METHODS AND KITS FOR SCREENING NUCLEIC ACID DUPLEX STABILITY

PROCEDES ET KITS PERMETTANT DE DETERMINER LA STABILITE DE DUPLEX D'ACIDE NUCLEIQUE

English Abstract

Simple methods and kits for determining the thermodynamic stability of nucleic
acid duplexes and single polynucleotide polymorphisms via competitive
equilibria are provided.

French Abstract

Cette invention concerne des procédés et des kits simples permettant de déterminer la stabilité thermodynamique de duplex d'acide nucléique et de polymorphismes polynucléotidiques simples via des équilibres concurrentiels.

Claims

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What is claimed is:


1. A method for screening for nucleic acid duplex
stability by competitive equilibria comprising:
(a) producing a solution containing a known amount
of an initial nucleic acid duplex with a known stability, said
initial nucleic acid duplex comprising a first nucleic acid
strand having a sequence wholly or in part homologous to a
target strand and a second nucleic acid strand having a
sequence wholly or in part complementary to the target strand;
(b) titrating the solution with a second solution
comprising a known concentration of the target nucleic acid
strand which competes with the first nucleic acid strand for
binding to the second nucleic acid strand, said target nucleic
acid strand being single- or double-stranded;
(c) subjecting the titrated solution to conditions
which disrupt the initial nucleic acid duplex and any duplex
or triplex formed between the target strand and the second
nucleic acid strand, but which do not disrupt the target
strand when double-stranded;
(d) subjecting the titrated solution to conditions
which promote duplex or triplex formation; and
(e) monitoring the titrated solution for changes in
the amount of initial nucleic acid duplex formed as a function
of the amount of target nucleic arid strand added.

2. The method of claim 1 wherein the conditions in
step (c) comprise heating the titrated solution to a
temperature high enough to disrupt the initial nucleic acid
duplex and any duplex or triplex formed between the target
strand and the second nucleic acid strand, but which do not
disrupt the target strand when double-stranded and the
conditions of step (d) comprise cooling the titrated solution
to a temperature wherein duplex formation occurs.

3. A method for screening for nucleic acid duplex
stability comprising:



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(a) producing a solution containing an initial
nucleic acid duplex comprising an initial nucleic acid duplex
with a known stability, said initial nucleic acid duplex
comprising a first nucleic acid strand and a second nucleic
acid strand, each strand being capable of forming a duplex
with a double-stranded target strand;
(b) titrating the target strand into the solution to
compete with initial nucleic acid duplex formation by forming
duplexes of target strand and first nucleic acid strand and
target strand and second nucleic acid strand;
(c) subjecting the titrated solution to conditions
which disrupt the initial nucleic acid duplex, the double-
stranded target strand, and any duplex between the disrupted
target strands and the first and second nucleic acid strands;
(d) subjecting the titrated solution to conditions
which promote duplex formation; and
(e) monitoring the titrated solution for changes in
the amount of initial nucleic acid duplex formed as a function
of the amount of target nucleic acid strand added.

4. The method of claim 3. wherein the conditions in
step (c) comprise heating the titrated solution to a
temperature high enough to disrupt the initial nucleic acid
duplex, the double-stranded target duplex and any duplexes
formed between the disrupted target strands and the first or
second nucleic acid strands and the conditions of step (d)
comprise cooling the titrated solution to a temperature
wherein duplex formation occurs.

5. A method for extracting enthalpy data from the
competitive equilibria method of claim 2 or 4 comprising
controlling temperature during step (d) so that changes
monitored in step (e) can be collected as a function of
temperature to produce a family of titration curves that can
be used to extract enthalpy (.DELTA.H°) data.




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6. A method for detecting a single nucleotide
polymorphism comprising:
(a) producing an initial nucleic acid duplex
comprising a first and second nucleic acid strand, wherein the
first or second strand of the duplex is designed to identify
a single nucleotide polymorphism in a single- or double-
stranded target nucleic acid sequence;
(b) measuring the amount of the initial nucleic acid
duplex;
(c) adding a fixed excess amount of a target nucleic
acid strand into the solution;
(d) subjecting the solution to conditions which
disrupt the initial nucleic acid duplex and any duplex or
triplex formed between the target strand and the first or
second nucleic acid strand, but which do not disrupt the
target strand when double-stranded;
(e) subjecting the titrated solution to conditions
which promote duplex or triplex formation; and
(f) measuring the amount of initial duplex formed
after addition of the target strand wherein the measured
amount after addition of the target strand is indicative of
the target strand containing the single nucleotide
polymorphism.

7. The method of claim 6. wherein the conditions in
step (c) comprise heating the titrated solution to a
temperature high enough to disrupt the initial nucleic acid
duplex and any duplex or triplex formed between the target
strand and the second nucleic acid strand, but which do not
disrupt the target strand when double-stranded and the
conditions of step (d) comprise cooling the titrated solution
to a temperature wherein duplex formation occurs.
8. A method for detecting a single nucleotide
polymorphism comprising:
(a) producing an initial nucleic acid duplex
comprising a first and second nucleic acid strand, wherein the



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first or second strand of the duplex is designed to identify
a single nucleotide polymorphisms in a double-stranded target
nucleic acid sequence;
(b) measuring the amount of the initial nucleic acid
duplex;
(c) adding a fixed excess amount of a target nucleic
acid strand into the solution;
(d) subjecting the solution to conditions which
disrupt the initial nucleic acid duplex, the double-stranded
target nucleic acid sequence and any duplex formed between the
target strand and the first or second nucleic acid strand;
(e) subjecting the titrated solution to conditions
which promote duplex formation; and
(f) measuring the amount of initial duplex formed
after addition of the target strand wherein the measured
amount after addition of the target strand is indicative of
the target strand containing the single nucleotide
polymorphism.

9. The method of claim 8 wherein the conditions in
step (c) comprise heating the titrated solution to a
temperature high enough to disrupt the initial nucleic acid
duplex, the double-stranded target duplex and any duplexes
formed between the disrupted target strands and the first or
second nucleic acid strands and the conditions of step (d)
comprise cooling the titrated solution to a temperature
wherein duplex formation occurs.

10. The method of claims 6 through 9 wherein one
nucleic acid strand of the duplex formed in step (a) contains
a sequence corresponding to the targeted single nucleotide
polymorphism; and the measured amount of initial duplex formed
after addition of the target strand indicative of the target
strand containing the single nucleotide polymorphism in step
(f) decreases as compared to the amount measured in step (b).



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11. The method of claims 6 through 9 wherein one
nucleic acid strand of the duplex formed in step (a) is a wild
type sequence; and the measured amount of initial duplex
formed after addition of the target strand is indicative of
the target strand containing the single nucleotide
polymorphism in step (f) is approximately equal to the amount
measured in step (b).

12. A method for determining the concentration of a
target nucleic acid sequence comprising:
(a) adding a known volume and concentration of an
initial nucleic acid duplex with a known stability to a known
volume of a solution containing a target strand;
(b) subjecting the solution to conditions which
disrupt the initial nucleic acid duplex and any duplex
between the target strand and a strand of the initial nucleic
acid duplex;
(c) subjecting the solution to conditions which
promote duplex formation; and
(d) determining the relative change in the amount of
initial duplex formed in the solution.

13. A method for determining the concentration of a
target nucleic acid sequence comprising:
(a) adding a known volume of a solution of target
strand to a known volume of a solution containing a known
concentration of an initial nucleic acid duplex with a known
stability;
(b) subjecting the solution to conditions which
disrupt the initial nucleic acid duplex and any duplex
between the target strand and a strand of the initial nucleic
acid duplex;
(c) subjecting the solution to conditions which
promote duplex formation; and
(d) determining the relative change in the amount of
initial duplex formed in the solution.



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14. The method of claim 12 or 13 wherein the
conditions in step (c) comprise heating the titrated solution
to a temperature high enough to disrupt the initial nucleic
acid duplex and any duplex or triplex formed between the
target strand and the second nucleic acid strand, but which
do not disrupt the target strand when double-stranded and the
conditions of step (d) comprise cooling the titrated solution
to a temperature wherein duplex formation occurs.

15. A method for assessing stability of various
selected target strands comprising:
(a) selecting various target strands;
(b) performing the method of claim 1 with the same
initial nucleic acid duplex and each of the selected target
strands; and
(c) comparing monitored changes in the amount of
initial nucleic acid duplex formed as a function of the amount
of the selected target nucleic acid strand added to ascertain
differences in stability of duplexes or triplexes formed by
the various target strands.

16. The method of claims 1 through 15 wherein
changes in the amount of initial nucleic acid duplex as a
function of the amount of target nucleic acid strand added are
monitored optically.

17. The method of claim 16 wherein fluorescent dyes
are attached to the first and second nucleic acid strands of
the initial nucleic acid duplex and changes are monitored
optically via eximer fluorescence.

18. The method of claims 1 through 15 wherein the
first nucleic acid strand comprises a donor nucleic acid
strand labeled with a donor of a FET pair and the second
nucleic acid strand comprises an acceptor nucleic acid strand
labeled with an acceptor of the FET pair and changes in the
amount of initial nucleic acid duplex in the titrated solution
are monitored by measuring changes in FET donor or acceptor
intensity.



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19. The method of claims 1 through 4 wherein
multiple distinguishably labeled initial nucleic acid duplexes
are produced in step (a) and monitored for changes in step (e)
or (f).

20. The method of claim 19 wherein each
distinguishably labeled initial nucleic acid duplex comprises
nucleic acid strands labeled with different FET pairs to
differentiate so that changes can be monitored via selective
fluorescence excitation with different wavelength light and
detection of emission at different wavelengths.

21. The method of claim 20 wherein at least one of
fluorescent dye is used as a FET donor in one duplex and a FET
acceptor in another duplex.

22. The method of claim 19 wherein the multiple
initial nucleic acid duplexes are produced by addition of one
first nucleic acid strand which is wholly or in part
homologous to the target strand and multiple second nucleic
acid strands which are wholly or in part complementary to the
target.

23. The method of claim 2 2 wherein the first nucleic
acid strand is labeled with an FET donor and the multiple
second nucleic acid strands are labeled with different FET
acceptors.

24. The method of claim 22 wherein the first nucleic
acid stand is labeled with an FET acceptor and the multiple
second nucleic acid strands are labeled with different FET
donors.

25. The method of any of claims 1 through 24 wherein
at least one nucleic acid strand of the initial duplex
comprises an internal loop, a modified base, a modified
backbone, or a non-Watson-Crick nucleotide base variation.

26. The method of claim 25 wherein the modified
backbone comprises peptido-nucleic acids (PNA) or oligomers
incorporating modified phosphate or sugar moieties.




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27. The method of claim 26 wherein the non-Watson-
Crick nucleotide base variation comprises an intra strand
crosslink, an abasic site, a naturally occurring or synthetic
base variant, a base mimetic or a base adduct.

