Nanopore sequencing by hybridization of probes to form ternary complexes and variable range alignment

Technical Field

0001The present invention relates generally to biopolymer sequencing. More particularly, in certain embodiments, the invention relates to the determination of biopolymer sequence information using sequence-specific probes capable of binding to double-stranded biopolymers. For example, positional information of one or more binding locations of the probes along the target biopolymer molecule is determined and a sequence of the biopolymer is derived based on the positional information.

Background

0002There is great interest in identifying the composition and sequence of various biomolecules, such as human DNA, with accuracy and specificity. Sequencing technology, however, is time consuming and expensive to develop and implement. For example, sequencing the DNA of a single individual for the Human Genome Project required over $3 billion of funding.

0003It is estimated that each person's DNA varies from one another by approximately 1 base in 1000. Knowledge of such genetic variations among human populations may allow the scientific community to identify genetic trends that are related to various medical predispositions, conditions, or diseases, and may lead to the realization of truly personalized medicine where treatments are customized for a given individual based on that individual's DNA. A reduction in the time and cost of DNA sequencing is needed to develop such knowledge and to tailor medical diagnostics and treatments based on the genetic makeup of individual patients.

0004One particular obstacle inherent in known methods is the inability to accurately position repetitive sequences in DNA fragments. Furthermore, known methods cannot determine the length of tandem short repeats, which are associated with several human genetic diseases.

0005One emerging sequencing technology employs nanopore or micropore devices. Nanopores are substantially cylindrical holes formed in a membrane or solid media, said holes having diameters that range from about 1 nm to about 200 nm. Some existing methods using nanopores have attempted to detect single DNA bases as they move through a nanopore under a bias voltage. However, it is difficult to detect single DNA bases as each base passes through the nanopore. Furthermore, the use of nanopores small enough to track single stranded DNA are unreliable and difficult to form.

0006Other methods have attempted to use nanopores to detect DNA hybridization probes or oligonucleotides on a DNA molecule and to recover the DNA sequence information using the method of Sequencing-By-Hybridization (SBH). SBH is a two-step procedure, wherein the collection of all subsequences that make up a target sequence is first determined by detecting hybridization of sequence-specific probes or a pool of probes to the target sequence and then using an algorithm that relies on the use of combinatorial methods to reconstruct the full sequence of the target using the collection of subsequences. Most of the SBH methods have relied on standard DNA probes, termed k-mers <i>(see e.g.,</i><nplcit id="ncit0001" npl-type="s"><text>E.M. Southern. "DNA chips: analysing sequence by hybridization to oligonucleotide on a large scale" Trends in Genetics, 12(3),110-115 (1996</text></nplcit>)). <patcit id="pcit0001" dnum="US2006287833A"><text>US 2006/287833</text></patcit> discloses SBH and nanopore sequencing carried out with oligonucleotide probes binding to ssDNA or zinc finger proteins binding to dsDNA

0007SBH procedures can also be used to attach a large set of single-stranded fragments or probes to a substrate to form a sequencing chip. When a solution of labelled, single-stranded target DNA fragments is exposed to the chip, the target fragments hybridize with complementary sequences on the chip. The hybridized fragments can be identified using a radiometric or optical detector depending on the selected label. Each hybridization provides information about whether the fragment sequence is a subsequence of the target DNA. The target DNA can then be sequenced based on which strings are and are not substrings of the target sequence.

0008The efficiency of SBH methods is poor. For example, large probe arrays are required to sequence modest target lengths. Furthermore, the information regarding the binding position along the target sequence of a given fragment with respect to other fragments is not generated using this experimental approach, and the number of times that a fragment binds a target is also undetermined. While SBH may be a useful for sequencing variants of known molecules, it is not useful for sequencing organic biomolecules at high throughput and accuracy. Still further, the algorithms that are used to reconstruct the target sequence from the hybridization data have not prove useful in practice because known SBH methods do not return sufficient information to sequence long fragments. Thus, these limitations have prevented the adoption of SBH as a primary sequencing method. There is therefore a need for improved methods of sequencing <ul id="ul0001" list-style="none" compact="compact"><li><patcit id="pcit0002" dnum="US20020028458A"><text>US 2002/0028458</text></patcit> discloses a sequencing method using magnifying tags.</li><li><patcit id="pcit0003" dnum="WO0146467A"><text>WO 01/46467</text></patcit> discloses a fluorescent intensity assay for duplex and triplex nucleic acid hybridization in solution utilizing fluorescent intercalators.</li><li><patcit id="pcit0004" dnum="WO0131063A"><text>WO 01/31063</text></patcit> discloses hybridization-triggered fluorescent detection of nucleic acids.</li></ul>

Summary

0009The present invention methods for determining the whole or partial sequence of a gene as set forth in the appended claims.

