"
Vitamin A
Models
Graphical model
Modeling:beta-carotene graphic.jpg
Note that lycopene and beta-carotene are representing by their characteristic colors. "hh" stands for "dihydro" and "pp" stands for "pyrophosphate".
LBS model
Our full LBS model includes both gene expression and the metabolic pathway.
The full pathway+expression beta-carotene model in LBS
We developed a simplified LBS model to examine the metabolic pathway in isolation from gene expression.
The beta-carotene pathway model in LBS
Matlab model
We chose to port our model to Matlab's SimBiology Toolbox in order to facilitate complex analysis. To speed computations, this model has been simplified by taking enzyme concentrations as constant, assuming that the gene expression component of our system has reached a steady state.
The full beta-carotene model exported from the Matlab SimBiology Toolbox
Note: all parameters for these models are listed here.
Sensitivity Analysis
Sensitivity analysis attempts to determine how the output changes with respect to small changes in the model parameters. In this case, we can represent this as $d[beta-carotene]/d[input_i]$. We found that for the beta-carotene system. Sensitivity to the Michaelis-Menten binding constant km is nearly zero. We can interpret this as meaning the substrate concentration is high enough to saturate the enzyme at each step of the pathway. Vmax, which is the product of kcat and the enzyme concentration, controls the reaction rate. Thus we show the sensitivities with respect to kcat. The plot has been normalized so that maximum sensitivity is 1.
Modeling:bc sensitivity.png?800
Notice that sensitivity to the GGPP synthases is reduced since GGPP can be synthesized by either of two enzymes. As you might expect, the sensitivities for each GGPP synthase sum to 1. Further, notice that beta-carotene production is not sensitive to the maximum turnover rate of neurosporene cyclase, the enzyme which causes leakage from the pathway. This is a result of the leakage being minor to begin with. Also, as mentioned before, all the enzymes are saturated, so a small leakage will not cause the next reaction to slow down.
Optimization
For a discussion of the optimization techniques used and the nitrogen allocation analysis which follows, see our optimization techniques.
Pareto frontier
Modeling:beta-carotene opto points.png
Nitrogen allocation
Marginal nitrogen allocation
Modeling:bc nitro marginal.png
