GROWTH EQUATIONS

Biot 309Fall, 2012

Generation TimeGeneration Time

N = (log10Nf – log10No ) / .301

N Number of generationsNfFinal Concentration of Cells

No Original concentration of cells

.301 Conversion Factor to Convert Log2 to Log10

generation (doubling) time

What is a Logarithm?What is a Logarithm?

• Logarithm is a function that gives the exponent in the equation bn = x. It is usually written as logb x = n.

• For example:

34 = 81 Therefore log3 81 = 4

Example 1Example 1N = (log10Nf – log10No ) / .301

Measure Culture at 9:00 a.m. 10,000 cells / mlMeasure Culture at 3:00 p.m. 100,000 cells / mlCalculate N

N = (log10Nf – log10No ) / .301

N = (5-4)/0.301

N = 1/0.301

N = 3.33 Generations in 6 Hours

We Know: 6 Hours = 360 Minutes

Therefore: Generation Time = 360 Minutes / 3.33 Generations

N = 108 Minutes to Generate

Example 2Example 2N = (log10Nf – log10No ) / .301

Measure Culture at 9:00 a.m. 10,000 cells / mlMeasure Culture at Noon 1,000,000 cells / ml

Calculate N

Example 2Example 2N = (log10Nf – log10No ) / .301

Measure Culture at 9:00 a.m. 10,000 cells / mlMeasure Culture at Noon 1,000,000 cells / mlCalculate N

N = (log10Nf – log10No ) / .301

N = (6-4)/0.301

N = 2/0.301

N = 6.64 Generations in 3 Hours

We Know: 3 Hours = 180 Minutes

Therefore: Generation Time = 180 Minutes / 6.64 Generations

N = 27 Minutes to Generate

Example 3Example 3N = (log10Nf – log10No ) / .301

Measure Culture at 9:00 a.m. 2000 cells / mlMeasure Culture at 1:00 p.m. 18,000 cells / ml

Calculate N

Example 3Example 3N = (log10Nf – log10No ) / .301

Measure Culture at 9:00 a.m. 2000 cells / mlMeasure Culture at 1:00 p.m. 18,000 cells / mlCalculate N

N = (log10Nf – log10No ) / .301

N = (4.25-3.30)/0.301

N = .95/0.301

N = 3.16 Generations in 4 Hours

We Know: 4 Hours = 240 Minutes

Therefore: Generation Time = 240 Minutes / 3.16 Generations N = 75.9 Minutes to GenerateN = 1.27 Hours to Generate