iGEM SORBONNE
NAWI
Model
Can we predict the metabolic changes in our mutant algea?
Our main goals when building our model was to be able to:
Predict heme production
Predict the impact of increased heme production the rest of the cell metabolism
See the impact of growth under different condition (light/dark)
Our model is based on Danos's 2015 paper “Mechanistic links between cellular trade-offs, gene expression, and growth” this model approximates cell functioning by the protein machinery. We thus have a dynamic system composed of differential equations representing the kinetics of nutrient uptake from the extracellular medium to enzymatic production and protein production.
Now we'll take a look at the model itself. We will show you the different parts of it and explain them step by step.
Figure 1: Diagram of the model described in the article
(1) external nutrients; (2) transporter protein; (3) internal nutrients; (4) metabolic enzymes; (5) ATP; (6) RNAs; (7) ribosome; (8) proteins
[Created with BioRender.com]
This system of equations is an assembly of kinetic equations, evolution equations and equilibrium equations between the different substrates.
These equations describe the different steps leading to the production of proteins:
The transport of nutrients from the extracellular medium to the intracellular medium
Their transformation into ATP
The production of mRNA and their translation by ribosomes into proteins.
Table 1: Table of reactions in the model.
Figure taken from Weiße, Andrea Y et al. “Mechanistic links between cellular trade-offs, gene expression, and growth.” Proceedings of the National Academy of Sciences of the United States of America vol. 112,9 (2015)
More specifically, in this model, we only consider four different types of proteins:
- transporter proteins
- metabolic enzymes
- ribosomes
- growth-independent proteins
We simulate the metabolism by considering:
(A) external nutrients are introduced into the cell by transporter proteins
(B) internal nutrients are transformed into ATP by metabolic enzymes
(C) with ATP, there is the formation of RNAs coding for each of the different proteins considered
(D) ribosomes bind to the RNAs
(E) ribosome-binded RNAs give proteins using ATP
Using this very simple model of the metabolism, we can introduce a new protein: our protein of interest (in our case heme) and the ARN that ncodes this protein. Therefore, by introducing these elements into our model, we can verify that the overexpression of our gene of interest does not have a negative impact on cell development and allows us to predict the production of our target protein: heme
Figure 2: Model with protein of interest (heme)
(8) ARNs coding for protein of interest, (9) protein of interest (here, heme which has encapsulated an iron molecule), (10) free iron molecules present in the cytoplasm
[Created with BioRender.com]
We were therefore able to write the system of differnetial equation governing this model and solve it using odeint from python in order to visualize how the overall mass of the cell evolves over time (which we approximated by the sum of all the proteins) and how the amount of heme evolves over time. We can also see the effect that increasing the parameter which determines the amount of RNAs which will eventually produce heme has on the metabolism of the cell.
Figure 3 : System of differential equations describing the model
VARIABLES: s_i : internal nutrients, a : ressources (ATP), r: ribosomes, e_t: transporter enzymes, e_m: metabolic enzymes, q: growth-independent proteins, m_x: mRNAs, c_x: ribosome-bound mRNAs, p: protein of interest (heme)
Table 2: Table of parameters in the model.
Figure taken from Weiße, Andrea Y et al. “Mechanistic links between cellular trade-offs, gene expression, and growth.” Proceedings of the National Academy of Sciences of the United States of America vol. 112,9 (2015)
We succeeded in implementing the model in python and using the parameters in Danos et al., we were able to obtain growth curves for the control cells (normal thb1 expression) and mutant cells (overexpression of thb1). We're are currently working on a more complicated model version of the model where we would be able to simulate cell multiplication by considering that cells divide after reaching a certain size. We are also working on implementing a stochastic version of the model with parameters distributed around a mean value. There are no curves because we are currently trying to calibrate the model to the recent control datas from our lab and from the IGEM-UESTC team’s lab. After calibration we should be able to predict the production, deduce the best production environment and thus give a better estimation of the final product cost.
For more information, visit our gitlab: https://github.com/IGEM-Sorbonne/Cell-model
