What is the purpose of intensive protein synthesis in G1 phase of mitosis, and what purposes do these synthesized proteins serve? Why are lipids and carbohydrates not synthesized intensively as well?
The G1 phase of eukaryotic cell cycle is part of interphase, which is when the cell is replicating its DNA ready for division. To understand the need for intense protein synthesis, we first need to understand how DNA is organised during mitosis.
Before DNA is condensed into chromosomes ready for nuclear division it is in the form of chromatin, a long fiber-like structure inside the nucleus. In order to condense into chromosomes, this chromatin must undergo a process of coiling and folding in order to create the chromosome 'X' structure we are familiar with. A major part of this DNA 'miniaturization' is the folding of the double helix around proteins called Histones - this creates new structures called nucleosomes.
In order to fully condense the roughly 3 meters of DNA in the average human cell down to a singular chromosome, millions upon millions of these Histone proteins are required.
And that answers your question; intense protein synthesis during the G1 phase is required in order to produce the extremely large amount of Histone proteins that are needed for packaging DNA into chromosomes ready for cellular division.
As for carbohydrates, these are constantly being processed by the body in order for the production of ATP for use as energy. The use of said energy for mitosis is a just another constantly required use of ATP within the body. Therefore there isn't any noticeable increase in carbohydrate processing/production, as it is happening regardless of the cell's stage in its cycle.
-See the image below (from shmoop.com) that explains the process of getting DNA into a chromosome.