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ALTERNATE ARRAY CONFIGURATIONS

315

Figure 9.23

Estimates of

the ideal pool sizes and dimensions for screening libraries with different

 

numbers of clones and different extents of redundancy. The actual characteristics of the CEPH YAC

 

 

library are

indicated by a dot. (

a ) Where

one false positive is tolerable for

each true positive. (

b )

Where only

0.01

false positive

is tolerated per screen.

Note that the shaded area represents

situa-

 

tions where pooling strategies are not useful. (Taken from Barillot et al., 1991.)

316 ENHANCED METHODS FOR PHYSICAL MAPPING

calculated results for two realistic cases. These results cover cases where one false positive per true positive is acceptable, and where only 0.01 false positive per screen will be seen. In general, the results indicate that for small numbers of clones, pooling is not efficient. The larger the library, the higher is the dimensionality of effective pools; however, the higher the redundancy, the worse is the problem of false positives, and the lower is the optimum dimensionality.

ALTERNATE ARRAY CONFIGURATIONS

There is a generally applicable strategy to distinguish between true and false positives in pools of arrayed clones. This strategy is applicable even where the density of true positives becomes very high. The basic principle behind the strategy is illustrated in Figure 9.24 for a two-dimensional array with two positive clones. Suppose that one has two versions of this array in which the positive clones happen to be at different locations, but the relationship between the two versions is known. That is, the identity of each clone at each position on both versions of the array is known. When row and column pools of the array

are tested, each configuration gives two positive rows and two positive columns, resulting in four potentially positive clones in each case. However, when the actual identity of the

putative positive clones is examined, it turns out that the same true positives will occur in both configurations, but usually the false positives will be different in the two configura-

tions. Thus they can be eliminated.

 

 

 

The

use

of multiple configurations of the array is

rather foolish and inefficient for

small arrays and small numbers of false positives. However, this process becomes very

efficient for large arrays with large numbers of false positives. Procedures exist called

transformation

matrices

or

Latin squares

that each show how to reconfigure an original

two-dimensional array into informative alternates. It is not obvious if efficient procedures

are known for arrays in higher dimensions. It is also not clear that any general reconfigu-

ration procedure is optimal, since the best scheme at a

given point may depend on the

prior results. Suffice it to say that the use of several alternate configurations appears to be

a very powerful tool. This is illustrated by the example shown in Figure 9.25. Here five

positive clones are correctly identified using row and column pools from three configura-

tions of a 7

7 array. This requires testing a total of 42 pools, which is only slightly less

than the 49 tests needed if the clones were examined individually. Again, however, the ef-

ficiency of the approach grows tremendously as the array size increases. Additional dis-

cussion

of quantitative aspects of

pooling

strategies can be found in Bruno et al., (1995).

Figure 9.24 A simple example of how two different configurations of an array can be used to resolve the ambiguities caused by false positives.

INNER PRODUCT MAPPING

317

Figure 9.25

A more complex example of the use of multiple array configurations to distinguish

 

true and false positives. In this case three configurations allowed the detection of five true positives

 

(larger font characters at positions 0, 0; 1, 2; 2, 5; 3, 3; and 4, 1 in the first configuration) in a set of

49 clones. The

’s in the first configuration indicate positive rows and

columns. In the second and

third configuration the

’s indicate clones that could be positive;

the

’s indicate those that are ex-

cluded by the results of the first and second configurations, respectively. (Taken from Barillot et al., 1991.)

318 ENHANCED METHODS FOR PHYSICAL MAPPING

INNER PRODUCT MAPPING

The enormous attractiveness of large sample arrays

as genome mapping tools has been

made evident. What a pity it is that with most contemporary methods there is no way to

make these arrays systematically. Suppose that we had an arrayed library from a sample,

and we wished to construct the equivalent array from a closely related sample (Fig. 9.26).

The samples could be libraries from two different people, or from two closely related

species. Constructing an array from the second

sample that is parallel to the first sample

is really making a map of the second sample, as efficiently as possible. We could do this

one clone at a time, by testing each clone from the second library against the array of the

first library. We could do this more rapidly by pooling clones from the second library. But

ultimately we would have to systematically place each of the clones in the second library

into its proper place in an array. This is an

extremely tedious process. What we need, in

the future, is a way of using the first array

as a tool to order simultaneously all of the

clones from the second array. In principle, it should be possible to use hybridization to do

this; we just have to develop a strategy that works efficiently in practice.

One very attractive strategy for cross-correlating different sets of samples has recently

been developed by Mark Perlin at Carnegie

Mellon. The method has been validated by

the construction of a YAC map for human chromosome 11. The basic idea behind the pro-

cedure,

called

inner

product mapping

 

(IPM) is shown in Figure 9.27. Radiation hybrids

(RHs;

see Chapter

7) can

be analyzed relatively easily by PCR using STSs of known

order on a chromosome. Because each RH encompasses a relatively large amount of hu-

man DNA, relatively few STS measurements suffice to produce a good RH map. RHs in

turn provide an excellent source of DNA to identify YACs in corresponding regions. In

practice, what is done is inter-

Alu

PCR (Chapter 14) both on each separate YAC and each

Figure 9.26 Unsolved problem of efficiently mapping one dense array onto another.

