454
Yreliminnry
notes
12. Ponta, H, Ponta, U, Kraft, V & Wintersberger, E, Eur j biochem 46 (1974) 473. 13. Simchen, G, Genetics 76 (1974) 745. 14. Tonnesen, T & Friesen, J D, J bact I I5 (1973) 889. Received December 15, 1976 Accepted December 27, 1976
Analysis of RNA-DNA competition hybridization using the Scatchard plot SUSAN A. GERBI, versity,
Providence,
Biomedical RI 02912,
Divkion, USA
Brown
Uni-
The Scatchard plot is convenient for expressing RNA-DNA competition hybridization data because the maximum amount of competition is directly read as the X-intercept. The derivation which validates the use of this graphical method for competition hybridization data is presented.
Summary.
RNA-DNA hybridization can be a powerful quantitative tool. When an excess amount of radioactive RNA is used it will saturate all complementary DNA sites, yielding a certain amount of hybridized radioactivity. We assume throughout this report that the experimenter has determined that there is adequate time to allow the hybridization reaction to go to completion. If under these saturating conditions an equal amount of unlabelled but otherwise identical RNA molecules are added, then only half of the previously observed hybridized radioactivity will be obtained. With increasing amounts of unlabelled RNA relative to the radioactive RNA, less and less radioactivity will be hybridized until at an infinitely large amount of unlabelled RNA no radioactivity will be hybridized. The unlabelled RNA is acting as a competitor with identical radioactive RNA molecules, and addition of competitor RNA to the system effectively acts to dilute the specific activity of the radioactive RNA. When various ratios of competitor to radioactive RNA are plotted Exp Cd
Res IO6 (1977)
against the radioactivity hybridized, the theoretical isotope dilution curve should be achieved (fig. 1a). In order to test if a particular unlabelled competitor RNA is identical in sequence to the radioactive RNA species, one observes whether or not the experimentally obtained hybridized radioactivity follows the theoretical isotope dilution curve as the ratio of competitor RNA to radioactive RNA is increased. If there is not total sequence identity between unlabelled and radioactive RNA molecules, one must estimate the limiting value of percent competition as the radioactive RNA is diluted to infinity. Fig. 2a depicts a curve for a situation where only 50% of the radioactive RNA sequences are also represented in the competitor RNA. Differences in molecular weight between the intact unlabelled and radioactive RNAs are not important to this plot since the amounts of RNA can be expressed as moles. Moreover, under the usual hybridization conditions at 65°C the RNA is degraded into smaller fragments so that steric hindrance by non-homologous unlabelled RNA which has not hybridized does not prevent the hybridization of neighboring homologous sequences [l]. Even if the competitor and radioactive RNA differ in size, this seems to have no effect on the kinetics of hybridization [2]. Fig. 2a shows that it is difficult to estimate precisely the percent competition at addition of unlimited competitor RNA. Therefore, the Scatchard plot method [3] is presented here as the preferred method for depicting competition hybridization data. Marsh & McCarthy [4] have already recommended the use of the Scatchard plot for hybridization saturation data because it is convenient and the experimental points are spread more evenly along the line than with other graphical methods. Others have uti-
Preliminuty
notes
455
is the molar equivalent of radioactive hybrid, and [DR] is the molar equivalent of unlabelled hybrid.
0 0
5
10
I5
20
25
I, 2. Ahcissu: (a) R/R*; (6) I-DR’; odinme: (a) DR*; (6) (I -DR*)/R. Fig. I. Complete competition of saturating amounts of radioactive RNA by addition of unlimited unlabelled RNA. See “Definitions” for abbreviations. The theoretically derived isotope dilution curve is plotted in the usual way in (a), and by the Scatchard plot method in (6). Figs
lized this method to account for RNA selfannealing [5]. The use of the Scatchard plot has been extended in the present report for competition hybridization experiments. Figs 1h and 2h replot the complete competition data and 50% competition data respectively, using the Scatchard plot. With this method of depicting the data, the actual percent competition can be accurately determined since it is the X-intercept. Moreover, this value can be directly obtained without using reciprocals, as is necessary for other graphical methods for hybridization data [6, 71. Use of the Scatchard plot in this manner has already proven helpful for analysis of competition of heterologous ribosomal RNA-DNA hybrids [l]. The derivation which validates the Scatchard plot method for use with competition hybridization data is presented below. Definitions Let [D] be the molar equivalent of free DNA sites complementary to the radioactive RNA being used, [I?*] is the molar concentration of radioactive RNA before thermal degradation, and [R] is the molar concentration of unlabelled RNA. Also, [DR*]
Derivation With no competitor RNA present the hybridization reaction which occurs is D+R*
4 ’ DR*
With sufficient time and under the usual hybridization conditions of 20-30°C below the T,,, the reaction goes entirely to the right, favoring the hybrid form. The association constant for this reaction is
K = WR*l ’
(‘1)
[D][R*]
which can be rearranged to read (2) If hybridization is carried out with an excess of R* in order to saturate all complementary sites on the DNA, then the maximum radioactive hybrid, DR;,,, will form. En route to saturation, DR$,,, will be the sum of free and bound DNA sites, or [DR,&]=[DR*]+[D]
