A high resolution CEPH crossover mapping panel and integrated map of chromosome 11
A high resolution CEPH crossover mapping panel and integrated map of chromosome 11Pamela R. Fain, Edward N. Kort1, Cherine Yousry2, Michael R. James2 and Michael Litt3,*
Department of Medicine, University of Colorado Health Sciences Center, Denver, CO 80262, USA, 1Division of Genetic Epidemiology, University of Utah, Salt Lake City, UT 84108, USA, 2Wellcome Trust Centre for Human Genetics, Headington, Oxford, UK and 3Department of Biochemistry and Medical Genetics, Oregon Health Sciences University, Portland, OR 97201, USA
Received May 15, 1996;Revised and Accepted July 22, 1996
High resolution (0.1 cM) CEPH crossover mapping panels were constructed for chromosome 11. These panels will facilitate a transition from top-down physical and genetic mapping strategies to integrated breakpoint mapping strategies. Novel methods, which differ from other methods in overcoming the limitations of incomplete heterozygosity and variable marker density, were developed for creating the panels and integrated maps. This made it possible to identify and sublocalize the majority of crossovers in 61 families. The panels were used to map 139 microsatellite markers. A semi-integrated map and a fully-integrated map were constructed by combining these data with data from CEPH 7.1 and then integrating data from the radiation hybrid (RH) map. Genetic lengths estimated from the mapping panels were similar to the estimates obtained when all recombinant and non-recombinant offspring were included (189.4 cM in females and 126.1 cM in males), indicating that genetic distances are stable at this high marker density. The maps have a cM density of 0.62. The distance between ordered markers is 1.39-2.92 cM depending on the criterion for order and the extent of map integration. The 2D maps provide the resolution and flexibility needed to enhance current applications such as positional cloning and mapping complex disorders; while the mapping panels will greatly improve the resolution, reliability and efficiency of future genetic mapping.
Over the last 5 years, there has been significant progress in constructing genetic and physical maps of the human genome. As a result, the once arduous task of linkage mapping for monogenic disorders can be done with limited effort as the first phase of the Human Genome Project draws to a scheduled close (1 ). Previous efforts to construct physical and genetic reference maps have relied on top-down strategies and analyses, which have been effective in circumventing the problems of creating a map without any knowledge of position for either markers or breakpoints. However, the use of these methods has also had predictable repercussions including gaps in the map, poor reliability of local ordering, and difficulties in map integration. Such problems often impede progress in the critical steps between linkage detection and positional cloning and make it difficult to achieve the map resolution needed to detect linkage for complex disorders.
The development of a reliable high resolution map will require a shift from traditional methods to direct breakpoint mapping as a means of improving the reliability of local ordering on physical and genetic maps (2 ). A transition to breakpoint mapping will also improve the efficiency of physical and genetic mapping and the ability to integrate information from diverse sources (3 ). The substrates for breakpoint mapping may be the ends of tangible fragments such as YACs or radiation hybrids (RHs), or the ends of meiotic fragments which can be inferred by studying inheritance patterns in families (4 ,5 ). Public databases and published maps now provide the resources necessary to order markers and to construct maps by directly positioning the markers in intervals between breakpoints. In theory, the number of breakpoints and crossovers sets a strict upper limit to the resolution that can be obtained by breakpoint mapping (6 ,7 ); however, in practice, the low and uneven distribution of markers characteristic of most breakpoint or family resources are major barriers to achieving maximum resolution. In addition, inadequate marker density can limit the reliability of breakpoint resources and subsequent mapping inferences (3 ).
This study describes high resolution CEPH crossover mapping panels and integrated maps of chromosome 11, which were created using novel methods for combining genetic and physical mapping data from diverse sources. By giving special treatment to the problems of incomplete heterozygosity and uneven marker density, these methods preserve potential resolution, maximize efficiency and produce highly reliable maps. This approach to high resolution mapping is an extension of previous efforts leading to the first crossover-based map of a human chromosome (chromosome X; 3 ); however, the X map was generated using CEPH data for all family members, while the map of 11 (Fig. 1 ) was constructed using data from mapping panels with many of the non-recombinant offspring excluded.