INNER PRODUCT MAPPING

319

Figure 9.27 Inner product mapping (IPM). (See text for details.)

RH. An array is made of the YAC PCR products, and this is probed successively by hy-

 

 

 

bridization with each RH PCR product. This assigns the YACs to RHs.

 

 

 

 

In previous STS mapping strategies, PCR with STS primers had to be used directly to

 

 

 

analyze YACs in YAC pools. This is relatively inefficient for reasons that have been de-

 

 

 

scribed earlier in this chapter. Instead, in IPM, the STS-YAC correspondences are built

 

 

 

mathematically as shown in Figure 9.27. The inner product

 

C

of two matrices

A

and B is

computed as

 

 

 

 

 

 

 

 

 

C ij

A ik B kj

 

 

 

 

 

 

 

k

 

 

 

 

The YAC versus RH hybridization results can be scored as positive (

 

1) or negative (

1)

as shown for matrix

A. The RH

versus STS PCR results can also be

scored as

positive

 

 

( 1) or negative (

1) as shown in

matrix

B. The inner product

matrix

C

is computed

el-

ement by element in a very simple fashion. It is a matrix that describes comparisons be-

 

 

 

tween STS’s and YACs that reflects the separate RH results with each. The best estimate

 

 

 

for each YAC-STS

direct correspondence is

the largest (most positive) element in

each

 

 

 

row of matrix

C. This is shown as

or * in the simplified matrix

 

C which indicates only

320

 

ENHANCED METHODS FOR PHYSICAL MAPPING

 

 

the largest

elements of C. The

symbols in

C

indicate a YAC (column) that actually

contains

the

indicated STS (row). The * symbols in

 

C indicate a YAC does not actually

contain

the

STS (i.e., it would

be scored negative in a direct

PCR

test) but must be lo-

cated near this STS for the RH data to be self-consistent. This simple example indicates that IPM has more mapping power than direct STS interrogation of YACs even though the latter process would involve far more work.

The IPM mapping project of human chromosome 11 used 73 RHs, 1319 YACs, and 240 STSs to construct a YAC map. A total of 241 RH hybridizations of YAC clone arrays were required, and 240 STS interrogations of the 73 RHs were done with duplicate PCRs.

SLICED PFG FRACTIONATIONS AS NATURAL POOLS OF SAMPLES

Previous considerations make clear that working with pools of probes or samples is often a big advantage. Sometimes this is also unavoidable when a region is too unstable or too

toxic to clone in available vector systems. Cloning a region, even if

it is stable, may also

be too time-consuming or costly if one needs to examine the region in a large number of

 

different samples. This would be the case where, for example, a region

expanded in a set

 

of different tumor samples is to be characterized. One way to circumvent the problem of

 

subcloning a region is to find one or more slices of a PFG-fractionated restriction digest

that contains the region. With enzymes like

 

Not

I that have rare recognition sites, gener-

ally 1 to 2 Mb regions will reside on at most a few fragments. Only a few probes from the

region will suffice to identify these fragments. PFG separation conditions can then be op-

timized to produce these fragments in separation domains where size

resolution

is

opti-

mum. The resulting slice of separation gel will then contain, typically, about 2% of the to-

tal genome. For a 600-kb human DNA fragment, this slice will consist of 100 fragments,

only one of which is the fragment of interest. This is probably too

dilute to

permit

any

kind of direct isolation or purification. But the slice can serve as an efficient sample for

PCR amplifications that try to assign additional STSs or ESTs to the region. If the slice is

examined from a digest of a single chromosome hybrid, it will contain only 1 or 2 human

 

DNA fragments. Then, as shown in Chapter 14, PCR amplification based

on

human-

specific repeating sequences

can

be

used to produce numerous

human-specific

DNA

 

probes from the region of interest.

 

 

 

 

 

 

 

 

RESTRICTION LANDMARK

GENOME

SCANNING

 

 

 

 

 

 

An alternative method for systematically generating a dense array

of

samples

from

a

genome has been developed. This method is called

 

 

restriction landmark genome scanning

(RGLS). It was originally conceived as a way of facilitating the construction of genetic

maps by finding large numbers of useful polymorphic sequences. Thus it

is a

method set

 

up to reveal differences between two genomes, and as such it fits the spirit of the kind of

differential analysis that needs to

be developed. RLGS, as

currently

practiced, is

based,

however, on genomic DNA rather than

on cloned DNA. The basic idea behind RLGS is

illustrated in Figure 9.28. A genome is digested with a rare-cutting restriction nuclease

like

Not

I, and the ends

of the

fragments

are labeled. This generates about 6000 labeled

sites

because

there are about

3000

Not

I sites in the genome, and each fragment will be

RESTRICTION LANDMARK GENOME SCANNING

321

Figure 9.28 Steps in the preparation of DNA samples for restriction landmark genome scanning (RLGS).

labeled on both ends. The sample is then digested with a second restriction enzyme, one

 

