Smillie, R. M., Graham, D., Dwyer, M. R., Grieve, A., and
`Tobin, N. F. (1967), Biochem. Biophys. Res. Commun. 28,
`604.
`Spencer, D., Whitfield, P. R., Bottomley, W., and Wheeler,
`A. M. (1971), in Autonomy and Biogenesis of Mitochondria
`
`and Chloroplasts, Boardman, N. K., Linnane, A. W., and
`Smillie, R. M. Ed., Amsterdam, North-Holland, pp 372-
`382.
`Spencer, D., and Wildman, S. G. (1964), Biochemistry 3,954.
`Weisblum, B., and Davies, J. (1968), Bacreriol. Rer;. 32,493.
`
`S P I E G E L M A N , HABER, A N D H A L V O R S O N
`
`Kinetics of Ribonucleic Acid-Deoxyribonucleic Acid
`Membrane Filter Hybridiza tiont
`
`George B. Spiegelman,$ James E. Haber, and Harlyn 0. Halvorson*
`
`ABSTRACT: The kinetics of hybridization of RNA to DNA
`immobilized on membrane filters were examined. It was
`found that hybridization binding curves could not be described
`in terms of a single forward and a single reverse rate constant
`for the formation and dissociation of the hybrid. Detection
`of a new form of hybrid provided additional evidence that the
`adsorption process was more complex. This new hybrid form,
`although stable to conditions which removed nonspecific
`hybrid, was more readily dissociated and more sensitive to
`
`T he kinetics and the mechanism of association of single
`
`strands of nucleic acid when both strands are in solution have
`been widely studied (Wetmur and Davidson, 1968; Craig et al.,
`1971 ; Porshke and Eigen, 1971). While it has been found that
`the mechanism of association is complex, intermediates in the
`reaction do not accumulate, and thus the reaction appears to
`have only one kinetically significant step.
`DNA-RNA hybridization on membrane filters have also
`been assumed to be closely approximated by the kinetics of a
`one-step adsorption reaction (Perry et al., 1964; Mangiarotti
`et al., 1968; Lava116 and De Hauwer, 1968; Kennell, 1968).
`However, this assumption has not been precisely tested, and
`the actual mechanism of strand association in membrane filter
`hybridization remains obscure.
`For example, the annealing of RNA to membrane filter
`bound DNA is generally agreed to reach an apparent steady
`state after 24 hr (at 66" and 0.33 M sodium). However, Bishop
`(1970) has shown that the dissociation constant measured
`after 24 hr does not equal either the equilibrium constant
`calculated from the ratio of the reverse to the forward rate
`constant for the reaction or the equilibrium constant calcu-
`lated by extrapolating the dissociation constant to infinite
`time. The simplest explanation for this discrepancy is that,
`after 24 hr, hybridizations have not reached equilibrium. An
`alternative explanation is that Bishop's rate constants are
`distorted by the presence of fast and slow reacting DNA sites.
`Still another alternative is that this discrepancy reflects a more
`
`t From the Rosenstiel Basic Medical Sciences Research Center,
`Brandeis University, Waltham, Massachusetts 021 54. Receiued March
`30, 1972. Supported by a grant from the U. S. Public Health Service
`(GM-18904-01) and by funds from the Rosenstiel Basic Medical Sciences
`Research Center.
`$ National Institutes of Health Predoctoral Trainee. Present address:
`Department of Microbiology, University of Washington, Seattle,
`Washington 98105.
`1234 B I O C H E M I S T R Y , V O L . 1 2 , N O . 6, 1 9 7 3
`
`RNase treatment than the final hybrid form. The amount of
`this less stable hybrid bound to the filters was inversely related
`to the amount of stable hybrid bound. Furthermore, the un-
`stable hybrid could be converted into stable RNase-resistant
`hybrid under hybridization conditions. From these restilts we
`conclude that the unstable hybrid is a direct intermediate in
`hybrid formation and that both the formation and the con-
`version of the intermediate are rate determining in the kinetics
`of the overall reaction.
`
`complex kinetic mechanism for membrane filter hybridiza-
`tions. To examine these alternatives, we investigated in detail
`the kinetics of membrane filter hybridizations.
