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The notion of doubling time dates to interest on loans in Babylonian mathematics. Clay tablets from circa 2000 BCE include the exercise "Given an interest rate of 1/60 per month (no compounding), come the doubling time." This yields an annual interest rate of 12/60 = 20%, and hence a doubling time of 100% growth/20% growth per year = 5 years.
In comparison to batch culture, bacteria are maintained in exponential growth phase, and the growth rate of the bacteria is known. Related devices include turbidostats and auxostats. When Escherichia coli is growing very slowly with a doubling time of 16 hours in a chemostat most cells have a single chromosome. [1]
Therefore, the doubling time t d becomes a function of dilution rate D in steady state: t d = ln 2 D {\displaystyle t_{d}={\frac {\ln 2}{D}}} Each microorganism growing on a particular substrate has a maximal specific growth rate μ max (the rate of growth observed if growth is limited by internal constraints rather than external nutrients).
The Monod equation is a mathematical model for the growth of microorganisms. It is named for Jacques Monod (1910–1976, a French biochemist, Nobel Prize in Physiology or Medicine in 1965), who proposed using an equation of this form to relate microbial growth rates in an aqueous environment to the concentration of a limiting nutrient.
A graph of this equation creates an S-shaped curve, which demonstrates how initial population growth is exponential due to the abundance of resources and lack of competition. When factors that limit an organisms growth are not available in constant supply to meet the growing demand, such as RNA and protein amounts in bacteria, the growth of the ...
RGR is a concept relevant in cases where the increase in a state variable over time is proportional to the value of that state variable at the beginning of a time period. In terms of differential equations , if S {\displaystyle S} is the current size, and d S d t {\displaystyle {\frac {dS}{dt}}} its growth rate, then relative growth rate is
Luria and Delbrück [5] estimated the mutation rate (mutations per bacterium per unit time) from the equation = [ ()] where β is the cellular growth rate, n 0 is the initial number of bacteria in each culture, t is the time, and
A final striking feature of the organism is the extremely slow growth rate; the doubling time is anywhere from 7–22 days. [ 7 ] The anammox bacteria are geared towards converting their substrates at very low concentrations; in other words, they have a very high affinity to their substrates ammonium and nitrite (sub-micromolar range).