## Model of systems

**Part1: Abstract**

Modelling is a powerful tool in synthetic biology that allows us to get a deeper understanding of our system. In order to see whether our system can work and how our system will work, we build this model to simulate our system. This model shows us the details of our system and give our intelligent device software data so that we can change the environment to increase the efficiency and stability of Optopia.

**Part2: Overview**

**1.***Synechocystis*

*Synechocystis*

These are the main differential equations of the *Synechocystis* part of the model. The parameters and variables above will be introduced below.

These functions calculate the growth rate of *Synechocystis*. The two functions correspond to different concentrations of CO_{2} in the solution.andmake the growth rate decline when the concentration of CO_{2} in the solution is too high or too low. (David et al. 2015)^{[1]}. From the same reference we get the relationship between the light intensity and the growth rate. The functionis from another reference(XIONG et al. 2012) ^{[2]}. The parameter the decline of the growth rate caused by gene editing. This parameter is introduced to make the growth model of wild *Synechocystis* fit to the growth of edited ones in the reference (Henrike et al. 2010)^{[3]}.

This stands for the CO_{2} consumed by each unit of *Synechocystis*.is used for growth,is used for lactate producing, and is used for sustaining its life.

The O_{2} consuming is calculated by because the photosynthesis and respiration in *Synechocystis* have the same stoichiometric ratio.

This function shows the inhibit of CO_{2} to the metabolism of *Synechocystis*. The lack of carbon source will not only effect the growth rate of the bacteria, but also reduce the produce rate of lactate.

Parameter | Description | Value | Unit | Source |
---|---|---|---|---|

q_{Lac,Synec} |
Lactate produced by each unit of Synechocystis. | 6.582×10^{-4} |
h^{-1} |
Fitting from reference ^{[3]} |

Y_{CO2,Synec} |
Yield coefficient of Synechocystis related to CO_{2} consuming, showing the CO_{2} consumed for growth |
2.284×10^{2} |
1 | Fitting from reference ^{[1]} |

Y _{O2,CO2} |
O_{2} producing coefficient related to CO_{2} consuming. |
1.375 | 1 | Calculated by the stoichiometric in the chemical equation of the photosynthesis and respiration in Synechocystis and relative molecular mass of O_{2} and CO_{2} |

Y_{CO2,Lac} |
O_{2} producing coefficient related to lactate consuming. |
6.818×10^{-1} |
1 | Calculated by the stoichiometric in the chemical equation of lactate producing, and relative molecular mass of CO_{2} and lactate |

m_{CO2,Synec} |
The sustain coefficient of Synechocystis. Stand for the CO_{2} consuming by the unit dry weight of alive Synechocystis. |
1.164×10^{-1} |
h^{-1} |
Fitting from reference ^{[1]} |

μ_{max,Synec} |
The max growth rate of Synechocystis. | 5.210×10^{-2} |
h^{-1} |
Fitting from reference ^{[1]} |

k_{CO2,Synec,1} |
The semi-saturation constant of CO_{2} concentration when it is low. |
3.551×10^{-6} |
g⋅L^{-1} |
Fitting from reference ^{[1]} |

k_{CO2,Synec,2} |
The semi-saturation constant of CO_{2} concentration when it is high |
7.788×10^{-2} |
g⋅L^{-1} |
Fitting from reference ^{[1]} |

c_{l,CO2} |
The critical value of CO_{2} concentration. Different formulas are applied when CO_{2} concentration in the solution is above or below this value. |
7.788×10^{-2} |
g⋅L^{-1} |
Fitting from reference ^{[1]} |

c_{max,Synec} |
The max concertation of Synechocystis in the solution. | 3.160×10^{-1} |
g⋅L^{-1} |
Fitting from reference ^{[1]} |

I_{k,Synec} |
The light intensity constant of Synechocystis while the light intensity is lower than 8000Lux | 8.749×10^{2} |
Lux | Fitting from reference ^{[1]} |

k_{decline} |
The decline caused by the gene editing. | 4.209×10^{-1} |
1 | Fitting from reference ^{[1]} |

**2.***Rhodopseudomonas palustris*

*Rhodopseudomonas palustris*

These are the main differential equations about the modeling part of the * Rhodopseudomonas palustris* (abbreviated as “Rps”). Through these differential equations, we can calculate the concentrations of Rps, carbon dioxide and lactate. The parameters and variables above will be introduced below.This part is similar to that of

*, because in our experiment, they are both used to provide lactate to*

*Synechocystis**and have similar genetic modification.*

*Shewanella*The function calculates the growth rate of *Rhodopseudomonas palustris*. The function corresponds to different concentrations of CO_{2} in the solution. makes the growth rate decline when the concentration of CO_{2} in the solution is too high. This is gotten from the reference (David et al. 2015)^{[1]}.