`For these investigations we used as a model system the
`hybridization of bacterial ribosomal RNA (rRNA) to total
`bacterial DNA. This system offers the advantages of natural
`polynucleotides with little internal redundancy of sequences
`(Fellner, 1971). Furthermore, the polynucleotides are easy
`to isolate in highly pure radioactive form. While there are
`three distinct ribosomal RNA species in our hybridizations
`(23S, 16S, and 5S), the RNA species and their DNA sites are
`present in the ratios of 1 :1 :1, and thus the hybridization can
`be considered in terms of a single RNA species (Avery and
`Midgely, 1969).
`Our investigations showed that the kinetics of membrane
`filter hybridizations were not those expected of a one-step
`nonequilibrium adsorption process. We found no evidence
`of fast and slow reacting DNA sites which could explain our
`results. However, we detected a second, less stable form of
`DNA-RNA hybrid. The properties of this new form of hybrid
`suggest that it is a direct kinetic intermediate in the hybridiza-
`tion reaction.
`
`Methods
`DNA Isolation. All of the DNA used in these hybridizations
`was labeled with tritiated thymidine. Cultures of Bacillus
`cereus T were grown in YP medium (4 gjl. of Bacto-peptone
`(DIFCO), 0.5 g/l. of yeast extract (DIFCO)) containing 5
`mCi/l. of [3H]thymidine (New England Nuclear Corp., 6.7
`Cijmmol). DNA (final specific activity of 4.3 X lo4 dpm/@g)
`was isolated from stationary phase cultures by a modification
`of the method of Marmur (1961) in which redistilled phenol
`saturated with 0.05 M Tris buffer, pH 7.5, was used for de-
`proteinization.
`
`Enzo Exhibit 2112
`Hologic, Inc. v. Enzo Life Sciences, Inc.
`Case IPR2016-00822
`
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`K I N E T I C S O F D N A - R N A M E M B R A N E F I L T E R
`
`RNA Isolation. An overnight culture of B. cereus T grown
`in a low phosphate medium (Spiegelman, 1972) was used to
`inoculate low phosphate medium containing 120 mCi/l. of
`carrier free 32P04 (New England Nuclear Corp.). The culture
`was grown until an AeO0 of 0.45 on a Beckman DB spectro-
`photometer was reached, and then potassium phosphate,
`pH 7.0, was added to the culture to a final concentration of
`0.1 M. After growth for one generation, the cells were harvested
`by centrifugation, resuspended in magnesium acetate buffer,
`pH 5.0, and disrupted by one pass through a French Pressure
`Cell (Aminco) at 20,000 psi. Ribosomes were obtained from
`the pellet of a differential centrifugation at 105,OOOg for 90
`min. The RNA was purified by phenol extraction and MAK
`column chromatography (Spiegelman et ai., 1973l). Unlabeled
`RNA was obtained in a similar manner.
`Hybridization Methods. The filter method of hybridization
`was used (Gillespie and Spiegelman, 1965). The hybridization
`buffer (f30SS) was based on that of Bonner et al. (1967) and
`contained 0.3 M NaCl-0.03 M sodium citrate, 30
`(v/v) stabi-
`lized formamide (Fisher), and 0.4 % (w/v) USP grade sodium
`dodecyl sulfate. Hybridizations were carried out in paraffin oil
`sealed vials containing 1 ml of f30SS. DNA was immobilized
`on Schleicher and Schuell type B6 membrane filters (Gillespie
`and Spiegelman, 1965) which were cut to 13 mm diameter
`circles containing approximately 0.5 pg of DNA. Retention
`of the DNA by the membrane filters was always greater than
`98%. All of the hybridizations were carried out at 37' with
`vigorous shaking.
`All RNA used in the hybridizations was degraded by heating
`as an aqueous solution in a boiling water bath for 5 min and
`then chilling in ice immediately before preparing the incuba-
`tion mixtures. This treatment results in a population of RNA
`molecules with an average size of about lo2 nucleotides as
`polyacrylamide gels
`measured by electrophoresis on 2.5
`(Spiegelman, 1972; Spiegelman et al. l).
`Both the total amount of RNA hybridized to the filter and
`hybrid which was resistant to RNase were measured. After
`incubation, the reaction was quenched by immersing the
`filters in 0.3 M NaCI, 0.03 M sodium citrate, pH 7.0 (2 X
`SSC?) at room temperature and then washing each filter
`once on each side with 25 ml of 2 x SSC under suction.
