Simulation of L chain rearrangement

We model light chain (L chain) gene rearrangement. The key assumption is that all L chain alleles and isotypes act independently of each other.  The probability of k or l rearrangement controls the actions of the six possible targets, (two ks and four ls), all of which could (albeit rarely) rearrange simultaneously. One step represents the time it takes to rearrange at least one k or l chain, although the probabilistic aspect of rearrangement may also lead to cycles in which no allele is rearranged.  The result of the rearrangement event is then evaluated. If successful, the rearranged state is tallied.  If unsuccessful, the cell may either die or undergo further rearrangement. The probability of death is called the "crash factor".  Outcome categories for either k or l are: unrearranged (0), productively rearranged (+), unproductively rearranged (-), and anti-self (AS). RS deletion of the k locus is included in the (k-) category.  Along with these categories, the Jk usage of each k allele is tallied. In our earlier model, a cell produces one rearrangement and then tests the result for viability (see Figure 1A). Even though rearrangement at one allele may precede the other, there must be some temporal overlap and thereby examples of allelic and isotypic inclusion can be explained.