Although other groups have made progress in developing CEPH crossover/breakpoint panels and map construction algorithms (8 ,9 ), these methods differ from the present study in relying on fixed boundaries, a requirement which can cause a significant reduction in potential resolution. For example, empirical results have shown that the loss of crossovers due to uninformative boundary markers reduces the resolution of the CEPH resource to less than 30% of its potential (10 ). Further, the reliability of breakpoint/crossover mapping depends on informative marker density, which varies for different regions and for different recombinants in the same region. This makes it unlikely that reliable maps can be produced by non-statistical methods (8 ) which do not incorporate a marker density (gap) criterion. Statistical methods for breakpoint mapping which allow for marker density (9 ) do so at additional expense in terms of resolution. By comparison, the 2D maps of X (3 ) and 11 (this study) have a higher resolution than most other genetic or physical maps of polymorphic markers reported to date. Similar maps can be generated for all other chromosomes using mapping panels or other data, but this will require methods which eliminate reliance on a fixed set of markers. The development of such methods is among the goals of the new 5-year plan for the US Human Genome Project (11 ).
Chromosome 11 was selected as an ideal target for determining the feasibility and effectiveness of the mapping panel approach. The distal end of 11p was among the first mapped regions of the genome and many genes of medical significance have been mapped to chromosome 11 since that time. Five different regions of the chromosome (11p15, 11p13, 11q13, 11q22-q23 and 11q24) have been given extensive attention due primarily to their association with neoplasia (12 ). Chromosome 11 also houses the genes for several developmental disorders and has been implicated in a number of complex diseases, including atopy (q12-q13), schizophrenia (q14-q22) and insulin-dependent diabetes (p15 and q13-q14). Hailed as a gene-rich chromosome based on an excess of ESTs (2 ), chromosome 11 is likely to maintain the priority it has been given in physical and genetic mapping activities, including positional cloning. Based on the experience with the 2D map of the X, which has been used extensively as a primary reference map (13 ), the 2D map of 11 will provide the utility and flexibility needed to confirm and integrate information from many different sources. The maps of both chromosomes have been incorporated into a genetics database (GENLINK; H. Donis-Keller), which can be accessed using the URL http://www.genlink.wustl.edu.
Crossover mapping panels are created by identifying recombinant offspring and assigning each recombination event to a mapping interval. This requires data for an initial set of confidently ordered markers. The mapping panel for each interval consists of family units including a minimum of two parents, one recombinant offspring and a non-recombinant sibling (4 ). New markers which have also been sublocalized to a mapping interval can be efficiently mapped to higher resolution by typing the marker on the mapping panel for that interval. The use of the panels is based on a simple principle: markers on one side of a crossover are identical by descent (IBD) in the two offspring while markers on the opposite side of this crossover are non-identical by descent (NIBD) in the two offspring. This principle depends on the assumption of a minimum crossover solution to the recombination events and error-free data; i.e., there must be a one-to-one correspondence between recombination and crossing over. The resolution and reliability of the panels depends on the number of crossovers included and on marker density.
In practice, the creation and use of CEPH mapping panels is complicated by the complexities of the data, caused in part by incomplete heterozygosity but compounded greatly by significant (1-2%) error rates and by the typing strategies used in different labs. Data for 200 loci (255 markers after excluding nine with no known `D segment' assignment) were available from version 7.1 of the CEPH database; however, many of the markers were not typed in the complete set of families. DNAs from 541 individuals in 40 families (some of which are related) have been distributed to over 100 CEPH collaborators; and the majority of RFLP markers have been typed in this set of families. DNAs for an expanded panel of 863 individuals in 61 families are available; however, only a few labs have submitted typing data for these families. The reverse practice of typing a subset of eight families (136 individuals; 14 ,15 ) or 15 families (237 individuals; 16 ) has become common in recent years and the data for most of the microsatellite markers (excluding `index' markers) are restricted to these families.
The mapping panels for chromosome 11 were created using CEPH data for 61 families. The majority (172 loci) of the 200 loci from CEPH 7.1 could be confidently sublocalized to a 10-15 cM interval using the RH map (17 ) and/or by applying a series of standard prescreening and map construction routines (see Methods). The next step was to identify recombination events in 61 families and to assign each event to a mapping interval. The method relies on an adjacency matrix, which is generated by one of the prescreening routines (BINS; see Methods). The adjacency matrix stores the number of ordering events (crossovers) for all possible pairs of 172 bin-assigned markers in the form of a weighted directed graph. Conflicts in bin assignments or local ordering of markers are detected as loops in the graph. The information stored in the matrix can be used to sublocalize a recombination event between any pair of markers to an interval the size of the genetic distance between the markers. Unlike methods which rely on informativeness for a fixed set of ordered markers, the majority of crossovers are retained in the panel when the prescreening programs are used to identify recombinants and order the markers; and the adjacency matrix is then used to sublocalize the crossovers.
