Microbial growth: generation time, growth curves and continuous culture
During exponential growth, generation time can be calculated from population counts and elapsed time. Logarithmic counts plotted against linear time give a straight line. A typical closed batch culture passes through lag, exponential, stationary and death phases. A chemostat can maintain steady conditions through nutrient supply and culture outflow.
What a learner can do afterwards
- Calculates generation time from two counts and the time between them.
- Explains why constant exponential growth gives a straight line when logarithmic population counts are plotted against linear time.
- Says what a chemostat controls that a closed flask cannot.
1 · Read
Many bacteria and archaea reproduce by binary fission: one parent divides into two daughter cells. Mutations can occur, so genetic identity is not guaranteed. During constant exponential growth without cell loss, generation time g is the time for the population to double. Nutrients, temperature and oxygen conditions affect growth.
A population grows from 40 to 320 cells in six hours at a constant doubling rate, without cell loss. Trace 40, 80, 160, 320: three doublings. Divide elapsed time by doublings: g = 6/3 = 2 hours. To predict a later count, divide elapsed time by g, then double the starting count once per complete generation.
A typical closed batch culture has four phases. During lag, cells adjust and population size changes little. During exponential, or log, growth, generation time is roughly constant. Nutrient shortage or waste buildup can lead to stationarity, when new cells roughly balance deaths. During death, viable counts decline as deaths exceed divisions.
A logarithm gives an exponent: log2(8) = 3 because 2 × 2 × 2 = 8. Counts 1, 2, 4, 8 have base-2 logs 0, 1, 2, 3. Equal ratios have equal log spacing, so constant exponential growth plots as a straight line with linear time and logarithmic counts. For initial count N0 and later count N during exponential growth, doublings n = log(N/N0)/log(2). Use a calculator's log key with the same base throughout. Then g = elapsed time/n.
A chemostat supplies fresh medium and removes mixed culture at equal volume rates, keeping volume constant. At a suitable flow rate, nutrient limitation can maintain steady population density while cells divide. New cells replace cells removed in outflow. Temperature and oxygen must also suit the organism. Excessively fast flow can wash the population out.
Doublings per unit time equal 1/g. A strain doubling every 20 minutes has three doublings per hour; one doubling every 60 minutes has one. Natural logarithms use base e, approximately 2.718. A calculator's ln key gives ln(2), approximately 0.693. Each doubling adds ln(2) to the natural log of the count, so specific growth rate is ln(2)/g, about 0.693/g, not 1/g.
Use exponential-phase counts to find generation time. Define graph axes and rate units. A chemostat can keep density steady while cells divide and leave in outflow.
Lesson, questions, worked solutions and flashcards written for this dataset. OpenStax Microbiology was consulted for factual study.
Readings and flashcards written for this dataset. OpenStax Microbiology was consulted for factual study.
More to read
Count the intervals
Suppose a population rises from 30 to 240 cells in 45 minutes during constant exponential growth without cell loss. The count sequence is 30, 60, 120, 240. Four counts are connected by three doubling intervals. The generation time is therefore 45/3 = 15 minutes.
This calculation would not describe cell division correctly if it ignored large losses of cells. A stationary batch culture can have nearly unchanged viable counts while divisions roughly balance deaths.
Continuous culture adds another possibility. In a steady chemostat, new cells can replace cells carried away in the outflow. Always identify what enters and leaves the population before interpreting an unchanged count.
What the medium changes
A growth result depends on the medium used. Failure to grow in one medium does not prove that a sample contained no living organisms.
A chemically defined medium specifies its chemical components and their amounts. A complex medium contains materials such as extracts or digests whose complete chemical composition is not known precisely. Neither name guarantees that the medium suits a particular organism.
Selective media suppress some organisms while allowing others to grow. Differential media reveal differences in biological activity, for example through a color change. One medium can perform both functions.
Report the medium alongside counts and times so that another reader knows which growth conditions the measurement describes.
Record oxygen conditions
A generation time applies to the conditions tested. Giving two cultures the same nutrients does not make their oxygen conditions equivalent.
An obligate aerobe requires oxygen for growth. An obligate anaerobe grows without oxygen and can be harmed by exposure to it. A facultative anaerobe can grow with or without oxygen, using different metabolic routes as conditions change.
These categories help explain why oxygen belongs in a culture report. They do not make a flat growth curve an oxygen test. Nutrients, temperature and other conditions can also limit growth. Record the conditions and investigate possible causes instead of choosing a single cause from population counts alone.
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