QuestionMathematical modeling of an experiment: two competing bacterial strains x1 and x2 growing in a flask where nutrient S is supplied at input concentration S0.

QuestionMathematical modeling of an experiment: two competing bacterial strains x1 and x2 growing in a flask where nutrient S is supplied at input concentration S0.

We know that (a) at low nutrient concentration the rate of uptake and bacteria growth is limited by and proportional to nutrient concentration (b) at high concentration the uptake and bacterial growth rates saturate and become constant independent of nutrient concentration.
This type update and growth kinetics is typically described by Michaelis- Menten kinetics:
dx1= x1S dt 1 a1 + S
1. Draw a simple diagram of the conceptual model. 2. Write the differential equations for bacteria x1 x2 and nutrient S. 3. Bonus: add bacteria x2 killing x1 as additional food draw the diagram
and write the equations (for bacteria x1 x2 and nutrient S).

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