Work, in Bitcoin and biologically, is a measure of energy expenditure over an amount of time. Proof that work has been done in either system is probabilistic: You might generate a winning hash on your first try, but it's unlikely, and with a longer sampling size, the probability is apparent.

In biological systems, there is just chemistry, specifically receptors and ligands, that kind of thing, but we could just as easily be talking about a solution with two reagents of a specific reactivity. Given a concentration of reagents and their reactivity, at a given temperature their movement results in a predictable reaction speed. Two individual molecules might get "lucky" but on the whole, the rxn speed is probabilistic.

With all other variables held static, the only way to speed or slow the reaction rate, which is dictated by the collision rate of the constituents, which is dictated by the temperature of the solution... you can only vary the temperature, which requires an expenditure of energy over time: Work. Given identical concentrations and amounts of reagents in two separate experiments, where each takes place for a set period of time, but are heated at different but unknown amounts, at any given moment of examination, the one which has reacted further probably has had more work done on it. The shorter the inspection interval, the less confident you can be that a period of luck hasn't occurred, but over time, you are confident.

For simplicity, let us say that at each inspection interval, the precipitate is removed along with a quantity of pure solute such that the concentration of reagents remains the same. This way, we can look at the precipitate formed as a percentage of the total potential precipitate, and we can isolate the change in concentration, which we would normally need to do in real life.

For Solution A, I generated a random integer from 0 to 4, for each time period, simulating that quantity of energy input. (Whatever quantity is necessary to react 2% of the reagent in that inspection period, on average). For B, I generated a random integer from 0 to 3. (Over time, we'd expect to see a 1.5% RoR.)


Time | Sol'n A | Sol'n B
   0       0%        0%
   1       2%        3%
   2       4%        3%
   3       7%        6%
   4      10%        7%
   5      10%        10%
   6      14%        11%
   7      17%        11%
   8      20%        11%
   9      21%        13%
  10      24%        13%
  11      28%        16%
  12      30%        16%
 . . . .
  18      49%        26%
  24      66%        31%
  32      87%        46%
  40      99%        58%
  41     100%        61%
 . . . .
  46     [done]      76%
  52     [done]      81%
 . . . .
  58     [done]      92%
  59     [done]      92%
  60     [done]      94%
  61     [done]      96%
  62     [done]      99%
  63     [done]     100%


These numbers work out nicely to illustrate the point. I just generated them until the point became clear; even here, it wasn't until "block" 6 that B appeared to gain on A. This is analogous, in Bitcoin, to beginning with a block at height N, which here we can just call 0, and seeing how quickly a given hashpower progresses. If the power of A + B is 100%, the power behind "pool" B is about 43% of the total, and A, 57%. For the first few blocks, B was a bit luckier vs. its true power, but A caught up; over the course of the experiment, A ended up "luckier" overall even compared to its true power (progressing at ~2.44% per interval, to B's ~1.59%, also slightly "lucky").

Cellular signalling systems are all dependent on the probabilities of reaction which is governed by energy input. It is no coincidence that blockchained proofs of work proves a precise probabilistic amount of work was performed. PoS systems do something, perhaps, but I am not familiar with a scientific analogue to "stake". It's proof of possession, but I don't know of a way that is useful in a signalling context.