Team:Marburg/Modeling

Projects :: Syndustry - iGEM Marburg 2016

SynDustry Fuse. Use. Produce.

Quantitative evolutionary stability analysis of kill switches

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 $$\frac{d}{dt}\vec{X}(t) = \vec{f}(\vec{X},t,k)$$ 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

In the following, the function \(f\) is explained for different biological phenomena. It captures how the concentrations \(\vec{X}\) influences their own change over time.

In table 2 a summary of biological processes that are translated into their mathematical modeling equivalence is provided. Further reading on that can be found in [#]. The corresponding definitions can be found in table 1. This was used extensively in the modeling section and its application can be found in the notebook section.

Symbol Definition
\(S_i\) Concentration of substance \(i\).
\(k_i\) Parameter describing a process.
Table 1. Definitions of symbols.

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

Figure 1
FIG TEXT HERE

Literature

  1. [1] RW, Brownsey, R. Zhande, and A. N. Boone. "lsoforms of acetyl-CoA carboxylase: structures, regulatory properties and metabolic functions." (1997).
  2. [2] Tehlivets, Oksana, Kim Scheuringer, and Sepp D. Kohlwein. "Fatty acid synthesis and elongation in yeast." Biochimica et Biophysica Acta (BBA)-Molecular and Cell Biology of Lipids 1771.3 (2007): 255-270.
  3. [3] Song, Chan Woo, et al. "Metabolic Engineering of Escherichia coli for the Production of 3-Hydroxypropionic Acid and Malonic Acid through β-Alanine Route." ACS synthetic biology (2016).
  4. [4] Grobler, Jandre, et al. "The mae1 gene of Schizosaccharomyces pombe encodes a permease for malate and other C4 dicarboxylic acids." Yeast 11.15 (1995): 1485-1491.
  5. [5] Chen, Wei Ning, and Kee Yang Tan. "Malonate uptake and metabolism in Saccharomyces cerevisiae." Applied biochemistry and biotechnology 171.1 (2013): 44-62.
  6. [6] Kai, Yasushi, Hiroyoshi Matsumura, and Katsura Izui. "Phosphoenolpyruvate carboxylase: three-dimensional structure and molecular mechanisms."Archives of Biochemistry and Biophysics 414.2 (2003): 170-179.
  7. [7] Song, Chan Woo, et al. "Metabolic engineering of Escherichia coli for the production of 3-aminopropionic acid." Metabolic engineering 30 (2015): 121-129.
  8. [8] Zhang, Guijin, Stephen Brokx, and Joel H. Weiner. "Extracellular accumulation of recombinant proteins fused to the carrier protein YebF in Escherichia coli."Nature biotechnology 24.1 (2006): 100-104.
  9. [9] Majander, Katariina, et al. "Extracellular secretion of polypeptides using a modified Escherichia coli flagellar secretion apparatus." Nature biotechnology23.4 (2005): 475-481.