This is a complicate process to understand. , Its suggested that to get best to induce at 0.6-0.8. which we call at log phase, where the bacterium will be actively dividing. Inducing time varies depending on the host you are using and how much protein they can handle ( some proteins are toxic and when you are expressing a foreign protein in the bacterial host in large amount you will create unstability in the dynamics of bacteria).
Ok, it's reasonable that we induce expression of protien in .8 or .6, because the bacteria are in log phase. But it's interesting for me induction of some protein was done in 1 or 2, even I read article about od=6!
Overexpressing proteins includes a lot of optimisation. Some proteins are easier to express in cells where the density is not to high, because the tend to get insoluble otherwise. Then there are proteins which are robust and get expressed in vast amounts so you can grow the cells for a longer time and get much higher concentrations of your target protein. And then there are proteins which are made only in small concentrations and where you need to grow the cells longer to get some yield (quite the contrary of the second case).
So there is no general recipe, the best thing to do for your protein is to induce them at some point and then take samples at different points (OD 1, 1.5, 2, 2.5 and so on) and then do a western and see where the best ratio between yield in the soluble fraction and yield in the insoluble fraction is.
When the cell density is 0,6-0,8 the bacteria are usually in the exponential growth phase. At this point the entire cell is wired for growth. This includes the expression of chaperones that help to remove misfolded proteins. If you induce expression of a recombinant protein (under the control of for example a T7 promoter) when the cells are not expressing these chaperones a large proportion of your protein will be misfolded may end up as inclusion bodies.
In addition, if you induce expression to early (for example immediately after inoculation) the high expression of your recombinant protein will inhibit bacterial growth and thus lead to reduced yield.
I will little differ with opinions of others. The reason being simple that whatever vector you may take or strain you may take, the thumb rule is cells should be vigorous. Also OD has significant role in protein expression because most of the protein we try to express are cytoplasmic protein, so they require low OD for induction but case changes when you try to express membrane proteins, eukaryotic proteins, nuclear protein. in those cases high OD is generally preferred as cells in stationary phase tend to help express recombinant proteins better.
as noted already, it is usually considered that bacteria are fittest in exponential growth phase.
However, if the protein expression is harmful (e.g. inclusion body formation, toxicity), it can be advantageous to induce at high OD. Even though the protein expression per cell might be lowered, more cells express your protein, hence sustaining yield.
This is particularly true if your recombinant protein expression reduces further bacterial growth (e.g. a toxic protein or through inclusion body formation).
When it comes to very high ODs (>6, >10 etc.), this is most commonly in a fermenter/fed batch. If you would do this in a batch culture, e.g. E.coli most often does not exceed an OD of 2 - 2.5. So be careful, the OD alone does not state in which growth phase the bacteria are in. While at 2.5 they might be in stationary phase in a batch culture, they could be in proper exponential phase under feeding conditions.
I found after inoculating an overnight culture (1:100 dilution) to my 0.5 L culture, it grew very slowly to OD ~0.4, taking 4-6 hours. After reaching OD 0.3, it takes two hours to reaching 0.38. The protein is likely to be toxic to the cells because the recombinant protein, expressed in pET29 vector, has a basic nucleic acid binding domain. Any good suggestions?