From the same reference we get the relationship between the light intensity and the growth rate. The function

is from another reference (Xiong et al. 2012)^{[2]}. The parameter the decline of the growth rate caused by gene editing. This parameter is introduced to make the growth model of wild * Rhodopseudomonas palustris* fit to the growth of edited ones in the reference ( Henrike et al. 2012 )

^{[3]}.

This stands for the CO_{2} consumed by each unit of *Rhodopseudomonas palustris*. is used for growth, is used for lactate producing, and used for sustaining its life.

This function shows the inhibit of CO_{2} to the metabolism of * Rhodopseudomonas palustris*. The lack of carbon source will not only impact the growth rate of the bacteria, but also reduce the production rate of lactate.

Parameter | Description | Value | Unit | Source |
---|---|---|---|---|

q_{Lac,Rps} |
Lactate produced by each unit of Rps per hour | 6.784×10^{-4} |
h^{-1} |
In this experiment, due to genetic modification, no correlation coefficient was found,so we run the simulation in a large range of parameters for many times and use the best data. |

μ_{max,Rps} |
Maximum growth rate of Rps per hour | 0.332 | h^{-1} |
Fitting from reference ^{[4]} |

k_{CO2,Rps} |
Yield coefficient of Rps | 4.124×10^{-6} |
g⋅L^{-1} |
Fitting from reference ^{[5]} |

I_{k,Rps} |
The light intensity constant of Rps while the light intensity is lower than 8000Lux | 8.892×10^{2} |
Lux | Fitting from reference ^{[6]} |

Y_{CO2,Rps} |
CO_{2} producing coefficient related to lactate consuming. |
2.340×10^{2} |
1 | Fitting from reference ^{[5]} |

q_{Lac,Rps} |
Lactate produced by each unit of Rps. | 6.784×10^{-4} |
h^{-1} |
Fitting from reference ^{[7]} |

Y_{CO2,Lac} |
Yield coefficient of Rps related to CO_{2} consuming, showing the CO_{2} consumed for growth |
0.6921 | 1 | Calculated by the stoichiometric in the chemical equation of lactate producing, and relative molecular mass of CO_{2} and lactate |

m_{CO2,Rps} |
The sustain coefficient of Rps. Stand for the CO_{2} consuming by the unit dry weight of alive Rps. |
0.1524 | h^{-1} |
Fitting from reference ^{[5]} |

k_{decline} |
The decline caused by the gene editing. | 0.4209 | 1 | Fitting from reference ^{[6]} |

c_{max,Rps} |
The max concertation of Rps in the solution. | 0.5211 | g⋅L^{-1} |
Fitting from reference ^{[7]} |

k_{s,met} |
the inhibition coefficient of CO_{2} to the metabolism of Rhodopseudomonas palustris |
0.122 | g⋅L^{-1} |
Fitting from reference ^{[5]} |

**3. ***Shewanella*

*Shewanella*

In generate, the three elements urgently needed to be modeled in *Shewanella* are the changes in biomass (Dry Weight, g/L), electricity production (mV), and lactate content (g/L) over time. Once the *Shewanella* modeling is completed, we only need to combine the model of *Shewanella* with the model of *Synechocystis* or *Rhodopseudomonas palustris* to determine which one is better to facilitate electricity produce. The process of deduction will write blow:

First, we need to simulate biomass function. Our biomass function is based on monod equation:

In this function, μ is specific growth rate of biomass.

Because there are two important growth factors in our model: lactate and oxygen content, we need some modifying tasks in this model. Noticing that the concentration of oxygen and lactate are both promoting biomass growth, with the inspiration of monod equation, we take the two factors into consideration so the function changes to:

In this function, c_{Lac} is concentration of lactate.

After this, we realized that a factor about oxygen competition is needed to add in the function. So we import a parameter to solve this problem, the function is modified to:

Taking the efficiency ratio of aerobic and anaerobic respiration (19:1) into consideration, we calculated two parameters:

The two parameters are used in our electricity production simulation:

The basic function is the famous Nernst equation:

In this function Ox is oxidized type, and Red is reduced type.

