I think the answer is really "it depends."

Let's look at just your body, because you are one of the many parts of nature that recycles dead organisms. You reuse some of the amino acids you eat, but you also burn a lot of them for energy. Even if you eat 100 g of protein every day, you don't put on 100 g of new muscle every day. So every day, you are burning at least some protein for energy -- turning it into basics like carbon dioxide and water and something nitrogenous. (In humans, the nitrogenous product is mostly urea.)

Also, most proteins in your body don't stick around forever. They are broken down and rebuilt. But the time frame can vary a lot. Collagen, for example, can have a very long half-life: over 100 years in cartilage and 15 years in skin according to [1]. At the other end of the spectrum, some enzymes have a half-life of hours [2]. So some of the amino acids currently in your proteins will be burned today and replaced by dietary protein. But because of the variability, it's very hard to say how long the average amino acid in your body stays an amino acid.

Similar things can be said for basically any biomolecule. For example, a nucleotide can "live" for a long time if it happens to be part of the DNA of a neuron or other long-lived cell, and for a much shorter time if it's in in the DNA of an erythroblast (red blood cell precursor) whose nucleus will soon be ejected and metabolized.

[1] Verzijl et al., "Effect of Collagen Turnover on the Accumulation of Advanced Glycation End Products," https://www.sciencedirect.com/science/article/pii/S0021925819558288

[2] Mathieson et al., "Systematic analysis of protein turnover in primary cells," https://www.nature.com/articles/s41467-018-03106-1

I think one of the biggest misconceptions that the average person has about chemical compounds is to think of them as unchanging. The reality is a lot more complicated. Exchange of like atoms (oxygen for oxygen, or hydrogen for hydrogen say) is always going on. We know this from stable isotope studies and even from radioactive tracer work, among many other reasons and evidence.

Systems are not static at the atomic level, at the molecular level. More like a giant square dance, where the overall form is constant but individual partners move around, trade places. The rate of trading (and how far a trade partner can migrate away) varies considerably depending on the physical state of the compound, whether solid, liquid, or gas. Solids are slowest and gases are fastest, as a general idea.

People talk about things like a water molecule, as if it is something that has existed since it first formed, maybe billions of years ago, but that is not exactly true. In bulk, sure, that mass of 10^23 (1 followed by 23 zeroes, perhaps a cup worth of water) has been water that long, perhaps, but each molecule is constantly smacking other ones and in the process, switching atoms (changing partners). Some of those changes involve other compounds too (the O in CO2 can end up as the O in H2O (water), and the reverse, with time).

It is certainly true that the rate of exchange is highly variable, and depends on the system and things like temperature (amount of energy shared around the system). It is also true that the distance over which such exchange occurs can be very tiny from our point of view. A hydrogen atom moving down a chain of carbon atoms in a solid over time is only moving on the order of nanometers (billionth of a meter), but it is moving. Which particular one is moving, or how many are moving at the same time, or what all is happening in detail is very hard to see or measure, but we can prove that it must have happened, and theory says it should anyway (the world at atom level is really busy).

This is pretty much the idea behind chemical equilibrium, that the compound is stable and persists even if the individual atoms move around. It is a dynamic process, but it is a steady state (what goes one way is offset by things going the other way, and not at all a case of once made, never changes, although some conditions can be, effectively, one-directional, going from all this to only that, when one form is way more stable than the original form). Basically, reactions will proceed primarily in one direction until the rate of reaction coming back gets to be about equal (that is what equilibrium means). Then things just dance together, switching partners (individual atoms or perhaps ion groups, particularly the anion complexes, which tend to migrate as a unit) but not switching the bigger forms that we call compounds.

As to the primary question, the persistence of an organic (or any) chemical compound through time depends on its chemical stability, which depends a lot on its circumstances (what else is nearby and competing for energy and electrons, and how easily can atoms change places, and whether the existing arrangement is more stable than alternatives using the very same atoms).

Some compounds are very easily broken and converted into something else. These compounds are the first to disappear. They also tend to be the simplest compounds (with organic molecules, the short chains will break down fairly easily, but they do get somewhat replaced by the breakdown of bigger chains into shorter chains).

When bacteria or bugs or whatever find these compounds in the environment, they tend to eat them all right up, really fast. These compounds will also break up just from non-biological reasons fairly quickly.

