Modeling
To model the Continuous Greening Cycle, we applied the biochemical engineering principle of mass balance. We defined a set of variables representing the various mass quantities involved in the system (biomass, nutrients etc), then constructed differential equations to describe their changes over time. We planned to use MatLab or R to run a simulation of the model.
Scope
For simplicity, the model is confined to a space of fixed volume and area. Therefore, all quantities involving concentrations or density can be simply expressed as absolute amounts present in this space.
Variables
To keep the model simple, we only considered the following set of absolutely essential quantities:
- x: live plant biomass
- y: yeast biomass
- z: E. coli biomass
- w: water content in soil
- c: cellulose
- e: active extracellular cellulase
- s: available glucose
- p: PGA
The model
Differential equations
Functions
Parameters
Results
Unfortunately, due to lack of information on the parameters involved, a satisfactory simulation could not be achieved. It might have been possible to use mathematical methods to find the optimum parameters, but such parameters would not accurately reflect real-world situations. Until further experimental data can be obtained, the simulation will have to be put on hold.
Suggested improvements
Measurement of parameters
Without experimental data on at least some of the quantities and/or parameters involved, we cannot hope to construct a realistic model. Plugging in arbitrary values to make the simulation work (i.e. get an increase over time of plant biomass) will not allow us to understand how the system will perform in a real-world situation, which is what we want our model to do.
Incorporation of glutamate
The above model excludes consideration of the quantity of available glutamate, which is the substrate required for PGA synthesis. This reflects an inherent weakness in our system: the lack of a discernible input for glutamate despite its requirement as a substrate. We assumed that the amount of glutamate will never be a limiting quantity; a more detailed treatment of its mass balance could have allowed us to verify if this is indeed the case.
Area-variable model
The area under consideration is held constant in this model. However the ultimate goal of our project is a cycle that not only renews itself but increases in scope as the greening effect spreads through the desert. To model such a cycle, we will need to incorporate area as a variable in the model, as well as identify the factors affecting its change.
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