The third and final step in the analysis is to evaluate each chromosome to determine if an offspring is eligible for the mapping panel. Eligibility depends on the density of informative markers, or more specifically, on a gap criterion. The map construction algorithms depend on the assumption that the correct marker order is one that minimizes the number of crossovers. Stated differently, any even number of crossovers (0, 2, 4, . . . ) may have occurred in the gap between a pair of non-recombinant markers but the map construction algorithms assume that no crossovers have occurred. Similarly, any odd number of crossovers (1, 3, 5, . . . ) may have occurred in the gap between a pair of recombinant markers but the map construction algorithms assume that exactly one crossover has occurred. Ordering errors caused by violations in the minimum crossover assumption can be reduced by adjusting the gap criterion.
By combining a gap criterion with the flexibility of the adjacency matrix, we were able to identify the majority of crossovers and to construct a highly reliable end map without sacrificing resolution. The initial gap criterion of 30 cM was based on theoretical models assuming a 1% error rate and different map functions (18 ). The criterion was later reduced to 25 cM based on empirical results described below. Using either criteria, the mapping panels for chromosome 11 created by these analyses include the vast majority of over 1500 crossovers from 61 families. The upper limit to the resolution of the mapping panels is given by the average distance between the crossovers, which is ~0.1 cM. However, the resolution that can be obtained in practice depends on the informative marker density for specific recombinants.
Mapping panels for 40 CEPH families were typed for 139 markers, which had been sublocalized to 10-15 bins based on RH mapping (17 ). The set of 139 markers included 51 markers for which the data duplicated or supplemented data from CEPH 7.1. In addition to potentially adding 88 new markers to the genetic map of chromosome 11 and improving the map resolution for 51 other markers, these data proved very useful for validating the algorithms for panel creation and map construction, determining a `hit rate' for identifying errors, replacing the initial gap criterion with a value based on empirical findings, and determining the empirical efficiency and resolution of the mapping panel approach.
The index map of chromosome 11 (19 ) was used as a starting point for this application. The recombinants were identified by visual inspection of an output from the CHROMPIC option of CRI-MAP, which displays the grandparental origin of the index markers on each offspring chromosome. All recombinants involving any pair of informative markers were included in the panels provided the recombinant markers were <15 cM apart. As summarized in Table 1 , a total of 583 recombinants meeting the 15 cM gap criterion were identified. The recombination events were positioned into 13 overlapping intervals averaging 10-15 cM in length with ~45 recombinants per interval. The recombinants account for 55% of the expected crossovers in the 40 families screened and 37% of the expected crossovers in 61 families.
Table 1 gives the approximate location of each interval based on the flanking index markers which were informative in recombinants. In the absence of fixed boundaries, the localization of some of the recombinants (crossovers) overlapped two intervals; e.g., the crossover in an offspring who is recombinant for HBB and D11S419 was arbitrarily assigned to region B in Table 1 ; however, the crossover in this case may have occurred proximal to the most distal crossover in region C. The mapping panel for each interval consisted of an average of 123 samples.
The data for the panel-typed markers were merged with the data for 61 families, which had been processed in the previous analysis. The combined data were used to update the adjacency matrix in preparation for conflict resolution and map construction. Prescreening routines report two types of suspicious observations: (i) pairs of non-recombinant offspring should have the same inheritance pattern (IBD or NIBD) for all markers; pairs which disobey this rule are flagged; and (ii) a loop in the adjacency matrix signaling a conflict in marker order is flagged. Suspicious data may be caused by errors or by hidden crossovers. Inconsistencies and order conflicts caused by hidden crossovers can be eliminated by using a more stringent gap criterion. Using a gap criterion of 30 cM, 25 pairs of non-recombinant offspring were flagged and the marker data were reevaluated. Errors were found in 18 (72%) cases. In cases of order conflicts, the data for both markers were flagged. The hit rate in these cases was much lower (34%), as expected since the conflict usually resulted from an error in only one of the markers. Nearly all of the other observations flagged as suspicious could be removed by reducing the gap criterion to 25 cM. Based on these results, the analyses described in the previous section were done using a gap criterion of 25 cM.
