Nitrogen is utilized by bacteria to generate terminal groups containing nitrogen or synthesize main chain if carbohydrate is there, amino acid polymers and carohydrate complexes in cell wall also form complexes of nitrogen. It is also used in formation of main cytoskeletal framework. 

Nitrate is reduced(Nitrate and nitrite reductase) and incorporated in aminoacids (see the exact schema of this process in a book of biochemistry. The aminocid are used for the synthesis  of   all proteins. Moreover Nitrogen is also involved in the synthesis of the linear tetrapyrrol of the phycocyanin..

Cyanobacteria utilize nitrate by using the two key enzymes nitrate and nitrite reductases (NR and NiR). The reduced nitrogen in the form of ammonia is incorporated in amino acids, the building blocks of proteins. Part of the amino acids enter in the biosynthetic route of the pigments like chlorophyll and phycocyanin.  The linear tetrapyrole of the phycocyanin is also synthesized from amino nitrogen. Thus, in the presence of optimum concentration of nitrate cyanobacteria synthesize maximum amount of phycocyanin, however, nitrate at higher concentration is toxic and may inhibit the growth of cyanobacteria as well as the synthesis of phycocyanin.

I recommend you to read the following paper "Dynamic Simulation and Optimization for Arthrospira platensis Growth and C‑Phycocyanin Production"

Question:

Dears

Have you already seen a positive correlation between biomass and Nitrate. If you see it in a N and P limitation mixotrophic culture in Spirulina what it means?

Nitrate is needed for the synthesis of aminoacids via nitrate-nitrite reductase complex.

Phycocyanin is decresing in absence of nitrogen source in medium