28. The method of claims 1 through 27 wherein at
least one nucleic acid strand of the initial nucleic acid
duplex is immobilized to a solid support.

29. The method of claim 28 wherein changes in
initial nucleic acid duplex are monitored via surface plasmon
resonance spectroscopy.

30. A method for determining the concentration of
a target nucleic acid sequence comprising:
(a) measuring fluorescence of a known volume of a
solution containing a single- or double-stranded target
nucleic acid sequence;
(b) adding a known volume and concentration of an
initial nucleic acid duplex to the solution;
(c) subjecting the solution to conditions which
disrupt the initial nucleic acid duplex and any duplex or
triplex formed between the target strand and strands of the
initial nucleic acid duplex, but which do not disrupt the
target strand when double-stranded;
(d) subjecting the solution to conditions which
promote duplex or triplex formation; and
(e) measuring the fluorescence of the solution after
step (d) so that a relative change in the fluorescence can be
determined.

31. A method for determining the concentration of
a target nucleic acid sequence comprising:
(a) measuring fluorescence of a solution containing
a known volume and concentration of an initial nucleic acid
duplex;
(b) adding a known volume of a single- or double-
stranded target nucleic acid sequence to the solution;



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(c) subjecting the solution to conditions which
disrupt the initial nucleic acid duplex and any duplex or
triplex formed between the target strand and strands of the
initial nucleic acid duplex, but which do not disrupt the
target strand when double-stranded;
(d) subjecting the solution to conditions which
promote duplex or triplex formation; and
(e) measuring the fluorescence of the solution after
step (d) so that a relative change in the fluorescence can be
determined.

32. The method of claims 30 or 31 wherein the
conditions in step (c) comprise heating the titrated solution
to a temperature high enough to disrupt the initial nucleic
acid duplex and any duplex or triplex formed between the
target strand and the second nucleic acid strand, but which
do not disrupt the target strand when double-stranded and the
conditions of step (d) comprise cooling the titrated solution
to a temperature wherein duplex formation occurs.

33. A kit for screening for nucleic acid duplex
stability by competitive equilibria comprising a known
concentration of an initial nucleic acid duplex with a known
stability, said initial nucleic acid duplex comprising a
first nucleic acid strand having a sequence wholly or in part
homologous to a target strand and a second nucleic acid strand
having a sequence wholly or in part complementary to the
target strand.

34. A kit for screening for nucleic acid duplex
stability comprising a FET-labeled nucleic acid duplex wherein
a first nucleic acid strand of the duplex is labeled with a
1 donor of a FET pair and a second nucleic acid strand of the
duplex is labeled with an acceptor of the FET pair.

35. A kit for screening for single nucleotide
polymorphisms comprising an initial nucleic acid duplex
wherein the first or second strand of the duplex is designed


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to identify a single nucleotide polymorphism in a single- or
double-stranded target nucleic acid. sequence.

36. The kit of claim 35 wherein the initial nucleic
acid duplex is FET-labeled.

37. The kits of claim 33 through 36 wherein a
strand of the initial nucleic acid duplex is immobilized to
a solid support.

Description

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METHODS AND KITS FOR SCREENING NUCLEIC ACID DUPLEX STABILITY
Introduction
This invention was made in the course of research
sponsored by the National Institutes of Health. The U.S.
Government may have certain rights :in this inventian.
Background of the Invention
Mutagenic lesions in DNA frequently result from
structural modifications of the hete;rocyclic bases (exocyclic
adducts, free radical-induced modiifications) and/or from
complete removal of the base (abasic sites). Further,
cellular processing of lesion containing DNA can lead to
mismatches, additions, deletions or base pair Substitutions.
Thus, by lesion, it is meant to inc7.ude mismatches, additions
and deletions. A wide range of lesion-induced thermodynamic
effects have been observed. Typically, the free energy
stabilizing the duplex is reduced significantly by inclusion
of the lesion: Methods of determining lesion effects on
duplex free energy are limited. Typically, the effect of a
DNA modification on the energetic~s of duplex formation is
measured by comparison of independently measured association
constants for the modified and unmodified duplex or by
comparing Tm values, which are commonly but erroneously
believed to represent thermodynamic stability. Therefore,
there is a need for a simple, rE~producible and sensitive
method for rapidly screening for duplex stability.
The assays of the invention have two novel features
which, when combined, provide a powerful and rapid method to
assess the consequences upon duplex formation of perturbations
to localized and/or global chemical'~features of nucleic acids.
The first unique aspect is using two simultaneously competing
equilibria to identify differences in equilibrium constants;
between formation of two different nucleic acid duplexes.


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Typically, the effect of a DNA moclification on the energies
of duplex formation have been measured by comparison of
independently measured association constants for the modified
DNA and the unmodified duplex requiring two separate
experiments. A second novel feature of the present invention
is that these assays require only one experiment.
Furthermore, there is a large technical barrier for
direct measurement of single duplex association events. In
conventional titration experiments, a solution of one strand
is added to a solution of its comp:Lement with formation of a
duplex monitored by any of a variety of methods, including
spectroscopic and calorimetric mei~.hods. To extract useful
information from a conventional titration, the experiment must
be devised such that a significant: fraction of free titrant
will be present throughout the titration. Satisfaction of
this condition leads to the familiar sinusoidal shape of the
titration curve. To satisfy this condition, typically the
product of the initial titrate concentration, c, and the
association constant, K, is in the range 10<cK<1000. Due to
the high association constant for :nucleic acid duplexes, the
component concentration must be: below the association
constant, the components are likely to be too dilute to be
detected by standard spectroscopic means. Having nucleic
acids compete for duplex formation, as in the present method,
creates a second equilibrium, i:eferred to herein as a
"competition" for duplex formation, that is measurable at
essentially any concentration range. Thus, the concentrations
can be tailored to virtually any method of detection.
Further, the competition is measured directly from a single
experiment rather than having to compare the results of two
independently measured experiments.
Another innovative aspects of this invention is the
ability to discriminate between the two duplexes being formed.
In one embodiment of the present invention fluorescence energy
transfer is used to facilitate this discrimination. A common


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spectroscopic method for monitoring duplex formation relies
on the hyperchromicity of duplex: formation. However, the
extinction coefficients of duplexes of similar length is not
a very sensitive~reporter of the small differences in DNA
content that are of most interest, as in the case of
oligonucleotide duplexes with damage to only a single base.
Even a technique such as circular dichroism is not
sufficiently sensitive and also suffers from difficulties in
interpretation of spectral variation which can be due to
factors other than duplex formation. FET provides a unique,
extremely sensitive, and essentially binary means of
discrimination because only a duplex with both the donor and
acceptor dyes will have the spectroscopic signature of the
energy transfer.
Competitive equilibrium assays of the present
invention are more widely adaptable to a variety of nucleic
acid systems than are assays than are based on changes in
intrinsic spectral characteristics of the dyes. For example,
the FET assay of the invention is dependent only on the
presence of the two dyes and is lirnited only by the necessity
of modifying DNA to bear the dyes and the fact that the
distance between the dyes increa~~es substantially when the
initial FET duplex is disrupted. Any spectral changes that
accompany the disruption of the FET duplex can be easily
treated during data analysis and do not cause any significant
complication for the FET assay.
Thus, the present invention has a number of
significant advantages over prior art techniques for
determining duplex stability.
Summary of the invention
An object of the present invention is to provide
methods for screening for nucleic: acid duplex stability by
competitive equilibria. Tn these methods, a solution is first
produced containing a known amount of an initial or reference
nucleic acid duplex with a known stability. The initial


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duplex is comprised of a first nu~clei.c acid strand having a
sequence; wholly or in part, homologous to a target strand and
a second nucleic acid strand having a sequence, wholly or in
part, complementary to the target strand. A series of
additions of target strand are then made by titrating the
solution with a second solution comprising a known
concentration of the target nucleic acid strand. This target
nucleic acid strand competes with the first nucleic acid
strand for binding to a nucleic acid strand of the initial
nucleic acid duplex. After each addition or titration, the
solution is subjected to conditions which disrupt some or all
of the nucleic acid duplexes and triplexes in the solution;
subjected to conditions which promote duplex or triplex
formation, and then monitored for any changes in the amount
of initial nucleic acid duplex formed as a function of the
amount of target nucleic acid strand added. This method can
be used for extracting entha7.py data by controlling
temperature during duplex or triplex formation and monitoring
changes as a function of temperature so that a family of
titration curves can be made and used to extract enthalpy
(oH° ) data .
Another object of the present invention is to provide
a for detecting a single nucleotide polymorphisms. In this
embodiment of the invention, the initial nucleic acid duplex
comprises a first and second nucleic acid strand, wherein the
first or second strand of the duplex is designed to identify
a single nucleotide polymorphism in a single- or double-
stranded target nucleic acid sequence. In this method, the
amount of the initial nucleic acid duplex in a solution is
first determined. A fixed excess .amount of a target nucleic
acid strand is then added to the solution. The solution is
then subjected to conditions which disrupt some or all
duplexes or triplexes in the solution followed by conditions
which promote duplex or triplex formation. The amount of
initial duplex formed after addition of the target strand is


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then measured. This measured amount,. after addition of the
target strand, is indicative of the target strand containing
the single nucleotide polymorphism.
Another object of the present invention is to provide
methods for determining the concentration of a target nucleic
acid strand which comprises ad<3ing a known volume and
concentration of an initial nucleic acid duplex with a known
stability to a known volume of a solution containing a target
strand. Alternatively, a known volume of a solution of target
strand can be added to a known volume of a solution containing
a known concentration of an initial nucleic acid duplex with
a known stability. The solution is then subjected to
conditions which disrupt the initial nucleic acid duplex and
any duplex between the target strand and a strand of the
initial nucleic acid duplex fol7Lowed by conditions which
promote duplex formation. The relative change in the amount
of initial duplex formed in the solution after addition of the
target strand is used to determine concentration of the target
strand.
Another object of the pre~~ent invention is to provide
a method for assessing stability of various selected target
strands. In this method competitive equilibrium assays are
performed with the same initial nucleic acid duplex for each
selected target strands. Change~~ in the amount of initial
nucleic acid duplex formed as a function of the amount of the
selected target nucleic acid strand added are compared for
each target strand to ascertain differences in stability of
duplexes or triplexes formed by the various target strands.
In this embodiment of the invention it is not necessary to
know the stability of the initial nucleic acid duplex.
In a preferred embodiment of these methods of the
invention, the first nucleic acid strand comprises a donor
nucleic acid strand labeled with a donor of a FET pair and the
second nucleic acid strand comprises an acceptor nucleic acid
strand labeled with an acceptor of the FET pair and changes


