A cell is like a library where thousands of books are copied every day. Molecular machines, polymerases and ribosomes, slide along a template chain and assemble a copy, link by link. These machines have several states: they can slow down, make mistakes, or switch. Previously, calculating such a process took hours.
The authors found an exact mathematical solution. They represented the growth of the copy as the motion of two iterations: one runs forward along the template, the other backward. Together they converge to the answer, like two hands counting beads on a rosary. This is not an approximation but a rigorous formula. The method was tested on a numerical example: it turned out to be many times faster than conventional computer simulations.
Now biologists will be able to predict more quickly how often the machine makes mistakes and how template length affects speed. This is important for understanding diseases related to malfunctions of the cell's copying apparatus.
A single ribosome can add up to 20 amino acids per second — faster than you can blink.