Modelling Glucose Transport and Population Growth

Below are the model equations defined by the class. First, an equation accounting for uptake of glucose in solution by the yeast population, with a potential correction term for osmotic back-flow from the cells:

$$\dot{g}_o = %%y \left[ \underbrace{-\alpha g_o y}_{\mbox{... ...uad \overbrace{ \gamma ( g_i - g_o) y }^{\mbox{osmosis}} ,$$ (6)

and another equation describing changes in internal glucose in the population (which is not changed by budding - the buds still have the same glucose as their parents):

$$\dot{g}_i = \overbrace{\alpha g_o y}^{\mbox{uptake}} \quad... ...is}} \quad -\underbrace{\beta g_i y.}_{\mbox{respiration}}$$ (7)

The class accounted for yeast population growth using a per-capita growth model, with growth rates inhibitted by the presence of alcohol:

$$\dot{y} = \overbrace{\epsilon y g_i}^{\mbox{budding}} \quad - \quad \underbrace{\omega a y.}_{\mbox{alcohol inhibition}}$$ (8)

Finally, production of alcohol as a waste product must be accounted for using a proportionality-to-respiration argument:

$$\dot{a} = \delta g_i y .$$ (9)

Together, equations (6 - 9) form a complete model for the yeast-sugar system.