File:Messages-Do-Diffuse-Faster-than-Messengers-Reconciling-Disparate-Estimates-of-the-Morphogen-Bicoid-pcbi.1003629.s004.ogv

English: Free particle diffusion. This video shows the results of a simulation of a system of freely diffusing particles with . In this simulation a bolus of 1,875 fluorescent particles is added to the central cube in a background of 20,000 particles that are uniformly distributed over the cubic simulation volume (see Materials and Methods for details). The video has three panels. In each of them we project the dimension into the plane that is shown. The left-most movie shows the local deviation in concentration of all particles above the equilibrium concentration. The fluctuations in the equilibrium baseline are apparent near the borders. The center movie shows the concentration of the added (fluorescent) particles. In this case the concentration of added particles near the borders begins at zero so the fluctuations of this quantity in the early part of the movie are small near the borders. As time passes and the particles spread those fluctuations grow. The right-most movie shows the actual (2D projection of the) positions of the added particles. We quantify the rate of spread of the distributions in the left and center panels by means of the second moments, , (Eq. (12)) computed using all the particles () and only the (fluorescent) added ones (), respectively. Both second moments grow linearly with time with the same slope as shown in Figs. 1 A and 1 B. This slope coincides with that of the averaged mean square displacement of the individual particles Fig. 1 C. From the slopes we obtain which agrees, in turn, with the diffusion coefficient of the particles that was used in the simulation. In the case of free diffusion the rate at which a perturbation spreads out with time and at which the mean square displacement of the individual particles increases is ruled by the same diffusion coefficient.