The Nernst equation is very clear and easy to use, but we have to add a *Shewanella* biomass factor to show the macroscopic electricity production. The lactic consuming value is closely related to the concentration of *Shewanella*. In addition, after the metabolic analysis of lactic in *Shewanella*, we promoted the function by modifying (or simplifying) the section. As a result, the electricity production function is:

In this function,

The last work in *Shewanella* modeling is the lactic consuming simulation:

The concentration of lactate dominates largely on electricity production. Similarly, with the inspiration of Monod equation, we notice that the concentration of lactate acid and *Shewanella* itself is in a positive correlation to lactic consuming rate. So we have summarized the lactic consuming equation:

Parameter | Description | Value | Unit | Source |
---|---|---|---|---|

μ_{Shewa,max} |
maximum specific growth rate of biomass | 1.192×10^{-1} |
g/(L·h) | Fitting from reference ^{[8]} |

c_{Shewa,max} |
maximum biomass (dry weight) of Shewanella | 1.531×10^{-3} |
g/L | Fitting from reference ^{[8]} |

k_{Shewa,O2} |
a parameter influencing the relationship between substances and biomass | 1.332×10^{-5} |
g/L | Fitting from reference ^{[9]} |

k_{Shewa,Lac} |
a parameter influencing the relationship between substances and biomass | 4.869×10^{-1} |
1 | Fitting from reference ^{[5]} |

k_{Shewa,1}
| correction term regarding the rate of consumption of lactate | 7.325×10^{1} |
1 | Fitting from reference ^{[9]} |

k^{'}_{Shewa,2} |
simplified coefficient about the Nernst equation | 1.235×10^{-1} |
1 | Fitting from reference ^{[9]} |

T | current temperature | 298 | K | Experiment data |

v_{Shewa,max} |
maximum lactate consumption rate per unit biomass | 7.012×10^{-1} |
g/(L·h) | Fitting from reference ^{[9]} |

k_{Shewa,3} |
constant value about lactate consuming | 3.056×10^{-1} |
g/L | Fitting from reference ^{[9]} |

**Part3: Result**

The voltage output of the three systems (Rhodopseudomonas palustris- Shewanella, Synechocystis - Shewanella and Shewanella only) are shown in the following figure:

The figure shows that because Rhodopseudomonas palustris and Synechocystis can produce lactate, these two systems can produce electricity more efficiently and steadily, which demonstrates the value and feasibility of our project. In the beginning of the Synechocystis-Shewanella system, oxygen produced by Synechocystis inhibited the electricity production of Shewanella, so this system doesn’t have peak value.

After molecular engineering, we get experiment data. It can fit our model result well. This demonstrates our model is right, so we can design a software based on model to tell us a better application experiment protocol which can get better result.

**Part4: Disscussion**

Based the insight we have gained from modeling, we find that concentration of carbon dioxide is the major limitation of Synechocystis-Shewanella system. Because low concentration of carbon dioxide will limit photosynthesis of Synechocystis, producing less lactate. Finally it leads to low electricity production. (Rhodopseudomonas can utilize the metabolic waste of Shewanella, so it need less carbon dioxide) Therefore, we add carbon dioxide to system and find that it can improve the electricity production. However, if we add too much carbon dioxide, the production will decrease, because excess carbon dioxide will inhibit the photosynthesis. (David et al. 2015)[1]1Finally, we find that the system has the highest voltage output when we add carbon dioxide 2.103×10^{-4}g⁄h.

**Reference **

[1]David Kuan, Sheldon Duff, Dusko Posarac, et al. Growth Optimization of Synechococcus elongatus PCC7942 In Lab Flasks and a 2-D Photobioreactor[J]. Can. J. Chem. Eng., 2015, 9999: 1–8

[2]XIONG Wen, QIAN Xin, YE Rui, et al. Eco-model based analysis of Lake Taihu cyanobacteria growth factors[J]. Lake Science, 2012, 24( 5) : 698-704

[3]Henrike Niederholtmeyer, Bernd T. Wolfstädter, David F. Savage, et al. Engineering Cyanobacteria To Synthesize and Export Hydrophilic Products[J]. APPLIED AND ENVIRONMENTAL MICROBIOLOGY, June 2010, 76(11): 3462–3466

[4]Song Zhiyong, Qu Yuanyuan, Zhou Jiti, et al. Identification of wild plasmids in Rhodopseudomonas palustris by reverse PCR [J]. Journal of Dalian University of Technology, 2009,01: 33-37

[5] Cuihong Du.Cloning and Expression of RubisCO Gene from Rhodopseudomonas palustris and Its Characteristics of Fixed Carbon Dioxide[D].Dalian University of Technology,2003. DOI:10.7666/d.y665688.

[6]Linghua Zhang,Zheshi Kuang,Wei Chen, et al.Preliminary study on culture characteristics of high activity photosynthetic bacteria Rhodopseudomonas palustris[J].Journal of South China Normal University(Natural science edition),2001,(4):37-39. DOI:10.3969/j.issn.1000-5463.2001.04.008.

[7] Huinong Cai,HuiNi,Wenjin Su.Optimization of Culture Media of Rhodopseudomonas palustris and Effect of Ammonia Reduction[J].Journal of Jimei University (Natural Science Edition),2007,(3).

[8]. Li F, Li Y, Sun L M, et al. Modular engineering intracellular NADH regeneration boosts extracellular electron transfer of Shewanella oneidensis MR-1.[J]. Acs Synthetic Biology, 2018, 7(3).