Analysis of DNA-RNA hybridization data using the scatchard plot

BIOCHEMICAL

Vol. 55, No. 3,1973

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ANALYSIS-OF --~DNA-RNA-I_-HYBRIDIZATION-DATA--USING-THE SCATCHARD PLOT ---- ---J. Lawrence Marsh and Brian J. McCarthy* Departments of Biochemistry and Genetics University of Washington Seattle, Washington 98195 Received

October

15,1973

SUMMARY: DNA-RNAhybridization experiments, especially in eukaryotic systems, ----are complicated by such factors as large genomesize and the difficulty of separating RNAfractions. Current analytical ;.lethods can lead to erroneous conclusions since heterogeneity is often obscured and data in the most useful concentration ranges are not readily obtainable. Someof these difficulties can be overcome by using a Scatchard plot which is superior to other methods in preventing commonmisinterpretations of data resulting from heterogeneous RNAsamples or non-specific reaction. In principle,

the titration

provides a quantitative that particular

of single-stranded

estimate of the fraction

DNAwith excess RNA

of the genomecoding for

species or group of RNAmolecules.

Ideally

the binding

should be measured over a broad range of RNAand DNA concentrations. practice, specific solubility.

however, the experimental design is limited

by such factors

as the

radioactivity

of the RNAor DNA, the amount of RNAavailable

and its

It

to achieve saturating

is often difficult

Decreasing the amount of DNAin the reaction detection activities

RNAconcentrations.

is not always practical

since

of very small amounts of binding requires rather high specific or excessively

in such reactions

saturation

in extrapolation

radio-

The approach to saturation presenting

Indeed, in order to determine the

(l-3).

values, experiments are often performed at the highest possible

RNA concentrations. bution of dilute

long periods of incubation.

is asymptotic with increasing RNAconcentration,

obvious difficulties final

In

It

is exactly

these data which tend to maximize the contri-

contaminants and non-specific

A method of anlaysis allowing a linear

reaction.

extrapolation

to infinite

RNA

*Present address: Department of Biochemistry and Biophysics, University California at San Francisco, San Francisco, California 94122.

Coprrikht 0 1973 by Amdemic Press, Inc. All rights of reproduction in any form reserved.

805

of

BIOCHEMICAL

Vol. 55, No. 3, 1973

concentration

is therefore

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desirable.

Although the double reciprocal

as applied by Bishop to DNA/RNAhybridization,

partially

fills

this need (4),

Scatchard's analysis of the binding of small ions by proteins this purpose in a manner superior to other available function

concentrations

can be conveniently

and usefully

are spread more evenly along the line. distinguishing

between specific

displayed;

It is particularly

and non-specific

(5) serves The

treatments.

is bounded on both ends by meaningful intercepts;

plot,

any range of and the points advantageous for

binding and for analyzing

the binding of an enriched component in the presence of heterogeneous contaminants. THEORETICAL: The equation describing

the function

can be derived as follows:

a DNA-RNAhybridization

reaction,

either

of the DNAon filters

by imobilization

mixtures containing

self reaction

increasing concentrations

allowed to come to equilibrium is measured. The reaction [Dl + [RI

and the fraction

of the DNAis prevented or by dilution.

Reaction

of RNArelative

to DNAare

of DNA in heteroduplex

equation can be written +

as:

[DRI

It should be noted here that the reaction

In

(1) described in equation (1)

considers only those sequences of DNAwhich can react with RNA, hence the term [D] or unreacted DNArefers could eventually

react with RNA. [R] refers

free RNA. [DR] is the concentration concentrations association

only to that unreacted DNAwhich to the concentration

of hybridized

DNA-RNAcomplex, all

being in terms of moles of nucleotides per liter.

The

constant K, is given by: Ka = [DRl/ IDI [RI

(2)

The maximumpossible extent of hybridization

1~~1~~ is by definition

sumof the bound DNA [DR] and the unreacted DNA [D], i.e.,

@RI + IDI.

of

Multiplying

equation (2) by [D] and substituting

for D yields:

806

equal to the

[DR]~~ = [DRmx - DRI

Vol. 55, No. 3,1973

BIOCHEMICAL

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Figure 1. Binding of a single RNA species to a single DNAsite is depicted in 4 ways. (A) direct plot, (B) semi log plot, (C) double reciprocal plot, (D) Scatchard plot.

