Likewise for the V and J segments of light chain genes. Using similar calculations, there are about 1200 possible kappa chains. There is also variability of the exact position at which different segments join. See Kuby Figure 5-14. This flexibility can lead to nonproductive rearrangements ie when the gene segments are joined out of phase.
Nonproductive rearrangements appear to occur at high frequency.
If one allele rearranges nonproductively, the cell can go on to rearrange the other allele and may generate a productive rearrangement. J rearrangement must take place before a light chain V-J rearrangement can occur. The kappa light chain is thought to rearrange after the heavy chain. If kappa rearrangement is nonproductive for both alleles, the lambda chain genes will rearrange. If all light chain arrangements are nonproductive, the B cell presumably ceases to mature.