraction methods that apply steady-state approximations to reduce the complexity and improve the analysis time of these models.Ìý The second module describes piecewise approximations to simplify non-linear reaction-based models of genetic circuits.Ìý The third module presents Markov chain models and methods for analyzing them.Ìý The fourth module provides methods to abstract models even further using state-based abstraction methods.Ìý Finally, the fifth module demonstrates methods, such as infinite-state stochastic model checking, to determine the likelihood that a genetic circuit hazard will cause circuit failure.
Learning Outcomes
- Explore abstraction methods and how they can accelerate the simulation of genetic circuit models.
- Describe abstract models for the binding of transcription factors to operator sites.
- Describe traditional enzymatic abstractions like the Michaelis-Menten equation.
- Construct stochastic finite state machine models of genetic circuits.
- Describe piecewise linear differential equations and how to analyze them.
- Review hill functions and how to decompose a state space into regulatory domains.
- Explain transient analysis methods for continuous-time Markov chain models.
- Summarize steady-state distribution analysis methods for continuous-time Markov chain models.
- Describe discrete and continuous-time Markov chain models.
- Explain qualitative logical models.
- Describe stochastic model checking methods.
- Detail a workflow for state-based abstraction.
- Calculate the likelihood of failure due to a genetic circuit hazard using infinite-state stochastic model checking.
- Calculate the likelihood of failure due to a genetic circuit hazard using stochastic simulation.
- Describe genetic circuit hazards.
- Demonstrate mastery of the material presented in this course.
Syllabus
Duration: 5Ìýhours
During this module, you will learn traditional enzymatic abstractions like the Michaelis-Menten equation, abstract models for the binding of transcription factors to operator sites, and additional abstraction methods and how they can accelerate the simulation of genetic circuit models.
Duration: 2Ìýhours
This module will introduce methods for abstracting models using piecewise linear representations.
Duration: 3 hours
This module will introduce Markov chains and analysis methods for them.
Duration: 3Ìýhours
This module will introduce a state-based abstraction workflow and analysis methods for these abstracted models.Ìý
Duration: 5Ìýhours
This module introduces genetic circuit hazards and how to determine the likelihood that they cause circuit failure.
Duration: 24ÌýhoursÌý
This module contains materials for the final project. If you've upgraded to the for-credit version of this course, please make sure you review the additional for-credit materials in the Introductory module and anywhere else they may be found.
Grading
Assignment | Percentage of Grade |
| Enzymatic Approximation | 1% |
| Operator Site Reduction | 6% |
| Abstraction Using iBioSim Assignment | 6% |
| Logical Encoding | 1% |
| Piecewise Linear Differential Equations | 1% |
| Stochastic FSM | 1% |
| Discrete-time Markov Chain | 6% |
| Steady-state Distribution Analysis | 6% |
| Transient Analysis | 6% |
| Abstraction Methods | 1% |
| Stochastic Model Checking | 1% |
| Qualitative Logical Models | 1% |
| Genetic Circuit Hazards | 1% |
| Hazard Simulation Using iBioSim | 6% |
| Hazard Verification Using STAMINA | 6% |
| Final Genetic Circuit Abstraction Project | 50% |
Letter Grade Rubric
Letter GradeÌý | Minimum Percentage |
| A | 93% |
| A- | 90% |
| B+ | 86% |
| B | 83% |
| B- | 80% |
| C+ | 76% |
| C | 73% |
| C- | 70% |
| D+ | 66% |
| D | 60% |
| F | 0% |