To infect your 60mm dish with 100 plaque-forming units (PFU) from a virus stock with a concentration of $7.7 \times 10^9 \, \text{pfu/ml}$, you need to calculate the appropriate dilution factor and volume to achieve the desired number of PFUs.

Step-by-step solution:

1. Determine the volume of stock required for 100 PFUs: $\text{Volume of stock} = \frac{\text{desired PFUs}}{\text{stock concentration}} = \frac{100 \, \text{pfu}}{7.7 \times 10^9 \, \text{pfu/ml}}$

2. Calculate the volume: $\text{Volume of stock} = \frac{100}{7.7 \times 10^9} = 1.2987 \times 10^{-8} \, \text{ml}$ This is a very small volume, approximately $0.000012987 \, \text{ml}$ or $12.987 \, \text{nL}$.

3. Choose a practical dilution: To make this volume measurable, you'll need to dilute the stock solution. One common approach is to perform serial dilutions.

   • For example, you can perform a $10^{-5}$ dilution (1 part stock + 99,999 parts diluent).
   • In this case, the new concentration of your diluted solution would be: $\frac{7.7 \times 10^9 \, \text{pfu/ml}}{10^5} = 7.7 \times 10^4 \, \text{pfu/ml}$

4. Determine the volume to take from the diluted stock: Now, using this new diluted concentration, calculate the volume needed to infect the dish with 100 PFU: $\text{Volume of diluted stock} = \frac{100 \, \text{pfu}}{7.7 \times 10^4 \, \text{pfu/ml}} = 0.0013 \, \text{ml} = 1.3 \, \text{µl}$

Dilution process:

• Perform a $10^{-5}$ dilution of your stock solution.
• Use $1.3 \, \mu\text{l}$ from this diluted solution to infect your dish with 100 PFUs.

Let me know if you'd like more details or have questions! Here are some follow-up questions:

1. What is the best practice for preparing serial dilutions?
2. How do you accurately measure small volumes like $1.3 \, \mu\text{l}$?
3. How would the calculation change if you needed 1000 PFU instead of 100?
4. What factors could affect the efficiency of virus infection in this experiment?
5. How would you adjust the dilution if you wanted to use a 100mm dish instead?

Tip: Always mix dilutions thoroughly to ensure an even distribution of viral particles.