[DRl/ [RI = Ka([DRlmax - [DRI) A plot of DNAhybridized/free whose x intercept

(3)

RNAagainst DNAhybridized

is [DR]-

is a straight

line,

the value for the maximumamount of DNAin

hybrid. DISCUSSION: There are four methods of plotting the association are [DR] (Fig. 1). prefered

VS.

DNA-RNAbinding data to obtain

constant K, and the maximumextent of hybridization.

[RI,

[DRI

VS.

Of these four,

log [RI, l/[D~l the last,

for both theoretical

[DRI vs. [R] suffers

vs. l/[Rl,

vs. [DRI

as described in this paper, is to be

(6) and practical

Prohibitively

are sometimes needed to approach saturation

reasons.

The direct

plot

the linear

or logarithmic

high RNAconcentrations

and extrapolation

in all but the simplest cases. Heterogeneity

reciprocal

and [DRI/[Rl

from the fact that the curve approaches the limiting

value of [DR]~~ asymptotically.

apparent in either

These

in a sample is not readily presentation.

plot is useful in that it gives a straight

binding sites are equivalent.

However, it

807

is difficult

is difficult

The double

line if all to plot all

the of the

BIOCHEMICAL

Vol. 55, No. $1973

Figure 2. Hybridization nitro-cellulose filters. Filters containing (7).

data

number.

the right slope

where

ordinate

they

have a disproportionately

reaction,

and the

slope

makes heterogeneity reactions. titrate a pure were

incubated

it

determining

of

limited

displaced

[R] are

for

of

by a far

to

on the

so close

to the

is

the

labeled

the

Furthermore,

function difficult.

the curve

described

components,

experiments

"28s"

rRNA in

saturation

808

DNA (7).

value

amounts

of complex designed

to

Using of RNA

The difficulty

by extrapolation

be the which

the chicken.

RNA, increasing chicken

will

a feature

consider

"28s"

of

goes to infinity

analysis

for

the y

maximum extent

and facilitates

containing final

linear

individual

coding

theoretically

manner.

[DRlmax,

systems

of illustration,

filters

of the

intercepts:

extrapolation

apparent

genes

all

in a useful

Any other

making

lines

of highly with

values

not

influence

ends by meaningful

-K . a

thus

For purposes

fraction

accurately

is

readily

the number

is

[R] being

hand weights

case of multicomponent straight

of

axes

large

the x intercept

one axis,

In the sum of the

on both

Ka[DR],,,

on at least

high

and displays

bounded

is

values

on the other

evenly

intercept

of both

curvature.

plot

is

in low

Conversely,

data

function

scale

results

as to obscure

obtainable

the

This

A Scatchard

the

way since

of the line.

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of chicken 28s rRNA to chicken DNA immobilized on RNA was labeled with 12'1 to 2.64 x 10' cpm ug-' 12.5 ug DNA were incubated in .l ml 2xSSC at 7O'C.

in a meaningful

finite

AND BIOPHYSICAL

of of the

BIOCHEMICAL

Vol. 55, No. 3,1973

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Figure 3. Binding behavior was calculated for a sample containing 2 RNA species, A and B, in 1O:l relative concentration. The K for both species was taken to be 10'. The total concentration of DNAwas&taken to be 50 ugfml 0.1% of which was complementary to each site A and B. A single RNAspecies binding to two DNAsites with different K in a 1O:l ratio produces the same result. -Ibinding of the mixture, --e-8- binding of the individual components as a function of total [R] = [RA] + [s].

binding curve (inset, concentration

Fig. 2) is clear.

A ten-fold

was necessary to increase binding from 75% to 99%of saturation.