Other different bacteria ("bugs") come along later and try to eat the residues. Some compounds do not yield enough energy to make it worthwhile for bacteria or whatever to even attack them and break them up. Costs more to do that than they get out of it. Those molecules just sit there for eons. No energy benefit for breaking them up even if they might not be the most stable form for what they are made from. The energy wall they need to cross to get to the more stable forms is simply too high for it to happen except rarely.

Other compounds are so stable, or so difficult to split apart, that the still exist after millions of years, changing only slightly between burial and our return to surface in crude oil.

Some compounds persist for so long that we use them as markers, as indicators of which plant (or animal) types are the probably source.

What is the lifespan of an organic molecule? It depends very much where that molecule ends up going and how unstable that molecule would become for new conditions. If you do not change conditions, the stuff will not change very fast if at all. Might still change atoms with near neighbors every so often, but the compound WILL persist.

If you take something like butane (a fairly simple organic molecule), it will last as long as you keep it in a container, but as soon as you flick your bic and press the lever to let gas out, POOF, it is destroyed in flame. Some compounds like PCBs and dioxins are so complex, and so noxious to life, that they persist almost forever, as far as we can tell. That is actually what some compounds we make are called, "forever chemicals", because nothing around our near-earth situation will break them up. We can only break them up at extremely high temperatures in the presence of oxygen or some similar electron-grabber, or in some other fairly difficult way.

How long does an organic compound last? from seconds to billions of years, and pretty well any time in between, depending on what you do to them.

It's extremely variable, of course. Some proteins have half-lives of a few seconds, others can be in the millions of years.

Dinosaur proteins have been (debatably) discovered:

>Ancient proteins dating back 195 million years have been found inside a dinosaur bone. ... The discovery pushes back the oldest evidence for preserved proteins by 100 million years. ... "This discovery tells us that yes, you really can probably preserve soft, microscopic proteins inside dinosaur bones for tens or hundreds of millions of years," Dr Brusatte added.

--'Startling' dinosaur protein discovery

The record for identifiable, sequence-able DNA is around a couple million years:

>Here we report an ancient environmental DNA (eDNA) record describing the rich plant and animal assemblages of the Kap København Formation in North Greenland, dated to around two million years ago.

--A 2-million-year-old ecosystem in Greenland uncovered by environmental DNA

Of course these are not the normal circumstances. DNA in a rain forest would be completely gone in probably a year or less. Most proteins are far less stable than the collagen found in dinosaur fossils. But it gives you a sense of the upper limits.

Challenging to answer this generically for all biomolecules.

Biochemical systems are always in some kind of dynamic flux. Think about proteins on the surface of a cell. Those proteins are regularly turned over - old ones get internalized (then broken down into amino acids to be repurposed for new proteins), and newly synthesized proteins get trafficked to the cell surface. This turnover happens constantly and the time scale depends on the specific protein. However this generally happens on the order of hours to days.

The added complexity to this is that the conversion of one biomolecule to another often does not happen spontaneously, but is facilitated by enzymes. A protein suspended in some kind of tissue will likely degrade faster compared to it being suspended in pure water.

If we ignore enzymes, there are all sorts of factors that affect a compound's stability. Temperature, exposure to specific wavelengths of light, presence of water or dried as a powder, pH, salt concentration, etc. Note that many research chemicals (including proteins) are stored as powders because they are more stable in that form compared to being dissolved in solution. This all to say the lifetime of a given biomolecule depends on a variety of conditions.

To your main question - how long do biomolecules get passed around by nature? Potentially indefinitely and infinitely. In nature, it's unlikely that a given biomolecule will just be left alone to passively degrade into individual atoms. Another organism will likely do something with that biomass. That being said, we fight nature all the time to slow this down, ex: we keep meat on ice and covered in salt dry it out and slow down the decaying process. With enough effort and $$, you could certainly slow down the degradation of any compound to keep around longer.

There is a very cool experimental method where you make a version of a compound you care about but use radioactive isotopes for some of the atoms. If you treat cells in a dish with this compound, you can then measure where that radioactivity is and then infer what biochemical pathways it went through to get converted into something else. This is called a pulse-chase experiment (you pulse the system with the radio-labeled compound).

TL;DR - Biomolecules generally do not exist in a vacuum where they have a chance to passively decay. Barring specific laboratory settings, biomolecules are basically always part of some network of biochemical reactions and constantly being converted into other compounds.

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