Question

If a single bacteriophage infects one \(E\). coli cell present in a culture of bacteria and, upon lysis, yields 200 viable viruses, how many phages will exist in a single plaque if three more lytic cycles occur?

Short answer

Answer: 1,600,804,200 phages

Step-by-step solution

Understand the lytic cycle and initial values

A lytic cycle is a process in which a bacteriophage infects a bacterial cell and produces multiple copies of itself. In this case, the initial number of phages after the first lytic cycle is 200. We need to find the total number of phages after three more subsequent lytic cycles.

Calculate the number of phages produced after the second lytic cycle

If 200 phages are produced after the first lytic cycle, we can assume that each of these phages will go on to infect another E. coli cell, and yield 200 new phages each. We need to multiply the initial number of phages (200) by the number of phages produced in the subsequent cycle (also 200): Number of phages after second lytic cycle = \(200\times200 = 40000\).

Calculate the number of phages produced after the third lytic cycle

Now we have 40000 phages after the second lytic cycle, and each of these will infect another E. coli cell, yielding 200 new phages each. We need to multiply the number of phages after the second lytic cycle (40000) by the number of phages produced in the subsequent cycle (200): Number of phages after third lytic cycle = \(40000\times200 = 8000000\).

Calculate the number of phages produced after the fourth lytic cycle

After the third lytic cycle, we have 8000000 phages. Each of these will infect another E. coli cell, yielding 200 new phages each. We need to multiply the number of phages after the third lytic cycle (8000000) by the number of phages produced in the subsequent cycle (200): Number of phages after fourth lytic cycle = \(8000000\times200 = 1600000000\).

Finding the total number of phages in the culture

The total number of phages at the end of four lytic cycles is \(200+40000+8000000+1600000000\). Adding these values gives us the total number of phages in the culture: Total number of phages = \(200 + 40000 + 8000000 + 1600000000 = 1,600,804,200\). So, there will be 1,600,804,200 phages in a single plaque after three more lytic cycles.