0010Embodiments of the present invention provide methods for sequencing a biopolymer by forming local ternary complexes along the length of the double-stranded biopolymer target molecule using one or more probes and obtaining information about the location of the probe(s) using a detector. These methods offer particular advantage when implemented with nanopore (including micropore) detection systems.

0011It is now appreciated that a key problem of analyzing single stranded biopolymers through a nanopore is that single-stranded biopolymers tend to self-hybridize and fold into secondary or higher-order structures. This may prevent entry of the single stranded sequence into the nanopore or stall its migration through the nanopore. Single-stranded DNA has a short persistence length and a measure of the DNA polymer rigidity is at a local level. Thus, folding of single-stranded DNA may falsely provide a signal similar to the presence of a binding probe.

0012Sequencing organic biopolymers comprising double-stranded DNA has several advantages over the use of single-stranded DNA. Double-stranded DNA, in contrast to single stranded DNA, does not have a tendency to fold into secondary structures, is easier to manipulate prior to the introduction into a nanopore channel, has a consistent transmission speed through nanopore channels, and has a longer persistence length. In addition, higher affinity probe molecules with greater sequence selectivity may be used with double-stranded DNA, than with single-stranded DNA.

0013There is disclosed a method for determining a whole or partial sequence of a target biopolymer. The method includes the step of providing a double-stranded biopolymer target molecule. The target molecule (or fragment thereof) is contacted with a first probe or a first collection of probes having specificity for one or more first recognition sites of the target molecule, thereby forming one or more first local ternary complexes along the double-stranded biopolymer target molecule (or fragment thereof), the one or more first recognition sites each having a first known sequence. At least a subset of the one or more first local ternary complexes along the double-stranded biopolymer target molecule (or fragment thereof) is detected to determine a first probe map. The whole or partial sequence of the target biopolymer may be determined using at least the first probe map. In the invention, the detecting step includes passing the double-stranded biopolymer target molecule (or fragment thereof) through a nanopore and detecting an electrical signal indicative of one or more locations of the one or more local ternary complexes along a length of the double-stranded biopolymer target molecule, thereby determining the first probe map.

0014The first probe map may include one or more of the following: (a) relative positional information of two or more first local ternary complexes along the double-stranded biopolymer target molecule (or fragment thereof); (b) absolute positional information of one or more first local ternary complexes along the double-stranded biopolymer target molecule (or fragment thereof); and/or (c) error of positional information of one or more first local ternary complexes along the double-stranded biopolymer target molecule (or fragment thereof). In the invention, the target molecule (or fragment thereof) is contacted with a second probe having specificity for one or more second recognition sites of the target molecule, thereby forming one or more second local ternary complexes along the double-stranded biopolymer target molecule (or fragment thereof), the one or more second recognition sites each having a second known sequence. The detecting step may further include detecting at least a subset of the one or more second local ternary complexes along the double-stranded biopolymer target molecule (or fragment thereof) to determine a second probe map. The determining step may include determining the whole or partial sequence of the target biopolymer using at least the first probe map and the second probe map.

0015At least one of the first probe map or the second probe map may comprise one or more of the following: (a) relative positional information of two or more first local ternary complexes along the double-stranded biopolymer target molecule (or fragment thereof), (b) relative positional information of two or more second local ternary complexes along the double -stranded biopolymer target molecule (or fragment thereof), (c) relative positional information of one or more first local ternary complexes and one or more second local ternary complexes along the double-stranded biopolymer target molecule (or fragment thereof), (d) absolute positional information of one or more first local ternary complexes along the double-stranded biopolymer target molecule (or fragment thereof), (e) absolute positional information of one or more second local ternary complexes along the double-stranded biopolymer target molecule (or fragment thereof), (f) error of positional information of one or more first local ternary complexes along the double- stranded biopolymer target molecule (or fragment thereof), and/or (g) error of positional information of one or more second local ternary complexes along the double-stranded biopolymer target molecule (or fragment thereof).

