# Modelling

Our Models | Ocean Model | Density Predictions

## Density Predictions

'So how many E. coli would you need 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 microplastic/m3 1 .

In this model we shall consider only low-density PE, which makes up 21% of the microplastic particles found in the ocean2. 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.

The laccase produced by our bacteria has a molar mass of 600004, so 1mg of laccase contains 1.66E-8 moles or 1.003E16 molecules of the enzyme. Our experimental results show that our laccase has a specific activity of 0.0006 mol/mg/min. This means that 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 LDPE present in a cubic metre of water would take 1 bacteria almost 3000 years! This result is given by the equation where T is the time taken in minutes to degrade laccase in 1m3 of seawater and B is the number of bacteria. To degrade polyethylene in one hour, then, would require 25 million E. coli cells (a colony weighing 0.0251 mg) per m3 of seawater.

## References

1. Goldstein, M., Rosenberg, M., Cheng, L. (2012) Increased oceanic microplastic debris enhances oviposition in an endemic pelagic insect, Biology Letters 10.1098

2. Andrady AL (2011) Microplastics in the marine environment. Marine Pollution Bulletin 62: 1596-1605

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

4. 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