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Team:Paris Bettencourt/Project/Sabotage/Model
From 2013.igem.org
Introduction
Synthetic biology relies on the addition of foreign genetic elements into organisms for their manipulation. This has the advantage to introduce orthogolous systems, avoiding many unwanted interactions with the organism's own processes citep{Guttinger2013}. However, every introduced system will consume cell's resources and compete for the molecular machinery responsible of replication (DNA level), transcription (RNA level), and translation (protein level). In case the device provides no direct benefit for the organism, the burden of the device will lead to a decrease in growth rate, and therefore a lower fitness citep{Shachrai2010}.
One way to avoid out-competition by lower growth rate is by horizontal transfer. Here we will study the behavior of a the phagemid/helpel system, which is a derived from from the non-lytic bacteriophage M13. This systems propagate throught E. coli F+ via two vectors: a phagemid carrying the desired device, and a helper carrying the necessary machinery for production of the bacteriophage. Only when both vectors are present in a cell, this will produce bacteriophage (see figure 1). Furthermore the system is designed such that the phagemid is produced in higher abundance than the helper.
We took the M13 infection model of cite{Wan2012} as a reference, and adapted to the phagemid/helper system. EXPLAIN SOMETHING ON RNA AND PROTEIN COSTS.
Notation: through this document we will use capital letter to denote cell populations, lower case to denote phagemid populations, and greek letters to denote functions and parameters.
Figure 1:
Model
Cell populations can growth up to a maximum concentration that depends on the media, called carrying capacity (κc). Furthermore cells share the resources used for growth ($S$). Here following classic work in bacterial population dynamics we have chosen to represent bacterial growth as a logistic function ($\lambda$) together with an asymptotic dependency on the substrate concentration ($\beta$), commonly known as Monod's equation.
Introduction
Introduction
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