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ellermeyer

# ellermeyer - Mathematical Models of Microbial Growth Sean...

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Mathematical Models of Microbial Growth Sean Ellermeyer Modeling in Mathematical Biology (MAP4484/MAP4484) (MAP4484/MAP4484) University of Florida

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The Basic Model for Microbial Growth ( d d h ) (Monod and others, 1940s 50s) Hypotheses Microbial growth rate is determined by the concentration of a single growth limiting substrate concentration of a single growth limiting substrate (nutrient) in the growth medium. The growth rate adjusts itself instantaneously in The growth rate adjusts itself instantaneously in response to changes in the substrate concentration.
s t concentration of substrate at time t x t concentration of microorganism at time t x t is called the specific growth rate of the colony x t is called the specific growth rate of the colony. Monod hypothesized that x t x t s t  where is a continuous and increasing function that satisfies 0 0 and lim s s m where m is called the maximal specific growth rate.

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Specifically, Monod hypothesized that has the form   m s s K h s where m is the maximal specific growth rate and K h is called the half-saturation constant (because it is the value of s for which s m /2 ).
One more hypothesis is: The rate of decrease of substrate is instantaneously proportional to the rate of increase of microorganism. Thus x t Ys t where Y mass of organism formed mass of substrate consumed is called the yield constant . By combining all of our modelling hypotheses, we obtain:

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The Monod Model for Microbial h h l Growth in Batch Culture t 1 m s t t 0 0 s Y K h s t x , s s 0 x t m s t K   x t , x 0 x 0 0 h s t This solutions of this model are in agreement with what would be expected based on the modelling hypotheses: The substrate decreases. The microbe increases (as an increasingly slower rate as substrate becomes depleted) and lim t s t 0 , lim t x t x 0 Ys 0 .
Continuous Culture A chemostat (also called a continuous culture device or a A chemostat (also called a continuous culture device or a CSTR) is a device that allows us to continuously refresh the culture medium and simultaneously remove the contents of the culture vessel (at the same rate so that the volume of the culture vessel remains constant at all times).

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ellermeyer - Mathematical Models of Microbial Growth Sean...

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