Genomics- The Science and Technology Behind the Human Genome Project. Charles R. Cantor, Cassandra L / genomics1-10 / 9

PROBE POOLING IN

S. POMBE

MAPPING

305

ing to increase the throughput

of experiments even further. However, the most efficient

ways to do this have not yet been worked out.

A caveat for all pooling approaches concerns the threshold between background noise

or cross-hybridization and true positive hybridization signals. Theoretical, noise-free

strategies are not likely to be viable with real biological

samples. Instead of striving

for

the most ambitious and efficient possible pooling strategy, it is prudent to use a more

overdetermined approach and sacrifice a bit of efficiency for a margin of safety. It is im-

portant to keep in mind that a pooling approach does not need to be perfect. Once poten-

tial clones of interest are found or mapped, additional experiments can always be done to

confirm their location. The key idea is to

get the map approximately right with a mini-

mum number of experiments. Then the actual work involved in confirming the pooling is

finite and can be done regionally by groups interested in particular locales.

PROBE POOLING

IN

S.

POMBE

MAPPING

An example of the power of pooling is illustrated by results obtained in ordering a cosmid

library

of the

yeast

S. pombe.

This organism was chosen for a model mapping project

because a low-resolution restriction map was already available and because of the interest

in this organism as a potential target for genomic sequencing. An arrayed cosmid library

was available. This was first screened by hybridization with each of the three

S. pombe

chromosomes purified by PFG. Typical results are shown in Figure 9.14. It is readily

apparent that most cosmids fall clearly

on one chromosome by their hybridization.

However there are significant variations in the amount of DNA present in each spot of the

array. Thus a considerable amount of numerical manipulation of the data is required to

correct for DNA sample variation, and for differences in the signals seen in successive

hybridizations. When this is done, it is possible to assign, uniquely, more than 85% of the

clones to a single chromosome based on only three hybridizations.

The next step is to make a regional assignment of the clones. Here purified restriction

fragments are labeled and used as hybridization probes with the cosmid array. An exam-

ple is shown in Figure 9.15. Note that it is inefficient to use only a single restriction frag-

ment at a time. For example, once one knows the chromosomal location of the cosmids,

one can mix restriction fragments from different chromosomes and use them simultane-

ously with little chance of introducing errors. After a small number of such experiments,

one has most of the cosmids assigned to a well-defined region.

To fingerprint the cosmid array further, and begin to link up cosmid contigs, arbitrary

mixtures of single-copy DNA probes were

used. These were generated by the method

shown in Figure 9.16. A FIGE separation of a total restriction enzyme digest of

S. pombe

genomic DNA was sliced into fractions. Because of the very high resolution of FIGE in

the size range of interest, these slices should essentially contain nonoverlapping DNA se-

quences. Each slice was then used as a hybridization probe. As an additional fingerprint-

ing tool, mixtures of any available

S. pombe

cloned single-copy sequences were made and

used as probes. For all of these data to be analyzed, it is essential to consider the quantita-

tive hybridization signal, and correct it

both for background and for differences in the

amount of DNA in each clone, the day-to-day variations in labeling, and overall hy-

bridization efficiency.

The

hybridization profile of

each of the

cosmid clones with the various probes used is

PROBE POOLING IN

S. POMBE

MAPPING

307

restriction enzyme-digested

S. pombe

genomic DNA.

up clones with similar hybridization

profiles

that indicate possible overlaps (Box 8.3).

analysis, and the method sketched in Box 9.2. In general, we

found

that

the different

methods gave consistent results. Where inconsistencies were seen,

these

could

often be

must

be located

nearby,

and

in fact they form a contig. The clones show some hybridiza-

tion

differences

when

very

simple probe

mixtures are used, since they are not identical

clones. An example of the kinds of contigs that emerge from such an analysis is shown in

Figure 9.19. These are clearly large

and redundant contigs of the sort one hopes to see in

a robust map.

Figure 9.17

Even when complex pools

of probes are used (e.g., pools

a and

b ) overlapping clones

will still tend to show a concordant pattern of

hybridization.

Figure

9.18

Hybridization profile of three different

S. pombe

cosmid

clones,

with a series of 63

different pools of probes.

Figure 9.19

S. pombe

cosmid map

constructed from

the patterns of probe hybridization to the

S.

pombe

cosmid

array. Cosmids

are indicated

by horizontal

lines along the maps. Letters shown

above the map and fragment names (e.g., SHNF

Sfi I fragment H and

Not

I fragment F). Gaps in

contigs are indicated by a vertical bar at the right end. Positions of LTRs, 5S rDNAs, and markers

are indicated by *, #, and

, respectively.

