Page 252 - Applied Probability

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11. Radiation Hybrid Mapping
The Cox et al. [10] data mentioned earlier involves 99 hybrids typed at 14
marker loci on chromosome 21. Examination of these data [5] shows that
the markers D21S12 and D21S111 are always concordantly retained or lost.
Since order cannot be resolved for these two loci, locus D21S111 is excluded
from the analysis presented here. Table 11.1 presents the 10 best orders
based on the maximum likelihood criterion. The difference in maximum
loglikelihoods between the best order and the current order is given in the
column labeled ∆L. Logarithms here are to the base 10, so a difference of
3 corresponds to a likelihood ratio of 1,000. The minimum obligate breaks
criterion is given in the column labeled Breaks. It is encouraging that the
three best maximum likelihood orders are also the three best minimum
obligate breaks orders. Evidently, some of the better orders involve complex
rearrangements of the best order.
The diagram below gives the estimated distances between adjacent pairs
of loci under the best order. These distances are expressed in the expected
numbers of breaks × 100 between the two loci per chromosome. (One ex-
pected break is one Ray, so the appropriate units here are centiRays,
abbreviated cR.) In Table 11.1 and the diagram, the loci D21S16, D21S48,
D21S46, D21S4, D21S52, D21S11, D21S1, D21S18, D21S8, APP, D21S12,
D21S47, and SOD1 are numbered 1 through 13, respectively.
Interlocus Distances for the Best Order

7.6 7.9 19.4 27.3 64.4 18.0 55.6 34.9 11.1 23.5 36.2 25.3
1 − 2 − 3 − 4 − 5 − 6 − 7 − 8 − 9 − 10 − 11 − 12 − 13

11.6 Polyploid Radiation Hybrids

Polyploid radiation hybrid samples can be constructed in several ways. For
instance, one can pool different haploid clones and test each of the pools
so constructed for the presence of the various markers to be mapped. If c
clones are pooled at a time, then a pool contains fragments generated by
c independently irradiated chromosomes. The overlapping nature of a pool
obscures fragment retention patterns. Balanced against this information
loss is the information gained by attaining a higher effective retention rate
per locus per pool.
Another method of generating polyploid samples is to expose normal
human diploid cells to a lethal dose of gamma irradiation. Some of the
irradiated cells can again be rescued by hybridization to unirradiated cells
from a rodent cell line. If the rodent cells are deficient in an enzyme such as
HPRT, then only the hybrid cells will grow in a culture medium requiring
the enzyme. Thus, the design of the diploid experiment is almost identical to
the original haploid design. The diploid design carries with it the advantage