0016In certain embodiments, the determining step comprises determining a spectrum map from at least the first probe map and the second probe map. Determining the spectrum map may optionally either comprise using a combinatorial sequence reconstruction algorithm or determining a candidate sequence by ordering at least two probe sequences using positional information and error of positional information.

0017The first recognition site sequence and the second recognition site sequence may overlap, and determining the spectrum map may include aligning the recognition site sequences. The first probe may be an <i>n</i>-mer probe, with <i>n</i> being an integer from 3 to 10.

0018The first probe may be a member selected from the group consisting of an oligonucleotide, a peptide nucleic acid and a polyamide.

0019The contacting step may further include contacting the target molecule (or fragment thereof) with the first probe in the presence of at least one of a recombinational protein or are combinational enzyme so as to facilitate hybridization of the first probe with the target molecule.

0020Conveniently, the providing step comprises enzymatically synthesizing at least a portion of a second strand upon a single-stranded template. The contacting step may comprise binding the first probe to a minor groove of the target molecule (or fragment thereof) or the first and second contacting steps are performed separately with different aliquots of the same target molecule. Preferably, a sequence of the first recognition site and a sequence of said second recognition site may overlap.

0021The description of elements of the embodiments of other aspects of the invention may be applied to this aspect of the invention as well.

0022In another aspect, the invention features a method for determining a whole or partial sequence of a target biopolymer, as defined in claim 11. The method for determining a whole or partial sequence of a target biopolymer comprises the steps of: (a) providing a double-stranded biopolymer target molecule, (b) contacting said target molecule or fragment thereof with a plurality of <i>n</i> probes each having specificity for one or more recognition sites of said target molecule, thereby forming local ternary complexes along said double-stranded biopolymer target molecule or fragment thereof, each of said recognition sites having a known sequence, wherein each of the n probes individually consists of a member selected from the group consisting of an oligonucleotide, a peptide nucleic acid and a polyamide, (c) detecting at least a subset of said local ternary complexes along said double-stranded biopolymer target molecule or fragment thereof to determine one or more probe maps, by (i) passing said double-stranded biopolymer target molecule or fragment thereof through a nanopore and detecting an electrical signal indicative of locations of said local ternary complexes along a length of said double-stranded biopolymer target molecule, thereby determining said one or more probe maps, and/or (ii) repeating for each of said <i>n</i> probes, and (d) determining said whole or partial sequence of said target biopolymer using at least said one or more probe maps.

0023Conveniently, the method further comprises fragmenting the double-stranded biopolymer target molecule prior to performing the contacting step and in which case, optionally determining said whole or partial sequence of said target biopolymer step comprises constructing a probe map by matching a pattern between overlapping regions of multiple fragments to arrive at an aggregated hybridization pattern for each probe.

0024The description of elements of the embodiments of other aspects of the invention may be applied to this aspect of the invention as well.

0025A method for detecting the sequence of a target nucleic acid includes contacting a target molecule with a first probe to create at least one probe-target complex at a recognition site of the target for which the first probe has a known specificity, while leaving uncomplexed, regions of the target for which the first probe is not specific. The target molecule is contacted with a second probe to create at least one probe-target complex at a recognition site of the target for which the second probe has a known specificity, while leaving uncomplexed, regions of the target for which the second probe is not specific. Complexed and uncomplexed regions of the target are detected and recorded to create a first probe map of the first probe and a second probe map of the second probe, the first probe map and the second probe map incorporating information on the relative position of the hybridization of the probes. A candidate sequence is determined by ordering at least two probe sequences using positional information or a combination of overlapping sequences of the probe molecules and positional information.

0026One of more of the following features may be included. Detecting the first probe map and detecting the second probe map may be performed sequentially or concurrently.

0027At least one of the first probe and the second probe may include a tag so as to allow discrimination of bound first probe from bound second probe. The first probe and the second probe may be comprised of mixtures of nucleic acid sequences. Detection may include using a single molecule detector, which may include a nanopore detector.

0028The description of elements of the embodiments of other aspects of the invention may be applied to this aspect of the invention as well.