Marker order information can be treated as a weighted, directed graph represented by an adjacency matrix; the 2D map may be viewed as a graphically processed adjacency matrix. The 2D maps were constructed using graph theory to generate a consistent linear order for all markers (see Methods). Based on previous studies (3 ), a confidence criterion of two crossovers was used to establish marker order; the order of markers separated by only one crossover is considered provisional. Marker order derived from crossovers, physical breakpoints, or any other criterion can be used to construct an adjacency matrix which is then merged with the matrix generated from genetic data. For the 2D maps, the adjacency matrix for the CEPH data was merged with an adjacency matrix generated from marker orders on the RH map (17 ). Two types of maps were generated: a semi-integrated map which distinguishes different sources of information (available from the GENLINK database, URL http://www.genlink.wustl.edu) and a fully-integrated map (Fig. 1 ) which does not distinguish different sources of information. The RH and genetic maps were in conflict for six pairs of markers, all of which were provisionally ordered (one crossover) on the genetic map. Based on previous studies (3 ), markers separated by one crossover will often surpass a likelihood criterion of 1000:1 odds for order at this marker density. The results presented here substantiate previous conclusions that this criterion should be abandoned for high resolution genetic mapping.
Maximum likelihood estimates of map distances gave genetic lengths of 126.1 cM in males and 189.4 cM in females. These estimates are similar to the estimates obtained for the 172 CEPH 7.1 loci with all family members included in the analysis (125.8 cM in males; 189.5 cM in females). The length estimates are also comparable to the estimates reported in other studies (16 ,18 ,20 ). These results indicate that distance estimates are stable at this marker density despite an overrepresentation of recombinant offspring for the panel-typed markers. The most distal marker on 11p (D11S2071) is derived from a telomeric YAC clone and is probably within 140 kb of the telomere. The distance between the telomere and the most distal marker on 11q is unknown.
Map resolution, measured as the distance between adjacent markers is 2.92 sex-averaged cM for confidently ordered markers (>1 crossover) and 1.75 cM for provisionally ordered markers (one crossover) on the semi-integrated map. When the physical and genetic maps are completely integrated (Fig. 1 ), the distance between confidently ordered markers is reduced to 2.3 cM. Taking a less stringent criterion of one crossover or 10:1 odds on the RH map, the distance between adjacent markers is 1.39 cM. The average distance to the nearest marker was similar for panel-typed markers and other markers.
The results of comparing the resolution of different maps understate the importance of informative marker density in determining map resolution. The most recent CHLC map of chromosome 11 shows 43 uniquely ordered markers (>1000:1 odds) with an average of 3.6 cM between markers (16 ). Data for 261 markers typed in 15 families (310 meioses) were reportedly included in this analysis. Nearly half of the markers (126/261) are genes or RFLPs with relatively low heterozygosities (~30%) while the remainder are STRPs with higher heterozygosities (~70%). The set of 261 markers thus provides ~132 informative markers per meiosis. By contrast, the most recent Genethon map has an average distance of 1.5 cM between confidently ordered (>1000:1 odds) markers (20 ). This analysis included 273 markers with an average heterozygosity of 70%. Although the markers were typed in only eight families, there were ~191 informative markers per meiosis. The 2D analysis reported here included 61 families with extreme variation in informative marker density between different families. The relatively poor resolution of the CHLC map can be attributed to lower marker density to begin with and to the use of computer algorithms which eliminate 75-85% of the data during the process of map construction. The higher resolution of the Genethon map compared to the 2D map is partly due to differences in informative marker density and partly due to the use of a less stringent (>1000:1 odds ~1-2 crossovers) criterion for ordering markers on the Genethon map. The effect of slight differences in genetic length estimates for the three maps is negligible. It should also be noted that a much higher density of markers will be needed to approach the potential resolution of the CEPH crossover resource (0.5, 0.3, 0.15 and 0.1 cM for the 8-, 15-, 40- and 61-family sets, respectively).
