Figure 7. Probabilistic analysis of Pcdh and Dscam1 recognition.

(A) Probabilities of incorrect non-self recognition between two cells as a function of the number of isoforms expressed per cell. Lines in the plot appear jagged due to the integer number of tolerated isoforms.

(B) Schematic representation of recognition units for different cis-multimeric states. Two cells share one common Pcdh isoform (blue) and one distinct isoform (red and yellow). Unique multimers are shown and the number of permutations for each multimer (e.g. ×2) are given.

(C) The relationships between common-isoforms and common-recognition units for different multimeric states. Vertical dotted lines mark the cases of 67% common Pcdh isoforms and show the corresponding percentage of common recognition units for monomers, dimers, trimers and tetramers. For the same percentage of common isoforms, larger multimers have a smaller percentage of common recognition unit.

(D) Monte-Carlo simulations were used to estimate the average number of copies of each multimer in a single cell. For the case of 15 Pcdh isoforms expressed per cell, the average number of copies of each multimeric recognition unit generated by the stochastic assembly of Pcdh isoforms into multimers is shown as a function of the number of copies of each isoform.