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Bacterial growth dynamics

You are walking on the beach when you step on a shell and cut your foot. Thirteen cells of Vibrio vulnificus bacteria are transferred from the shell and deposited deep inside the cut. 36 hours later, the cut has become extremely painful and you go to the doctor. If the generation time of this species is 90 minutes under these conditions,

1) How many bacteria are present at the time you go to the doctor?

(Enter the answer in Blackboard either as the full number typed out, or in scientific notation in the format X.XEx Do not add any spaces or other punctuation except the decimal point. If you do, Bb will count it wrong. In Bb terms, this is a ‘calculated numeric' question.)

Not realizing the severity of the infection and that he/she should use intravenous dual-drug antimicrobial therapy, the doctor prescribes only oral doxycycline and sends you home.

2) What class of antibiotic is doxycycline? (Hint: Look in Chapter 8 and Chapter 27 of your book for this information)

3) With what general bacterial process do antibiotics in the class that contains doxycycline interfere?

At this time, the bacteria are not just in the wound. 29 cells of V. vulnificus have gotten into your blood. However, the doxycycline does slow the growth of the bacteria considerably to a generation time of 6 hours. Over the next few days, you take all of your doses of doxycycline, but become increasingly ill. Eventually, you collapse and are rushed to the hospital. It is determined that you have 7 cells/mL of bacteria in your blood. If you have 5 L of blood in your body,

4) How many total bacterial cells are in your blood?

(Enter the answer either as the full number typed out, or in scientific notation in the format X.XEx)

5) How many generations have the bacteria been through from the time they entered your blood until you arrived at the hospital?

6) How many days have passed since the bacteria entered your blood? (Assume a constant generation time of 6 hours with continued doxycycline treatment)

Because you are unconscious and the friend who brought you to the hospital does not know you were on oral doxycycline, the medical team that treats you initially does not realize that doxycycline is unlikely to be effective in fighting your infection because the bacteria have developed resistance to it.

The usual treatment for V. vulnificus "septicemia" would be an intravenous combination of doxycycline and a third-generation cephalosporin derivative. (Cephalosporins are beta-lactam antibiotics, which are considered most effective against Gram-positive organisms, but 3rd generation cephalosporins are effective against Gram-negative organisms such as Vibrio.)

Because they don't have access to your recent medical history, the critical care team puts you on a combination of intravenous doxycycline and a third-generation cephalosporin derivative before they have been able to make contact with your primary care doctor.

7) With what general bacterial process do beta-lactam antibiotics interfere? (Hint: Look in Chapter 3 and Chapter 27 of your book for this information)

8) With what specific activity(ies) in the process you chose in Question 7 do beta-lactam antibiotics interfere? (8 pts) (multiple choice)

You keep getting worse. Five days after arriving at the hospital, your blood titer of bacteria is determined to be 19 cfu/mL. The generation time has slowed again due to the dual-drug treatment, but the bacteria are still growing. Using this new 19 cfu/mL titer, the titer given in the set-up for question 4 above, and the fact that this growth took 5 days, calculate the new slower generation time on the dual-drug treatment.

9) What is the new generation time in hours?

The critical care medical team finally makes contact with your primary care physician and finds out that you had already been on oral doxycycline. Privately, they suggest that this might not have been the best option given the severity of the initial wound infection. Your primary care physician hangs his/her head in shame, but that does not help you. Due to the initial inappropriate antibiotic treatment, you are likely to die.

Your critical care team decides to switch your treatment to intravenous ciprofloxacin.

10) What class of antibiotic is ciprofloxacin? (Hint: Look in Chapter 7 and Chapter 27 of your book for this information)

11) With what general bacterial process does ciprofloxacin primarily interfere?

Soon after this treatment begins, the growth rate of the V. vulnificus becomes negligible due to the ‘bacteriostatic' activity of ciprofloxacin.

Because ciprofloxacin has ‘bacteriocidal' activity as well as ‘bacteriostatic' activity, it will be able to assist your immune system in actually killing the bacteria (not just stopping their growth as would an antibiotic with only bacteriostatic activity).

Given that the bacteria reached a titer of 21 cfu/mL in your blood before ciprofloxacin caused cessation of growth, if the death rate is 65% per day,

12) How many days of uninterrupted ciprofloxacin treatment would it take for the infection to clear? (8pts) (Assume that growth is completely arrested at the time the death starts, and assume that 21 cfu/mL is the highest concentration they reached before they began to die.) (Multiple choice)

(Hint if you get stuck: To get a rough idea of the length of treatment needed, you don't need to use calculus. You can do it the long way by calculating the cumulative effect of the given daily death rate over successive days.)