Figure 2 shows a comparison of distances in cM from the genetic map (Fig. 1 ) and physical distances in cR9000 (a 1 percent frequency of radiation-induced breaks between a pair of markers after exposure to 9000 rads of X-rays) from the RH map (17 ). Estimated lengths of 2867 cR and 144 Mb for chromosome 11 lead to an estimate of ~50 kb per cR, which may be distorted in the centromere region due to preferential retention of centromere-proximal DNA in RHs. Genetic lengths of 189.4 cM in females and 126.1 cM in males lead to estimates of ~762 kb per cM in females and 1143 kb per cM in males. The relationship between the cM and cR distances differs for males and females, with excess recombination at the telomeres apparent only in males. In females, there is a linear relationship between distances in cM and distances in cR except for a slight restriction in recombination near the centromere. If the observed trends extend to the telomeres, the difference between genetic lengths in males and females is likely to diminish or disappear as more distal markers are found. The results of comparing genetic and physical distance are consistent with cytological evidence for chiasma localization at the telomeres in male meioses (21 ), and to some extent, with cytological evidence that male and female genetic maps are complementary (22 ).
All of the 139 panel-typed markers were genotyped by PCR in the one lab (ML) using conditions previously described (23 ). Briefly, unlabeled PCR products were separated on DNA sequencing gels, blotted to nylon membranes and detected by autoradiography following probing with a 5' 32P-labeled oligo corresponding to the microsatellite motif present.
Three analyses were used for detecting errors, sublocalizing markers and creating an initial adjacency matrix. Markers from CEPH 7.1, which could not be sublocalized using the RH map (17 ), were positioned among the RH-mapped markers using the BUILD option of the CRI-MAP linkage package (24 ). A drop analysis was used to identify markers which caused significant map expansion. Drop analyses were performed using the `fixed' option of CRI-MAP. Total sex-average map length was compared to map length with each marker, one at a time, dropped. A marker was removed if dropping it from the map decreased the map length by >= 3 cM. The BINS program (18 ) uses bin assignments for the markers to create an initial adjacency matrix. The adjacency matrix represents a weighted directed graph in which each node is a marker and each edge is the number of order events (crossovers) between two markers.
The map construction algorithms operate on the adjacency matrix as follows.
(i) Perform transitive closure using the following rule: if A is ordered to B with nAB crossovers, B to C with nBC crossovers, and A to C with nAC crossovers, the transitive ordering confidence of A to C is max[nAC, min(nAB, nBC)].
(ii) Eliminate conflicts in local ordering of pairs of markers based on the difference, NC, in the number of crossovers (edges on the weighted directed graph) favoring one order (pter -> A -> B) over the other (pter -> B -> A) with NC varied in successive passes from 8, 6, 4, . . . crossovers and with the adjacency matrix rebuilt after deleting data in each pass.
(iii) Using a recursive depth-first search algorithm to traverse the adjacency matrix (weighted directed graph), construct a comprehensive (all markers) linear order which is free of conflicts.
Map distances are estimated by maximum likelihood using the layered EM algorithm (25 ). Two final routines translate the adjacency matrix built from genetic data into the graphical format shown in Figure 1 , using a specified confidence criterion for marker order. One of these routines (2D-MAP) was described previously (3 ). 2D-MAP outputs a map with information from other sources of marker order superimposed on the CEPH map (semi-integrated map, available from the GENLINK database, URL http://www.genlink.wustl.edu). The other routine (2D-ADD) completely merges the adjacency matrices from different sources leading to a fully-integrated map (Fig. 1 ). Most of the algorithms for panel creation and map construction have recently been integrated into one program (PANELS). The URL for software distribution (excepting CRI-MAP and the drop analysis) is ftp://morgan.med.utah.edu/pub/panels (anonymous ftp to morgan.med.utah.edu in the directory /pub/panels). Both PC and generic UNIX versions are available.
We are indebted to over 100 laboratories who have generously contributed data to the CEPH collaboration. We thank Dante LaMorticella, Eric A. Smith and Thas Phromchotikul for excellent technical assistance. This work was supported by NCGHR #HG00022 to M.L.. Partial support was provided by NCGHR HG#00360 (EK) to P.F. and by NCI #CA58860 (PF). P.F. gratefully acknowledges support from the Barbara Davis Center for Childhood Diabetes and the University of Colorado Cancer Center.
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