Marc Roussel, Department of Chemistry and Biochemistry, University of Lethbridge
28 October 2007
Howe's paper presents a very interesting comparison of directed active transport of a signal to diffusional transport, both without and with inactivating dephosphorylation of the signal. The results highlight the limitations of diffusional transport, particularly in large cells.
In his simulations of diffusion, Howe apparently chose his spatial step length, and hence the length of his time steps, by a scaling argument involving the mean speed and diffusion coefficient. This resulted in spatial steps of about 10-12m. This is exceedingly conservative: The radius of an atom is of the order of an Angstrom (1Å = 10-10m). Thus, Howe's diffusional steps are two orders of magnitude smaller than the size of a single atom. Since he is modeling the diffusional motion of a macromolecule as a whole (and not of side chains or other atomic-scaled features), it would be entirely reasonable to use a step size of the order of 1Å. Another way to think about this issue is that distances between molecules in solution are of the order of a few Angstroms. For example, hydrogen bonding distances are typically about 3Å. That being the case, moving a molecule an Angstrom in each step, and perhaps even a few Angstroms, is certainly not unreasonable. Using these much larger step sizes would allow for much more efficient simulations. Indeed Howe noted that he was strongly limited by computational time in what he could accomplish.
Theoretical Biology and Medical Modelling
Step sizes in simulations of diffusion
28 October 2007
Howe's paper presents a very interesting comparison of directed active transport of a signal to diffusional transport, both without and with inactivating dephosphorylation of the signal. The results highlight the limitations of diffusional transport, particularly in large cells.
In his simulations of diffusion, Howe apparently chose his spatial step length, and hence the length of his time steps, by a scaling argument involving the mean speed and diffusion coefficient. This resulted in spatial steps of about 10-12m. This is exceedingly conservative: The radius of an atom is of the order of an Angstrom (1Å = 10-10m). Thus, Howe's diffusional steps are two orders of magnitude smaller than the size of a single atom. Since he is modeling the diffusional motion of a macromolecule as a whole (and not of side chains or other atomic-scaled features), it would be entirely reasonable to use a step size of the order of 1Å. Another way to think about this issue is that distances between molecules in solution are of the order of a few Angstroms. For example, hydrogen bonding distances are typically about 3Å. That being the case, moving a molecule an Angstrom in each step, and perhaps even a few Angstroms, is certainly not unreasonable. Using these much larger step sizes would allow for much more efficient simulations. Indeed Howe noted that he was strongly limited by computational time in what he could accomplish.
Competing interests
None.