# OptoFlux - Making designing a breeze

## A mathematical model that optimizes the dimensions of the LIT bulb to maximize its productivity

# Model Aims

1. Determine the optimum concentration of Cyanobacteria cells in the LIT bulb

2. Determine the concentration of E.coli cells required in the LIT bulb in order to produce a luminescence of 160W

3. Determine the diameter of the LIT bulb for optimal luminance

4. Design a 3D prototype of the LIT bulb with the dimensions we determined with OptoFlux

# The Science behind the LIT bulb

We developed our OptoFlux model to determine the optimum shape for our LIT bulb. The LIT bulb is powered by the co-culture of photosynthesizing Cyanobacteria cells and luminescing E.coli cells. In order to maximize the amount of luminescence our E.coli cells can produce we need to maximize the amount of photosynthesis taking place by the Cyanobacteria cells.

Essentially, when the Cyanobacteria cells photosynthesize they produce glucose. A portion of the glucose they produce is then taken up by the E.coli cells to produce luminescence. OptoFlux works by ensuring the rate of photosynthesis is the same in all the cells regardless of their position in the LIT bulb, hence it assumes that the same light intensity will reach all the cells. We are modelling the optimal dimensions (diameter of the LIT bulb) that minimize the shading effects within the bulb. Finally, we used the optimal dimensions obtained from OptoFlux to create a 3D model of our LIT bulb in Autodesk Fusion 360.

Figure 1: Demonstrates the bacterial co-culture in the LIT bulb

# Outlining the steps for the LIT bulb design

Step 1: Use OptoFlux to determine the optimal LIT bulb diameter that maximizes the amount of glucose produced

Step 2: Determine the number of E.coli cells required to produce a high enough luminescence which can compete with a conventional 160W light bulb

Step 3: Evaluate if the amount of glucose produced from the Cyanobacteria cells is sufficient to culture the required number of E.coli cells

# Step 1: Use OptoFlux to determine the optimal LIT bulb diameter that maximizes the amount of glucose produced

# Modelling step outline

1) Determine the Incoming Photon Flux Density (Iph) at the edge of the LIT bulb that is closest to the light source

2) Determine the Iph at each position in the LIT bulb

3) Determine the rate of photon uptake by the Cyanobacteria cells at each position in the LIT bulb

4) Determine the average sugar production rate at each position in the LIT bulb

# Modelling steps

# 1) Determine the Incoming Photon Flux Density (Iph) at the edge of the LIT bulb that is closest to the light source

Figure 2: Demonstrates light being shown onto the bacterial co-culture in the LIT bulb

We determined the number of photons entering our LIT bulb by employing the Planck-Einstein relationship . This relationship enabled us to use radiometric units to quantify the number of photons entering our LIT bulb. We only focused on quantifying the photons within the Photosynthetically Active Radiation (PAR) part of the light spectrum, as those are the only light wavelengths used for photosynthesis. Through quantifying the number of photons entering our LIT bulb we could determine the levels of photosynthesis that could take place by our Cyanobacteria cells.

Where:

I_{phλ} = Incoming photon flux density at a particular wavelength (λ)

I_{ph} = Total Incoming photon flux density over the PAR light spectrum

E_{nl} = Amount of light absorbed by the Cyanobacteria cells at different Iph values

# 2) Determine the Iph at each position in the LIT bulb

Figure 3: Demonstrates that different amounts of light reach different positions in the LIT bulb

We then decided to divide the LIT bulb into a number of imaginary segments (z), and to determine the Iph entering each of the imaginary segments of the LIT bulb. This way, we could evaluate the number of photons available for the photosynthesis of our Cyanobacteria cells at each position within the bulb.

Where:

α_{x,λ} = Specific light absorption coefficient for Cyanobacteria cells

C_{x} = Concentration of Cyanobacteria biomass in the LIT bulb

z = Zone, i.e. Location in the LIT bulb

AF = Accumulation Factor (accounts for the photoaccumulation state of the cells)

Δλ = Wavelength intervals

# 3) Determine the rate of photon uptake by the Cyanobacteria cells at each position in the LIT bulb

Figure 4: Demonstrates photons entering the LIT bulb

We determined the photon uptake rate at each position in the LIT bulb using forward and backward finite differences. The finite differences allowed us to estimate an approximation.

Where:

Δ_{z} = Distance between two positions in the LIT bulb

q_{ph}(z) = Rate of photon uptake by the Cyanobacteria cells at each position in the LIT bulb

# 4) Determine the average sugar production rate at each position in the LIT bulb

Figure 5: Demonstrates photosynthesis and respiration taking place by the co-cultured bacteria in the LIT bulb

We determined the average rate of sugar production within the LIT bulb by determining
the specific rate of sugar production and the yield of biomass on sugar at each position in the bulb.

