The argument that blood plasma resembles sea-water, in essence, relies on the notable similarity in concentration of two ions in plasma and sea-water, compared with their intracellular concentration: sodium and potassium.
- The concentration of sodium-ion in sea-water is about 450 mM, whereas the concentration of potassium-ion is only about 10 mM (ref)
- The plasma concentration of sodium-ion is about 140 mM and the concentration of potassium-ion is about 3-5 mM (ref, but many clinical biochemistry sources will confirm)
That is, both plasma and sea-water are 'high-sodium, low-potassium' and the concentrations are remarkably similar. If we contrast this with the intracellular concentration of these ions:
- The intracellular concentration of potassium-ion is about 150 mM, whereas the concentration of sodium-ion is about 10-20 mM (ref)
That is, the 'intracellular milieu' is 'high-potassium, low-sodium'. Blood plasma, of course, is considered an extracellular fluid.
We can generalize further and say (Skou, Nobel lecture):
- The intracellular concentration of potassium-ion is about 150 mM whereas extracellular concentration is about 4 mM.
- The intracellular sodium-ion concentration is 10-20 mM whereas the extracellular concentration about 140 mM
Thus sea-water, in terms of sodium-ion and potassium-ion concentrations, resembles the extracellular milieu, leading to the somewhat hyperbolic view that "blood can also be thought of as a private ocean...".
But the similarities are striking.
At one time it was thought that this concentration difference was due to cells being impermeable to sodium-ion, a hypothesis first put forward by E.J. Conway.
It is it now known, of course, that concentration imbalance is maintained by the sodium-potassium pump, which is present in animal cells but not in plant cells (W.D. Stein). The presence of this pump allows animal cells to be in osmotic equilibrium (no change in osmotic pressure) with their surroundings. (Plant cells, in contrast, have developed a cell wall that allows high internal osmotic pressures and which may (to again quote Stein) "have condemned [them] to a largely sessile life")
The history of its discovery (and much more) is given in The Identification of the Sodium Potassium Pump, the Nobel lecture by J.C. Skou
Addendum 1: Historical Origins
According to a review by Mulkidjanian and colleagues, it was Macallum in 1926 that first drew attention to the similarities in inorganic composition of sea-water and plasma and its significance as evidence that the first animals emerged from the sea.
I think R.L. Berg (see Addendum 3), at a famous conference in 1957, also drew attention to this, but I do not have access to the reference.
But just because animals emerged from the sea does not necessarily mean that life began in the sea. Mulkidjanian and colleagues point to the fact that "inorganic composition of the cell cytosol dramatically differs from that of modern sea water" (which was also first pointed out by Macallum in 1926) may indicate that life began in a high-potassium, low-sodium environment and that life in the sea only became possible after the evolution of the sodium-potassium pump allowed organisms to maintain their 'fundamental biochemical architecture' (the chemical conservation principle).
These authors suggest condensed geothermal vapours as a likely environment for life's origin but not everone agrees.
I notice from the comments that the similarity and blood plasma and sea-water is considered somewhat heretical and perhaps not sufficiently backed up by evidence. This viewpoint has a long history in 'mainstream' science.
Pearse in The migrations of animals from sea to land (1936), for example, has this to say:
The general similarity of the bloods of animals to seawater has been interpreted as indicating that all animals originated in the sea.
While there are many discrepancies to be explained, it is a common belief that "blood is modified seawater" (quoting Pantin,1931).
Another good source with some great references is The Oceans, Their Physics, Chemistry, and General Biology (1942) by Sverdrup, Johnson and Fleming, which is available as an e-book, especially the section in Chapter VIII on Sea Water and the Body Fluids.
Finally, there is nothing 'creationist' about the above arguments, but creationists, in the main, don't like them. See Is the Sodium Chloride Level in the Oceans Evidence for Abiogenesis? by Bergmann, for example.
Although I do not agree with any of the views expressed in this article (especially the view that the Flood "likely carried to the earth’s surface many tons of pulverized crustal material containing large amount of salts and other minerals"), it contains many good references to the 'mainstream' point of view (which the author attempts to debunk).
Addendum 2: Serum and Plasma
Plasma is liquid component of blood that is clinically obtained as the supernatant (upper 'layer') generated by centrifuging blood collected in the presence of an anti-coagulant such as heparin or EDTA.
Serum is plasma without clotting factors and is clinically obtained by first letting blood clot, centrifuging, and then collecting the supernatant.
Both serum and plasma are considered extracellular fluids, in contrast to cytoplasm, which is the intracellular fluid that 'holds' the organelles and other cellular components.
There is no clinical difference in serum and plasma sodium levels, but serum concentrations of potassium are somewhat lower (about half-millmolar or thereabouts) than those of plasma (ref)
It appears that the R.L. Berg quoted above is Raisa L Berg, the eminent Russian Darwinist and geneticist who, among many other achievements, wrote In Defense of Timoféeff-Ressovsky.
As I stated above, I do not have access to the original reference but R.L Berg is quoted in Bergman's article (also quoted above) as follows:
Berg (1959, pp. 169–170) notes, “The most important arguments in favor of the hypothesis that life originated exclusively in the ocean” are, first, “the similarity between the salt composition of the body fluids of land animals and that of the waters of the ocean.”
He [sic] then adds that the “similarity in the salt composition of the waters of the ocean and that of the body fluids of land animals could be accounted for” only by evolution (Berg 1959, p. 170).
It would be very nice to have her views recorded 'first hand' here (the OP question has generated a lot of interest).
Perhaps someone with access to the article could post a separate answer?