Specific growth rate

Specific growth rate is defined as the increase in cell mass per unit time, e.g., grams cells (g) per gram cells (g) per hour: ( $\text{g}\cdot\text{g}^{-1}\cdot\text{h}^{-1}$ ). The specific growth rate is commonly given by the symbol, µ (mu), and the most common units are in reciprocal hours (h⁻¹); however, it can also be expressed in reciprocal seconds (s⁻¹) or minutes (min⁻¹) or any other units of time.

Formula

Specific growth rate can be calculated from:

$\mu = K' = \frac{\ln (m_{t_2} / m_{t_1})}{t_2 - t_1};\quad t_2 > t_1$ ,

where $m_{t_\cdot}$ are biomasses at the different timepoints (t₁ and t₂) respectively^[1]

When looking for doubling time, then use that $m_{t_2}/m_{t_1} = 2$ and the doubling time t_d is t₂ - t₁.

Specific growth rate constant

Specific growth rate constant is a way of measuring how fast the cells are dividing in a culture. It is defined on the basis of doubling rate, and mathematically it can be explained by the following formula:

k = 1/Log 2 x 1/t x (Log N_t - Log N_o)

it can be modified as:

k= 3.32 x 1/t x (Log N_t - Log N_o)

where k= growth rate constant

N_t = number of bacteria at a time t

N_o = number bacteria at start

t = time.

References

^ "Physiological acclimation of marine phytoplankton to different nitrogen sources". Levasseur et al. Journal of Phycology, 1993, Vol 29 (5), pages 587–595.