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in the amount of initial nucleic <~cid.duplex in the titrated
solution are monitored by measuring changes in FET donor or
acceptor intensity.
Yet another object of t:he present invention is to
S provide kits for screening for nucleic acid duplex stability
and single nucleotide polymorphisrns by competitive equilibria
methods.
Detailed Description of the Invention
The present invention is a method and kit for
IO screening the impact on nucleic acid duplex stability of
alterations in base structures, e.g. due to carcinogen
exposure or synthetic modification; the role of sequence
context on such effects; and any other such alterations in
Watson-Crick pairing such as mismatched base pairs or
15 bulged/unpaired bases. Modifications of the phosphodiester
backbone may also be detected. TY:~e small amounts of material
required, speed of execution and applicability to a wide range
of test strands make the assay useful for detailed
thermodynamic characterizations and for screening
20 applications. These features make the methods and kits of the
present invention superior to ca7_orimetry and other optical
methods, with significant savings in the amount of test
material necessary to perform a free energy determination.
The range of effects an duplex stability of a particular
25 defect or modification can be r~'adily determined with the
methods of the invention. With this information, the most
interesting duplexes can be identified for further study.
Thus, large investments in time and materials will be made
only for systems of real interest.
30 One of the key features of the invention is the
flexibility in the nature of the test nucleic acid components
that can be evaluated. In one experiment, two 13 mer DNA
oligonucleotides, each bearing one of the FET fluorophores,
referred to herein as donor (D) and acceptor (A) strands,
35 form a duplex. The test or target strand competitor is a


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third DNA oligonucleotide of the same length bearing a single
damaged site at the central position. However, application
of the method is general, encompassing virtually any variation
in the nature of the nucleic acid duplex and test strand
competitor. The donor (D) and acceptor (A) strands need not
be the same length nor must the target, whether single strand
' or duplex. Further, as used herein, the terms "DNA", "nucleic
acid", "oligonucleotide" and "strand" are meant to include
other variations as there is no requirement for any of the
three nucleic acid strands to be DI~fA. Accordingly, the terms
"DNA", "nucleic acid", "oligonuc7.eotide" and "strand" are
meant to include DNA, RNA, and .analogues including those
comprised, in whole or in part, of modified bases and/or
modified backbones such as peptido-nucleic acids (PNA) and
other oligomers, incorporating modi:Eied phosphate and/or sugar
moieties (e. g. PNAs, methyl phosphonates, phosphorothioates)
that maintain duplex-forming abilit:Y may be used in the method
of the invention. Further, these germs are also inclusive of
the vast number of non-Watson-Crick nucleotide base variations
that may be incorporated into any o:E the components, including
intra strand crosslinks, abasic sites, naturally occurring or
synthetic base variants, base rni.metics and base adducts,
including, for example, carcinogen-induced adducts. There is
also no need to limit the system to three independent strands
of the same length competing for formation of two possible
duplexes.
Most nucleic acid amplification techniques, such as
polymerase chain reaction produce duplex target. The
technique of the present invention can be used on such targets
in one of two ways.
In a first embodiment, a triple helix is formed
between the target duplex and one of the strands of the
reference duplex. The sequence requirements for triple helix
formation are well known. Typically, triple helices involve
stretches of pyrimidines on one strand of a Watson-Crick


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duplex, a complementary stretch of purines on the other strand
of the Watson-Crick duplex, and a third strand comprised of
stretches of either complementary purines or pyrimidines which
resides in the major groove of the duplex. Details of the
sequence requirements and tolerated substitutions are well
known and widely described in the art. The target duplex need
not be disrupted and all calculation equations provided in the
Examples are applicable to this embodiment without
modification.
The second embodiment is more complex and applicable
only when sequences do not meet the requirements for triple
helix formation. In this embodiment, the target duplex must
be disrupted, i.e. melted, so that bath the donor-labeled and
acceptor-labeled.oligonucleotide ca.n bind to the complementary
strand of the target duplex. The addition of two equilibria
(the formation of the target duplex: and the interaction of the
donor strand with one of the target. duplex strands) makes this
formalism .inappropriate for deriving quantitative data.
However, due to the law of mass action, the equilibrium
distribution of complexes will still depend on the relative
values of the equilibrium association constants and the
various concentrations. Therefore, the FET observable will
also depend on these values. As a consequence, qualitative
information on the relative stability of complexes formed by
the target duplex's component stra:n:ds and various sets of DNA
duplex probes can be obtained.
The method is also usefu7L for structures that might
include large bulging/unpaired regions, competing internal
loops and/or hairpins or other deviations from simple duplex
formation. The above-mentioned variants may occur in
combination, thereby increasing the number of potential
targets of study.
The only limitations are that the FET donor and
acceptor be within resonance distance in the initial duplex
and that formation of the competing complex prevents energy


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transfer by displacement of either donor or acceptor. Any FET
donor and acceptor pair can be u~~ed and such dyes are well
known in the art and commercially available. The fluorescent
dyes may be at opposite ends of the duplex (-5' and -5' or 3'
and 3'), the same end of the duplex: (-5' and -3'), or with one
or both fluorophores in the interior of the strands}. The
fluorophores may be linked after oligonucleotide synthesis or,
when the phosphoramidites are available, incorporated during
synthesis.
Further, FET, monitored either by fluorescence of the
acceptor or by quenching of the donor, is not the only usable
means of monitoring the amount of the reference or donor-
acceptor duplex. Any method by which the amount of reference
or initial duplex can be monitored as a function of the amount
of target can be used. Eximer fluorescence or other optical
means can be used. In fact, nucleic acid strands of the
initial duplex can be labeled with any pair of species with
properties or characteristics dependent upon proximity.
Examples include, but are not limited to, fluorescent dyes,
antibody-antigen pairs, enzyme-inhibitor pairs and enzyme-
coenzyme pairs. Further, if the assay is carried out on a
surface, surface plasmon resonance; (SPR) spectroscopy may be
employed with the label being a ch:romophore at the wavelength
used in the SPR measurement.
The high throughput nature of this assay, in
comparison to the more time and maiterial intensive techniques
generally used for thermodynamic analysis, makes the assay
applicable to various problems in biotechnology and
pharmaceutical research. For example, this assay can be used
to evaluate nucleotide mimetics as drugs such as the anti-HIV
drugs ddC and AZT; to evaluate the effects of
carcinogen/chemical exposure an the stability of DNA and DNA-
RNA hybrid duplexes; and for screening of various parameters
for hybridization studies (e. g. temperature, buffer,
sequences). Screening of non-natural nucleic acid analogs as


CA 02355920 2001-06-21
WO OOI37686 . PCTJUS99130751
_ lp _
antisense or antisense agents can also be addressed by this
method. The assay of the invention can be a companion
technique to help improve existing hybridization techniques.
The method of the invention can a7.so be used for screening,
in solution, for the presence: of single nucleotide
polymorphisms (SNPs or "snips") which are used in
pharmacogenetic research targeted at identifying the genetic
basis of disease and genetic diagnosis of the potential for
such disease in individuals. The latter aspects have
particular importance in the biotechnology industry. Many
companies are currently involved in developing and marketing
hybridization assays for a wide variety of research and
development efforts. Virtually al.l of the assays currently
in use rely on immobilization of ate least one participant in
the hybridization reaction. Significantly, the immobilization
introduces a host of complications, including non-specific
interaction of any/all of the components with the immobilizing
platform; possible distortion of the biochemically important
equilibrium due to immobilization; the possibility that the
chemical linkage of the immobilizalwion can partially occlude
the necessary interactions with the non-immobilized
components; and the necessity of additional steps in the
protocol for the immobilization itself prior to running the
binding experiments. The method of the invention, being
entirely in solution, eliminates tlZe complications caused by
immobilization. Further, because i~he method uses titration,
control experiments with standardized DNA can be run
frequently or in parallel with test compounds to eliminate
spurious results. Such standardized DNA is a component of a
kit for carrying out the method of the invention.
The competing equilibria which are the basis of this
assay provide a greatly enhanced method for detecting
differences in stability between two nearly identical
duplexes. Studying the association of two strands forming one
duplex and comparison of the association of two other strands


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- 11 -
in a separate experiment, as is done in current methods,
requires two experiments with th.e inherent compounding of
experimental error. The present. invention advantageously
requires only one.
The calculations used for data analysis are derived
from the general equations for three component, two-equilibria
systems as taught by Linn and Rigg:~ (J. Mol. Biol. (1972), 72,
671-90) .
Two equilibrium association constants are defined
below, with subscripts f and t indicating free and total
concentrations, respectively, arid AD, AX, D, A, and X
represent the donor/acceptor complex, the competitor/acceptor
complex, donor strand, and acceptor strand, and the competitor
or "test" strand, respectively:
K '~f - l~
X fAl X~_~) A _~D _AK
(Equation 1)
K ~ -
"° - DfAt Dc-~ A=-~tD -~K
(Equation 2)
These equations are for the "test" or "target" strand forming
a complex with the acceptor strand. In this and the models
that follow, the opposite competition, with X binding to D,
can also be described by simple substitution of the terms.
These basic expressions for the equilibrium constants
can be combined and rearranged to the following equation:


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- 12 -
lAJ ~ (lDJ ~ -l~~ Jy
1 + X -1~f K
+(~D~ ~ _UD J)
K
(Equation 3)
The loss of energy transfer is monitored as the AD
complex is disrupted by the formation of AX. The
complementary measurement of emission of the acceptor
subsequent to energy transfer also may be used. Which
approach works better will depend on the photophysical
properties of the fluorescent dyes. As discussed, the value,
8 is the fraction of the initially observed fluorescence
energy transfer at each point in the titration and is related
to the relative concentrations of the donor/acceptor complex
( [AD] ) to (total donor strand] ( LD~ t) ( [AD] - [D] t at the
beginning of the titration):
.L o
- -
" D 1 -I
a
(Equation 4)
with relative fluorescence readings for the dilution-corrected
relative fluorescence at each point n, I", fluorescence of the
fully formed FET duplex, Ice, and the fluorescence of the donor
strand alone , ID .
In equation 5, the dilution corrections are added
explicitly, where Vo is the initial volume of the D-containing
solution, VA, the volume of the added A-containing solution,
and vs, the volume of the ith aliquot of the X-containing
solution.