0029A further method for detecting the sequence of a target nucleic acid includes contacting a target molecule with a first probe to create at least one probe-target complex at a recognition site of the target for which the first probe has a known specificity, while leaving uncomplexed, regions of the target for which the first probe is not specific. The target molecule is contacted with a second probe to create at least one probe-target complex at a recognition site of the target for which the second probe has a known specificity, while leaving uncomplexed, regions of the target for which the second probe is not specific. Complexed and uncomplexed regions of the target are detected and recorded to create a first probe map of the first probe and a second probe map of the second probe, the first probe map and the second probe map incorporating information on the relative position of the hybridization of the probes and incorporating information on the error of the positional information for each probe. A candidate sequence is determined by ordering at least two probe sequences using positional information and parameters relating to the error in positional information or a combination of overlapping sequences of the probe molecules and positional information and error in positional information.

0030One or more of the following features may be included. A parameter relating to error in measured position of a probe may define a range of positions for the probe. The target sequence may be determined by overlapping sequences of at least two probe molecules only when the range of one of the probes overlaps with the range of another probe. The range may be selected so as to be proximal to a sequence position. The range may be different for every probe. Choosing the range further may include using a correlation between the size of the error and the size of the range. Detecting may include using a single molecule detector. The detector may include a nanopore detector.

0031The description of elements of the embodiments of other aspects of the invention may be applied to this aspect of the invention as well.

0032A method for determining a sequence of a nucleic acid target includes creating multiple aliquots of a target molecule solution. Each of a plurality of the aliquots is combined and stringently incubated with a different corresponding probe, with each probe-aliquot combination having a plurality of probe molecules having a known specificity for a given subsequence of the target so as to create a probe-target complex for each aliquot. The probes are predominantly complexed with their corresponding subsequences for which they have specificity. The probe-target complexes are detected with a single molecule detector capable of distinguishing regions of the target that are complexed and uncomplexed with the probe so as to generate a probe map that estimates, to within an error, the positions of the multiple instances of the subsequence within the target sequence. The probe maps generated from the multiple aliquots are preliminarily aligned, and a model sequence created that estimates the actual sequence of the target, the model sequence having a growing end. A range of candidate sequences proximal to the growing end are selected from within the set of aligned probe maps. A probe- specific sequence is selected from within the range that has an overlapping region of substantial homology or identity to a sequence at the growing end of the model sequence, yet has at least one base in a non-overlapping region beyond the growing end. At least one base from the non-overlapping region is appended to the growing end.

0033One or more of the following features may be included. The range may be selected based on at least one estimated probe map positional error. The size of the range may be related to the error. The same range may be used to select sequences from each probe map. A different range may be used to select sequences from each probe map. The detector is a nanopore detector. Aligning the probe maps from the multiple aliquots may include using at least one of a reference probe, a reference sequence and a reference protein. The target may be fragmented prior to creating the aliquots. Multiple fragment probe maps for a given sequence-specific probe may be aligned and assembled into a target probe map for that probe. The probes may be chosen so as to bind to all possible sequences of DNA. Creating a model sequence may include choosing a starting probe-specific sequence and from a probe map. The multiple probe maps may be aligned in relation to at least one of each other and the target sequence.

0034The description of elements of the embodiments of other aspects of the invention may be applied to this aspect of the invention as well.

0035A method for detecting a sequence of a target biopolymer includes providing a double-stranded biopolymer target molecule. The target molecule is contacted with a first probe having a first probe specificity for recognition sites of the target molecule to form a first plurality of local ternary complexes, the first probe having a first predicted recognition site sequence. A detector is used to determine positional information of the first plurality of local ternary complexes.

0036One or more of the following features may be included. The positional information may include a parameter related to a spatial distance between two local ternary complexes. The target molecule may be contacted with a second probe having a second probe specificity for recognition sites of the target molecule to form a second plurality of local ternary complexes, the second probe having a second predicted recognition site sequence, and a detector may be used to determine positional information of the second plurality of local ternary complexes. The positional information of at least the first and second plurality of local ternary complexes may be aligned to determine a DNA sequence of the target.

0037A method for detecting a sequence of a target biopolymer includes providing a double-stranded biopolymer target molecule. The target molecule is contacted with a first probe having a first probe specificity for recognition sites of the target molecule to form a first plurality of local ternary complexes, the first probe having a first predicted recognition site sequence. The target molecule is contacted with a second probe having a second probe specificity for recognition sites of the target molecule to form a second plurality of local ternary complexes, with the second probe having a second predicted recognition site sequence. The formation of the local ternary complexes is detected. A sequence of the target biopolymer is determined by assembling at least the first and second predicted recognition site sequences.

