Depends on what are you chasing at. If you want to find whether the gene is there or not like in case of a transformation experiment DNA isolation and PCR is enough for checking the integration. But sometimes even when gene is present in the genome there can be several other factors for the gene to not express like genomic imprinting, position effect, gene silencing, chromatin modifications etc. So, if you really want to find out whether transcription of gene occurs or not and if occurs at what rate; then you can go for RNA isolation and realTime PCR. Sometimes the transcripts are unable to give out functional proteins due to codon bias or other post-translational modifications. This is where you have to check for the presence of the protein even when we already know that transcription is occurring.

Hi Deng,

To answer your questions,

1. Gene expression is a step wise process. Genes are functional units in DNA which encode for either just RNA or a step ahead, a protein. Like previously mentioned, a gene can have two fate (depending on what it is and what it encodes!), a) it may be transcribed to be an mRNA or b) other RNAs like tRNA or rRNA.

Among these the mRNA will be further subjected to translation into protein. Others will remain as tRNA and rRNA. For the genes whose end products are proteins, it involves 2 steps (transcription and translation) for its expression.

Experiment wise, it is better to check both the products of the 2 steps as, for fine tuning of gene expression, both of these steps are tightly regulated (especially in eukaryotes). So, even if you get a positive RT PCR product doesn't  mean your gene will have the desired protein expression. After transcription also it can be down-regulated. Hence, it is better to check the transcript by RT PCR and the protein (end product) by Western blot to have better confirmation.

2. The relation between gene expression and protein expression as I said is the process that the gene goes through. It largely depends on the gene and its cellular functions. If it is a rRNA encoding gene it will not be translated after transcription but if it is a gene encoding ribosomal proteins, then it'll be translated and it'll have a functional protein product. 

Hope it helps!

Dear

I purpose you some interesting articles concerning your question.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC55876/

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4459080/

https://kendricklabs.com/wp-content/uploads/2016/08/WP1_mRNAvsProtein_KendrickLabs.pdf