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- 13 -
v+v-~~v
r -r
D Lr
e=
V +V
r -r -
D AD
(Equation 5)
Substituting Equation 3 into Equation 4, assuming
that [X] t » IAxJ , and rearranging yields Equation 6
~A~ . t1-~j~
1+X ~~ ,
+LL~). C1-el
(Equation &)
A program (written in the Microsoft vBA language) that
computes a function theta ( fA] t, fD] t, CXJ t, K"~, K~) to
calculate the isotherms (6 vs. Xt or logXt) using equation 6
is depicted in Example 5. The value of 6 is found by
iteration to satisfy the equation RHS(equation 6) - 8 -
0, where RHS means right-hand side. The entire
experimental isotherm can be fit using equation 6 to find a
value for the desired parameter K,~. This is, however, not
necessary as shown in the following section.
Xo.s is defined as the concentration of competing
strand X at which 8 = 0.5, or exactly half of the
acceptor/donor duplex, AD, has been disrupted. The value
of Xa.s can be interpolated from a plot of 8 versus log [X] t.
When 6 = 0.5, a simple relation between the desired
equilibrium constant K,,~, the measured value Xo.s, and the
known values CDJ t and KAD results :in:


CA 02355920 2001-06-21
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- 14 -
K _ K ~D~'
2X
o.s
(Equation 7)
Application of the well known relation between ~G° and K
yields Equation 8:
D G = -.F~t2 K ~D~ '
2.X
° . 5
(Equation 8)
The value of K,~ will have been previously determined by
independent methods such as differential scanning calorimetry
and UV-absorbance melting. Alternate representations of
equation 8 can be used to evaluate the free energy changes
associated with the formation of the duplexes and the defects.
D
L1GA,° =~G,~ -Rf ln. 2X'
° . 5
(Equation 9)
D
~G ° --FCC' 1nK -Rf In 2X'
(Equation 10)


CA 02355920 2001-06-21
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- 15 -
D
OG,~ -~G,~ =-Fd' 1n 2X'
° . S
(Equation ll)
Alternatively, the impact of a difference between two
oligonucleotides (X1 & XZ) on duplex stability, ~oG°, can be
evaluated by titration (in separate experiments) of the two
competitors against the same reference AD duplex at the same
AD concentration {Equation 12).
X
~~G,°_ , =DG,° -~Gx° =-I~' 7n ° . ~ . s
X
o.s,.
(Equation 12)
In Equation 12, the value far K"~ is canceled. Therefore, one
can evaluate the free energy impact of a single defect, or
multiple defects, without thorough thermodynamic
characterization of the AD duplex.
The assumption of [X]t » [AX] in equation 6 can be
relaxed thereby leading to
~AJa1-e)
e=
1+ X ~ -~ K +~D~a1-el
K
(Equation 13)
An unknown parameter [AX] must be: evaluated as part of the
calculation of 8. This is accomplished by iteration over [AX]
with the restriction that [A] t = [A,X] + [AD] + [A] f. A second
root finding problem is executed with the objective being
finding a value of [AX] that sati~~fies the equation


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- 16 -
_ 6
~~ [~~-8D~ - K (11-a =0
(Equation 14)
A second program is also shown in Example 5 that calculates
theta { [A] t, [D] t, [X] t, K~, K~) wiithout the restriction that
[X]t » [AX]. While a useful reduction of equation 13
(similar to equations 7 and 8) cannot eliminate the need for
iterative solution, values of Xt at B - 0.5 are readily
calculated. Values of Xt so calculated are compared to
experimental values and K~ adjusted to produce the
experimental value of Xt
Comparison of isotherms calculated using equations
6 and 13 reveal that the error ini~roduced by the assumption
of negligible [AX] is small and only significant when K"~ ~K,~.
For K"~/K~ - 1, the error in free energy is about 0.4
kcal/mole; for K~ /K"~ = 0.1, 0.06 kcal/mole; and for K~/K~ =
0.01, 0.005 kcal/mole. Therefore, the assumption is in most
cases reasonable. Those cases where it is not totally without
adverse consequence, that is where K"~ ~K~, are readily
predictable, can be addressed easily by application of the
full equation 13.
As is clear from the equations 7 and 8, the K~ and
DG°,,~ values that are measured are' relative to the value of
K"~. As a practical matter, titration of X into the solution
to a concentration of 1000 [D] t is convenient . An Xo.S value of
1000[D]t corresponds to a o~G° val.ue of about 4.5 kcal/mole
(~~G° - -RTln(1/2000). This is a rather large range and
should accommodate most single ba;ae defects. The range can
easily be extended by performing additional titrations using
less stable AD duplexes. The stability of the AD duplexes can
be modulated by inclusion of modified bases and/or mismatches.
A series of AD duplexes can therefore be designed to cover


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- 17 -
essentially any range of oG° values, i.n intervals of 3 to 4
kcal/mole.
Analysis of the para7_1el titrations can be
accomplished independently or collectively to determine the
free energy values using the analysis described above.
Equation & can be rearranged and used to determine
the concentration of a target seqv.~ence (X), when the values
of K~ and K,~ are known. In this example, a known volume and
concentration of AD duplex is added to a known volume of an
X containing solution. Alternatively, a known volume of X
containing solution is added to a known volume of AD duplex
containing solution of known concentration. Thus [A]t=[D]t is
known. The concentration of X, [X:]t, can be calculated from
the relative change in fluorescence, 8, using the formula
CX] ~ = K ~LA] ~ (1-.8)~ _6~/8
M
(Equation l5)
When the temperature is controlled during the
annealing process of a titration, additional information can
be obtained. The cooling process can be performed in steps
so that values of 6 are collected as a function of
temperature. Data at each temperature are used to produce a
family of titration curves. Each curve is analyzed
independently and values for K~ are determined as a function
of temperature. The van't Hoff equation,
off°=-R(a~c /a(1/~) )
(Equation 16)


CA 02355920 2001-06-21
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1$ _
can be used to extract enthalpy (1~H°) data. The thermodynamic
description, at a given temperature is completed by using
DG°=-RTlnK and ~S°=(~H° - DG°)/T.
Direct detection of formation of DNA duplexes by
titration is extremely difficult because of the very low
concentrations required for monitoring the equilibrium which
are well below the operating range of traditional in-solution
methods. A competition assay is usable over a wide range of
instrumentally accessible concentrations. The method of the
invention provides a more reliable measurement of nucleic acid
complex stability over a very wide range of free energy values
because the titration depends an the difference in stability
between the initial donor/acceptor-containing duplex and the
resulting competitor-containing duplex and not on their
absolute free energy values. Therefore, the range of
accessible free energy values can be tuned by choice of the
initial danor/acceptor-containing duplex. Relative free
energies are usually the desired experimental result and the
method of the invention provides them directly. The lower
detection limits of the fluorophores define the maximum
difference in free energy that can be detected by the method.
The use of fluorophore detection provides great sensitivity.
The emission spectrum of the donor strand at 10 pM
concentration has been visualized. reliably using a photon
counting fluorometer.
Free energies calculated from the assay of the
present invention have been demonstrated to be in agreement
with those measured by extensive thermodynamic studies on
individual duplexes. In these ea~periments, two titrations
were performed at the same Dt concentration, for two starting
Watson-Crick FET duplexes, designated A~T and T~A, which
differ only by the central base pair, out of the 13 pairs in
the duplex. Competition on each duplex is from nearly the
same single strand as present in the FET duplexes, except this
single strand is unlabeled and has a tetrahydrofuranyl abasic


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- 19 -
"lesion" site (F) at the central base pair. Free energy
values measured by this method corr~pare quite favorably to
those measured by extensive differential scanning calorimetry
and W absorbance melting experiments on these 13-mer duplexes
containing a single tetrahydrofuran~~1 abasic site (F) in the
central position. Specifically, using the FET assay, a value
of -14.5 ~ 0.1 kcal/mole for formation of the F-T duplex was
determined, compared with a value of -15.1 ~ 0.6 kcal/mole
determined using DSC/W melts. Similarly, using the FET assay
a value of -16.2 ~ 0.1 kcal/mole was determined for formation
of the F-A duplex compared with <~ value of -16.0 ~ 0.4
kcal/mole by DSC/W melts. These results correspond to ~~G°
values of -1.7 a- 0.2 kcal/mole from FET and -0.9 ~ 1.0
kcal/mole from DSC/UV melting studies for substitution of an
A residue for a T residue opposite t;he abasic site.
Because measurement depends on relative
concentration, [D]t/[X], the method of the present invention
can be used in any concentration regime. The appropriate
concentration range is determined b;y the sensitivity of the
detection system. Accordingly, [D]t is selected by one of
skill to optimize the detection method. Due to practical
limitations on the volume of Citrant that can be added to the
Citrate, there are some practical limitations to the range of
free energy values that can be coverE~d by a single titration.
However, this range is quite large. A convenient limit of the
ratio [D] t/ [X] 0.5 is about 0. 001. This corresponds to a factor
of about 0.002 in association constant or 3.7 kcal/mol in free
energy. Most defects for which reliable free energy data are
available fall into this range.
However, since the measured free energy values depend
on the ratio of K~ and K"~ (o~G°), the appropriate choice of
donor-acceptor duplex must be made for each titration.
Because the complementarity of the component strand of the
donor-acceptor reference duplex need be only sufficient to
form the duplex and achieve moderate thermal stability, the


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- 20 -
assay may be tuned over a wide range of free energy values by
introducing mismatches in the donor-acceptor reference duplex.
By judicious choices of donor-acceptor duplexes, a series of
three donor acceptor duplexes can cover a range of 11
kcal/mole in free energy. If titrations are done in parallel,
use of such a family of duplexes relieves one of estimating
the magnitude of K,~ prior to perfoa~ming the titration. In
this embodiment of the method of the present invention,
several donor/acceptor complexes are formed simultaneously.
Each different donor or acceptor oligonucleotide differs
slightly, while maintaining complementarity of the acceptor
with the target (X) or employing an analogous system where X
binds to the donor, to produce donor/acceptor pairs of
differing stability. By appropriate selection of donor and
acceptor dyes, it is possible to conduct multiple simultaneous
titrations of X into a single solution. Spectroscopic
discrimination of the various donor acceptor pairs provides
multiple free energy determinations simultaneously.
The assay of the present invention can be adapted by
immobilization to a variety of inert solid supports using
technologies established for standard hybridization studies.
In this embodiment, one of the strands of the reference duplex
(either donor(D) or acceptor (A)) can be attached to the
surface. The reference duplex can then be formed on that
surface. Exposure to target will release the unattached
strand, thereby producing the signal. Because concentration
cannot be defined at a surface in the same way as in solution,
comparison to a standard of known stability is required for
quantitative results. Hawever, immobilization facilitates the
miniaturization and adoption of this assay to high throughput
screening while providing the benefit of using FET and the
competing equilibria to increase the sensitivity of
measurement of differences in duplex stability.
Immobilization may also allow for the construction of an
array of donor/acceptor duplexes of differing stability. Such


CA 02355920 2001-06-21
WO OOI37b86 . PCT/US99J30751 .
- 21 -
an array assures appropriate selection of the initial complex.
Further, because ranges of the free energy differences
measurable using the various initial complexes overlap,
multiple complementary measurements can be made
simultaneously.
Simultaneous titrations provide a number of
additional advantages to this assay. With appropriately
designed donor-acceptor reference complexes, the range of
accessible free energy is multiplied by the number of duplexes
titrated simultaneously. Thus, employing three simultaneous
donor-acceptor duplex titrations means that the effective
range of a single titration experiment becomes 9-12 kcal/mol,
without expending any extra test strand. The enhanced range
also means that a favorable outcome is likely in a single
experiment, rather than having to explore various single donor
acceptor duplexes to find one which has a free energy less
than 3-4 kcal/mol higher than the test duplex. Second, this
application provides a degree of multiplexing that reduces the
time involved in each assay, and thereby enhances the ability
to perform high throughput scrf~ening of nucleic acid
variations. Thus, the simultaneous titrations are truly
simultaneous rather than merely in parallel, meaning that all
of the information is gathered using a single cuvette. The
detailed theory supporting the simultaneous titration
experiment is described below.
Single Acceptor/ Multiple Donox or Multiple Acceptor/Szngle
Donor Me shod
In principle, any number of donor-acceptor pairs
could be included with selective ex<:itation of the donors and
a single acceptor. The limitation is imposed by the necessity
of finding several donors with non-overlapping excitation
spectra and sufficient Stokes shift: such that their emission .
spectra each overlap sufficiently i~he excitation spectrum of
the acceptor. This method allows a series of AD complexes
with varying K~ to be used simultaneously.