0
5
10
I5
(3)
20
25
0
.2
4
6
.6
1.0
Fig. 2. Fifty percent competition of saturating amounts of radioactive RNA by addition of unlimited unlabelled RNA. Abbreviations as in fig. I. The theoretically derived curve is plotted in the usual way in (a), and by the Scatchard plot method in (h). ET/J Cc/l Hes 106 (1977)
456
Preliminary
notes
It follows that
Rearranging
Pl=PKLl-DR*l Substituting
(4)
eq (4) into eq (2) we obtain
([DR&,]-[DR*])
*K,=
[DR*] [R*]
[DRI -=-K,[DR]+K,[DR,,,] PI Substituting
eq (7) into eq (10) gives us
(5) [DR$,,,]-[DR”]
We now focus our attention on the effect that unlabelled competitor RNA has on the observed [DR;t;,,.; [R*] is still maintained in saturating amounts. Let us first consider the situation in which the sequence of R is identical to R*. In this case we will observe an isotope dilution effect. Any unlabelled hybrid, DR, will form at the expense of DR*, and [DR;ax]=[DR*]+[DR]+[D]
terms yields
(6)
LRJ
=
-K,([DR~,,I-[DR*l)+K,[DR,,,I
(11)
This fits the equation of a straight line r=mx+h For ease in plotting this, we may multiply values of either axis by a constant, such as the volume, so that we can express our units as moles rather than molarity. Since saturating amounts of R* are used, we can normalize DR&,, to 1, and substituting this into eq (7) we define the mole fraction of competed hybrid as
This is an extended version of eq (3), which was the special case of [DR]=O (i.e., no competitor RNA present). When the competition hybridization reaction has gone to completion under these saturating conditions, then [D]=O. Hence, for this case we can rewrite eq (6) as
Hence, in our straight line plot, for the left hand term
[DR]=[DR$,,]-[DR*]
4’= J-m*
(7)
for the situation at complete saturation. Similarly with only unlabelled RNA and no radioactive RNA, the reaction is L)+R
Yreliminnry
notes
12. Ponta, H, Ponta, U, Kraft, V & Wintersberger, E, Eur j biochem 46 (1974) 473. 13. Simchen, G, Genetics 76 (1974) 745. 14. Tonnesen, T & Friesen, J D, J bact I I5 (1973) 889. Received December 15, 1976 Accepted December 27, 1976
Analysis of RNA-DNA competition hybridization using the Scatchard plot SUSAN A. GERBI, versity,
Providence,
Biomedical RI 02912,
Divkion, USA
Brown
Uni-
The Scatchard plot is convenient for expressing RNA-DNA competition hybridization data because the maximum amount of competition is directly read as the X-intercept. The derivation which validates the use of this graphical method for competition hybridization data is presented.
Summary.
RNA-DNA hybridization can be a powerful quantitative tool. When an excess amount of radioactive RNA is used it will saturate all complementary DNA sites, yielding a certain amount of hybridized radioactivity. We assume throughout this report that the experimenter has determined that there is adequate time to allow the hybridization reaction to go to completion. If under these saturating conditions an equal amount of unlabelled but otherwise identical RNA molecules are added, then only half of the previously observed hybridized radioactivity will be obtained. With increasing amounts of unlabelled RNA relative to the radioactive RNA, less and less radioactivity will be hybridized until at an infinitely large amount of unlabelled RNA no radioactivity will be hybridized. The unlabelled RNA is acting as a competitor with identical radioactive RNA molecules, and addition of competitor RNA to the system effectively acts to dilute the specific activity of the radioactive RNA. When various ratios of competitor to radioactive RNA are plotted Exp Cd
Res IO6 (1977)
against the radioactivity hybridized, the theoretical isotope dilution curve should be achieved (fig. 1a). In order to test if a particular unlabelled competitor RNA is identical in sequence to the radioactive RNA species, one observes whether or not the experimentally obtained hybridized radioactivity follows the theoretical isotope dilution curve as the ratio of competitor RNA to radioactive RNA is increased. If there is not total sequence identity between unlabelled and radioactive RNA molecules, one must estimate the limiting value of percent competition as the radioactive RNA is diluted to infinity. Fig. 2a depicts a curve for a situation where only 50% of the radioactive RNA sequences are also represented in the competitor RNA. Differences in molecular weight between the intact unlabelled and radioactive RNAs are not important to this plot since the amounts of RNA can be expressed as moles. Moreover, under the usual hybridization conditions at 65°C the RNA is degraded into smaller fragments so that steric hindrance by non-homologous unlabelled RNA which has not hybridized does not prevent the hybridization of neighboring homologous sequences [l]. Even if the competitor and radioactive RNA differ in size, this seems to have no effect on the kinetics of hybridization [2]. Fig. 2a shows that it is difficult to estimate precisely the percent competition at addition of unlimited competitor RNA. Therefore, the Scatchard plot method [3] is presented here as the preferred method for depicting competition hybridization data. Marsh & McCarthy [4] have already recommended the use of the Scatchard plot for hybridization saturation data because it is convenient and the experimental points are spread more evenly along the line than with other graphical methods. Others have uti-
Preliminuty
notes
455
is the molar equivalent of radioactive hybrid, and [DR] is the molar equivalent of unlabelled hybrid.