`Ribonuclease (RNase) resistant hybrid was determined by
`the method of Gillespie and Spiegelman (1965). An identical
`procedure was used to measure the total amount of hybrid,
`except that the RNase incubation was omitted.
`The amount of hybrid on the filter was calculated from the
`ratio of [32P]RNA to [3H]DNA radioactivity. The filters were
`washed with 1 ml of distilled water to remove excess salt
`(Spiegelman, 1972; Spiegelman et al. l), dried, and dissolved
`in 1 ml of ethyl acetate. Ten milliliters of toluene scintillator
`containing 4 g/l. of 2,5-diphenyloxazole (Packard) and 0.05
`g/1. of 1,4-bis[2-(5-phenyloxazolyl)]benzene (Packard) was
`added to each dissolved filter and the radioactivity measured
`with a Packard Tri-Carb scintillation counter. Parallel sets of
`filters without DNA were used as blanks to correct for non-
`specific association of [ 32P]RNA to the membrane itself.
`
`Results
`Eoaluation of Hybridizations as a Nonequilibrium One-Step
`Reaction. If membrane filter hybridizations occur by a one-step
`
`1 Spiegelman, G. B., et al. (1973), manuscript in preparation.
`* Abbreviation used is: SSC, standard saline-citrate.
`
`H Y B R I D I Z A T I O N S
`4.0 I
`
`-
`n
`0
`* 3.0
`a
`Z
`n
`rn 2.0
`
`2 00
`
`400
`
`600
`
`min.
`
`Pl ao,4t-
`
`a
`
`0.3
`
`,
`
`,
`
`40
`
`,
`
`,
`
`80
`
`,
`
`,
`
`I 2 0
`
`hr
`FIGURE 1 : Measurement of the rates of formation and dissociation
`of the RNA-DNA hybrid. (a) Kinetics of formation of RNA-DNA
`hybrid on membrane filters. Labeled rRNA (2 pg/ml) was hy-
`bridized to aH labeled DNA in f30SS at 37". At intervals, sets of
`filters were removed and the amount of RNase-resistant RNA
`bound was measured. The specific activity of the RNA was 6 X
`lo8 cpm/pg. Each point of the graph represents the average of three
`DNA membranes. The initial rate of formation of the hybrid was
`used to measure the rate constant, ken. (b) The dissociation of RNA
`hybridized to DNA filters. DNA filters were hybridized with 2 pg/ml
`of 3*P-labeled RNA in f30SS at 37". After 20 hr two sets of six
`filters were used to measure the amount of RNase-resistant hybrid.
`The remaining filters were rinsed, blotted, and returned to hy-
`bridization buffer containing 10 kg/ml of unlabeled rRNA. At
`intervals, filters were removed from the second incubation and the
`amount of RNase-resistant hybrid remaining was measured. Each
`determination of the amount of RNA remaining bound to the filter
`is the average of four filters. The rate of dissociation, kofr, was de-
`termined from the slope of the dissociation curve.
`
`reaction as do liquid associations, then they should be ade-
`quately described by the mechanism
`RNA + DNA
`
`kon
`
`koa
`
`hybrid
`
`(1)
`
`If, as indicated by Bishop (1970), the reaction has not reached
`equilibrium, data relating the degree of hybridization to the
`input concentration of RNA should be described by the time-
`dependent form of a Langmuir adsorption curve (Laidler,
`1965), using the measured values for the rate constants k,,
`and koff. The rate constant for formation (ken) was determined
`from the initial linear slope of the time course shown in
`Figure la, yielding a value of 0.142 ml/(pg hr). The rate con-
`stant for dissociation (k,ff) was measured from the slope
`of the decay curve (Figure lb) and equaled 0.0022 hr-l.
`In Figure 2 the theoretical hybridization binding curve based
`on the measured rate constants is compared in the form of a
`double reciprocal plot with data from several hybridization
`experiments carried out for 20 hr. The theoretical curve is
`B I O C H E M I S T R Y , V O L . 1 2 , N O . 6, 1 9 7 3 1235
`
`
`Exhibit 2112 Page 2
`
`

`
`3.0 1
`
`I
`
`I
`
`I
`I .o
`[RNA]-' ml /pg
`
`,
`
`I
`
`I
`2.0
`
`FIGURE 2 : Comparison of saturation hybridization data with a
`theoretical nonequilibrium, one-step adsorption curve. Several
`saturation curves for the hybridization of rRNA to DNA were
`measured after 20 hr of incubation at 37" in f30SS. The data are
`presented in the form of a double reciprocal plot. The maximum
`saturation level was determined by extrapolation of the saturation
`curves; the extent of hybridization is expressed as a per cent of the
`was calculated
`maximum saturation level. A theoretical curve (-)
`from the nonequilibrium form of a one-step binding reaction as dis-
`cussed in the text using the measured rate constants, k,, = 0.145
`ml/(pg hr) and k,ri = 0.0025 hr-1.
