Team:Tokyo Tech/Collaborations
Collaborations
1. Collaboration with Kanagawa Institute of Technology
1.1. Overview
Our team collaborated with iGEM 2016 team KAIT Japan and other teams, as we were asked to help them with the modeling in an early stage. From iGEM 2016 team KAIT Japan we were asked to help them create a mathematical model for their project.
1.2. Project
Team KAIT wanted to increase the production of Bacterial Cellulose (BC) produced by the bacteria A. xylinum. To do so, we have to take in account the cellulose synthesis pathway.
Fig. 8-2-1. Cellulose synthesis pathway of an Acetobacter
Taking this pathway in consideration iGEM 2016 team KAIT Japan planned to increase the amount of cellulose production by diminishing the amount of G6PDH and PGI enzymes by the antisense method.
1.3. Mathematical Model
Cellulose is produced basically by a series of enzyme reactions, so in order to create a mathematical model for this project, we have to take in account the principal reactions taking place in this production. By doing this we obtain the following equations.
$$ \displaystyle \frac{d[Glc]}{dt} = - \frac{V_{max_1}[Glc]}{K_{m_1} + [Glc]} $$
$$ \displaystyle \frac{d[Frc]}{dt} = - \frac{V_{max_5}[Frc]}{K_{m_5} + [Frc]} - \frac{V_{max_6}[Frc]}{K_{m_6} + [Frc]} $$
$$ \displaystyle \frac{d[G6P]}{dt} = - \frac{V_{max_1}[Glc]}{K_{m_1} + [Glc]} - \frac{V_{max_2}[G6P]}{K_{m_2} + [G6P]} - \frac{V_{f_3} \frac{[G6P]}{K_{s_3}} - V_{s_3} \frac{[F6P]}{K_{P_3}}}{1 + \frac{[G6P]}{K_{s_3}} + \frac{[F6P]}{K_{P_3}}} - \frac{V_{max_4}[G6P]}{K_{m_4} + [G6P]} $$
$$ \displaystyle \frac{d[F6P]}{dt} = \frac{V_{max_5} [Frc]}{K_{m_5} + [Frc]} + \frac{V_{max_8} [FDP]}{K_{m_8} + [FDP]} + \frac{V_{f_3} \frac{[G6P]}{K_{s_3} - V_{s_3} \frac{[F6P]}{K_{P_3}}}}{1 + \frac{[G6P]}{K_{s_3}} + \frac{[F6P]}{K_{P_3}}} $$
$$ \displaystyle \frac{[F1P]}{dt} = \frac{V_{max_6}[Frc]}{K_{m_6} + [Frc]} - \frac{V_{max_7} [F1P]}{K_{m_7} + [F1P]} $$
$$ \displaystyle \frac{d[FDP]}{dt} = \frac{V_{max_7} [F1P]}{K_{m_7} + [F1P]} - \frac{V_{max_8} [FDP]}{K_{m_8} + [FDP]} $$
$$ \displaystyle \frac{d[PGA]}{dt} = \frac{V_{max_2} [G6P]}{K_{m_2} + [G6P]} - \frac{V_{max_{11}}[PGA]}{K_{m_{11}} + [PGA]} $$
$$ \displaystyle \frac{d[G1P]}{dt} = \frac{V_{max_4} [G6P]}{K_{m_4} + [G6P]} - \frac{V_{max_9} [G1P]}{K_{m_9} + [G1P]} $$
$$ \frac{[UDP - Glc]}{dt} = \frac{V_{max_9}[G1P]}{K_{m_9} + [G1P]} - \frac{V_{max_{10}}[UDP-Glc]}{K_{m_{10}} + [UDP-Glc]} $$
$$ \frac{d[Cell]}{dt} = \frac{V_{max_{10}}[UDP-Glc]}{K_{m_{10}} + [UDP - Glc]} $$
Were each equation represents the concentration of each molecule. \( V_{max_n} \) and \( K_{m_n} \) represent the maximal velocity and the Michaelis constant of reaction n respectively. In the case of the concentration of G6P and F6P we have to consider the reversibility of the reaction.
However in this case, since it was considered to only use glucose and not fructose, we can simplify the equations to the following ones.
