We know that everything, living or non-living, is made out of molecules. Molecules are random walkers that keep bumping into each other and changing their trajectory, shape and even their chemical identity. How, then, does a collection of such random walkers assemble into incredibly organized and precise molecular machines that make a living system function? In this course we will learn how to describe random walkers using probability theory and primarily computer simulations. Using the Python programming language, we will simulate the behavior of biological molecules inside a living cell.
GAMBLER'S RUIN
Two gamblers (G1 and G2) are playing a game where they each start out with some money (M1 and M2). The players flip a single coin to decide who wins one round of their game. The loser has to give the winner $1. They keep repeating the coin flip until one player has all the money and one player has no money - they have been ruined.
What is the probability that Gambler 1 is ruined in a game?
How many rounds will they play until a gambler is ruined?
RANDOM WALKS AND MOLECULAR MOTION
In very small cells, such as bacteria, completely random walks are very efficient, and the molecules can move from wall to wall multiple times in a short time period. However, in larger human cells complete randomness is too slow. This issue is solved by making many many copies of molecules (like how there are many many copies of the same enzyme and substrate in a molecule), which increases the chances of collision. However, there is a limit to the efficiency of the copies. Instead, the random walks are biased heavily in one direction, an example of which can be seen in neuron cells.