The document discusses diauxic growth and calculating growth rate constants in bacteria. It notes that during diauxic growth, bacteria will utilize carbon sources in a certain order and require a lag phase to produce enzymes for a secondary source. The growth curve shows two exponential phases separated by a lag phase. It also explains that the growth rate constant K represents the number of generations per hour and can be calculated using population measurements taken at two time points during exponential growth. An example calculation is provided.

1. Bacterial Growth II Diauxic Growth Growth Rate Constant

2. Bacterial Growth II

3. Bacterial Growth II

4. Diauxic Growth Key features of diauxic growth: Microbes have a choice of carbon source in the medium They will utilise first the one which is closest to the one they were using before inoculation, or They will use the simplest structure first (usually glucose)

5. Diauxic Growth Key features of diauxic growth: Initially the growth curve is the same as a standard growth curve The stationary phase is in fact another lag phase In this second lag phase new enzymes are being synthesised by the bacteria to utilise the secondary carbon source

6. Diauxic Growth Key features of diauxic growth: The second lag phase is then followed by a second exponential phase followed by the stationary phase and death phase

7. Growth Rate Constant During exponential growth The number of microorganisms doubles at regular intervals. The time taken for the population to double is called the generation time The number of generations per hour is called the exponential growth rate constant , represented as K .

8. Growth Rate Constant The growth rate constant and the generation time for a culture can be found as follows:

9. Growth Rate Constant Two measurements of the population size (N) are taken during the exponential phase t hours apart We call the first measurement N 0 , and the second N t . During time t . there were a certain number of divisions (or generations) which we will call n .

10. Growth Rate Constant Then n = log 10 N t - log 10 N 0 log 10 2

11. Growth Rate Constant As log 10 2 is always equal to 0.301 n = log 10 N t - log 10 N 0 0.301 YOU ARE NOT EXPECTED TO KNOW HOW THIS EQUATION IS DERIVED OR TO MEMORISE IT – BUT WILL BE REQUIRED TO USE IT!

12. Growth Rate Constant Once we know there are n generations in t hours, we can find the growth rate constant, K (number of generations per hour): K = n / t generations -1 We can also find the generation time, which is equal to 1 / K hours, or 60 / K minutes

13. Growth Rate Constant A students counts the number of bacteria in a liquid culture at 10 am, and again at 3 pm. Her cells counts are as follows: 10am 25 000 cell cm -3 3 pm 200 000 cell cm -3 Calculate the growth rate constant (K) and the generation time for this culture.