$$ \frac{d[Glc]}{dt} = - \frac{V_{max_1} [Glc]}{K_{m_1} + [Glc]} $$
$$ \displaystyle \frac{d[G6P]}{dt} = - \frac{V_{max_1}[Glc]}{K_{m_1} + [Glc]} - \frac{V_{max_2}[G6P]}{K_{m_2} + [G6P]} - \frac{V_{f_3} \frac{[G6P]}{K_{s_3}} - V_{s_3} \frac{[F6P]}{K_{P_3}}}{1 + \frac{[G6P]}{K_{s_3}} + \frac{[F6P]}{K_{P_3}}} - \frac{V_{max_4}[G6P]}{K_{m_4} + [G6P]} $$
$$ \frac{d[F6P]}{dt} = \frac{V_{f_3} \frac{[G6P]}{K_{s_3}}}{ 1 + \frac{[G6P]}{K_{s_3}} + \frac{[F6P]}{K_{P_3}}} $$
$$ \frac{d[PGA]}{dt} = \frac{V_{max_2} [G6P]}{K_{m_2} + [G6P]} $$
$$ \frac{d[G1P]}{dt} = \frac{V_{max_4} [G6P]}{K_{m_4} + [G6P]} - \frac{V_{max_9} [G1P]}{K_{m_9} + [G1P]} $$
$$ \frac{d[UDP- Glc]}{dt} = \frac{V_{max_{9}} [G1P]}{K_{m_{9}} + [G1P]} - \frac{V_{max_{10}} [UDP-Glc]}{K_{m_{10}} + [UDP-Glc]} $$
$$ \frac{d[Cell]}{dt} = \frac{V_{max_{10}} [UDP-Glc]}{K_{m_{10}} + [UDP-Glc]} $$
1.4. Antisense Method
The antisense method consists in inhibiting the production of certain proteins by using an antisense RNA that is perfectly complementary to the target nucleotide sequence, thus preventing its transcription.
In this case we are using the antisense method to prevent the production of the enzymes G6PD and PGI so by representing the binding of the antisense mRNA to the nucleotide sequence by a hill equation we get the following equations.
$$ \frac{d[G6P]}{dt} = \frac{V_{max_1} [Glc]}{K_{m_1} + [Glc]} - \left(1 - \frac{\alpha_1[mRNA_1]^{n_1}}{K_1^{n_1} + [mRNA_1]^{n_1}} \right) * \frac{V_{max_2}[G6P]}{K_{m_2} + [G6P]} \\ - \left(1 - \frac{\alpha_2[mRNA_2]^{n_2}}{K_2^{n_2} + [mRNA_2]^{n_2}} \right) * \frac{V_{f_3} \frac{[G6P]}{K_{s_3}} - V_{s_3} \frac{[F6P]}{K_{P_3}}}{1 + \frac{[G6P]}{K_{s_3}} + \frac{[F6P]}{K_{P_3}}} - \frac{V_{max_4}[G6P]}{K_{m_4} + [G6P]} $$
$$ \frac{d[F6P]}{dt} = \left( 1 - \frac{alpha_2[mRNA_2]^{n_2}}{K_2^{n_2} + [mRNA_2]^{n_2}} \right) * \frac{V_{f_3} \frac{[G6P]}{K_{s_3}} - V_{s_3} \frac{[F6P]}{K_{P_3}}}{1 + \frac{[G6P]}{K_{s_3}} + \frac{[F6P]}{K_{P_3}}} $$
$$ \frac{[PGA]}{dt} = \left(1 - \frac{\alpha_1[mRNA_1]^{n_1}}{K_1^{n_1} + [mRNA_1]^{n_1}} \right) * \frac{V_{max_2}[G6P]}{K_{m_2} + [G6P]} $$
Where ɑn and Kn and nn are constants from the hill equation. The concentration of the mRNA depend on the conditions of the experiment.
1.5. Results
Applying this mathematical model we got the following graphs.
(a)
(b)
(c)
(d)
(e)
Fig. 8-2-2. (a) Concentrations without applying the antisense method, (b) Concentration while inhibiting G6PD enzyme, (c) Concentrations inhibiting PGI enzyme, (d) Concentrations inhibiting both G6PD and PGI enzymes, (e) Concentrations strongly inhibiting both enzymes
We can see that the production of BC increases the more we inhibit the enzymes G6PD and PGI, so we can assume this model is correct. However, we cannot say it is the most appropriate to our case since it has not been corroborated with the experiments. We managed, though, to create the basis for a future more precise model.
2. A workshop of modeling
On August 16th, we hosted a workshop of dry teams. The participating universities were Gifu University, Tokyo University of Agriculture and Technology, University of Tokyo and Kanazawa Institute of Technology. The iGEM Tokyo Tech team and the iGEM UT-Tokyo team taught modeling methods to the other iGEM teams. We exchanged our ideas, and thereby we gained new knowledge of modeling.
Helping a New iGEM High School Team
We visited The American School in Japan on September 14th and gave a modeling lecture. We explained our project’s overview and taught modeling methods. We also talked about what iGEM is because The American School is a new iGEM team. The iGEM Tokyo Tech team had collaborated with many universities so far. This visit enabled us to collaborate with high school.
4. Developing an application
5. May Festeval
The Japanese iGEM teams took part in the school festival at the University of Tokyo. Our team shared ideas and gave each other feedbacks. We introduced iGEM and synthetic biology to the public.
See the Human Practice page for further information.