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As an example, the case wherein there are 3 donors
(D1, D2, D3) and a single acceptor dye (A) is described;
however, the number of donors is not limited to 3. The donors
are discriminated by the excitation wavelengths, 1~1, A2, A3-
The initial concentrations are [Dl] t = [DZ] ~ _ [D3] t = [A] t~3 .
The Donor and acceptor labeled strand can form any or all of
the complexes AD1, AD2, AD3, and AX. The equilibrium
constants for the various complexes that form are enumerated
below.
DA DA
K , _ a.
"° 1- D A D -DA A -DA-DA-DA-~
a t z a c z a a
r a
(Equation 17A)
DA DA
K _ '
D A D -DA A -DA-DA-DA-~'
a t z z c n z a
t a
(Equation 17B)
DA DA
K _ a _
D A D -DA A -DA-DA-DA-1~
a L r ~ a a a z a
t a
(Equation 17C)
K __ A'~ - A~C
X A X -~A' A -DA-DA-DA-~
r : v m a y~. .as t t ~ a ~ ' s ~ ~ y
{Equation 18)
Analogously, three theta values, which differ by the
excitation wavelength, can be defined.


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- 23 -
IA 1-Im
ai ~ ai "
° D ~ I.~_Im
a 1 .gin 1
(Equation 19A)
I"z-~.'z
A2 : a2 n
n D t IA z-IA z
2
a 2 "° 2
(Equation 19B)
IT'-.I~'
A D a, "
~' 3 - 3 a _
" r
s
Ia3-~.p3a3
(Equation 19C)
and thus
~~ _ ~-e" 1LD1
(Equation 20A)
~~2~~e"zLD2JL
(Equation 20B)
~ 3 ~ e" 3LD ~ t
(Equation 20C)
Combining equations 20 with equations Z7 and 18 and knowledge
of the three K~, values, allows for fitting for the value of
K,~. In principle, not all K~ value, need be known. In this


CA 02355920 2001-06-21
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- 24 -
case, the increased number of unknowns complicates the
analysis significantly.
An alternate model, in which AD1, ADz and AD3 are in
equilibrium with XD1, XDZ and XD3 can. be derived analogously.
Fitting here is more complex as the number of unknowns is
larger - including
K
2
K
xa
K
xa
A treatment in which a single donor and multiple
acceptors can be used when fluorescence energy transfer can
be observed directly (when acceptor emission is observable)
and the acceptor emission spectra, do not overlap
significantly. Derivation of appropriate equations for this
case is straightforward and analogous to those derived for the
above case.
Multiple Acceptor/Multiple Donor Methods
Several donor acceptor/cornplexes can be monitored in
solution simultaneously. Each donor must have a unique
excitation wavelength and each acceptor an absorbance spectrum
corresponding to the emission of it.s donor. If emission of
the acceptor is to be monitored, thEe emission spectra of the
acceptors must be unique. Some correction for overlap can be
made; however, such necessity complicates the data analysis
significantly. °The number of donor acceptor pairs is, in
principle, unlimited.
Multiple donor acceptor pairs are designated A1D1,
AZDz, A3D3, etc. An example is provided using three AD pairs,.
but any number is possible. Equations accounting for the
multiple simultaneous equilibria are described below.

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AD AD
_ 1 y y a
D A - D -A D -A D -A D A -A D -A D -A D -A
y ( y f 1 y' 1 1 7 1 3 7 1 L y y 1 Z 1 3 y
(Equation 21A)
AD AD
z z 1
K
"2D2 D A D -A D -A D -A D A -A D -A D -A D -A
a a z 1 Z s : 7 : a = y x s s 7 7
y
(Equation 21B)
AD AD
K __ 7 7 _ :~ 7
"s"3 D A ~~-A D'-A D -A D A -A D -A D -A D -A X
7 f 1 r 3 L 7 1 1 3 7 3 C 3 1 7 3 7 1 7
(Equation 21C)
AX AX
K - _ 7
"1X X A X -AX-AX-AX A -AD -AD -AD -A
t 1 c 1 s 7 y y 1 a ~ a 7 7
,.
(Equation 22)
It is assumed that each X sequence wall bind to Al, A2, and A3
with equal affinity, since the three acceptor oligonucleotides
have identical sequences . Therefore, [XA1] - fXA2] - f~31 and
K =K =K
A 1X " ZX A 3X
(Equation 23)
Similar reasoning leads to the assertion that CD1A1] - fDlAa]
- [D1A3] and so forth for the other donor sequences . Defining
expressions for 8 and substituting t:he following expressions
for the equilibrium constants it is found that:


CA 02355920 2001-06-21
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- 26 -
I"1_rn 2
8Ax A=D ~ °.r
D D < l~A~_IA~
D I A 1D 1
(Equation 24A)
-,-A 2-IA 2
eA2_ A=D
D _ D < l a 2 -.L a 2
D 2 A zD 2
(Equation 24B)
IA:lTTA3
ea3- A= D= D3 1D
D D < - ~A 3-IA 3
s
03 A3o3
(Equation 24C)
Therefore,
8D 1LD=J< LA=D=J fA=D. J LA=D=I
(Equation 25A)
8., ZLD ~ < -LA1 D= ~-LA= D: J-LA= D= J
(Equation 25B)
8D 3LD= J -_LA, D= ~-LA= D~ ~-LA= D= J
(Equation 25C)
Further assume that ~D~~r = (D211= rD3lf , which is determined by
the experimental setup.


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A D a~1
K _ x '
"1°1 D A 1_38~~ [A,x-E~xl+6x2+6x3 D ~ -~A X
x f x ' x i x
(Equation 26A)
A D exz
K T x x
x2°z Dx 'Ax ' 1-36x2 [A, -fax'+8xz+8x' D ~ -[A X]
x x x
c o
(Equation 26B)
A~ Dx 8x 3
K -
"3~' Dx ' A, ' 1-36x' [A ~~ -f3x 1+6x 2+8x ~ D' -[A X]
x 7 3
t
(Equation 26C)
AX AX
K _ ~ -
x lx X ' As ' ~X, 3~A X,l LA ~ ~ ex 1+ex z+ex 3 D ~' IA X,
s .~
(Equation 27)
Equations for
K
w Zx
and
K
a 3x
assume similar forms and as noted above are assumed equal to
K
A lx


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This system of equations (Equations 26 & 27) must be
solved by iterative methods to rind a value of K~ which
satisfies, at each Xt, the constr<~ints imposed by the known
concentrations of the AD complexes; derived from the measured
6 values.
A fundamentally different: strategy for simultaneous
monitoring of multiple donor/acceptor pairs is to use the dyes
as acceptor and donor, but on different duplexes: Again,
discrimination is made optically. Here, an example is
provided using three donor/acceptor complexes, but the method
is not limited in the number of complexes that can be
employed.
The nomenclature is altered slightly from that used
above. Here, each fluorescent dye is designated as D, with
superscript A indicating that dye D is acting as an acceptor
and superscript D indicating that dye D is acting as a donor.
Dyes are attached to oligonucleotides such that three FET-
capable duplexes can form: DAZD°1, Dx'3DD2, and DA4DD3. Dye D1 acts
only as a donor and D4 only as an acceptor; however, dyes Dz
and D~ act as acceptor and donor, but on different duplexes.
Again, the oligonucleotides are designed so that DA2Dpl, DASD°2.
and DA4DD3 vary in stability systematically and so that the X
strand can form duplexes with the acceptor bearing strands,
namely DAZX, DA3X and D''4X .
As in the cases described above, equilibrium
constants can be derived relating the concentrations of the
various solution components.
Da DD DADD
D A D t- A D _ A A , A D Z Alt A D A D A D
Dl Dz f Dl Dz Dl D3 Dl - D4 Di Dz - Dz Dl - Dz Dz - Dz Ds Dz
(Equation 28A)

CA 02355920 2001-06-21
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- 29 -
A D
D3 Dz D3 Dz
'~D~D° D A D A A A ~D A A D A D A p
D D Ds t - Dz r _ Dz Dz _ D3 D2 _ D4 Dz~ D3 r _ D3 Di _ Ds Dz _ Da D3 _ D3
(Equation 28B)
Da DD Da DD
D D D A f D3 t _ Dz D3 _ D3 D3 - D4 D3~ D4 t - D4 Dl - Dq Dz - D4
D D D A D A D A D A A D A D A D
(Equation 28C)
Because the acceptor strands are not identical (the dyes
differ although the oligonucleot~ides to which they are
attached are identical), there are three additional
equilibrium constants to define.
Dz"X D"X
K A =
z
°z" D" ,LX~f ~" -D,".D° -D,"D° --D="DS° -D"X LXy
.D"X -DS"X -I7".X,
(Equation 29A)
DJ"X D"X
K A = -
" 1I
/I D" D"D°. D"D° D"D° D"X LXy-D"X-D"X-IJ,"X,
DS" f LXJ f 1 ' 1 ' E 1 3 3 T 1
t
(Equation 29B)
17"X _ D,"X
K A = - _
I7," LX~f D," - D," DS° D," DJ° D " DS° - D," X X -
D " X - D " X D "
f a L ~ C 2 1 -
(Equation 29C)
If the dyes do not perturb the equilibria significantly, it
is reasonable to assume that ~~RX KD3 X K°4 X . The


CA 02355920 2001-06-21
WO 00137686 _ PCT/US99/30751
- 30 -
assumption that the acceptor dyes are equally perturbing or
non-perturbing is reasonable and testable.
D.Da IA~_Ia ~
A D
= A _'~1
° D D A 1 A 1
i I D I A D
°1. °2°1
(Equation 30A)
A z A 2 A z A
I D+I A~ _~ I" ~I A~ LAD_In z
z Dz Dz z - z
a ,
A A '/ A A 2 A z A 2
° D r ~ I D+I A J ~ I A D+I A ~ D I A D
02 OZJ D3D2 OZ Dz D3a2
(Equation 30B)
A D D a- A .~ I 3 .... I 3
A3- D D - (ID3 ID3~-~In3~ aA D A
3 3 3 _ 3
D o A 3 A 3 '/ a 3 a 3 A 3 A 3
a ~ D+I Al ( I JI~DPI A ~ D I A D
D3 03 a4a3 a3 D3 aAD3
(Equation 30C)
Note that in the expressions for n and n , the measured
quantities (shown in parentheses) contain contributions from
the fluorescence of the acceptor of the previous (as in the
assigned index) donor acceptor pair. This is assumed to be
independent of the formation of the' complex. This assumption
is testable, should it not be valid appropriate corrections
can be applied.
As in the above analyses, the concentrations of the
donor/acceptor complexes can be determined by measurement of
the 8 values and knowledge of the total concentrations of the
donor strands.


