Second moments of particle distributions and mean square displacements obtained from a simulation of particles that diffuse and react with immobile binding sites.

<p>Similar to Fig. 1 but for the simulation of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003629#pcbi.1003629.s005" target="_blank">Video S2</a> which corresponds to a system of particles that diffuse with and react with immobile binding sites according to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003629#pcbi.1003629.e004" target="_blank">Eq. (1)</a>. The simulation parameters are such that the effective diffusion coefficients defined in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003629#pcbi.1003629.e010" target="_blank">Eq. (2)</a> are and . As in the simulation with the freely diffusing particles, the simulation starts when a bolus of fluorescent particles is added to a background of (non-fluorescent) particles that are initially spatially uniform and in chemical equilibrium with the binding sites. Also in this case we compute two second moments and the averaged mean square displacement of the added particles to quantify relevant properties of the simulation. For more details see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003629#s4" target="_blank">Materials and Methods</a>. <b>A</b>: (shown in gren) computed using <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003629#pcbi.1003629.e479" target="_blank">Eq. (12)</a> with the number of all particles in the box. Linear fit (shown in black). <b>B</b>: (shown in red) computed using <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003629#pcbi.1003629.e479" target="_blank">Eq. (12)</a> with the number of fluorescent particles in the box. Linear fit (shown in black). <b>C</b>: The mean of the squared displacements of the added particles (shown in red) computed using <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003629#pcbi.1003629.e461" target="_blank">Eq. (11)</a>. Linear fit (shown in black). As explained in supplementary text 0.3, in this case, the diffusive behavior sets in after a transient. Once this behavior is reached, diffusion coefficients, , and , can also be estimated by taking 1/6 of the slope of the three fitting curves. Differently from the situation of freely diffusing particles, in this case, the estimates differ from one another. They yield A: , B: , C: . According to the theory (see supplementary text 0.3), and and should be given by <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003629#pcbi.1003629.e010" target="_blank">Eqs. (2)</a>. In fact, the values derived from the simulation satisfy and are pretty close to the theoretical values, and .