53. One hundred E. cli cells are each infected by a single λ phage particle. The ratio of the number of
phage particles committing to lysogency to those committing to lysis is 4:1. Assuming that the average
burst size is 80, the number of free phage particles released after one round of infection is __________.
Problem Breakdown
Total infections: 100 phage particles, one per E. coli cell.
Given a 4:1 lysogeny-to-lysis ratio:
- Total ratio parts = 5
- Lytic infections = 100 ÷ 5 = 20 cells
- Lysogenic infections = 80 cells (no free phage production)
Calculation
Each lytic infection produces a burst size of 80, but subtract the infecting phage.
Net phage per lytic cell = 80 - 1 = 79
Total free phage = 20 × 79 = 1580
Final Answer: 1580 free λ phages
Key Concepts: Lytic vs Lysogenic Cycles
Lytic Cycle
- Phage replicates within host
- Produces **80 virions per cell**
- Cell lyses, releasing ~79 net free phages
Lysogenic Cycle
- Phage genome integrates as a prophage
- No lysis or free phage production in a single round
Step-by-Step Free Phage Calculation
- Lytic cells: 1/5 of 100 = 20
- Lysogenic cells: 80
- Net release per lytic infection: 79
- Total free phages = 20 × 79 = 1580
Result Summary Table
| Parameter | Value | Explanation |
|---|---|---|
| Total cells | 100 | Each infected by 1 λ phage |
| Lysis fraction | 1/5 (20 cells) | From 4:1 lysogeny:lysis ratio |
| Burst size | 80 | Average phage output per lysed cell |
| Net phage per lysis | 79 | 80 minus infecting phage |
| Free phages | 1580 | Final answer |
Exam Relevance for Biotechnology Students
This mirrors GATE Biotechnology PYQs and tests:
- Lytic vs lysogenic decision
- Burst size interpretation
- Correct ratio computation
Common mistakes include using 20 × 80 = 1600 instead of subtracting input phage.