0038One or more of the following features may be included. Detection may include measuring the relative positions of the local ternary complexes, and/or creating at least one of a probe map or a spectrum map. Assembling may include overlapping the recognition site sequences. One of the first probe and the second probe may include a collection of probe molecules of substantially similar specificity. The probe molecules may include moieties such as polyamides, nucleic acids, and/or peptide nucleic acids. A recombinational enzyme or protein may be added to aid hybridization. Detection may include using a nanopore detector. Providing the double-stranded biopolymer target molecule may include enzymatically synthesizing at least a portion of a second strand upon a single stranded template.

0039The description of elements of the embodiments of other aspects of the invention may be applied to this aspect of the invention as well.

0040A library of probes adapted for determining a sequence of a biopolymer target may include polyamide molecules. The library may also include gapped polyamide molecules. All of the probes may be gapped polyamides.

0041A method for determining a sequence of an unknown sequence of a biopolymer target includes: (i) contacting the target with a polyamide probe having a specificity for a recognition site of the target; and (ii) detecting whether the probe and target are bound.

0042One or more of the following features may be included. A predicted sequence of the recognition site may be recorded if the probe is bound. A probe map may be determined. The probe molecule may bind to the minor groove of the target molecule.

0043A method for determining sequence information of a nucleic acid having a sequence includes providing a double-stranded nucleic acid target molecule having a sequence and a plurality of binding sites disposed along the sequence. A plurality of probe molecules having a first sequence specificity are added to the double-stranded nucleic acid target molecule. The probe molecules having the first sequence specificity and the target molecule are incubated so as to effectuate preferential binding of the first probe molecules to both a first binding site and a second binding site of the target molecule. A parameter related to a distance between the first binding site and the second binding site is measured.

0044A second probe molecule may be added to the double-stranded nucleic acid target molecule, and the second probe molecule and the target molecule may be incubated so as to effectuate preferential binding of the second probe molecule to both a third binding site and a fourth binding site of the target molecule. A parameter related to the distance between the third binding site and the fourth binding site may be measured. The parameter is measured by passing the target molecule and bound probe molecules through a nanopore.

<u>Brief Description of the Drawings</u>

0045The foregoing features of the invention will be more readily understood by reference to the following detailed description, taken with reference to the accompanying drawings, in which: <ul id="ul0002" list-style="none" compact="compact"><li><figref idref="f0001">Fig. 1</figref> is a flow chart for a method of sequencing DNA in accordance with an embodiment of the present invention;</li><li><figref idref="f0002">Fig. 2</figref> is a schematic drawing showing a double-stranded DNA target complexed with multiple probe molecules to form local ternary complexes;</li><li><figref idref="f0002">Fig. 3</figref> is a schematic drawing showing a double-stranded DNA target complexed with multiple strand- invading probe molecules to form local ternary complexes;</li><li><figref idref="f0002">Fig. 4a</figref> is a schematic drawing showing an idealized kinetic trace of an impedance measurement generated as local probe-target complexes passes through a nanopore;</li><li><figref idref="f0003">Figs. 4b</figref> and <figref idref="f0004">4c</figref> each show a graph of an exemplary current signal determined in accordance with an embodiment of the invention;</li><li><figref idref="f0005">Fig. 5a</figref> is a schematic diagram of a nanopore detector in accordance with an embodiment of the invention;</li><li><figref idref="f0006">Fig. 5b</figref> is a schematic diagram of the detector of <figref idref="f0005">Fig. 5a</figref> with a local complex within the nanopore in accordance with an embodiment of the invention;</li><li><figref idref="f0007">Fig. 5c</figref> is a schematic diagram of the detector of <figref idref="f0005">Fig. 5a</figref> with an uncomplexed region of target DNA within the nanopore in accordance with an embodiment of the invention;</li><li><figref idref="f0008">Fig. 6</figref> is a flow chart illustrating a reconstruction algorithm in accordance with an embodiment of the present invention; and</li><li><figref idref="f0009">Fig. 7</figref> is a flow chart illustrating an algorithm for reducing possibilities during DNA sequencing in accordance with an embodiment of the present invention.</li></ul>

