Team:Virginia/Modeling

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Models

Goals of model

The goal of the Nygone project is to grow modified E. coli cells on filters that will be put in water treatment plants to remove microplastics. However, due to time constraints, we are unable to engineer the final product. Hence a mathematical model was built in order to:

  1. Give predictions on the amount of bacteria required to produce a sufficient amount of MnP enzyme to degrade micro-particles of nylon in water
  2. Simulate the distribution of MnP enzyme produced by bacteria
  3. Simulate the degradation of nylon micro-particles by MnP particles in water
  4. Analyze the sensitivity of MnP production and nylon degradation to various factors including concentration of bacteria, production rate of MnP by unit bacteria, volume, and flow rate of waste water.

General model

The model was separated into two parts:

  1. Kinetics of MnP enzyme in water
    • Rate of change of MnP concentration in water = rate of diffusion + rate of production - rate of elimination
    • c is the current concentration of MnP, dp/dt is the rate of production of MnP, and J is the flow rate.
    2. 2. Reaction of MnP particles with nylon Michaelis-Menten Equation
E is the MnP enzyme, S is the nylon substrate. kf and kr are forward and reverse reaction constants of enzyme-substrate complex formation. kcat is the reaction coefficient for oxidation of nylon substrate, and the turnover number, defined as the maximum number of substrate molecules converted to product per enzyme molecule per unit time.

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