0 0
5
10
I5
20
25
I, 2. Ahcissu: (a) R/R*; (6) I-DR’; odinme: (a) DR*; (6) (I -DR*)/R. Fig. I. Complete competition of saturating amounts of radioactive RNA by addition of unlimited unlabelled RNA. See “Definitions” for abbreviations. The theoretically derived isotope dilution curve is plotted in the usual way in (a), and by the Scatchard plot method in (6). Figs
lized this method to account for RNA selfannealing [5]. The use of the Scatchard plot has been extended in the present report for competition hybridization experiments. Figs 1h and 2h replot the complete competition data and 50% competition data respectively, using the Scatchard plot. With this method of depicting the data, the actual percent competition can be accurately determined since it is the X-intercept. Moreover, this value can be directly obtained without using reciprocals, as is necessary for other graphical methods for hybridization data [6, 71. Use of the Scatchard plot in this manner has already proven helpful for analysis of competition of heterologous ribosomal RNA-DNA hybrids [l]. The derivation which validates the Scatchard plot method for use with competition hybridization data is presented below. Definitions Let [D] be the molar equivalent of free DNA sites complementary to the radioactive RNA being used, [I?*] is the molar concentration of radioactive RNA before thermal degradation, and [R] is the molar concentration of unlabelled RNA. Also, [DR*]
Derivation With no competitor RNA present the hybridization reaction which occurs is D+R*
4 ’ DR*
With sufficient time and under the usual hybridization conditions of 20-30°C below the T,,, the reaction goes entirely to the right, favoring the hybrid form. The association constant for this reaction is
K = WR*l ’
(‘1)
[D][R*]
which can be rearranged to read (2) If hybridization is carried out with an excess of R* in order to saturate all complementary sites on the DNA, then the maximum radioactive hybrid, DR;,,, will form. En route to saturation, DR$,,, will be the sum of free and bound DNA sites, or [DR,&]=[DR*]+[D]
0
5
10
I5
(3)
20
25
0
.2
4
6
.6
1.0
Fig. 2. Fifty percent competition of saturating amounts of radioactive RNA by addition of unlimited unlabelled RNA. Abbreviations as in fig. I. The theoretically derived curve is plotted in the usual way in (a), and by the Scatchard plot method in (h). ET/J Cc/l Hes 106 (1977)
456
Preliminary
notes
It follows that
Rearranging
Pl=PKLl-DR*l Substituting
(4)
eq (4) into eq (2) we obtain
([DR&,]-[DR*])
*K,=
[DR*] [R*]
[DRI -=-K,[DR]+K,[DR,,,] PI Substituting
eq (7) into eq (10) gives us
(5) [DR$,,,]-[DR”]
We now focus our attention on the effect that unlabelled competitor RNA has on the observed [DR;t;,,.; [R*] is still maintained in saturating amounts. Let us first consider the situation in which the sequence of R is identical to R*. In this case we will observe an isotope dilution effect. Any unlabelled hybrid, DR, will form at the expense of DR*, and [DR;ax]=[DR*]+[DR]+[D]
terms yields
(6)
LRJ
=
-K,([DR~,,I-[DR*l)+K,[DR,,,I
(11)
This fits the equation of a straight line r=mx+h For ease in plotting this, we may multiply values of either axis by a constant, such as the volume, so that we can express our units as moles rather than molarity. Since saturating amounts of R* are used, we can normalize DR&,, to 1, and substituting this into eq (7) we define the mole fraction of competed hybrid as
This is an extended version of eq (3), which was the special case of [DR]=O (i.e., no competitor RNA present). When the competition hybridization reaction has gone to completion under these saturating conditions, then [D]=O. Hence, for this case we can rewrite eq (6) as
Hence, in our straight line plot, for the left hand term
[DR]=[DR$,,]-[DR*]
4’= J-m*
(7)
for the situation at complete saturation. Similarly with only unlabelled RNA and no radioactive RNA, the reaction is L)+R