CA 02355920 2001-06-21
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- 31 -
LD"D°J 9°~~D°J
(Equation 31A)
lD"D°J-BnZLD°~
3 2
t
(Equation 31B)
lD"D °J-e° 3LD'°~,
(Equation 31C)
Again substituting values for the 8 terms and assuming that
which is determined by the experimental
setup, a system of equations is presented that can be solved
as a function of [X] t to find valves for
K A =K A =K A
°zx o3x y4x
D"D° 8A1
K t = - n
A D-
r r
a
D1° D=" 1-38°1~~~D'"J~-~~6°1+~"2+g"' ~jT°~ -
~D'"XJ
(Equation 32A}
D"D° 9~2
K A D= ~
°3°2 D° D'" 1 36°2 [D'" (6n1+6n2+8~3 D2° -
D"X
r r ) ( )x ~ Jr C J


CA 02355920 2001-06-21
WU 0~I376$6 PCT/US99I307S1
- 32 -
(Equation 32B)
DAD.D. VA3
1 1
K A D= -
D'D t DIx , 1-36n' [DI"~ -~~1+6~2+0~3 [D~D~~ ~~xXJ
t
(Equation 32C)
D"X DZ°X
K A = -
aZx DZA 'LX,f LD"~° 8al+~a2+ea3 ~D'"~~ ~D'AX~ (~X~~ 3~D'"X~~
(Equation 33)
Expressions for
KA
a3x
and
KA
04 x
are derived similarly and, as described above, their values
are assumed to be identical to
KA
a2x
The advantage of this method of multiple simultaneous
titration, where some of the dyes act as both donor and
acceptor (although on different oligonucleotides), over the
method described above, in which all donors and acceptors are
unique, is that the probability of identification of a set
of fluorescent dyes with the necessary photophysical
properties is enhanced.


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While there are restricti.ons.on the properties of a
set of dyes usable in simultaneous titratians, there are
likely to be many sets of usable dyes. One such set of dyes
is described in the table below. Each of them is available
from Molecular Probes, Inc. of Eugene, Oregon.
Donor Acceptor F a rescent Dye
DD
----- Ale~:a 350
2 2 Alexa 430
DD DR
Ale~;a 488
-- D4 Alexia 594
When one of the reference duplex strands is attached
to a surface, only the other strand need be labeled. In this
embodiment, the measurement is not FET, but rather
fluorescence. A washing step must be included in this
embodiment to remove released label. However, this
modification may disturb the equilibria rendering this
embodiment of the assay more qualitative than quantitative.
Multiple measurements can :be conducted simultaneously
on a surface. A series of different strands can be attached
to a surface so as to identify a particular oligonucleotide
with its location on the surface;. This kind of spatial
distribution of different oligonucle~otides is well known. The
fluorophore can be attached post-synthetically or as a
phosphoramidite; either method is compatible with methods for
producing an oligonucleotide array on a surface. A single
oligonucleotide with sufficient complementarily to form
reference duplexes with each of the immobilized strands can
be used to form a series of reference duplexes. The surface
is then exposed to a single target that simultaneously
equilibrates with all of the reference duplexes. A series of
standards can be routinely incorporated into this assay.


CA 02355920 2001-06-21
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The method of the present invention is of particular
use in single nucleotide polymorplhism (SNP) screening. The
theory behind the application of this FET assay to SNP
screening is based upon two segments of DNA, the first being
a "wild type" sequence (does not. contain a SNP), and the
second being a variant sequence {a SNP) that, for example, may
be a marker for disease or disease tendency. Standardized
methods abound for amplifying a :mall genetic sample (e. g.
from a few microliters of~blood), and the result would be one
amplified strand, which would become the unlabeled competitor
(X) strand in our FET assay. When amplification of the target
is performed the quantity of the target can be determined by
use of labeled primers. Either fluorescently labeled, so as
not to interfered with the subsequent FET measurement, or by
any of the many well known methods for l~.beling amplification
products.
Since SNP screening is merely a detection of a SNP,
and not a quantitation of energetic impact per se, FET-based
SNP screening does not even require a full titration of target
(X) into the donor-acceptor duplex. Merely adding a fixed
excess amount of the X strand is sufficient, in effect making
a two-point titration wherein the: fluorescence is measured
before and after X addition. The amount of X strand needed
should be in the range of 10- to :100-fold excess over donor
(D). In these experiments, when the sequences of X and D
match, X will efficiently displace D from the donor acceptor
duplex, causing an efficient, and probably complete, reduction
in 8. When X and D do not match, 8 will remain high. In
theory, either experiment would be sufficient to prove the
presence or absence of wild-type sequence. However, it is
generally preferable to guarantee that a positive and negative
signal will be achieved in clinical assays, so it would be
preferable to run two experiments in parallel, monitoring
donor-acceptor duplexes of wild-type and SNP sequences, one
of which should have high B and one low 8. Additionally, a


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- 35 -
heterozygous sample would score as an efficient competitor for
both donor-acceptor duplexes.
The assay is further applicable to situations where
there may be multiple SNP sites within a single gene, with
5 each variation occurring at low frequency. In this embodiment,
a much longer sequence can be screened similarly, still in a
single experiment. In such a case, the donor-acceptor duplex
has the wild-type sequence of the full length of the region
of interest. The amplified target: strand, X, is judged, from
10 a single 10- to 100-fold addition, to either compete or not
for the donor-acceptor duplex. If FET is reduced, and X is
a good competitor, then further screening could be done using
additional assays more specific in nature to the sequences in
question. Even if another specific screening method is
15 preferred, the global nature of the~FET assay is useful as a
first screen, eliminating the cost and expense of screening
by other more detailed methods for every single patient being
tested. If, among all SNPs identified within a gene, the
frequency runs as high as 20o fo:r having any one variation,
20 the single screen using a very long sequence would still
eliminate the need for extensive testing on 80% of the
samples. This would represent a large savings in material,
and would greatly improve the throughput of testing
facilities.
25 The SNP assay is not limited by the length of the
strands (e. g. number of bases long) that are being screened.
The actual length limitation is a theoretical barrier
attributable to a kinetic situation whereby very long uniquely
complementary sequences may not ever form a complete duplex.
30 This limitation is similar to the fact that long sequences
such as complete bacterial genomes cannot be completely
reannealed after thermal disruption. The barrier for this
assay is estimated to be in the range of several hundreds of
bases, such that sequences of interest in the range of up to
35 100 bases can be easily accommodated. Clearly, longer


CA 02355920 2001-06-21
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- 36 -
sequences, however, are considered within the scope of this
assay.
The relevance of a strand length of about 100 bases,
however, is that regions bearing even one SNP may be assessed
by a single assay, using this method. As SNP identity becomes
linked to disease potential in humans, such screening becomes
an extremely valuable technique for rapid diagnosis of
individual patients, both fox diagnosis of ailment, infection,
drug sensitivity, drug resistance, etc:, and early detection
of conditions that can lead to timely application of
preventative treatments. Regions of genes already identified
as having relevant SNPs are generally in the range of 100
bases or less, meaning that the theoretical length limitation
will not become a factor in practice.
The key feature of this method that eliminates length
of the oligonucleotides as a limitation, unlike in other
assays under commercial development, is that this method
depends on competition between two different equilibria
characterized by two different equilibrium constants. Thus
the actual measurement is the ratio of the two equilibrium
constants, and thus the differe:n.ce in free energies for
formation of these alternative duplexes . The difference in
free energy caused by a defect, :>uch as a single base pair
mismatch (i.e. not a canonical Wat:son-Crick pairing), is the
same whether the defect is within a very long duplex or a
short one, so lang as the bulk of t:he duplex generally remains
stable. Thus, the magnitude of ~G° is not a consideration,
since the fluorescence assay measures the difference in two
~G° values (~~G°) directly. Mismatches of the four canonical
bases will generally exhibit ~~G° values of about 1 or 2
kcal/mol, but this 1 to 2 kcal/mol is the actual magnitude of
the measurement itself. Thus, whether the absolute values are
20 kcal/mol of duplex, as in a 10-15 base pair
oligonucleotide, or 600 kcal/mo7. of duplex, in something


CA 02355920 2001-06-21
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_ 37 _
perhaps as long as a gene, the assay is silent to these
magnitudes, because it is reporting ~L1G° directly.
Fluorescently labeled strands used in the present
invention may be provided in a kit form. A researcher
interested in adapting their test DNA lesion could do so
simply by synthesizing a small amount of test DNA within a
sequence predefined by the kit DNi~. A kit would include at
least one FET-labeled starting duplex and the appropriate
buffer along with simple instrucaions for performing the
experiment and analyzing the data. The kit may also include
a standardized competitor strand to ensure reproducibility and
to facilitate comparisons over time. As an example, the
strands of a kit could be designed with specific targets in
mind. A specific kit could be designed, for example, to
1.5 screen for a single mutation in a gene.
The following nonlimitinc~ examples are provided to
further illustrate the present invention.
EXAMPLES
Example 1: Purification and dye-labeling of 5'-amino-linker
oligonucleotides
Standard phosphoramidite DNA synthesis with an amino-
linker phosphoramidite as the last (5") residue is performed.
The intact synthesis column is dried under vacuum. The column
is then cracked open and the glass support beads are
transferred to a screw top plastic bottle. Aqueous NH40H (1
ml) from the freezer is added to each tube and the DNA is
deprotected for three days at room temperature for standard
amidites. Tubes are then cooled in the freezer and the NH40H
is pipetted off. The supports are; then washed with 2 x 200
3 0 ~l water or a mixture of EtOH : CH3C:L~ : H20 ( 3 :1: 1 ) ; the samples
and washes are combined; and then dried in a Speed--Vac. The
dried samples are then dissolved in H20 at low temperature
(<40°C) and floating non-soluble materials are removed. At
this step, the sample may be purified by reverse phase, using
high performance liquid chromatography (HPLC ) and a PRP-

