Well, there are plenty of large single celled organisms. Many are algae, but some, like Gromia sphaerica are grape sized amoeba. And they move! 🙂
Whether there’s a maximum size isn’t really known. Since we already know that plants and protists can grow pretty large, let’s focus on animal cells.
The largest single celled animals aren’t much larger than a couple of millimeters. The reason for this may have to do with the chemistry of growth and reproduction.
In order for a cell to metabolize and divide it needs its DNA just about everywhere within its volume otherwise the cell won’t be able to “communicate” the right chemicals where they need to be when they need to be there. That’s why the nucleus of an animal cell is the largest organelle and takes up a good chunk of the cell’s volume.
In order for an animal cell to get larger, its nucleus must grow proportionally. But there’s almost no reason for the nucleus to do this because there’s a finite amount of DNA. So it may come down to the “peanut butter spreading too thin”. If the nucleus becomes too large, it’s possible that the proteins the DNA is synthesizing won’t be in the right locations or right proportions when another organelle needs them, and the cell dies.
Every cell has the problem of “surface area” vs “energy/water needed” for all the cells inner components to run.
If you make a cell (and it’s insides) too big, it becomes less and less efficient to move water in and out. Imagine a football sized mitochondria with the same energy transfer system as the tiniest one. Instead of requiring a few drops of water in a week, it now needs gallons a day. And the cell doesn’t have an internal storage system for gallons of water. Or plumbing to get it in or out. And then you have issues with things like water evaporating from a giant membrane. Basically every energy & water problem a small cell has, but on such bigger scales cells would need to fundamentally “re-evolve” to address these bigger problems.
The current largest known single cell is an algae that can grow up to a foot long. And, “It independently evolved a form that resembles the organs of land plants. A stolon (a vein like stiff water tube) runs along the surface that the cell is growing on and from the stolon arise leaf-like structures…” So it can grow this large because it lives in water, which solves the evaporating problem, and it HAS started to fundamentally change how it’s structured compared to most other cells.
Most single celled organisms figured out a better way to increase in size is to just clump a bunch of smaller cells together so the same mechanisms can still work for each cell individually.
Cells are typically small because of the square-cube relationship. The stuff inside the cell is proportional to the cube of the length, but each bit of stuff needs to exchange energy and waste with the environment, and this happens at the surface, which is proportional to the square of the length. If the cell gets too big the amount of access to the environment per bit of stuff inside the cell drops below a sustainable level and the cell dies.
Say you have a factory, do you want one mega factory that only has one manufacturing machine, one HR department, one parking lot and one breakroom to share with everyone or have two smaller factories each with their own set of amenities and half the amount of workers each
The bigger the cell gets, the more work it has to do to move stuff from one side to the other, remove trash, supply energy and maintain itself. It just makes more energetic sense to have two smaller independent cells that can talk to each other instead.
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