 

that cuts more frequently, say at a six base site. The resulting fragments are then fraction-

 

ated by agarose gel electrophoresis in the size range of 1 to 20 kb. The agarose lane is ex-

 

cised and digested in situ with a third, more frequently cutting enzyme, one that recog-

 

nizes a four-base sequence. The resulting small DNA fragments are now separated in a

 

 

second electrophoretic dimension on polyacrylamide, which fractionates in the 0.1 to

1

 

kb size range. The result is a systematic pattern of thousands of spots, as shown in Figure

 

9.29 a. Each spot reveals the distance between the original

Not

I site and the nearest site

Figure 9.29

Example of

the results seen by RLGS. (

a ) Two-dimensional electrophoretic separa-

tion of DNA

fragments. (

b ) Sites where polymorphisms can be detected on a typical fragment.

322

ENHANCED METHODS FOR PHYSICAL MAPPING

 

 

 

for the

second and third enzymes (Fig. 9.29

b ). Any polymorphisms in these distances,

caused either by altered restriction sites or by DNA insertions or deletions, will appear as

displaced

spots in the two-dimensional fractionation. The method

appears to

be

very

powerful

because so many spots can be resolved, and the patterns,

at least

for

mouse

DNA where the method was developed, are very reproducible.

PROGNOSIS FOR THE FUTURE OF GENOME MAPPING

In the human, mouse, and other species officially sanctioned as part of the human genome project, genetic mapping is proceeding rapidly and effectively. Indeed the rate of progress appears to be better than originally projected. Dense sets of polymorphic genetic markers have been generated. These have served well to order megaYACs. Finer maps are still

needed because

of the difficulties in handling

megaYACs

and

the

need

to

break

them

down into smaller samples for subsequent manipulations. These finer maps, however, will

 

 

be more easy to construct by using preexisting megaYAC

contigs, just as

the preexisting

S. pombe

restriction map allowed the design of efficient strategies

to

order an

S. pombe

cosmid library. BAC, PAC, or cosmid maps are still needed for current direct DNA se-

quencing technology. Direct sequencing from YACs or from genomic DNA is possible, as

 

we will describe in Chapter 10, but it is not yet reliable enough

to be routinely used in

large-scale sequencing projects. As the genome project concentrates on DNA sequencing,

 

the notion of a sequence-ready map has become important. Such a map consists of sam-

 

ples ready for DNA sequencing. Detailed order information on these samples could be

 

known in advance, or it could be obtained

in the

process

of

DNA

sequencing.

See

Chapter 11 for further discussion.

 

 

 

 

 

 

 

 

 

 

For species other than those already intensively studied, the best strategies will depend

on the kinds of samples that are available. If

radiation hybrids and mega clone

libraries

are made, these will obviously be valuable resources. If dense genetic maps can be made,

 

the probes from these will order the megaYACs. If a genetic map is not feasible, FISH

provides a readily accessible alternative. In other cases it may be possible to purify the

chromosomes or fragments efficiently by flow sorting, improved microdissection, or other

 

 

tricks to be described in Chapter 14.

 

 

 

 

 

 

 

 

 

 

The notion of having to make a map of a person for diagnostic purposes is still awe-

somely difficult. Mapping methods are complex and make major demands on both instru-

 

 

mentation and skilled personnel. New approaches will be needed before diagnostic map-

 

ping can be considered at all realistic. The use of radioactive

 

 

 

 

 

 

32 P pervades most current

mapping methods, and this is surely something to be avoided in a technique proposed for

 

widescale clinical use. One area that may impact heavily on the prospects for diagnostic,

mapping is the development of improved, sensitive, nonradioactive detection techniques.

 

These will be described as we deal with DNA

sequencing

methods

because

it

is

here

 

where these methods have first been used or tested.

 

 

 

 

 

 

 

 

 

 

SOURCES AND ADDITIONAL READINGS

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6: 55–64.

 

 

 

 

 

 

Ashworth, L. K., Hartman, M.-A., Burgin, M., Devlin, L., Carrano, A. V., and Batzer, M. A. 1995.

 

 

Assembly of high-resolution bacterial artificial chromosome, P1-derived artificial chromosome,

 

 

 

and cosmid contigs.

Analytical Biochemistry

 

224: 565–571.

 

 

 

Barillot, E., Lacroix, B., and Cohen, D. 1991. Theoretical analysis

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N -

dimensional pooling strategy.

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19: 6241–6347.

 

Bruno, W. J., Knill, E., Balding, D. S., Bruce, D. C.,

Doggett,

N. A., Sawhill, W. W., Stallings,

 

 

R. L., Whittaker, C. C., and Torney, D. C. 1995. Efficient pooling designs for library screening.

 

 

Genomics

 

26: 21–30.

 

 

 

 

 

 

Green, E. D., Riethman, H. C., Dutchik, J. E., and Olson, M. V. 1991. Detection and characteriza-

 

 

tion of chimeric yeast artificial-chromosome clones.

 

Genomics

11: 658–669.

 

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Grothues, D., Cantor, C. R., and Smith, C. L. 1994. Top-down construction

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