Of course Nature "tries" to pack in as much meaningful signal as possible!
The bases (the letters in the four letter DNA alphabet), mostly built up of light atoms, weigh each just a bit over 100 of such tiny parts of a gram (atomic units, or g/mol, to be exact)    .
They appear in pairs, but still, even given that a pair weighs around 300 * 6 * 10^-23 g, you can fit quite a few of such base pairs in a few grams. Ca 3.3×10^20 / g, or ~ 330 000 000 000 000 000 000, given this rough esti-calculation.
 A: https://en.wikipedia.org/wiki/Adenine
 C: https://en.wikipedia.org/wiki/Cytosine
 G: https://en.wikipedia.org/wiki/Guanine
 T: https://en.wikipedia.org/wiki/Thymine
"Capable of storing 215 petabytes (215 million gigabytes) in a single gram of DNA, the system could, in principle, store every bit of datum ever recorded by humans in a container about the size and weight of a couple of pickup trucks."
Not sure what they base it on though. Perhaps we'll have to do a more proper calculation ourselves ...
Do you disagree? Back of the envelope-wise (depending on their definition of "digital data"), that seems to be about within two or three zeroes of correct, no?
That's pretty dense.
It is a collection of papers from a symposium on the topic at Cornell University.
Heck, even the TCP/IP protocol has its counterpart with the addresstags (post translational modifications), for sorting in the biological router called "golgi apparatus" .
We never observed a process creating these structures that doesn't start from already existing such structures, and it's not like we see these structures popping up spontaneously everywhere in the universe. No, we didn't find them elsewhere than on this very planet, out of the hundreds we can observe.
The combination of such ingenuity on every level -- physical and abstract -- with such an astonishing beauty and such purposefullness, also on every level, makes me cringe when the cred for all of this is given to this unobserved idea of evolution .
No, I'm not talking about the changes we do observe in nature today which also go under this term, but on the origin of these solutions and structures.
In other words, it's the anthropic principle again: If the universe operated differently, and different patterns were evolved and led to us, then we would consider different patterns to look intelligent.
Given the heavy biases of the anthropic principle, odds don't look good (... when we can't take back on some intentionality towards anything, behind anything).