Introduction

The fact that Synthetic Biology not only opens doors to a new era of science but also threatens humankind and the ecosystem we live in is widely known. The impact of genetically modified organisms (GMOs) in nature can not be foreseen and are practically irreversible once having been in contact with nature.

Genetic constructs designed to kill GMOs on purpose once they have unintentionally escaped the lab environment are a great way to reduce the threat through these organisms [1]. These constructs are called killswitches in analogy to their industrial equivalent. It might be implemented into an otherwise already genetically modified organism. Once the organism escapes the lab, it will die. This way, it cannot harm the environment.

However, one has to keep in mind that all organisms underlie natural occurring mutation. Therefore the killswitch might be destroyed through mutations while the organism is under lab conditions. This problem causes subsequently that the GMO might threatens nature due to its survival after an accidental escape.

A killswitch is a genetic regulatory network. Such a network is built from biological components such as promoters and genes which are interlinked with each other. The network’s structure – also called its topology – plays a crucial role for killswitchs: Weakly design killswitch topologies are prone to destruction through mutation. Therefore, a GMO’s safety classification depends on its killswitch topology. This raises the need for a tool to quantify a killswitch topology’s robustness against mutation. Such a tool does not only provide help for a biologist designing a GMO how to design a specific killswitch but it can be also used to derive general design guidelines.

In the following, we will describe how the escape rate of a killswitch is computed. The escape rate is defined as the probability that a killswitch is destroyed due to mutations during lab conditions such that the organism survives in wild life.

Genetic regulatory networks

Genetic regulatory networks (GRN) describe how genes are expressed inside an organism [1]. This is very comprehensively summarized in wiring diagrams. Taking electrical circuits as comparison, the electrical current is equivalent to the flow of gene expression in GRNs. Genetic promoters represent nodes with different logical behaviors that lead to gene expression and therefore proteins being built. Subsequently, these proteins control promoters again such that a complex behavior arises.

A common way to put this into a context so that quantitative statements are possible is to use the modeling of GRNs based on ordinary differential equations (ODEs) [2].

First, a vector of all involved substances is defined $$\vec{X} := sum_{ i=1 }^{ n } X_i cdot \vec{e}_i$$ with \(X_i\) being the concentration of the \(i\)th substance. Substances span from mRNA over proteins to intermediate complexes. This vector \(\vec{X}_i\) depends on the degree of model detail and the precise biological processes (for instance dimerization or cooperativity).

The time derivative of the vector \(\vec{X}_i\) is then formulated as a continuous function that might depend on the concentrations of all involved substances $$\fraq{d}{dt}\vec{X}(t) = \vec{f}(\vec{X},t,k)$$ where \(t\) is a given point in time and \(k=(k_i)_i\) encapsulates all constant parameters used in the time derivative. The parameters \(k_i\) are of very high relevance: They capture the biological processes and determine if the mathematical model in return resembles the involved biology.

Continuous genetic regulatory network modeling

Modeled killswitches

(a) BNU China 2014

(b) Parallel (OR) regulation

(c) Serial regulation

(d) Parallel (AND) regulation

General genetic algorithms

Adapted genetic algorithm

Implementation

Summary