`
`nonlinear, as expected for a nonequilibrium condition. While
`the data for the 20-hr saturation experiments are also non-
`linear, the data points do not fall on the theoretical curve.
`This lack of correspondence between the theoretical curve
`
`and the saturation data far exceeds experimental error (8 z); a
`
`fit of the data could be obtained either by decreasing the value
`of k,, by a factor of 10 or by raising the value of koff by a
`factor of 10. Since measurement of k o f f did not appear to be
`subject to much experimental error, only a systematic error
`could cause an underestimation of koff. Such an error, which
`would result in an abnormal stabilization of duplexes, seemed
`unlikely to us; thus, systematic errors in the measurement of
`k,, were sought.
`One possible explanation for a systematic overestimation
`of k,, is that the RNase treatment used to eliminate regions of
`RNA not in heteroduplex (Gillespie and Spiegelman, 1965)
`might distort the early kinetics of the reaction. If, at the be-
`ginning of the hybridization reaction, a subfraction of the
`RNA binds more rapidly and with significantly higher RNase
`resistance (i.e., more complete duplex formation), the initial
`slope determination of k,, would be too high. Such a situation
`could be detected by taking the ratio of RNase-resistant
`hybrid to total hybrid formed during a time course (Figure 3a).
`The total hybrid can be directly measured in the absence of
`RNase treatment by washing the membranes extensively with
`2 X SSC, so that essentially all nonspecifically bound RNA
`is removed. Under the conditions used for these washings
`only molecules which are hybridized for approximately 15 or
`more continuous nucleotides are retained
`(Niyogi and
`Thomas, 1967; Niyogi, 1969). Thus, molecules which are
`retained meet requirements for specificity (McCarthy and
`Church, 1970).
`As seen in Figure 3b, the RNase resistance of bound RNA
`has a low initial value which can be extrapolated to 15 % at
`zero time. This resistance increases to approximately 65
`as
`the hybridization proceeds. This final value is in agreement
`1236 B I O C H E M I S T R Y , V O L . 1 2 , N O . 6, 1 9 7 3
`
`S P I E L G E L M A N , H A B E R , A N D H A L V O R S O N
`
`l a
`0 4.0 1
`
`m
`
`I
`
`X
`
`2.0
`
`0
`
`O I
`
`I .o ,I
`60 c"
`
`600
`
`0
`
`200
`
`400
`
`min.
`
`i
`
`2 0
`
`40
`
`60 80 100
`
`min.
`FIGURE 3: Rate of formation of hybrid in the presence and absence
`of RNase treatment. (a) Hybrid formation with 2 pu&/ml of labeled
`RNA was measured in the presence ( 0 ) and absence (0) of RNase
`treatment, as described in Methods. (b) The degree of RNase
`resistance was calculated as the ratio of RNase-resistant hybrid
`to total hybrid formed, as measured in part a.
`
`with other measurements of RNase resistance of hybrids
`formed on filters using rRNA (Gillespie and Spiegelman,
`1965; Fry and Artman, 1969). Since the initial RNase resis-
`tance is low, it is extremely unlikely that the measured value of
`k,, reflects selective binding of high RNase resistant mole-
`cules.
`Chuructevization of a Rupidly Dissociating Class of' Specific
`Hybrids. A one-step binding mechanism for membrane filter
`hybridization predicts that the degree of RNase resistance will
`remain constant throughout hybridization. In the data pre-
`sented in Figure 3, it does not. The predominance of bound
`RNA with low RNase resistance at the beginning of hybrid-
`ization suggests that there may be a class of specifically bound
`RNA molecules which are hybridized for only a small portion
`of their length. These molecules, although stable to washing
`procedures which remove all nonspecifically associated RNA,
`should dissociate much more rapidly than molecules hybrid-
`ized over a greater portion of their length.
