Development of mutual information given different initial and stationary distributions.

<p>Three different initial probability distributions (A1-3) and three different stimulation-conditions each yielding a specific stationary distribution (B4, C4 and D4). Dependent on the different combinations of these distributions and conditions, the development of the probability distribution of synapses <i>p</i>[<i>S</i>(<i>t</i>)] differs (gray scale in central panels). This results in different time courses of the mutual information (red) between initial number of synapses <i>S</i>(0) and number of synapses <i>S</i>(<i>t</i>) at time point <i>t</i>. In general, for all conditions, except <i>wp</i>-condition, mutual information decays to zero after 10⁷ to 10⁸ time steps. For the <i>wp</i>-condition (panels C1-3) the same decay occurs, but to a non-zero plateau. On this plateau information about the initial number of synapses is preserved up to 10⁹ to 10¹⁰ time steps. The height and duration of this plateau can be reproduced by analytical methods from a simplified system (blue dashed line, see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004684#sec010" target="_blank">Models and Methods</a>).