Microbes and Society HW

Microbes and Society Bacteria Calculations Assignment Homework 4 25 points Please turn in your assignment on March 24th at the beginning of class. I will take off two points for each day it is late, including turning it in at the end of class.

Calculating Bacterial Growth

By knowing three simple formulae, problems related to calculating the number of bacteria growing during the logarithmic phase can easily be solved. Use the formula explanations and the worked examples here to help solve the homework problems below. The number of bacteria cells in the log phase of growth can be determined by;

X = X0 * 2y (1) where: X = the total # of bacteria present after y generations; X0 = the initial number of bacteria; y = the number of generations (or doublings)

Example: Bacillus subtilis (right) is a bacterium that divides every 30 minutes. Assume you inoculate a culture with exactly 100 B. subtilis cells. After 3 hours, how many bacteria are present if you assume all log-phase growth? Answer: In 3 hours, B. subtilis will divide 6

times (180 min/30 min per doubling).

Therefore, y = 6. X = X0 * 2y X = 100 * 2

6

X = 6400 cells

Let’s say that you didn’t know how many generations resulted in the bacteria growth calculated above, but you did know the number of cells present at the beginning and end of the logarithmic growth (100 and 6400 cells, respectively). How do we calculate the number of generations that occurred? In this situation (when you know the starting and final numbers of cells, but do not know y), use;

y = [(log x) - (log x0)] / 0.301 (2) where: y = the number of generations (or doublings); X = the number of cells at the end of incubation; X0 = the number of cells at beginning of incubation

Therefore,

y = [(log 6400) - (log 100)] / 0.301 y = (3.81 - 2) / 0.301 y = 6 generations…just like we calculated for use in formula (1) above.

Sometimes we want to know how much time it takes for a generation to occur. This information can be very important for understanding how quickly an infection might spread. The generation time for a population can be calculated by dividing the number of minutes of logarithmic growth (t), by y. In our example:

t = 60 min x 3 hours t = 180 min generation time = t / y (3) where; t = total logarithmic growth time (minutes); y = number of generations

Therefore, generation time = 180 min / 6 generations generation time = 30 min per generation

Use the formulae and examples above to solve these problems. 1. A worker at a deli neglects to wash his hands before preparing potato salad. He unintentionally

contaminates the salad with 12,000 Salmonella cells. How many bacteria will be present in 12 hours if the generation time is 15 minutes (assume all logarithmic growth)?

2. You determine that a coconut cream pie contains 3 million (3 x 10 6 ) Staphylococcus aureus cells.

You assume that the food preparer did not wash his hands and probably inoculated the cream with 500 S. aureus. If the pie was made 6 hours ago, (i) how many generations have occurred, and (ii) how long is each generation?

3. Using the generation time from Problem 2, how many S. aureus would be present after eight hours of logarithmic growth?

4. Streptococcus pyogenes (below) are often referred to as “flesh eating bacteria” (it’s true, look it up). It is estimated that more than 700 million S. pyogenes infections occur world wide each year, including over 650,000 cases of severe, invasive infections with a mortality rate of 25%. The bacterium can divide every 40 minutes at body temperature. Assume that you fall down and scrape your knee and get infected with five S. pyogenes cells. You think nothing of this minor accident, and avoid seeking medical attention.

i) After 24 hours of logarithmic growth, how

many S. pyogenes will be infecting your body?

ii) For every one million S. pyogenes in an

infection, a cubic millimeter of flesh is consumed in a day. After 24 hours, how much tissue (in cubic mm) would be lost?