Team:BGU Israel/Model1.html

Overview

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.

How does it work?

In both P.A.S.E 1 and P.A.S.E 2 a common critical element is that a protein is produced while the bacterium is in the lab, keeping the cell alive, and stops being produced when it is released from the lab:

1. In P.A.S.E 1, a protective protein- the CI repressor, represses the production of the Holin & Endolysin toxins.
2. In P.A.S.E 2, an Essential protein- tyrosine tRNA synthetase, a protein that the cell requires to function.

This protein concentration directly affects the probability of each individual bacterium to die or to proliferate.

So what are the mathematics behind the model?

There is evidence [2][3] that the distributions for cell division times and death times are similar to the Gamma distribution.

In the time frame [0,t], 0 is the moment the cell has finished its last division, and ‘t’ is either the time of death of the cell, or its proliferation time.

In lab

Initialization

In the lab, when the production of critical proteins in P.A.S.E 1 and 2 is fully induced, protein concentration remains constantly 100% of its possible concentration. This is the initialization state, and in this state each option, dying or proliferating, was assigned a unique time-dependent gamma PDF (Probability Density Function). The PDF’s assigned were such that a higher probability is given to cell proliferation (assuming infinite resources in the lab), and produced a typical bacterial growth curve with generation time of 40 minutes- similar to that of engineered E. coli.

In vivo