Progress in Biophysics and Molecular Biology, Volume 121, Issue 1, May 2016, Pages 35-44.

Consider a virtual beacker constitued of \(500\times 500\) loci, all initally at the stage \(0\). Each of these loci is subject to evolve through a double discrete in time random walk, with forward and backward evolutions, and with absorbing final stages \(n_1\) and \(n_2\) at the end of these two chains. These chains have respective length \(n_1\) and \(n_2\) and are figured just below.

\[ \begin{matrix} n_2 & \leftarrow[]{p_2} & \dots & 2_2 & \leftrightharpoons[1-p_2]{p_2} & 1_2 & \leftrightharpoons[1-p_2]{1/2} & 0 & \rightleftharpoons[1-p_1]{1/2} & 1_1 & \rightleftharpoons[1-p_1]{p_1} & 2_1 & \dots & \rightarrow[]{p_1} & n_1\\ \\ \end{matrix} \]

Loci at the stage \(0\) evolve

- with probability \(1/2\) to the stage \(1_1\),
- with probability \(1/2\) to the stage \(1_2\).

- with probability \(p_j\), it evolves forward to the stage \(i_j+1\),
- with probability \(1-p_j\), it evolves backward to the stage \(i_j-1\).

- Choose a set of parameters (\(p_1\), \(p_2\), \(n_1\) and \(n_2\)) or one in the predefined list.
- Click 'Complex formation' to initiate the evolution of the whole beacker.
- Click 'Competitive binding' to count the repartition of loci through the chains (normalized abscissae).