<u>Detailed Description</u>

0046As used in this description and the accompanying claims, the following terms shall have the meanings indicated, unless the context otherwise requires: <ul id="ul0003" list-style="none" compact="compact"><li>A "target" means a biopolymer, for example, having sequence information which is to be determined using embodiments of the present invention;</li><li>A "probe" means any molecule or assembly of molecules capable of sequence-specific covalent or non-covalent binding to a target molecule;</li><li>In connection with a target bound to one or more probes, a "ternary complex" means a complex formed from three or more biomolecules. For example, a complex of two complementary strands of DNA (i.e., double-stranded DNA or dsDNA) with a third probe strand is a ternary complex. Higher order complexes also include ternary complexes; for example, a complex of double-stranded target DNA with two probe molecules bound to the same stretch of sequence, with two probe molecules bound to each other and in turn to a stretch of sequence, with two identical probe molecules bound to different subsequences, or with a probe molecule and a protein bound to a stretch of sequence are quaternary complexes that also include a ternary complex.</li></ul>

0047A "local ternary complex" means a ternary complex that is localized to a particular stretch of biopolymer. For example, multiple local ternary complexes may exist when probe molecules bind to a target molecule in multiple locations separated by stretches of bases to which the probe is not bound (i.e., uncomplexed regions).

0048A "polyamide" refers to the class of DNA binding polyamides originally developed by the Dervan laboratory at the California Institute of Technology. Polyamides are molecules containing heterocycle ring structures that can be combined in a modular fashion to recognize DNA sequences by binding in the minor groove of duplex DNA. Typical heterocycle ring structures in this class are, but not limited to, N-methylimidazole, N-methylpyrrole, 3-hydroxy-N-methylpyrrole, N-methylpyrazole, 3-methylthiophene, benzimidazole, hydroxybenzimidazole, imidazopyridine. The rings may be connected via carboxamide linkages, by the amino acid β-alanine, or directly joined by single bonds. Other ring structures and linkages can be envisaged by practitioners familiar with the art.

0049The polyamides may include spacers that are not sequence specific and that allow the curvature of the polyamide to stay in register with the curvature of double-stranded DNA ("gapped polyamides"). The spacer may be used as a gap when the polyamide is used as a probe for sequence determination. Gapped probes are more efficient at reconstructing sequence information than a non-gapped probe.

0050In connection with a target and a probe, a "probe map" means a data set containing information related to the sites along a target sequence at which a probe preferentially binds. The data set may include absolute positional information referenced to a known sequence, relative information related to distances between binding sites, or both. The data set may be stored in computer media.

0051A "spectrum map" means a collection of probe maps determined for a target sequence.

0052A probe recognition site refers to a target sequence, structure, or conformation that is preferentially recognized by the probe in the presence of other target sequences, structures, or conformations. The probe may interact with the recognition site through non-covalent, covalent, or mixtures of covalent and non-covalent interactions.

0053In connection with a probe map or a spectrum map, "dynamically weighted spectrum" means the collection of probes under consideration for the extension of a growing sequence with weights as to the likelihood that they should be chosen next. These weights will be based on a parameter related to the measured positions of the probes. The dynamically weighted spectrum may or may not include sequence information. For example, in the case of six-mers, if the growing sequence ends in ATACG, the dynamically weighted spectrum may include only the probes ATACGA, ATACGC, ATACGG, and ATACGT with weights based on their (relative) positions. Alternatively, the dynamically weighted spectrum may be thought of as a collection of probes, independent of sequence, whose probability of being next in the sequence is based on their measured distances from the current growing end of the strand. (In this case sequence-specific information would be incorporated subsequently.)

0054Illustrative embodiments described herein relate to detecting and analyzing probe maps, to gather sequence information. More particularly, illustrative embodiments described herein relate to creating and detecting specific ternary complexes along double-stranded biopolymer target molecules to gather sequence information. For simplicity, the embodiments described below use DNA as a target, but other biopolymers such as RNA may also be sequenced. In an embodiment, probes that are selective for one or more sequences are hybridized to a target sequence. The target sequence may be double-stranded DNA and the probes are chosen for the ability to bind to one or more sites of double-stranded DNA. The binding of the probe is then detected using a nanopore to generate a probe map in computer media. By detecting probe binding at multiple subsequences along the target, a spectrum map may be constructed. Information contained in the spectrum map may then be aligned an assembled into a finished sequence.

