File:Messages-Do-Diffuse-Faster-than-Messengers-Reconciling-Disparate-Estimates-of-the-Morphogen-Bicoid-pcbi.1003629.s005.ogv

English: Effective diffusion. This video shows a simulated experiment in which a bolus of fluorescent particles is added to the central cube in a cube in which particles diffuse and react with immobile binding sites according to Eq. (1). Particles and sites are initially uniformly distributed and at chemical equilibrium (see Materials and Methods for details). As in Video S1 the left-most panel shows the concentration of all the particles above equilibrium. The center panel shows the concentration of the added (fluorescent) particles. The right-most panel shows (a 2-dimensional projection of the) positions of the added particles. This is what would be observed if each of the added particles could be identified. The deviation from equilibrium of the concentration of all the particles smooths out so fast that is only obvious in the earliest frames of the left most panel. This smoothing occurs much faster, on the other hand, than that of the deviations in the fluorescent particle density. This difference becomes quantifiable in Fig. 2 where we show the second moments (Eq. (12)) computed using all the particles () in A and only the (fluorescent) added ones () in B. In both cases the second moments eventually depend linearly on time. From the slopes we obtain a diffusion coefficient that is more than 10 times faster in Fig. 2 A than in Fig. 2 B. The latter, on the other hand, is roughly the same as the one that is derived from the slope of the mean square displacement shown in Fig. 2 C. These observations agree with the results of [5] (see also supplementary text S3). Namely, according to the theory, the deviation from equilibrium of the total particle concentration spreads with the collective diffusion coefficient, , and that of the (fluorescent) added particles with the single molecule coefficient, , which also rules the time dependence of the individual particles mean square displacement. For the simulation parameters, it is about 14 times faster than the single molecule diffusion coefficient, , which agrees with what is observed in the panels and in Fig. 2.