Simulating a Genetic Ring Oscillator: A Synthetic Biology Approach with Python

Field: Synthetic Biology, Computational Modeling
Focus: Genetic Circuits, PoPS Modeling, Numerical Integration

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 Overview

In this project, I simulate the behavior of a genetic ring oscillator, a synthetic circuit built from gene regulatory inverters. This work is inspired by the MIT 20.180: Biological Engineering Programming, which introduces the fundamentals of gene circuit modeling and protein regulation through computational tools.

The simulation is implemented entirely in Python using numerical methods, offering an educational and research-grade foundation for exploring time-based genetic dynamics.

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 Biological Background

Synthetic biology treats DNA-based logic circuits much like digital electronics. At the core of this simulation is the inverter, a genetic NOT gate. These gates are modeled using:

1. Protein Generator:

$$\frac{dR}{dt} = \text{ProductionRate} \times \text{PoPS}_{\text{in}} - k_d \cdot R$$

Where:

• $R$: Repressor protein concentration

• $k_d = \frac{\ln 2}{t_{1/2}}$: First-order decay rate

• $\text{PoPS}_{\text{in}}$: Polymerase per second signal (transcription rate)

2. PoPS Regulator:

$$\text{PoPS}_{\text{out}} = \text{PoPS}_{\text{max}} \cdot \frac{k_D}{k_D + R}$$

This models transcriptional repression where proteins bind DNA to reduce the outgoing signal.

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Ring Oscillator Circuit

By chaining three inverters in a closed loop, we create a genetic ring oscillator. An odd number of NOT gates causes signal inversion to propagate over time, leading to oscillatory protein expression—a biological clock.

This behavior is central to many real-world synthetic constructs, including toggle switches and biostable memory units.

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Implementation Highlights

• Built in Python, simulating each inverter with its internal protein generator and repression logic.

• Used Euler’s method for solving ODEs governing protein concentrations and signal flow.

• Configurable parameters: half-life, production rate, repression constant $k_D$, PoPS max, and time steps.

• Simulates both steady state and transient oscillatory dynamics.

   

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  Example Output

   Input Signal : 70.0 PoPS
  Repressor Protein (Inverter 1): 1014.49
   
  PoPS Out (Inverter 1): 0.0689
  PoPS Out (Inverter 2): 35.0172
  PoPS Out (Inverter 3): 0.1376
  ...
   

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  Conclusion

  This project reflects a broader vision of programmable biology. By modeling genetic circuits computationally, we gain early insight into their behavior—empowering researchers and students to design biological systems with the same logic we use for digital machines.

  This also opens pathways toward more advanced sequence-based modeling, which I plan to pursue as part of my future research in bioinformatics and computational genomics.