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I haven't been able to find any good order-of-magnitude estimates for how many photosystems (e.g. how many PSII complexes, how many PSI complexes) are in an average chloroplast (or perhaps per area of thylakoid membrane).
Textbooks always just show a small area of membrane, and I'm interested to know whether there are say hundreds of complexes or millions. Is there any published data on this?
This article states that in plants at 15-25% relative water content (RWC), the PSII density is around ~700 complexes/µm$^2$, and in hydrated plants ~1500 complexes/µm$^2$.
They also have some nice Cryo-SEM images of grana membranes and the changes in PSII complexes density depending on their RWC. Which is also an important aspect of the question, since the amount of PSI and PSII complexes will vary depending on the environmental stimuli.
Additionally, given that biological material is variable even within the same species (different tolerances might have a different effect on the amount of complexes/µm$^2$), I would expect variability in the complexes density among different species of plants too.
Regarding PSI, I found an article where mass spectrometry analysis approximates the average of PSI in the thylakoid of a Prochlorococcus MED4 ecotype to 4303/μm$^2$. However, the thylakoids of another ecotype had more densely PSI organizations of crystalline pseudo-hexagonal arrays and the average was estimated at 5583/μm$^2$. In fact, the article tested growth under different conditions (low-light, high-light, poor-nutrient) of the different ecotypes and supports the hypothesis that the second ecotype adapted to low-light conditions (by maximizing the amount of pigments in its thylakoid membrane) while the first one adapted to high-light conditions. In this case, the observed part of the membrane with cryo-EM tomography was ~6 μm$^2$and ~22 μm$^2$ of thylakoid membrane area for the first and the second ecotype.
I think the right answer is that there are still many factors affecting the distribution of PSI and PSII that are still unknown and a better approximation cannot be made.
References
Charuvi, Dana & Nevo, Reinat & Shimoni, Eyal & Naveh, Leah & Zia, Ahmad & Adam, Zach & Farrant, Jill & Kirchhoff, Helmut & Reich, Ziv. (2015). Photoprotection Conferred by Changes in Photosynthetic Protein Levels and Organization during Dehydration of a Homoiochlorophyllous Resurrection Plant. Plant physiology. 167. 10.1104/pp.114.255794.
MacGregor-Chatwin C, Jackson PJ, Sener M, Chidgey JW, Hitchcock A, Qian P, Mayneord GE, Johnson MP, Luthey-Schulten Z, Dickman MJ, Scanlan DJ, Hunter CN. Membrane organization of photosystem I complexes in the most abundant phototroph on Earth. Nat Plants. 2019 Aug;5(8):879-889. doi: 10.1038/s41477-019-0475-z. Epub 2019 Jul 22. PMID: 31332310; PMCID: PMC6699766.
