Why are most cells small with many convolutions in their membranes?
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Each cell has to be able to exchange materials with its environment in order to stay alive and do its job(s). Cells need to intake things like nutrients, water, and oxygen, and they need to be able to export things like metabolic products and waste materials. No matter which direction the material is moving in, it needs to cross the cell membrane at some point. This means that the total area of the cell membrane sets a limit on how quickly a cell can exchange things with its surroundings.
The larger the cell, the more materials it has to move. For this reason, most cells stay relatively small. In order to maximize the amount of cell membrane available for exchange, cells can be flattened or can develop convolutions or extensions such as villi.
The way we describe this mathematically is by calculating the cell's surface area to volume ratio. The more surface area (i.e., cell membrane) a cell has per unit of volume, the easier it is fro that cell to move materials in and out.
It has everything to do with their surface area. A cell with convolutions in its membrane has much more surface area, so a greater amount of proteins can enter it at the same time.
A large cell has a greater volume compared to its surface area, and if this is too large, it will not get enough proteins/oxygen or whatever it needs.
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