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- 38 -
column, equilibrated with 50 mM ammonium bicarbonate. Elution
is performed by a linear (5-500) gradient of acetonitrile in
50 mM NH4HC03. Following freeze-drying, the fractions
containing the purified tritylated N-modified oligonucleotide
are heated to 95°C for 5 minutes to remove the MMT-(trityl)
group and subjected to ethanol precipitation in the presence
of sodium ions, as fallows.: the volume is adjusted to 300 to
400 ~l water; NaCI (100 ~.1, 2M) or sodium buffer is then added
along with 950 ~.1 of EtOH; samples are then placed in the
freezer for at least 30 minutes, preferably one hour.
Following freezing, the sample is centrifuged for 12 minutes
at 14,000 rpm. The resulting pellet is dried to remove any
residual ethanol. Trityl is then removed by addition of 200
~.l of 80 o acetic acid for one hour at room temperature and
evaporating the liquid in a Speed -Vac for 2 to 3 hours until
a glassy residue is observed. Thi~~ step is critical to ensure
elimination of any residual free amines that might interfere
with the labeling reaction. For the unlabeled
oligonucleotides, the trityl group is removed by addition of
80% acetic acid and incubation for one hour at room
temperature, followed by freeze drying. Both the purity of
the final product and the success of detritylation are
monitored by analytical reverse phase HPLC. If required,
additional purification of the detritylated oligonucleotide
is performed by reverse phase HPLC. The purified DNA is
subjected to ethanol precipitation/Na+ exchange to rid the
sample of any excess reactive amines from the HPLC buffer and
labeled as follows: DNA (30-40 OD-260) is dissolved in 270 ~.l
of H20 in an O-ring tube. NaHCO3 (30 ~.1, 1 M} at pH 8.3 is
then added. One mg of succinyl ester form of the dye is then
added for each 20 OD of DNA. This can be weighed as a dry
reagent into a glass vial, dissolved in 80 ~C1/mg of fresh
DMSO, and added into the plastic tube of DNA solution. The
glass vial is then rinsed with 20 ~,1 of additional DMSO and
added to the plastic tube. Alternatively, a 100 ~Cl aliquot


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_ 39 _
of dye is added. The dye and DNA are then allowed to react
at 37°C or higher at least overnight.
The DNA is then isolated from any unreacted dye with
a PD-10 Sephadex G-25 column (Pharmacia). The column is
5 equilibrated by rinsing with at least 25 ml of H20. The DNA
sample is diluted with H20 to a final volume of 1000 ~Cl and
loaded onto the column. The DNA is then washed using 1.6 ml
HzO. DNA is eluted in 600 ~l fra.ctions with H20. Generally
six fractions are sufficient.
The fractions are dried i~o at least ~ the volume and
adjusted to 300 ~C1 total volume with H20. Each fraction is
then independently subjected too ethanol precipitation.
Generally only the first three fractions will have appreciable
DNA. The free dye stays mostly dissolved in the ethanol.
15 The DNA containing precipitates are combined and the
labeled DNA purified using ion exchange HPLC (Mono-Q column)
with Buffer A being 50 mM Tris HC1 with 15% acetonitrile and
Buffer B being Buffer A with 1 M NaCI. The gradient profile
can be tailored but in general increases from 0 to 80% buffer
20 B over 25-35 minutes. Monitoring absorbance at both 260 nm
and the absorbance maximum of the attached fluorophore can
help to define the labeled and unlabeled DNA peaks.
The labeled DNA is further purified by HPLC using an
ion exchange column (e. g. Mono Q, Pharmacia) equilibrated with
25 50 mM Tris HCl and 15% acetonitrile (Buffer A) and a linear
gradient (0-100%) of Buffer B (i.e., Buffer A containing 1 M
NaCI). Absorbances at 260 nm and the wavelength corresponding
to the maximum absorbance of t:he fluorophore are use to
monitor and define labeled and unlabeled pools of
30 oligonucleotides.
Alternatively, a desalting column can be used in
place of the ethanol precipitation steps.
5!-labeled oligonucleot.ides forming duplexes have
been compared with the parent un:l.abeled duplexes, revealing
35 no alterations in their thermodynamic stability in the


CA 02355920 2001-06-21
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40 -
presence of the probes. Moreover, the ability to form Watson-
Crick duplexes in a stoichiometric ratio has been further
confirmed by HPLC analysis of the annealed mixtures, in
comparison to the free oligonucle~otide strands. Additional
evidence reveals that both labeled and unlabeled
oligonucleotides may be recovered upon completion of a FET
assay by repurification, with no indication of adulteration.
Time-dependent studies of the integrity of the labeled
oligonucleotides reveal no sign of: aggregation or degradation
within 1 year from sample px-eparation. The labeled
oligonucleotides may be stored as ;stock solutions in water and
working buffer at or below -20°f, for at least six months.
Preferably, the samples should be stored as a lyophilized
powder, for periods exceeding six months.
Example 2: Determination of labe:Led DNA concentration
Determination of the concentration of the labeled DNA
strands in stock solutions has been performed using an average
extinction coefficient of 1.1 x 105 M-lcm-1 at 25°C. The
intrinsic DNA absorbance at 260 n.m has been demonstrated to
not be significantly altered by thE1 presence of the conjugated
dye.
Example 3: Formation of the FET duplex
A working stock solution of each of the labeled DNA
of complementary sequence in the range of 2 to 3 micromole DNA
strand is prepared. Fluorescence detection is performed as
follows: after each aliquot (of any titrant) the cuvette is
heated to about 90°C, using,an external heat block, and cooled
to 25°C via the intrinsic cooling of the jacketed cuvette
holder in the fluorometer. The: cuvette must be tightly
stoppered to minimize evaporation during heating. Wavelengths
must be tailored for the dyes used. For example, for the
fluorophore pair Oregon Green 514 and Rhodamine-Red-X, the
emission spectrum is collected over 510-650 nm with excitation
at 508 nm, with scanning at 100 nm per minute . The time
drive is set to collect, using the kinetics mode, 30 or 60


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seconds (at 0.1 second per reading) using 508 nm excitation
and 528 nm emission. These data points are then averaged,
resulting in a precise relative :Fluorescence intensity for
each reading, and an associated standard deviation for that
averaged value. The fluorescence of the buffer alone is read
to establish a blank for the instrument response.
The fluorescence of the 'free" donor strand is then
determined. A sample of 10 nM donor strand is prepared in 250
~.l total volume of buffer and fluorescence is measured. An
aliquot of the acceptor strand from the working stock
sufficient to achieve a final concentration of 100 nM is then
added to form the FET duplex and the fluorescence is
determined.
Example 4: Titration of the competing strand
A working stock of the competing strand is prepared
at a concentration appropriate to the expected
ability/inability to compete for duplex formation with the
formed donor/acceptor pair. In general, the concentration is
one order of magnitude higher than the donor and acceptor
working stocks for each 1 kcal/mol of free energy difference
(o~G) expected for the competing strand. In the event the
free energy differences are completely unknown, a number of
concentrations can be prepared, covering a wide range of
concentrations, i.e., 2 ~M, 20 ~.M, 200 ~,M, etc. solutions in
buffer. Titration is started with the most dilute solution
and more concentrated solutions are used as necessary.
For the first aliquot, thE: competing strand is added
to a final concentration of about i~ of the concentration of
the donor/acceptor concentration. The fluorescence is then
determined. If there is a significant change in the
fluorescence, titration is continued with the working stock.
If there is no change, titration i.s continued with a higher
working stock concentration. Additional aliquots are added
and the fluorescence determined until the fluorescence


CA 02355920 2001-06-21
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- 42 -
intensity recovers to at least ~ of: the intensity measured for
the free donor strand.
Example 5: Automation of competit:W a titration experiment
The FET.data acquisition protocol was automated on
an AVIV Model ATF-105 Automatic Titrating Fluorescence
Spectrophotometer. The customized software developed for the
FET assay on this particular instrument improved the overall
accuracy, precision, and data throughput compared to
conventional manual titration experiments. There are several
key features of the automated FET assay including programmed
titration of acceptor and competitor or target strands and the
ability to conduct successive heating/cooling cycles of the
sample solution in the cuvette. Selection of the upper
temperature limit is dictated by two important considerations,
namely that the parent and test duplexes are dissociated into
single strands and the covalently attached fluorophores are
stable at the desired upper temperature. Extensive control
studies conducted on the stability of the Oregon Green 514
(OG) and Rhodamine-Red-X (RdRX) labeled strands indicate that
these fluorophores retain their integrity during successive
heating/cooling cycles over the tennperature range of 0 - 75°.
The superimposition of W melting/cooling curves reveled that
the fluorescently labeled strands in the parent duplex are not
labile below 75°C. The overall reproducibility is compromised
when heating the identical duplex t.o temperatures above 75°C,
as noted in the family of non-superimposable UV
melting/cooling curves. It is incumbent upon the analyst to
judiciously evaluate and select the practical upper
temperature limit for a particular duplex and set of
fluorophores.
A typical experiment is initiated by placing a
cuvette containing a 100 nM solution of the Oregon Green 514
labeled donor strand in the sample compartment, heating the
cuvette to 75°C, maintaining the temperature at 75°C for three
minutes, and cooling the sample to 20°C over an equilibration


CA 02355920 2001-06-21
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period of five minutes. Durin~~ the cooling cycle, the
instrument is operated in the: kinetic mode and the
fluorescence emission intensity i;s recorded at 521 nm (i.e.
excitation wavelength - 508 nm) at five second intervals.
After the fluorescence intensity plateaus indicating that
equilibrium is achieved, a referE:nce spectrum of'the donor
strand is recorded over the wavelength range of 510-650 nm.
Activation of the first syringe drive dispenses fixed
microliter aliquots of the Rhodamine-Red-X labeled acceptor
strand in the sample cuvette to form the FET-active donor-
acceptor reference duplex. Upon addition of each aliquot of
acceptor, the sample is subjected to a heating/cooling cycle
identical to that above to ensure that the duplex anneals
properly. The donor strand (D) d(GCGTACACATGCG)-OG (SEQ ID
I5 NO:1) is titrated with its complementary acceptor strand (A)
d(CGCATGTGTACGC)-RdRX (SEQ ID N0:2) to form the FET-active
reference donor-acceptar duplex. The diluted corrected
fluorescence intensities are cast in the form of a Job Plot
to confirm that the stoichiometry o~f the single strands in the
reference duplex is 1:1 (i.e. mole fraction = 0.5). Although
the forward titration demonstrates that the single strands
associate to form a competent duplex, the experimental
protocol may be simplified by loading the pre-formed reference
duplex into the cuvette prior to conducting the automated
competition experiment. Elimination of the forward titration
increases the sample throughput by reducing overall
experimental time in the FET assay by approximately 50
percent.
Having formed the FET active reference duplex in the
initial part of the experiment, t:he second syringe drive is
activated to dispense fixed aliquots of the unlabeled
competing strand (X)d(CGCATGFGTACGC')(SEQ ID N0:3). The sample
solution containing the three strands is subjected to
heating/cooling cycles after each addition in the titration
experiment to facilitate annealing of the donor-acceptor and


