Population Growth of Bacteria

POPULATION GROWTH

When placed in favourable conditions populations of bacteria can increase at remarkable rates, given that each division gives rise to two identical daughter cells, then each has the potential to divide again. Thus cell numbers will increase exponentially as a function of time. For a microorganism growing with a generation time of 20 minutes, one cell will have divided three times within an hour to give a total of eight cells. After 20 hours of continued division at this rate then the accumulated mass of bacterial cells would be approximately 70 kg (the weight of an average man). Ten hours later the mass would be equivalent to the combined body weight of the entire population of the UK. Clearly this does not happen in nature; rather, the supply of nutrients becomes exhausted and the organisms grow considerably more slowly, if at all.

The time interval between one cell division and the next is called the generation time. When considering a growing culture containing thousands of cells, a mean generation time is usually calculated. As one cell doubles to become two cells, which then multiply to become four cells and so on, the number of bacteria n in any generation can be expressed as:

1st generation n = 1 × 2 = 2 ¹

2nd generation n = 1 × 2 × 2 = 2 ²

3rd generation n = 1 × 2 × 2 × 2 = 2 ²

x th generation n = 1 × 2 ^x = 2 ^x

For an initial population of N_o cells, as distinct from one cell, at the xth generation the cell population will be:

N= N_o × 2^x

where N is the final cell number, N_o the initial cell number and x the number of generations. To express this equation in terms of x, then:

log N = log N_o + x log 2

log N − log N_o = x log 2

x = (log N − log N_o )/ log 2 = (log N − log N_o )/0.301

.

= 3.3(log N − log N_o )

The actual generation time is calculated by dividing x into t where t represents the hours or minutes of exponential growth.