`A more rapidly dissociating class of specific hybrid duplexes
`
`
`Exhibit 2112 Page 3
`
`

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`K I N E T I C S O F D N A - R N A M E M B R A N E F I L T E R H Y B R I D I Z A T I O N S
`too
`75
`
`X
`
`h
`
`loo
`
`c
`
`40
`
`5
`
`IO
`
`20
`
`5 0
`
`15
`Hours
`FIGURE 4: Dissociation of RNA-DNA hybrid measured without
`RNase treatment. 32P-Labeled total rRNA (2 pg/ml) was hybridized
`to 3H-labeled DNA for 2 hr in f30SS at 37". The filters were then
`placed into f30SS buffer containing 5 p g / d of unlabeled rRNA.
`At intervals, sets of six filters were removed and the amount of
`total hybrid remaining was measured. The data were normalized
`by setting the initial amount of hybrid equal to 100%. The dotted
`line is an extrapolation of the slow dissociation part of the curve.
`
`could be detected by a measurement of the dissociation of
`total bound RNA in the absence of RNase treatment. The
`time course of dissociation of total specific hybrid (Figure 4) is
`biphasic when plotted semilogarithmically, suggesting that
`there are at least two classes of dissociating RNA molecules.
`The rapid initial rate of decay can be resolved by subtracting
`the contribution of the slow rate seen after 20 hr (dotted
`line, Figure 4) from the total decay curve. Three determina-
`tions of the fast rate showed linear kinetics when plotted
`semilogarithmically (Figure 5). While the slopes of the fast
`decay curves were somewhat variable in several experiments,
`the half-life of the rapidly dissociating hybrid is approxi-
`mately 1.5 hr.
`If this class of rapidly dissociating hybrids were binding
`nonspecifically, or were a contaminant of the RNA prepara-
`tion binding to nonribosomal cistrons, then the amount of
`this unstable hybrid would be independent of the saturation
`of the ribosomal RNA sites. The relation between the amount
`of unstable RNA and the saturation level was tested by
`measuring the amount of unstable hybrid as a function of
`RNA concentration after a 20-hr hybridization incubation.
`The amount of rapidly dissociating hybrid can be estimated by
`extrapolating the slow linear slope of the dissociation curve
`back to zero time (as in Figure 4). The amount of the fast
`component is then the difference between the total bound
`RNA at zero time and the point of extrapolation. In Figure 4
`approximately 35 of the RNA bound is rapidly dissociating.
`For each measurement, two sets of membrane filters were
`hybridized for 20 hr. One set of filters was used to measure
`the amount of total RNA bound. The second set of filters was
`washed free of unbound labeled RNA and placed in f30SS
`containing 10 pg/ml of unlabeled RNA for 20 hr. As seen
`above, after the second 20-hr incubation the amount of
`hybrid remaining on the filter represents approximately 95
`of the stable RNA which had been formed. Correcting the
`amount of hybrid remaining on the second set of filters by 5
`
`50
`
`-g 25
`3
`a
`0 -
`0 .-
`c -
`'E
`#
`
`IO
`
`5
`
`2.5
`
`X
`
`X
`
`I
`I
`
`I
`
`I
`5
`
`I
`3
`h r.
`FIGURE 5: Rate of dissociation of the unstable hybrid. The rate of
`dissociation of the unstable hybrid was measured by subtracting
`the slow rate of decay (dotted line, Figure 4) from total the rate
`during the first 10 hr of the reaction. Experimental conditions are
`the same as in Figure 4. Three independent measurements were
`made (0, A, X). Each set of data was normalized to 100% initially
`bound. The slope for the rapid dissociation is -0.49 hrr1.
`
`gives a measurement of the amount of stable hybrid present
`at the start of the 20-hr dissociation. Subtraction of the cor-
`rected stable hybrid from the total hybrid should yield a
`measurement of the amount of rapidly dissociating hybrid.
`In Table I, the amount of rapidly dissociating hybrid is
`measured as a function of both RNA concentration and the
`amount of total hybrid bound. The amount of unstable
`hybrid decreased as the DNA was saturated with the stable
`form. Such data strongly indicate that the rapidly dissociating
`RNA is neither nonspecifically bound nor a contaminating
`RNA species, but rather competes for the same sites on the
`DNA as the ribosomal RNA species.
