# Microbial growth

### From BioMineWiki

Growth implies that all chemical components of the cell increase with the same speed and after a certain time this leads to increase in cell number, which causes increase in size or number of the individuals. Growth is normally performed batch-wise or continuously.

Most bacteria have asexual growth, which means that no sex cells are involved. The bacteria divide binarily, usually perpendicularly to the length axis and thereby two new cells are produced.

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## Mathematical expressions of growth

If "growth" fits the definition that all chemical components of the cell increase with the same speed, a unicellular bacterium increases in cell number exponentially with base 2 (see figure Exponential growth):

**N _{t} = N_{0} x 2^{n}** (1)

N_{t} = cell number at time t

N_{0} = starting number at time zero

n = number of doublings (generations).

By designating generation time as *g* and total time as *t* equation (1) can be written:

**N _{t} = N_{0} x 2^{t/g}** (2)

Set μ=1/g, which is defined as the *specific growth rate* constant. Inserted into (2) gives:

N_{t} = N_{0} x 2^{tμ} and after taken the logarithm the equation can be written

**lg N _{t} = lgN_{0} + tμlg2** (3)

If equation (3) is plotted in a semi-logarithmic diagram you will have a straight line, which means that during exponential growth you obtain a straight line. However, during batch growth of a bacterial culture you can have four growth phases called lag, log, stationary and death.

## Balanced and unbalanced growth

The growth of a culture is related to the composition of the medium. If all the essential components are available, the growth is balanced. If, however, one or several essential components are missing the growth is terminated due to unbalanced growth, which often leads to death of the culture.

If two different energy sources are available in the growth medium, the growth curve normally shows two exponential phases - diauxi.

## Quantitative methods for measuring microbial growth

As bacteria are unicellular and divide asexually the growth of the population can be followed either by the changes in number of cells or weight of cell mass. Examples of methods are turbidimetric measurements, direct microscopic count or viable count.

Parameter | Method | Sensitiveness (cells/ml) | Note 1 | Note 2 |
---|---|---|---|---|

Cell mass (dry weight/ml) | Gravimeter | 10^{8} | Direct method | The method gravimeter uses ordinary balances after removal of the water content of the sample. Given a sample size of one ml and assuming that an average dry bacterium weighs 10-12 g and that a ordinary balance can detect 10-4 g this means that you must have >108 bacteria per ml in the sample to be able to use weighing. |

Cell mass (dry weight/ml) | Turbid meter (O.D.) | 10^{7} | Indirect method | The sensitivity given for any turbid meter, ordinary spectrophotometers measuring optical density, is arbitrary. |

Cell mass (dry weight/ml) | Chemical analysis | (depending on the compound) | Indirect method | |

Cell number, total | Microscopy | 10^{6} | Direct method | For microscopy the sensitivity value means that you have on average one cell in the smallest square on the special object glass used. |

Cell number, viable | Viable count (V.C.) | 1-10 | Indirect method | In a viable count you usually pour 0.1 ml of the sample onto the surface of a nutrient agar plate. If you get one colony after incubation then you have had 10 bacteria per ml in the sample. |