I have constructed a DNA library and I have got an insert of around 3.2 kb size showing desired phenotype. How does a gene this big in size, get ligated to a vector much lesser in size than it?
I assume you have a linear DNA molecule. My first question is: Do you know the sequence of it? The sequence is crucial for several cloning strategies.
If you know the sequence of it, you could use Gibson assembly. At first, you must design primers for the amplification of your DNA fragment. The primer sequences are extended at the 5' end with sequences which are homologous to your plasmid. Additionally, you construct primers for the amplification of your plasmid. These primers should have a 5' end which is homologous to your desired insert. Afterwards, you can produce two PCR products with homologous ends. The following procedure is described in the handbook of your selected Gibson assembly master mix supplier (e.g. NEB). This method is very reliable and should work well in your case. The size difference between your insert and the plasmid backbone should not be an issue.
If you do not know the sequence of your DNA fragment, you could use TOPO-TA or TOPO blunt end cloning (ThermoFisher Scientific). Afterwards, you can cut the TOPO plasmid with restriction enzymes and transfer the insert into your own vector. However, this is more complicated than using Gibson assembly. Again, the size difference between your insert and the plasmid backbone should not be an issue.
No, 500bp is not a size differences that should cause problems during ligation. You could try different ratios of insert to backbone in your ligation reaction e.g. 1:1, 3:1, 5:1 (backbone: insert).