`The rapidly dissociating hybrids which apparently occupy
`rRNA might be very short RNA pieces (12-20 nucleotides),
`which would be displaced by larger RNAs as the saturation
`level is approached. Such rapidly dissociating hybrids, com-
`posed of short RNA molecules, should have high RNase
`resistance since the greater part of each molecule would be in
`heteroduplex. We tested this possibility by measuring RNase
`activity during the first 20 hr of the dissociation reaction.
`Membrane filters were hybridized for 2 hr with 2 pg/ml of
`radioactive rRNA and then removed, rinsed, blotted, and
`placed into f30SS containing 10 pg/ml of unlabeled RNA
`at 37". At intervals, parallel sets of filters were removed. One
`set was used to determine the total amount of radioactive
`RNA remaining (curve a, Figure 6) and the second set was
`used to measure the amount of RNase-resistant radioactive
`RNA bound (curve b, Figure 6).
`As seen in Figure 6, two processes occur simultaneously in
`the second incubation. During the first 10 hr of the dissocia-
`B I O C H E M I S T R Y , V O L . 1 2 , N O . 6, 1 9 7 3 1237
`
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`
`S P I E G E L M A N , H A B E R , A N D H A L V O R S O N
`
`TABLE I: Stable and Unstable RNA-DNA Hybrid Formation after 20 Hr of Hybridization as a Function of RNA Concentration.'
`
`RNA Input (Fg/ml)
`3.00
`1 S O
`0.75
`0.10
`0.50
`0.25
`Unstable hybrid formed (pg of RNA/pg of DNA X lo3)
`0.011
`0.028
`0.038
`0.041
`0.047
`0.048
`0.352
`0.340
`0.295
`0.264
`0.205
`0.131
`Stable hybrid formed (pg of RNA/pg of DNA X lo3)
`a Parallel sets of DNA filters were incubated at 37" for 20 hr in f30SS containing various concentrations of anP labeled rRNA.
`The amount of stable and unstable hybrid was measured by the procedure described in the text.
`
`tion there is a 34% loss of total bound material (curve a).
`At the same time there is an increase of 31% in RNase-
`resistant hybrid (curve b). After 10 hr, both curves decrease
`at the rate previously found for the slow decay of total hybrid
`after 20 hr of dissociation (Figure lb). Exactly analogous
`conversions were obtained in cases where the second incuba-
`tion contained either 1 pg/ml or no unlabeled RNA. Since the
`increase in RNase-resistant hybrid takes place in the presence
`of a vast excess (10 pg/ml) of unlabeled RNA, the increase
`must represent further hybridization of RNA molecules al-
`ready partially hybridized. Further more, the half-life of decay
`of total hybrid and the half-life of increase of RNase resistant
`hybrid are identical. Thus, it seems that the two processes
`are acting on the same pool of hybrids; that is, the unstable
`hybrid is the same species as that converted to a more RNase-
`resistant form. Finally, it should be noted that the increase in
`RNase resistance observed here is analogous to the change in
`RNase resistance in
`the overall hybridization reaction
`(Figure 3).
`
`80
`
`0 c 60
`rn
`
`5
`
`15
`
`2 0
`
`10
`hr.
`FIGURE 6: Chase experiment. DNA membranes and blank filters
`were hydridized for 2 hr with 2 pg/ml of radioactive rRNA in
`f30SS at 37". The filters were then transferred to fresh f30SS con-
`taining 10 pg/ml of unlabeled rRNA. At intervals, parallel sets of
`filters were removed from the second incubation. One set was washed
`and then the total hybrid (without RNase treatment) remaining was
`measured (curve a). The second set was RNase treated and then
`the remaining RNase resistant hybrid determined (the chase curve.
`curve b). The data were normalized so that the total amount of
`hybrid on the non-RNase treated sample was 100% initially.
`1238 B I O C H E M I S T R Y , V O L . 1 2 , N O . 6, 1 9 7 3
`
`Eualuation of Membrane Filter Hybridization as a Two-
`Step Reaction. The data presented in Figures 3,4, and 6 sug-
`gested that there exists a class of RNA-DNA hybrids which
`are specifically bound but only partially hybridized. This
`class of hybrids can either dissociate to free RNA or hybrid-
`ize further, resulting in a more stable hybrid. The detection
`of this class of hybrid suggested that membrane filter hybridiza-
`tion might be kinetically a two-step reaction which can be
`described by the mechanism
`RNA + DNA e X e H
`
`ki
`
`kz
`
`k3
`
`kr
`
`(2)
`
`where the unstable class of hybrid is the intermediate stage
`in the reaction (X) and the stable class of hybrid is the final
`stage (H).
