# Introduction

The creation of our odorant producer and sensor arise us with interesting questions: Is the system feasible? And how fast would the sensing response be? Instead of costing too much time in the lab, we turned to modeling to give us an answer. We have built a kinetic model for our systems, diacetyl generation, oscillation and odr-10 pathway, to give us an estimate to observe a result.

Modeling of our system
Mathematical modeling was used to simulate different parts of a synthetic bacteria-yeast ecosystem (diacetyl producer, oscillation and odr-10 pathway).

1. Simplify the modeling of diacetyl producer to simulate production result easily.
2. We constructed deterministic and “degrade-and-fire” models to analyze oscillation.
3. With a systematic method which consists four parts (ODE pathway analysis, parameter sensitivity analysis, parameter sweep, stochastic analysis) to optimize the odorant sensing system.

How did modeling help our project?
Diacetyl production model makes it possible to compare conventional production.
Oscillation model can simulate the period and maximum production in the oscillation. It can give us an estimate and help to design the experiment.
Modeling of odr-10 pathway optimizes the project design of Sst2 gene. Through parameter sweep analysis made it possible to provide our best result of our pathway modeling. And it is possible to calculate required diacetyl production in a single cell.

# Diacetyl Producer

Our pathway model for diacetyl producer consists of two parts: ODE pathway analysis and parameter sensitivity analysis. ODE pathway analysis is to examine the feasibility of our pathway. It is the foundation of model analysis.

Figure 1. ODE pathway analysis

Figure 2. Reaction Rate sensitivity analysis

Diacetyl Producer

Oscillation

Odr-10 pathway

# Modelling of Oscillation

To describe the mechanisms of oscillation, we developed a deterministic and “degrade-and-fire” model, using delayed differential equations for protein and LuxI concentrations. Although the nature of oscillations is related to the degrade-and-fire oscillations observed in a dual delayed feedback circuit, an important difference in our model is the coupling in different cells through extracellular AHL. The model of this coupling, and the related cell-density dependence, allowed us to explain most of the oscillation mechanisms.