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- 44 -
acceptor-target (AX) duplexes. .?~ sufficient excess of the
target strand X (in this case approximately 100 fold) is
titrated into the cuvette to ensure that at least half of the
acceptor has been displaced from the reference duplex. The
dilution corrected relative fluorE~scence (6) is plotted as a
function of the concentrations of acceptor (A) and target (X)
strands. The concentration of competing strand (Xo_5) at which
exactly half of the acceptor/donor duplex (AD) is disrupted,
that is 8 = 0.5, is interpolated from this plot. Substituting
the value for Xo.s into the simplified relation:
KAx= (K~~Dt/2oXo.s)
yields a value for the acceptor/t.arget association constant
(K,,~) . Application of the thermodynamic relation between OG°
and K~~facilitates calculation of the free energy:
DG°=-R~T~lnK~
In this example, values of Xo,s - 1.1 x 10-5 for
d(CGCATGFGTACGC)(SEQ ID N0:3) and Dt=4.22 x 10-8 for
d(GCGTACACATGCG)-OG (SEQ ID N0:1), coupled with a K~=9.0 x
1014 determined independently for tYze reference duplex, results
in a K~=1.7 x 1012 for the formation of the AX duplex.
Substitution into the relevant relation yields a value of oG°
- 16.4 kcal/mol for the AX duplex that compares favorably with
the value determined previously (i.e. ~G° - 16.0 kcal/mol)
employing a combination of caloz-imetric and spectroscopic
technique.
Example 6: Equation Programs
Equa ti on 6 Procrram
'declare globals'
Dim At, Dt, Xt, Kad, Kax As Double
Function theta(zl, z2, z3, z4, z5) As Double
At = zl
Dt = z2
Kad = z3
Kax = z4
Xt = z5


CA 02355920 2001-06-21
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theta = ModRegFal{0#, 1#)
End Function
Private Function funcl(A) As Double
fund = At * ( 1 - A) / ( ( 1 + Xt * Kax) / Kad + Dt * ( Z - A) )
- A
End Function
Private Function ModRegFal.{X1, X2 As Double) As Double
'Modified Regula Falsi'
'(adapted from Conte & de Boor, 1980)'
'Finds root of function funcl, if bracketed '
Const xtol = 0.000000000001
Const ftol = 0.000000000000001
Const ntol = 100
Dim SignFl, n, PrvsF3 As Integer
Dim F1, F2, F3, X3 As Double
F1 = funcl (X1)
F2 - funcl(X2)
'test whether root is bracketed'
I f Sgn { F1 ) * F2 > 0 Then
Debug.Print "X1= ", Xl, "X2= ", X2
Debug.Print "funcl{X1)= ", F1, "funcl(X2)= ", F2
End
End If
X3 = X1
F3 = F1
'BEGTN ITERATION'


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Fox n = 1 To ntol
'TEST FOR CONVERGENCE'
"Is interval small enough?'
If Abs(X1 - X2) <= xtol Then
ModRegFal = X3
Exit Function
End I f
'Is F3 small enough?'
If Abs(F3) <= ftol Then
ModRegFal = X3
Exit Function
End If
'GET NEW GUESS BY LINEAR INTERPOLATION'
X3 - ( F1 * X2 - F2 * X1 ) / ( F1 - F2 )
25 PrvsF3 - Sgn(F3)
F3 - funcl (X3 )
'CHANGE TO NEW INTERVAL'
I f Sgn ( F1 ) * F3 >= 0 Then
Xl - X3
F1 - F3
If F3 * PrvsF3 >= 0 Then F2 = l~2 / 2#
Else
X2 - X3
F2 -- F3
If F3 * PrvsF3 >= 0 Then FI = 1?1 / 2#
End If
Next n
'END ITERATION'


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Debug.Print "X1= ", X1, "X2= ", X2, "X3= ", X3
Debug. Print "fund (X1) _ ", F1, "funcl (X2) _ ", F2, "funcl (X3) _
rr ~ F3
Debug. Print ntol, " iterations without convergence"
End Function
Equation 13 Program
'declare globals'
Dim At As Double, Dt As Double, Xt As Double
Dim XA As Double, Kad As Double, Kax As Double
Dim AX As Double
Function theta(zl#, z2#, z3#, z4#, z5#) As Double
At = z1
Dt = z2
Kad = z3
Kax = z4
Xt = z5
dummy = ModRegFal2(0#, zl) 'switch to At
theta = ThetaO()
Debug. Print "AX/Xt= "; AX / Xt; " Theta = "; theta
End Function
Private Function ThetaO() As Double
ThetaO = ModRegFall(0#. 1#)
End Function
Private Function funcl(A As Double;! As Double
funcl = At * (1 - A) / ( (1 + (Xt - .AX) * Kax) / Kad + Dt * (1
- A)) - A
End Function
Private Function func2(B As Double) As Double
Dim TO As Double
AX = B
TO = ThetaO()


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func2 = At - AX - TO / (Kad * (1 - TO}} - TO * Dt
End Function
Private Function ModRegFall(X1 A~; Double, X2 As Double) As
Double
'Modified Regula Falsi'
' (adapted from Conte & de Boor, 1580) '
'Finds root of function funcl, if bracketed '
Const xtol = 0.000000000001
Const ftol = 0.000000000000001
Const ntol = 100
Dim SignF1 As Integer, n As Integer, PrvsF3 As Integer
Dim F1 As Double, F2 As Double, F3 As Double, X3 As Double
F1 = funcl(Xl}
F2 = funcl(X2)
'test whether root is bracketed'
If Sgn(F1) * F2 > 0 Then
Debug. Print "root not bracketed"
Debug.Print "X1= ", X1, "X2= ", X2
Debug.Print "funcl(X1)= ", F1, "funcl(X2)= ", F2
End
End If
X3 - X1
F3 = F1
'BEGIN ITERATION'
For n = 1 To ntol


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'TEST FOR CONVERGENCE'
'Is interval small enough?'
If Abs (X1 - X2 ) <= xtol Then
ModRegFall = X3
Exit Function
End If
'Is F3 small enough?'
If Abs(F3) <= ftol Then
ModRegFall = X3
Exit Function
End If
'GET NEW GUESS BY LINEAR INTERPOLA,TTON'
X3 - ( F1 * X2 - F2 * X1 ) / ( F1 - F'2 )
PrvsF3 - Sgn{F3)
F3 - funcl (X3 )
'CHANGE TO NEW INTERVAL'
If Sgn(Fl) * F3 >= 0 Then
X1 = X3
F1 = F3
If F3 * PrvsF3 >= 0 Then F2 - F2 / 2#
Else
X2 - X3
F2 - F3
If F3 * PrvsF3 >= 0 Then F1 = F1 / 2#
End If
Next n
'END ITERATION'
Debug.Print "Xl= ", X1, "X2= ", X2, "X3= ", X3


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Debug.Print "funcl(X1)_ ", F1, "funcl(X2)_ ", F2, "funcl(X3}=
" F3
Debug. Print ntol, " iterations without convergence"
End Function
Private Function ModRegFal2(Y1 As Double, Y2 As Double) As
Double
'Modified Regula Falsi'
'(adapted from Conte & de Boor; 19g0)'
'Finds root of function func2, if bracketed '
Const xtol = 0.000000000001
Const ftol = 0.0000000001
Const ntol = 100
Dim SignFl As Integer, n As Integer, PrvsF3 As Integer
Dim F1 As Double, F2 As Double, F3. As Double, Y3 As Double
F1 = func2 (Y1)
F2 = func2(Y2)
'test whether root is bracketed'
I f Sgn ( F1 } * F2 > 0 Then
Debug.Print "Y1= ", Y1, "Y2= °, Y2
Debug.Print "func2(Yl)= ", F1, "func2(Y2)= ", F2
End
End If
Y3 = Y1
F3 - F1
'BEGIN ITERATION'
For n = 1 To ntol

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'TEST FOR CONVERGENCE'
'Is interval small enough?'
If Abs(Y1 - Y2) <= xtol Then
ModRegFal2 - Y3
Exit Function
End If
'Is F3 small enough?'
If Abs(F3) <= ftol Then
ModRegFal2 = Y3
Exit Function
End I f
'GET NEW GUESS BY LINEAR TNTERPOLATION'
Y3 = ( F1 * Y2 - F2 * Y1 ) / ( F1 - F2 )
PrvsF3 - Sgn(F3)
F3 - func2 (Y3)
'CHANGE TO NEW INTERVAL'
I f Sgn ( F1 ) * F3 >= 0 Then
Y1 = Y3
Fl = F3
Tf F3 * PrvsF3 >= 0 Then F2 = :F2 / 2##
Else
Y2 = Y3
F2 = F3
If F3 * PrvsF3 >= 0 Then F1 = :f1 / 2~
End If
Next n
'END ITERATION'
Debug.Print "Y1= "~ Y1, "Y2= ", Y2,, "Y3= "~ Y3


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Debug.Print "func2(Yl}= a, F1, "func2(Y2)_ ", F2, "func2(Y3}_
" F3
Debug. Print ntol, " iterations without convergence"
End Function

CA 02355920 2001-06-21
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SEQUENCE LISTING
<110> Breslauer, Kenneth J.
Gelfand, 'Craig A.
Plum, G. Eric
Rutgers, the State University of New Jersey
<120> Methods and Kits for Screening Nucleic Acid Duplex
Stability
<130> RU-0076
<140>
<141>
<150> 60/119,909
<151> 1999-02-12
<150> 60/113,731
<151> 1998-12-23
<160> 3
<170> PatentIn Ver. 2.0
<210> 1
<211> 13
<212> DNA
<213> Artificial Sequence
<220>
<223> Description of Artificial Sequence: Synthetic
<400> 1
gcgtacacat gcg 13
<210> 2
<211> 13
<212> DNA
<213> Artificial Sequence
<220>
<223> Description of Artificial Sequence: Synthet~:c
<400> 2
cgcatgtgta cgc 13
<210> 3
1


CA 02355920 2001-06-21
WO 00/37686 PCT/US99/30751
<211> 13
<212> DNA
<213> Artificial Sequence
<220>
<223> Description of Artificial Sequence: Synti~:etic;
n=abasic furan
<220>
<221> misc_feature
<222> (7}
<400> 3
cgcatgngta cgc 13
2