`If membrane filter hybridization does involve a signifi-
`cant intermediate step, it should be possible to calculate the
`various rate constants of eq 2 from the dissociation and hy-
`bridization curves of Figure 6. These constants should gen-
`erate a theoretical saturation curve which describes the mea-
`sured saturation data. In addition, measurement of the for-
`mation of both the intermediate and the final stable hybrid
`form should show that the intermediate is found prior to the
`stable hybrid according to classical precursor-product rela-
`tionships.
`In considering the hybridization as a two-step process,
`it becomes necessary to reexamine the manner in which the
`amount of stable hybrid (Hobsd) was measured above. In a
`two-step mechanism it is no longer sufficient to determine
`the amount of stable hybrid by extrapolating the slope of
`the slow decay part of the dissociation curve, as was illus-
`trated in Figure 4. The data in Figure 6 show that during the
`dissociation experiment some unstable hybrid continues to
`hybridize. Consequently, Hobad as measured by extrapolation,
`is an overestimate of the amount of stable hybrid actually
`present at the start of the dissociation experiment (Ho).
`HO can be related to Hobsd by solving the kinetic equations
`for the decay of both stable and unstable hybrid (which
`depend on Ho) for the intercept used to measure Hobad.
`The difference between HobEd and Ho depends on the Values
`of the rate constants kp, k3, and ka of eq 2. For the constants
`determined by the curve fitting procedure below, HobEd iS
`nearly equal to ((k2 + k3)/k2)H0. Since Hobsd is greater than
`Ho, the observed amount of unstable hybrid (Xobsd) Will
`be less than the true amount of unstable hybrid (XO). Xobsd
`Ho, since (Hobsd + Xobsd) must equal (Ho + XO).
`will underestimate Xo by the same amount as Hobsd exceeds
`
`Values for the rate constants kz, ks, and k 4 were determined
`by curve fitting, using the data in Figure 6. The appropriate
`kinetic equations describe the mechanism
`
`
`Exhibit 2112 Page 5
`
`

`
`K I N E T I C S O F D N A - R N A M E M B R A N E F I L T E R
`
`H Y B R I D I Z A T I O N S
`
`TABLE 11: First Approximation for Rate Constants kz, k3, and
`k4.a
`
`1.4
`
`Assumed
`Calculated Constants (hr- l)
`Relationship
`kz
`k3
`k4
`between kz and k3
`0.01
`kz = k3
`0.24
`0.24
`kz = 10k3
`0.40
`0.04
`0.004
`0.06
`kz = O.lk3
`0.04
`0.40
`a Values of k2, k3, and k4 were calculated from rate equations
`for a two-step adsorption process by first assuming a rela-
`tionship between kz and k8. The sum of these three constants
`(kz + k3 + k4) is approximately equal to the rapid dissocia-
`tion rate (0.50 hr-l)) while kzk4 is approximately equal to the
`slow dissociation rate (0.0025 hr-l).
`
`-
`
`kr
`WO)R
`ka
`
`(XO)R
`
`k2
`
`RNArree
`
`(3)
`
`where ( H O ) ~ and ( X o ) ~ are the RNase-resistant fractions of
`stable and unstable hybrids, respectively. The equations used
`are similar to those for consecutive first-order reactions (Ben-
`son, 1960). In using the equations two alterations had to
`be made. First, since the data were measured in terms of
`Hobsd and not Ho, the appropriate expressions relating those
`two quantities were substituted into the equation. Secondly,
`factors had to be included to account for the use of RNase
`treatment. This was accomplished by assuming that each of
`the two hybrid forms had a constant RNase resistance. The
`RNase resistance of unstable hybrids was measured by ex-
`trapolating the curve in Figure 3b to zero time (15%) since
`it is assumed that the very first hybrid formed would be of
`the intermediate unstable class. The RNase resistance of
`the stable hybrid was measured by the long time values in
`Figure 3a (65x), since it was assumed that little unstable
`hybrid would be present after a long incubation.
