Large-scale cell growth and protein expression - (Dec/03/2015 )

I used to inoculate 50 mL LB with 500 uL of incubated BL21(DE3) culture and it usually takes me 2 - 3 hours for OD 600 to reach between 0.6 and 1. Then for induction, it would take me 6 - 8 hours. Now I need to inoculate 200 mL LB with 5 uL of incubated culture and then induce the culture. How can I determine the time it takes for the inoculation and induction? Thank you for the answers in advance.

This sounds like a bad idea. You should probably grow up a larger volume from the 5 ul (perhaps 5-10 ml) and then inoculate the larger volume. This will give you more control over the growth. But to do the calculation, the culture volume ratio in your original experiment was 1:100, while the proposed experiment volume ratio is .005/200 or 1:40000, so it should take roughly twice as long for the culture to grow (a bit less).