I would test it out by plating BL21 DE3 with the protein plasmid and without the protein plasmid (preferably one with the same antibiotic resistance, to reduce variables). 3 - 5 plates each. I would vary the amount of inducer in the media (ex. plate 1 has .1% arabinose, plate 2 has .2%). Incubate overnight, count colonies in the morning. If the protein is toxic, you should see the colony count decreasing as the amount of inducer increases (it probably will decrease a bit because extra resources go into protein production, you can judge by how drastic the change is), and the control should have a constant count.
Protein toxicity will adversely affect the cloning and expression. Protein toxicity is the most important reason for DNA cloning or subcloning problems. Most expression problems are also the result of protein toxicity. You can judge out that the protein you are expressing is toxic to host cells if it has the following phenotypes:
1. Toxic Protein Cloning Problems
No colony in cloning
Fewer colonies than those in regular cloning experiments
Small percentage of positive clones
Wrong orientation
Mutations leading to defective products or no expression
2. Transformation Efficiency Problems
The transformation efficiency of the vector containing a toxic protein is lower or significantly lower than the control vectors or the vectors containing non-toxic proteins.
Transformation efficiency in a normal cell strain is significantly lower than that in a detoxification strain.
3. Host Cell Growth Rate and Cell Density Problems
Cell grows significantly slower and cannot reach its normal density in a given medium before induction.
Cell grows significantly slower and cannot reach its normal density after induction.
Growth rate and cell density are low in normal strain. In contrast, the growth rate and cell density are close to normal in a detoxification cell strain.
4. Toxic Protein Expression Problems
No expression
Low yield
Defective proteins
Inconsistent expression
For more information about problems and strategies of toxic protein expression, you can refer to this link: