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Methodology

Overview

The modelling methodology can be divided into two parts: Modelling Principles and Protocol. The modelling principles serve to describe the underlying mathematical equations that govern modelling in genetic circuits. It contains information about the basic parameters used in our models, the differential equations used to measure different parts, and an example of how we used those equations in our models.

The Protocol is the highlight of our modelling contributions. It contains information about the six-step framework we employ to make the modelling, and development of engineered customized kill switches easier.

1. Modelling Principles

a) General Kinetics Used in Modelling Genetic Circuits

The modelling of genetic circuits requires simulating differential equations that measure the kinetics and conditions changes in time. Despite different modelling softwares, the kinetics involved in modelling are mainly those found in or based upon the Hill Equationand Michaelis-Menten Equation (a special case of Hill Equation).

Where Vmax is the maximum rate of the reaction
Where KM is the concentration of substrate at 0.5Vmax
Where h is the number of binding sites
[s] is the concentration of the substrate

Some other useful terms include:
V0 is the minimum velocity of the rate of reaction
Kcat is the catalyst rate constant in enzymatic reactions
Kd is the dissociation rate between molecules
Ka is the association rate between molecules
DA is the degradation rate of A

b) How to Model the Parts of the Genetic Circuit

  1. [mRNA]

    2. Messenger RNA are RNA molecules that carry transcribed DNA to the ribosome for protein synthesis. The mathematical model for [mRNA], where the molecule is a repressor, is represented by the following ODE:

  2. [Peptide]

    3. Peptides are unfolded proteins. When they form a long chain, they form proteins. The mathematical model for [Peptide] is represented by the following ODE:

  3. [Protein]

    4. Proteins are molecules made from long chains of amino acids. Proteins also serve to perform various functions. The mathematical model for [Protein] is represented by the following ODE::

  4. [Complex]

    5. Complex or a protein complex, is formed when two proteins or two molecules or a protein and a molecule each bind together in an associative manner. The mathematical model for [Complex] formed by can be represented by the following ODE:

  5. [Other molecules]

    6. Other molecules refer to a chemical element, compound, or condition that interacts with other parts in the model. Depending on the formation of the molecule, it can be modelled by one of two ODEs:

    • Input Molecule
    • Enzymatic Reaction

c) Implementing Modelling

Using the principles described above in a) and b), below is the model for our human designed construct for probiotics (Stage 1 model). Our other models follow similar methods of modelling.

  1. pPhoB Phosphate Promoter
  2. Peptide of RBS34 after Phosphate Promoter
  3. TlpA36 Protein
  4. pTlpA36
  5. Peptide of RBS34 after pTlpA36
  6. IM2 Protein
  7. pCon Constituitive Promoter
  8. Peptide of RBS34 after pCon
  9. E2 Protein
  10. Phosphate Molecule
  11. Temperature36 Molecule (simulating temp. condition)
  12. TlpA36-Temperature36 Molecule (TlpA36 at low temp.)

d) What software did we use to model our genetic circuits?

We initially used MATLAB Simulink to model our genetic circuits and then migrated to AdvanceSyn Studio which became our preferred modelling software. AdvanceSyn Studio is an upcoming Singapore startup that offers a cloud-based platform to easily model, simulate and optimise genetic circuits. AdvanceSyn Studio kindly offered their support by letting our team use their software to model our genetic circuits. To find out more about AdvanceSyn Studio, click here.

We also used the CAD tool CELLO to generate the genetic circuits used in the Automated Circuit Design from our logic tables. To find out more about CELLO, click here.

2. Protocol

Kill switch can be developed simply by following the protocol below.

Specifications

  • Choose a combination of input sensors from our library/iGEM registry. Input sensors should enable scientists to differentiate different environments which bacteria live.
  • Characterize and calculate the Relative Promoter Unit (RPU) of sensors if sensors are not available in our toolkit. The protocol can be found here.
  • Create a truth table and a timing diagram mapping input sensors and toxin-antitoxin products for various stages.

Design and Modelling

  • Depending on the complexity of the circuit design,
    • Simple circuits – designed and modelled directly on Advancesyn Studio.
    • Complex circuits – generate kill switches circuits on CELLO and run simulation on Advancesyn Studio.
  • Run sensitivity analysis and combinatorial analysis to optimize circuit design based on the following criteria:
    • Response time (how fast the bacteria die)
    • Metabolic stress on cells
    • Toxin – antitoxin production

Optimization

  • Perform experiment with the optimized kill switch circuit.
  • Further improve kill switch design based on the feedback from experiment results.

We will demonstrate the use of NUSgem Kill switch Toolkit in the following case studies: