jotin gogoi

There are simple equations that reveal a lot about biology. For example, given the concentration of a molecule, one can quickly calculate the average spacing between those molecules in a cell. The equation involves an assumption; namely, that a cell can be sliced into a cube, with one molecule sitting in the center of each box. Each box has a side length of d, and a volume of d × d × d, or d³. Imagine zooming out of this hypothetical cell. The whole cell has a volume, V, and contains N molecules, which means it has N little boxes. So the total volume of the cell is given by the volume of one box times the number of boxes: V = N × d³ Rearranging this equation, we get: d³ = V / N Now, the term N/V is just the same thing as density, or the number of molecules per unit volume. We can therefore flip it around and call it c, or "concentration." Rearranging once more, then, we get: d³ = 1 / c, or equivalently, d = c^(-1/3) This is a beautiful little equation! Remember that c is the concentration of a molecule and d is the average spacing between those molecules. Now we can use this to figure out how tightly packed a particular molecule is within the cell. Consider glutamate, which has a concentration of about 100 millimolar, or 0.1 moles per liter. Multiply by Avogadro's number and convert (1 cubic meter = 1,000 liters), and we get c = 6.022 × 10²⁵ m⁻³. Finally, if we take the inverse cube root, we get d = 2.55 nanometers. So each molecule of glutamate sits, on average, about 2.55 nanometers from its neighbors, which is a distance smaller than the width of a typical protein. It's fun to repeat this with other things, too. Try it for water, ATP, ribosomes, and so on. If you wanted to recreate a David Goodsell painting (see below), you could also use this equation to calculate how far apart each object in the painting ought to be!