Why are cells so small?As Mendel describes in this story, cells are so small they cannot normally be seen with the naked eye. There are also a lot of cells in the average organism, a fact that astonished their discoverer, Robert Hooke, who calculated from his observations of cork cells that there must be over a billion cells in one "cubick inch", a fact most remarkable. The average adult human has a lot more than this, about 60 trillion according to one calculation  a fact even more remarkable. A pint of blood has over 5 billion specialized cells floating in it, and you scrape off your skin or slough off from your intestines close to 700 billion cells a day!!Why? Cells have a finite life span which, like any kind of complex machinery, occasionally breaks down. They can be repaired for a time, but sooner or later it is easier and more efficient to discard the older cell and recycle it constituents into a new cell with fewer problems. This renewal goes on constantly throughout the life time of a multicellular organism. Cells arise by division, specialize, function and carry out their roles, then age and eventually die or are lost. The total organism remains the same throughout this process, and (usually) has a longer time on earth than any one of its cells. For the body of an animal or plant, small, specialized cells are easier to replace and turnover without disruption than would be the case if an organism was made up of just a few very large cells. Imagine what it would be like if each of your eyes was a single cell. When it came time for the eye cells to be replaced, you would be either blind or have an extra eye growing in your face until the change over could take place. As it is, you have about 125 million cells in your eye which are responsible for capturing light rays, and as a few of them are replaced every day, you never notice the change.




One reason, therefore, why cells are so small, and there are so many of them, is simple logistics. But there is another reason and the one given in this story; the tyranny of mathematics. Two mathematical quantities rule the lives of every cell; their surface area and their volume. Each cell is a living globule of cytoplasm in which vast numbers of chemical reactions are taking place millions of times a second. These metabolic furnaces need fuel, everything from food to complex nutrients, and produce waste products that must be eliminated. Diffusion of these molecules seems to be the main way of getting a chemical compound where it is needed and somewhere else when it is not. Diffusion is very rapid over short distances, but much much slower over longer distances. Lacking a circulatory system (like out blood system), cells rely on diffusion to move their molecules around, and thus need to keep distances short. One of the most important exchanges that takes place is between the inside of the cell and the outside environment. This is how most cells get the food they need and eliminate the waste products of their metabolic reactions. This is where the second quantity comes in; surface area. All these exchanges take place across the surface of the cell, which is bounded and regulated by a cell membrane. Some of these exchanges are by simple diffusion, and many others are by selective pumps, but either way, the limiting factor is the amount of surface across which the movement of molecules takes place. To keep the calculation simple, let us imagine that Mendel and his class have just found a cell shaped like a cube. Each side of this cell measures 10 units (they are using a microscope to make these measurements), so they can calculate both the volume and the surface area of this cube/cell. The volume of a cube is obtained by multiplying the length by the width by the height, and the total surface area by adding together the surface area of the six sides, (obtained by multiplying the length and width of each side). Since Mendel is observing a cube where all the sides are the same size, the calculations are easy:
Volume:.........=...10 x 10 x 10...=...1000 cubic units. Surface Area....=...10 x 10 x 6....=....600 square units Mendel loved ratios. The basis of his whole theory of genetics was found in the ratios of offspring from genetic crosses, so he would have instantly grasped the importance of the ratio between the surface area and the volume of a cell. Ratio....Surface/Volume....600/1000 = 0.6 So far, so good. Now, if Mendel's cell begins to grow and the dimensions increase to 20 units per side, the calculations become:
Volume:.........=...20 x 20 x 20...=...8000 cubic units. Surface Area....=...20 x 20 x 6....=...2400 square units Ratio....Surface/Volume....2400/8000 = 0.3As Mendel showed, the ratio goes down (from 0.6 to 0.3) as the cell size increases. The practical effects of this change on the cell is dramatic, less and less surface is available to exchange the materials need by and produced by the increasing internal volume. Like commuters into and out of a growing city, if the roads stay the same, but the volume of traffic increases, sooner or later there will be gridlock. Cells cannot, therefore increase beyond certain practical limits to two reasons; speed of diffusion and surface area / volume ratios. There is, actually, a way cells use to limit the effects of the surface area / volume ratio. In cells specialized for exchanging materials to the outside (like those found in the intestines), the surface area is dramatically increased by tiny, fingerlike, extensions of the surface (called microvilli) which don't add much to the volume, but add a lot to the surface area. These cells need this extra surface to absorb nutrients from the intestines, but even they cannot change the rate of diffusion, so these cell to must also remain microscopically small. 
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