System Model

Our Models | Ocean Model | Density Predictions

1. Ocean Model

The fundamental idea behind our ocean model is the need to understand the movements of microplastics in the North Pacific ‘garbage patch’, so that we might decide how best our Plastic Republic bacteria should be used. Several studies have looked at large scale-movements of marine debris, both in the North Pacific gyre (Kubota 1994 and 2005; Liang, Wei, Zhang, and Huang 2010) and in the wider ocean (Lebreton, Greer, and Borrero 2012; Maximenko, Hafner, and Niiler 2012). We know that plastic debris accumulates in five subtropical gyres (in the North Pacific, the South Pacific, the North Atlantic, the South Atlantic, and the Indian Ocean) and that once in the gyre plastics will circulate for between 4-5 years (McNally, Patzert, Kirwan, and Vastano 1983). Our model, therefore, was written to show movements of microplastics at a smaller scale.

The model shows the microplastics found in a 10 000 m^2 area of water down to a depth of 25m, and their movements over a 12-hour period. These movements are predicted from data on currents taken from Port Allen in Hawaii, using a random weight to take account of differing speeds of movement due to particle density. We used the estimate of 0.116 microplastic particles m^3 (Goldstein, Rosenberg & Cheng, 2012), which for a model of this size means looking at around 29000 particles. An important function of our model is to tell us, as the simulation is running, how often collisions occur between the microplastic particles. The model estimates that significant numbers of collisions will occur only for particles larger than around 10cm^3 – yet microplastics are defined as plastic debris less than 1 mm^3. This tells us that our aggregation strategy will require further thought if we hope to aggregate particles through collision.

The model was written in MATLAB and the currents data on which the model is based was taken from the Hawaii 2011 Current Observation Project of the National Oceanic and Atmospheric Agency of the USA (www.noaa.gov). We would like to thank Miriam Goldstein of the Scripps Institution of Oceanography for her help in finding gyre data.

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

Kubota, M. (1994) A mechanism for the accumulation of floating marine debris north of Hawaii, Journal of Physical Oceanography

Kubota, M. (2005) Pleading for the use of biodegradable polymers in favor of marine environments and to avoid an asbestos-like problem for the future, Applied Microbiology and Biotechnology 67; 469-476

Lebreton, L C-M., Greer, S. D., Borrero, J. C. (2012) Numerical Modelling of Floating Debris in the World’s Oceans, Marine Pollution Bulletin 64; 653-661

Liang, H., Wei, H., Zhang, T., and Huang, J. (2010) The Simulation of Marine Plastic Debris Distribution Based on Cellular Automata, 2010 International Conference on Computer Application and System Modelling

Maximenko, N., Hafner, J., Niiler, P. (2012) Pathways of marine debris derived from trajectories of Lagrangian drifters, Marine Pollution Bulletin 65; 51-62

McNally, G., Patzert W., Kirwan Jr, A., Vastano, A. (1983) The Near-Surface Circulation of the North Pacific Using Satellite Tracked Drifting Buoys, Journal Of Geophysical Research 88; 7507-7518

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 microplastic/m^{3 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 <math>T = 1.51x10^{9}\over B</math> 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.

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