Figure 2.

The trajectory of a diffusing protein is a ‘random walk’. A 3-D random walk of 10⁶ steps, each of length 1, is shown here as a projection on a 2-D plane. The end-points of the walk are at (0,0) and at (–300,–300). The overall size of the random walk is roughly the square root of the number of steps, or ∼1000 steps, as expected from the mean square law R² = Dt. Although this law holds quantitatively only in statistical terms when applied to many random walks, the overall size of one random walk is usually reasonably well estimated by the mean square law. It is important to note that the random walk has many voids; it does not completely explore the 3-D region it extends through.