Part 1: Finding the specific rate of sugar production at each position of the LIT bulb:

Where:

q_{s}^{c}(z)= Specific sugar production rate at each position in the LIT bulb

q_{s,m}^{c}(z) = Maximal sugar production rate in the cells

Y_{phm}^{c} = Maximal yield of sugar on photons

**Part 2: Determine the yield of biomass on sugar production at each position of the LIT bulb **

Where:

Y_{sph}(z)= Yield of biomass on sugar at every position in the LIT bulb

Where:

q_{s average}^{c}= Average sugar production rate

# OptoFlux Results

With our OptoFlux model, we were able to determine the optimal: LIT bulb dimensions, Cyanobacteria cell concentration and Incoming Photon Flux Density

# Optimal LIT bulb dimensions

When optimizing the diameter for the LIT bulb we decided to focus on two aspects, the amount of sugar produced and the yield of sugar on biomass for each diameter tested.

Parameter | Inputted values |
---|---|

Concentration of Cyanobacteria cells in the LIT bulb (mol/m^{3}) |
1 |

Incoming Photon Flux Density (mol/m^{2}s^{-1}) |
5E-03 |

Figure 6: Outlines the parameters that were inputted into OptoFlux model to optimize the diameter of the bulb

Figure 7: Demonstrates the effect increasing the diameter of the bulb has on the average sugar production rate and the yield of biomass on sugar

As expected, Figure 7 shows the general trend of increase in LIT bulb diameter with a decrease in average sugar production rate. Increasing the diameter of the bulb, increases the area available for the Cyanobacteria cells, which again increases the probability of shading effects associated with the distribution of the cells along the diameter of the bulb. The higher the shading effect, the lower the amount of light that can reach all the cells in the cell culture. The point of intersection of the 2 lines represents the trade off of the 2 optimized conditions.

Parameters | Optimized values |
---|---|

Average sugar production rate (q _{s average}) (mol_{s}mol_{x}^{-1}s^{-1}) |
9.8E-05 |

Yield of biomass on sugar (Y _{s/ph}) (mol_{s}mol_{ph}^{-1}) |
1E-01 |

LIT lightbulb Diameter (m) | 9.8E-02 |

Figure 8: Outlines the optimized diameter for the LIT bulb

# Optimizing the concentration of the Cyanobacteria cells in the LIT bulb

Similarly, to optimize the concentration of Cyanobacteria cells needed for the LIT bulb we focused on two aspects: the amount of sugar produced; and the yield of sugar on biomass for each diameter tested.

Parameter | Inputted values |
---|---|

Diameter of the bulb (m) | 9.8E-02 |

Incoming Photon Flux Density (mol/m ^{2}s^{-1}) |
5E-03 |

Figure 9: Outlines the parameters that were inputted into OptoFlux model to optimize the Cyanobacteria concentration in the bulb

Figure 10: Demonstrates the effect changing the Cyanobacteria concentration has on the average sugar production rate and the yield of biomass on sugar

Figure 10 demonstrates that increasing the concentration of Cyanobacteria in the LIT bulb, decreases the average rate of sugar production. An augmentation in the concentration of cells in the bulb, leads to an increase in the overall number of cells. This causes the content of the LIT bulb to be more viscous. Therefore, it becomes harder for light to penetrate the cell culture and reach cells that are found further inside the bulb. As such, the average sugar production rate in the LIT bulb decreases. The yield of biomass on sugar increases as the concentration of Cyanobacteria cells increases. This occurs because, if the number of cells in the bulb increases there are a larger number of cells photosynthesizing. This in turn results in a larger amount of sugar being produced. Here again the intersection of the two lines represents the optimized conditions, i.e. the trade off between average sugar concentration and yield of biomass on sugar.

Parameters | Optimized values |
---|---|

Average sugar production rate (q _{s average}) (mol_{s}mol_{x}^{-1}s^{-1}) |
6.2E-06 |

Yield of biomass on sugar (Y_{s/ph}) (mol _{s}mol_{ph}^{-1}) |
9.7E-02 |

Concentration of Cyanobacteria cells (mol m^{3}) |
100 |

Figure 11: Outlines the optimized Cyanobacteria concentration for the LIT bulb

# Optimizing the Incoming Photon Flux density (Iph) for the LIT bulb

To optimize the incoming Iph for the LIT bulb we focused on two aspects: the amount of sugar produced; and the yield of sugar on biomass.

Parameter | Inputted values |
---|---|

Diameter of the bulb (m) | 9.8E-02 |

Concentration of Cyanobacteria cells (mol/m^{3}) |
100 |

Figure 12: Outlines the parameters that were inputted into OptoFlux model to optimize the Iph for the LIT bulb

Figure 13: Demonstrates the effect increasing the Iph has on the average sugar production rate and the yield of biomass on sugar

From Figure 13 we see that an increase in the Iph for the LIT bulb correlates with an increase in the average sugar production rate. This occurs because increasing the Iph for the bulb, essentially corresponds to an increase in the number of photons entering the bulb. Therefore, a larger number of photons is available for photosynthesis. This photon increase helps overcome any shading effects present in the LIT bulb and allows for more cells to photosynthesize. However, as the Iph increases the yield of biomass per photon decreases. This occurs because once the saturation point for photosynthesis is met, the maximum rate for photosynthesis is met, and the remaining photons will not be utilized by the cells for photosynthesis. The best Iph was identified as the point at which the graphs intersect. Although past the point of intersection the average sugar production rate increases there is such a significant decrease in the yield of sugar per photon the best trade-off between the two variables is identified as the point of intersection.