The extrapolation

to infinite

[R] is facilitated

according to equation 3 (Fig. 2). constant is 8.6 x lo6 M-l,

Several factors,

(8,9).

such as GC content, relative

base pair mismatching, non-specific

concentrations

influence

the value of the

With a mixture of several RNAspecies, the apparent binding

constant for each species depends on its relative This allows one to distinguish contaminants.

from non-specific

these data

a value consistent with the values of 2.6 x lo6 6'

association and differing binding constant.

by plotting

From the slope of the line the association

reported for g. coli RNA/DNAhybrids

dilute

increase in RNA

sections, one displaying

locus specific

hybridization

In both cases the curve will

a decreased slope reflecting

contaminants or non-specific

in the mixture.

between an enriched component Ind a number of

Similarly,

reaction.

concentration

association.

below. 809

can be distinguished

break into two

the binding of dilute

Two such cases will

be illustrated

BIOCHEMICAL

Vol. 55, No. 3,1973

Figure In the

4. first,

to two DNA sites resembles

containing

a 1O:l

same binding

displayed

ratio

plot

in Fig.

reactions

such as the

4.

thermal

(10).

are

grossly

deviates

strikingly

and must

be analyzed plot

stability

for

linearity

as a multiple

the direct

The Scatchard indicating binding

can be seen by comparing

of the same data

(Fig.

The Scatchard

Rather

in than

Fig.

3 and as a of the

can these offers

component

plot

of Fig.

the

two cases

no evidence

the

mixture.

It

sample

of 4

is

heterogenous

The advantages

4 to a double

for

of the

reciprocal

plot

3).

analysis

20 and 80% saturation

that

of

identical.

parameters

plot

of (A)

is

in Fig.

other

saturation

overestimated. from

plots

of the product

case

with

a 9% contamination

two cases

by considering

In either

and the values

interest

constants.

Only

of a sample

to two DNA sites

to simulate

reciprocal

binds This

the behavior

binding

of these

which

was calculated.

Secondly,

was calculated

method.

RNA species

constants

binding.

behavior

Scatchard

of a single

association

and double

Scatchard

Scatchard

behavior

by the

of two RNA species

as direct

heterogeneity

3 analyzed

non-specific

The binding

be distinguished

Fig,

different

constant

an RNA sample. is

from

the binding with

situation

the

Data

AND BIOPHYSICAL RESEARCH COMMUNICATIONS

makes maximum use of-the determining

maximizing

the the

final

effect

810

data

saturation of dilute

obtained

between

values

and association

contaminants

and

BlOCHEMlCAL

Vol. 55, No. 3,1973

non-specific

reaction,

these data make it possible to identify

of the component of interest unknown contaminants. percentage

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the binding

despite the concomitant binding of multiple

Moreover, these data are subject to the least

error and are theoretically

most significant

(6).

The fact that

this plot is bounded at both ends allows one to determine immediately by visual inspection what portion The best fit

of the total

titrant

has been performed.

to the data can be determined by any of several published

methods (11,12).

Acknowledgment Weare greatly

indebted to Dr. A. Tereba for the use of his unpublished

data (Fig. 2), and to Dr. David A. Deranleau for his stimulating This research was supported by a predoctoral

fellowship

discussions.

(IJSPHSGrant PGMOOO52)

and USPHSGrant #GM20287to B. J. McCarthy. REFERENCES: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Bishop, J. 0. (1972) Karolinska Symposia on Research Methods in Reproductive Endocrinology, 5th Symposium, Gene Transcription in Reproductive Tissue, pp. 247-273. Walker, P. M. B. (1969) Prog. Nucleic Acid Res. -Mol. -Biol. 2, --301-326. Birnstiel, M. L., Chipchase, M. and Speirs, J. (1971) m. Nucleic Acid Res. Mol. Biol. ---Bishop, J. 0. (1969) Scatchard. G. (1949) Deranleau, D. A. (196rJ. Amer. m. s. 9l, 4044-4049. (1973) Biochemistry, in press. Tereba, A. and McCarthy,B.r Bishop, J. 0. (1970) Biochem. J. 116, 223-228. Kennell, D. E. (1971) Prog. --Nucleic Acid Res. -Mol. -Biol. II-, 259-301. Farquhar, M. N. and McCarthy, B. J. (1973) Biochemistry (in press). Deranleau, D. A. (1969) I. Amer. Chem. Sot. 9l, 4050-4054. Feldman, H. A. (1972) -Anal.Biochcs%7-338.

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