Team:BGU Israel/Model1.html

A Stochastic Birth-Death Model

Overview

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The initial and most important goal of our model was to predict whether a system like ours will work.

In other words, will the system give the bacteria enough time to perform a certain biochemical function, but also ensure that the mechanism won't fail and the bacteria won't survive?

The model predicted

1. A possible overall time frame, working time frame, and generation range.
2. Limits of leakage rates and mechanism strengths parameters the system can handle.

At first, we aimed to construct a deterministic model that describes the population's behavior based on a set of differential equations.
We very quickly realized that a reliable deterministic model will require precise, deterministic parameters for the commonly used building blocks of SynBio.
We found out that the variation of these values can be enormous- what is the copy number of each plasmid and does it remain constant? What are the transcription and translation rates for each gene? What are the degradation rates for the different components? What is the promoter’s strength and what is its basal expression? And on top of all those complications, even if one can obtain a good estimation of the quantitative data, will it remain the same when integrated in a novel system with new interconnections and dependencies?
For example, it has been shown that gene expression can vary in response to changing the reporter gene alone by up to 44% in a simple expression circuit [1].
We decided that a factor of uncertainty had to be incorporated into the model, and therefore, we decided to construct a stochastic birth-death model that will model the behavior of the entire bacterial population, based on the probability of each and every individual to die or to proliferate.