Parameters | Optimized values |
---|---|

Average sugar production rate (q _{s average}) (mol_{s}mol_{x}^{-1}s^{-1}) |
1.3E-05 |

Yield of biomass on sugar (Y_{s/ph}) (mol_{s}mol_{ph}^{-1}) |
9.5E-02 |

Incoming Photon Flux Density (mol/m^{2}s^{-1}) |
2.5E-03 |

Figure 14: Outlines the optimized Iph for the LIT bulb

# OptoFluxes optimized conditions for the LIT bulb

From the OptoFlux model we were able to optimize the conditions within our LIT bulb to maximize the amount of sugar produced from our Cyanobacteria cells.

Parameters | Optimized values |
---|---|

Diameter of bulb (m) | 9.8E-02 |

Concentration of Cyanobacteria cells (mol/m^{3}) |
100 |

Incoming Photon Flux Density (mol/m^{2}s^{-1}) |
2.5E-03 |

Figure 15: Outlines the optimized parameters for the LIT bulb

###### Step 2: Determine the number of E.coli cells required to produce a high enough luminescence which can compete with a conventional 160W light bulb

1) Determine the number of E.coli cells required to produce the required luminescence

From literature we determined that each E.coli cell produces a luminescence equivalent to 10^{4} photons/s.
A 160 W light bulb produces a luminescence of 10^{18} photons/s. Therefore:

2) Determine the number of Cyanobacteria cells required to produce sufficient levels of glucose to co-culture the desired number of E.coli cells

The ratio of E.coli cells to Cyanobacteria cells in a co-culture is; 10^{7} E.coli cells to 10^{8} Cyanobacteria cells. Therefore:

3) Determine the concentration of Cyanobacteria cells required in the bulb and compare it to the maximum concentration of Cyanobacteria cells our OptoFlux optimized LIT design can handle

In order to determine the Cyanobacteria cells' concentration in the LIT bulb we first calculated the mass of the Cyanobacteria cells and then determined the moles of the Cyanobacteria cells. This enabled us to determine the concentration of Cyanobacteria cells present in the LIT bulb.

The OptoFlux LIT bulb design has the capacity to culture up to 100 mol/m^{3} of Cyanobacteria cells.
In order for our LIT bulb to produce a luminescence equivalent to a 160W light bulb we require a Cyanobacteria concentration of 0.15 mol/m^{3}, this
concentration is 100 fold lower than the maximum Cyanobacteria concentration that can be handled in the OptoFlux LIT bulb design.
Therefore, our OptoFlux LIT bulb is suitable to maintain our co-culture.

Step 3: 3D Prototype of the LIT bulb

We decided to create a prototype of the OptoFlux LIT bulb on Autodesk Fusion 360.

Figure 16: Demonstrates the 3D design of the LIT bulb

###### OptoFlux Assumptions

- Light will only hit the bulb from one side
- The diameter inputted into the OptoFlux model represents the longest distance light would need travel through the bulb
- E.coli cells and Cyanobacteria cells are homogeneously distributed within the LIT bulb
- As blue light activates the luminescence of the E.coli cells, the absorption coefficients for Cyanobacteria were taken at 450nm (13 m
^{2}mol^{-1}) light wavelength - The effects of light scattering, including reflection and refraction, are neglected
- All cells in the cell culture are in their exponential growth phase

###### OptoFlux Species

###### OptoFlux Parameters

###### Analytical steps used to calculate the concentration of Cyanobacteria

# Bibliography

Ducat D, Avelar-Rivas J, Way J, Silver P. Rerouting Carbon Flux To Enhance Photosynthetic Productivity. Applied and Environmental Microbiology. 2012;78(8):2660-2668.

Janssen M. Microalgal Photosynthesis and Growth in Mass Culture. Photobioreaction Engineering. 2016;:185-256.

Mahlmann D, Jahnke J, Loosen P. Rapid determination of the dry weight of single, living cyanobacterial cells using the Mach-Zehnder double-beam interference microscope. European Journal of Phycology. 2008;43(4):355-364.

Marr A. Growth Rate of Escherichia coli. Microbiological Reviews- American Society for Microbiology [Internet]. 1991 [cited 7 October 2017];55(2):316-333. Available from: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC372817/pdf/microrev00033-0134.pdf

Patel A, Mishra S, Pawar R, Ghosh P. Purification and characterization of C-Phycocyanin from cyanobacterial species of marine and freshwater habitat. Protein Expression and Purification. 2005;40(2):248-255.