`By assuming different relationships between k, and k3
`(Table 11)) curves were generated and then compared to curve
`b, Figure 6, which had been normalized to an initial value
`of 1.0. As seen in Figure 7, the comparison shows clearly
`that kz must be nearly equal to k3 and approximately equal
`to 0.25 hr-1,
`To measure the rate constant kl, the rates of formation
`of both stable and unstable hybrids were measured. DNA
`membranes were hybridized with 2 kg/ml of radioactive RNA.
`used to measure the total amount of hybrid bound (Hobsd +
`At intervals two sets of filters were removed. One set was
`Xobsd or HO + Xo) and the other set of filters was placed in
`a dissociation reaction (f30SS, 37”, 10 pg/ml of unlabeled
`rRNA, for 20 hr) to measure the amount of observed stable
`hybrid (Hobsd). The values of f f o b s d and &bsd obtained from
`the experiment were corrected to values Ho and X o as described
`above. The value for kl, taken from the initial slope of the
`curve for the formation of the unstable hybrid, is 0.3 * 0.1
`ml/(pg hr). The corrected time course data in Figure 8 con-
`firm one prediction of the hypothesis of the existence of an
`intermediate hybrid in the reaction: the kinetics of the two
`forms do follow a precursor-product relationship.
`Using the rate constants calculated for the two-step
`adsorption mechanism, theoretical saturation curves were
`generated. The kinetic equations used for these curves are
`
`1.2
`
`U .-
`L
`n
`I 1.0
`2.
`c c
`0 c .:
`a 0
`0
`
`0.8
`
`0 z
`K v, O6
`.- 5 0.4
`e 4- u
`IL 0.2
`
`t \
`
`10
`
`5
`h r.
`FIGURE 7: Comparison of theoretical and measured chase curves.
`Theoretical chase curves for a two-step reaction were calculated
`and compared with curve b in Figure 6 (0-0). In curve a, kz = k3;
`in curve b, kz = 0.1k3; and in curve c, kz = 1Ok3. The values of the
`rate constants in each case are given in Table 11. The RNase resis-
`tance of the intermediate form was taken from Figure 3 as 15%
`and the RNase resistance of the stable hybrid was taken at 6 5 z .
`The initial amounts of Ho and XO were calculated by extrapolation
`of the slow dissociation curve to give HDbsd and &bad and these
`values converted to Ho and Xo, as described in the text.
`
`similar to those published by Nossell and Ninham (1970)
`for multisite adsorption. These curves describe the reaction
`
`where ( X o ) ~ and (Ho)R are the RNase-resistant fractions of
`XO and Ha. Therefore, use of these equations requires inclu-
`sion of the RNase-resistance factors for the curve fitting pro-
`cedure described above. A theoretical curve, based on the
`calculated rate constants, is presented in Figure 9. The fact
`that the saturation data are well described by two-step ad-
`sorption curves is further evidence for the complex hybridiza-
`tion mechanism.
`
`Discussion
`The measured kinetics of ribosomal RNA hybridization
`to DNA immobilized on membrane filter do not conform to
`the generally assumed theoretical one-step mechanism. After
`examining several possible sources of systematic error in
`the measurement of either the forward or reverse rate con-
`stant, we concluded that the hybridization process must be
`more complex, with more than one kinetically significant
`step. Several experiments produced data which suggested
`the existence of an intermediate hybrid formed during hy-
`bridization. This intermediate hybrid is stable to procedures
`which remove nonspecifically bound RNA (Niyogi and
`Thomas, 1967), but dissociates 200 times more rapidly than
`“normal” hybrid under hybridization conditions. Since the
`rate of dissociation of double stranded nucleic acids with a
`B I O C H E M I S T R Y , V O L . 12, N O . 6, 1 9 7 3 1239
`
`
`Exhibit 2112 Page 6
`
`

`
`S P I E G E L M A N , H A B E R , A N D H A L V O R S O N
`
`2.0 t-
`
`-
`I
`n
`c 1.8
`.-
`0
`c
`2 1.6
`cn
`
`C o 1.4
`.-
`e
`0
`A 1.2
`
`I .o
`
`1.00
`
`C .? 0.75
`c
`Q
`L
`3
`e
`
`0.50
`
`C 0
`.-
`c
`V
`
`I&
`
`0.25
`
`5
`
`15
`
`2 0
`
`IO
`