Exponentially Growing Populations
Reproducibility from one day to the next and between different laboratories is necessary before meaningful measurements can be made on growing cells. Populations of cells that are not overcrowded or limited by oxygen, nutrients, or ions grow freely and can be easily reproduced. Such freely growing populations are almost universally used in molecular biology, and several of their properties are important. The rate of increase in the number of cells in a freely growing population is proportional to the number of cells present, that is,
In these expressions µ is termed the exponential growth rate of the cells. The following properties of the exponential function are frequently useful when manipulating data or expressions involving growth of cells.
Quantities growing with the population increase as eµt. Throughout this book we will use µ as the exponential growth rate. The time required for cells to double in number, Td, is easier to measure experimentally as well as to think about than the exponential growth rate. Therefore we often need to interconvert the two rates Td and µ. Note that the number of cells or some quantity related to the number of cells in freely growing populations can be written as Q(t) = 2t/Td, and since 2 = eln2, Q(t) can also be written as Q(t) = e(ln2/Td)t, thereby showing that the relation between Td and µ is µ = ln2/Td.
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