FALSE POSITIVES WITH SIMPLE POOLING SCHEMES

309

cosmid

map of

S. pombe.

The objective in this limited example is to test the evidence

in favor of particular schemes for ordering three clones A, B, and C. Various possible

arrangements of these clone are written as the columns and rows of a matrix, each ele-

ment of this matrix is represented by the maximum likelihood estimate that the clones

i and

j overlap by a fraction

f: L ij( f ). For each possible arrangement of clones, we cal-

culated the weight of the matrix,

W

m defined as

W m

i j L ij(f)

j i i

The

result for a simple case is shown in the figure. The true map will have an arrange-

ment of clones that gives a minimum weight or very close to this. The method is par-

ticularly effective in penalizing arrangements of clones where good evidence for over-

lap

exists, and yet the clones are postulated to be nonoverlapping in the final

312

ENHANCED METHODS FOR PHYSICAL MAPPING

MORE

GENERAL POOLING

SCHEMES

A

branch

of mathematics

called

sampling

theory

is

well developed and instructs us how

to

design

pools effectively. In the most

general case there

are two

significant

variables:

the

number

of dimensions used for the array and the pools,

and the number of alternate

pool configurations employed. In the case described in Figure 9.21, the array is two di-

mensional, and the pools are one dimensional. Rows and columns represent one configu-

ration of the array. Diagonals, in essence, represent another configuration of the array be-

cause

they

would be rows and columns if the elements of

the array were placed in a

different order. Here we want to generalize these ideas. It is most important to realize that

the

dimensionality of an

array or a pool

is a mathematical statement about how we

chose

to describe it. It is not a statement about how the

array is actually composed in space. An

example is shown by the pooling scheme illustrated

in Figure 9.22. Here plate pools are

used in conjunction with vertical pools, made by combining each sample at a

fixed

x-ylo-

cation on all the plates. The arrangement of plates appears to be three

dimensional;

the

plate pools are two dimensional, but the vertical pools are only one dimensional.

MORE GENERAL POOLING SCHEMES

313

We

consider

first

an

N

element library,

and

assume that we

have

sufficient

robotics to

sample it in any way we wish. A two-dimensional square array is constructed by assign-

ing to each element a location:

a ij

where

i 1, N

1/2;j 1, N 1/2

If we pool rows and columns, each of these one-dimensional pools has

N 1/2 components,

and

there are 2

N 1/2 different

pools if we

just consider rows and columns. The

actual

con-

struction of a pool consists of setting one index constant, say

i 3, and

then

combining

all samples that share that index.

The

same

N

element

library

can

be treated

as a

three-dimensional

cubic

array. This is

constructed, by analogy, with the two-dimensional array by assigning to each element a

location:

a ijk

where

i

1, N

1/3

1, N

1/3

1, N

1/3

;j

;k

If we pool two-dimensional surfaces of this array, each of these pools has

N 2/3 compo-

nents. There are

3

N 1/3 different

pools if

we

consider

three

orthogonal sets

of

planes. The

actual

process of constructing

these

pools

consists

of

setting

one

index

constant,

say

j 2, and then combining all samples that share this index.

We can easily generalize the pooling

scheme

to higher dimensions. These become

hard

to

depict

visually, but there is no

difficulty

at

handling

them

mathematically.

To

make a four-dimensional array of the library, we assign each of the

N

clones an index:

a ijkl

where

i

1, N

1/4

1, N

1/4

1, N

1/4

1, N

1/4

;j

;k

;l

This array is what is actually called a hypercube.

We

can

make

cubic

pools

of

samples

from the array by setting one index constant, say

k

4,

and then combining all samples

that share this index. The result is 4

N

1/4 different

pools,

each

with

N

3/4 elements. The

pools actually correspond to four orthogonal sets of sample cubes.

The process can be extended to five and higher dimensions as needed. Note that the re-

sult of increasing the dimensionality is to decrease, steadily, the number of different pools

needed, at a cost of increasing the size of each pool. Therefore the usefulness of higher-

dimension pooling will depend very much on experimental sensitivity. Can the true posi-

tives b distinguished among an increasingly higher level of background noise as the com-

plexity of the pools grows?

The highest dimension possible for a pooling scheme is called a binary sieve. It is defi-

nitely the most efficient way to find a rare event in a complex sample so long as one is

dealing with perfect data. In the examples discussed

above,

note that

the

range

over

which each sample index runs keeps dropping steadily, from

i 1,

N

1/2 to

i 1, N 1/4 as

the dimension of the array is increased from two to four. The most extreme case possible

would allow each index only a single value; in this case there is really no array, the sam-

ples are just being numbered. A pooling scheme one

step short of this extreme would be

to allow each index to run over just two numbers. If we kept strictly to the above analogy

we would say

i 1, 2; however, it is more useful to let the indices run from 0 to 1. Then

we assign to a particular clone an index like

a 101100. This is

just a

binary

number

(the

equivalent decimal is 44 in this case). Pools are constructed, just as

before,

by

selecting

all clones with a fixed index, like

a ijk 0mn .