In BIOL 182, we learned of secondary messengers, which are intracellular signaling molecules released in response to extracellular triggers. A molecule, perhaps a hormone of some sort, would bind to a receptor protein on the cell membrane, which would “turn on” proximal G-proteins by allowing them to switch their bound GDP with GTP. At this point, the G-proteins detach from the cell membrane, and bind to proteins classified as “primary effectors” along the inner cell membrane. These primary effectors can release their own signals via a biochemical reaction, signals being other molecules that can create a response within the cell by binding to other proteins. These signals, and all biochemical reactions in general, are governed at least in part by Brownian motion; without random walking, there can be no collisions between substrates and enzymes, or even between simple molecules to initiate chemical reactions.
Below is a simple calculation of the time it would take for the average cyclic adenosine monophosphate molecule, a common secondary messenger, may diffuse from near the cell membrane 1-dimensionally into the nucleus, where it will interact with DNA-binding proteins, under the assumption that there are no other larger particles hindering its random walk (a very ideal scenario!). All values were approximated with quick online research, with the radius of the substrate (assumed spherical) being calculated from the approximated surface area derived from a molecule calculator.
The time it would take without any helpful or detrimental interactions to reach the nucleus from near the cell membrane would be 0.61 seconds, assuming 1-dimensional motion. This seems a little slow, but as this value was obtained using approximations and discounting all possible cell process that could have hindered or progressed this substrate’s journey to the nucleus, it’s difficult to say what the actual time period will be.
Another thing to think about is how we can predict reaction rates in general; with a higher concentration of proteins and substrates would come greater rates of reaction, due to the larger number of particles participating in random walking, which would increase the chances of a collision and meaningful interaction occurring. Reaction rates in high school and early college courses are simply given to us as detached values to plug and chug, but it may be interesting to consider the underlying phenomenon behind these otherwise uninteresting numbers.
Though obviously cell processes are obviously much more mediated and complex than a mess of proteins and substrates colliding with one another, Brownian motion nonetheless sets the foundation for many cellular processes.