Model
In order to predict the intensity of electricity the StarchLight device would be able to generate, as well as the areas where our project needs improving, we decided to create a model of our device. Our model is inspired by graph theory models. The key components of the battery (i.e. starch, glucose, lactate, E.coli, S.oneidensis, amylases, and electrons) move and interact together within a confined three-dimensional space representing the device. We defined the nature and rules of these interactions by integrating the successive enzymatic reactions and metabolic pathways that occur in our device.
The theory behind the model
Starch gives out one molecule of glucose per interaction with the amylase (1). Theoretically, 1 molecule of glucose can generate 2 molecules of lactate via glycolysis and the reaction carried out by the LDH (2). In S.oneidensis, the conversion of lactate to formate can produce 4 electrons, and the conversion of lactate into citric acid can produce 12 electrons. It is hypothesized that 40% of the lactate is used to create formate, and 30% goes into the tricarboxylic acid cycle (TCA). Thus, on average, one molecule of lactate generates 5 electrons in S.oneidensis (3).The intensity of the generated electric current can be deduced from the results of this simulation.
- Starch-(n) + Amylase → Starch-(n-1) + Glucose
- Glucose + E.coli → 2 Lactate + E.coli
- Lactate + S.oneidensis → 5 electrons
The model can be finetuned by setting different values for each interaction, by modifying the number of each component and their relative speeds. The purpose of this model is to help us understand the bottlenecks of our design by tuning its parameters to fit experimental data. Moreover, once the model is close enough to experimental data, we could use it to predict the efficiency of our upscaled device.
Figure 1: Output visualization of the simulation.
The left panel represents the position of the particles at
each time step. The z axis is represented by the size and color of each particle. The right panel represents
the time evolution of each particle count. Initialization: N E.coli = 100; N SO = 100; N Starch = 900; Starch
and Shewanella speed = 0; other speeds= 1% of the box volume per time step, area of interaction: 1% of
the box volume.
Codee available at: https://github.com/LoPezous/StarchLight
How the model works
Initialization
The simulation is initialized by randomly placing starting particles (i.e S.oneidensis, E.coli, Starch, and amylases) in the working area.
Particle movement
At each time step and for each dimension of the 3D space (x, y, z), each particle randomly moves at a predetermined speed, meaning a certain distance at each time step.
Figure 2: Movement of the particles in 3D space (BioRender)
Area of interaction
Each particle has a predetermined area of interaction and interaction probability. If a particle enters the area of interaction of another particle which it can interact with, they will interact as described in the theory behind the model.
Figure 3: Particle interaction (BioRender). Red perimeters represent the areas of interaction. An amylase and a starch molecule are close enough for the interaction to occur.
Periodic boundary conditions
To prevent particles from stacking against the battery walls, we designed an “infinite box” adapted from the periodic boundary conditions used in gas simulations. It teleports particles as described by the figure below. Another advantage of this method is the improvement of the scalability of the model. In theory, the results of a box can be propagated to predict the behavior of a larger box.
Figure 4: Periodic boundary conditions. A particle crosses an edge of the box and travels back to the opposite edge.
Tunable parameters
In order to finetune our model, these are the parameters we could modify:
- Working area size
- Particles’ speeds
- Particles’ area of interaction
- Particles interaction probability
- Duration of the simulation
- Amount of each particle at initialization
Perspectives
This model has two main purposes:
- Finding which parameters limit the device by comparing experimental results to in silico results and fine tuning the model’s parameters.
- Using the model’s scalability to predict the expected output of a larger device, possibly at industrial scale.
Moreover, this model could be considered stochastic. A common alternative to this type of model would be to build a deterministic model of our device. To do so, we would model the successive reactions with a system of differential equations. It would be interesting to compare the stochastic model to the deterministic model of the battery to see how much the results differ and try to understand why.