Team:University College London/Modelling/SystemModel

From 2012.igem.org

Density Model

'So how many E. coli would you need, then, to make Plastic Republic work?'. This was the question, raised during a presentation of our project to UCL Engineering, that made us realise the need for the density model. This second predictive model aimed to find the mass of bacteria that would be needed to perform each of the functions of our Plastic Republic system.

Due to time constraints and lack of experimental results, our density model focuses on degradation rather than the more complex aggregation pathway. We wanted to find the mass of bacteria required to degrade the plastic in a cubic metre of seawater, using Goldstein, Rosenberg, and Cheng's estimate of 0.086 mg/m^{3 1} .

The laccase we used has a molar mass of 60000², so 1mg of laccase contains 1.003E16 molecules.

In this model we shall consider only low-density PE³, which makes up 21% of the microplastic particles found in the ocean. Assuming, however, that by the time Plastic Republic is ready to be released into the ocean, our bacteria will be able to degrade all types of plastic (and not just PE) we will continue to use the mass estimate of 0.086 mg/m³. LDPE has a molar mass of 191000³ so 0.086mg contains around 4.50E-10 moles of LDPE.

Our experimental results show that the laccase produced by our bacteria has a specific activity of 0.0006 mol/mg/min, so to degrade the LDPE present in 1m³ of water would require 7.5E-7 mg of laccase, or 7.5 billion molecules. Our SimBiology model tells us that we can expect one bacteria to produce 5 molecules of laccase per minute, so to produce enough laccase to degrade the 4.5E-7 molecules of PE present in a cubic metre of water would take 1 bacteria almost 3000 years!

So what density of bacteria should we have? We have other considerations than amount of plastic degradedWe should solve optimally T = 1.51E9 / B, where T is the time taken in minutes to degrade laccase in 1m³ of seawater and B is the number of bacteria, and in

1. Goldstein 2. 5. Ding Z, Peng L, Chen Y, Zhang L, Gu Z, Shi G, Zhang K (2012) Production and characterization of thermostable laccase from the mushroom, Ganoderma lucidum, using submerged fermentation. African Journal of Microbiology Research 6: 1147-1157. DOI: 10.5897/AJMR11.1257 3. Microplastics in tehn marine environment 3. Santo M, Weitsman R, Sivan A (2012) The role of the copper-binding enzyme - laccase - in the biodegradation of polyethylene by the actinomycete Rhodococcus ruber. International Biodeterioration & Biodegradation 208: 1-7