0055Like SBH, positional hybridization sequencing relies on the biochemical hybridization of probes to an unknown target. However, once the biochemical hybridization is substantially complete, a detector that determines the position of hybridization is utilized. In addition to determining the position of hybridization, the detector is capable of counting the number of times a probe hybridizes to the target. The positional information allows a combinatorial sequence reconstruction algorithm to be used that differs from those used in SBH. In standard SBH, the spectrum of the target sequence from which probes are selected during each step of sequence reconstruction includes all the probes that hybridized and this remains constant during the course of the reconstruction. That is, every probe in the spectrum can be used at any step during reconstruction. In the case of positional hybridization detection, the spectrum is a dynamically weighted spectrum. The dynamically weighted spectrum may include all the probes that bound to the target (with different weights). However, in most embodiments the dynamically weighted spectrum will only include a subset of the spectrum. A consequence of not including all the probes is that during reconstruction of the sequence the dynamically weighted spectrum must change at least once in order to encompass all probes in the spectrum.

0056Other illustrative embodiments relate to methods and computer algorithms for aggregating, aligning and assembling multiple probe maps into a model nucleotide sequence. In a specific embodiment, combinatorial sequence reconstruction algorithm is used to generate spectrum maps for determining sequence information. Due to the complex nature of the calculations and quantity of data generated, it is expected that the methods described herein be carried out in a substantially automated manner by an appropriate computer algorithm running on a computer of adequate speed.

0057In an illustrative embodiment, detection of local ternary complexes is accomplished by passing double- stranded biopolymer target molecule or fragment thereof through a nanopore and detecting an electrical signal indicative of the locations of the local ternary complexes along the double- stranded biopolymer target molecule. The use of nanopores to detect solution phase DNA hybridization reactions is described in <patcit id="pcit0005" dnum="US6537755B"><text>U.S. Patent 6, 537,755 to Drmanac</text></patcit>, and in <patcit id="pcit0006" dnum="US20060287833A" dnum-type="L"><text>U.S. Patent Application Publication No. 20060287833, to Yakhini</text></patcit>.

0058<figref idref="f0001">Fig. 1</figref> shows a flow chart for a method of sequencing a target in accordance with an embodiment of the present invention. For simplicity, this and other embodiments detailed herein use genomic DNA as the target to be sequenced, although other types of molecules, including cDNA, and RNA could be sequenced in this way. A target DNA sequence is extracted from a source and purified (step 100). The starting material may be any of a variety of double-stranded nucleic acids, for example, genomic DNA, PCR products, cDNA, RNA-DNA hybrids and the like. The use of double- stranded DNA as a target has several advantages over the use of single stranded DNA. These include a reduction in the amount of secondary structure present in the target strand to be sequenced, a more consistent transmission speed of the DNA through the nanopore, the ability to manipulate single molecules of double-stranded target DNA prior to introduction into the nanopore, a longer persistence length of the DNA, and the use of probe molecules that are of higher affinity and sequence selectivity. While the method may be most powerful with long pieces of DNA to which a probe may bind in multiple subsequence positions, the invention is also applicable to shorter nucleic acids such as viral genomes, plasmids, cosmids etc. The target DNA may be derived from any of multiple sources and may be the genome of an organism whose DNA sequence is unknown, or is known (resequencing). Alternatively, the DNA may be derived from several organisms. The target DNA may be of a known size or range of sizes; alternatively, the size of the target DNA may be unknown. The purification of step 100 may be the complete purification step or performed in conjunction with later steps. For example, a biochip that includes a nanopore may also accomplish further purification via electrophoretic or other methods. Optionally, the target may be amplified by PCR, rolling circle amplification, or other suitable method.

0059If chromosomal DNA or other large target DNA polymers are to be sequenced, it may be desirable to fragment the DNA. Target DNA may be fragmented by any of a number of commonly used methods including hydrodynamic shearing, sonication, ultrasonic fragmentation, enzymatic cleavage, nebulization, chemical cleavage, and heat induced fragmentation. Hydrodynamic shearing may be favorable if large nucleic acid fragments are desired. A commercially available device, HydroShear (Genomic Solutions, Ann Arbor, Mich., USA), is available that will shear DNA to a tight size distribution. To use this device, double-stranded DNA in solution is passed through a tube with an abrupt constriction. Fluid accelerates to maintain the volumetric flow rate through the smaller area of the constriction. During this acceleration, drag forces stretch the DNA until it snaps. The DNA fragments until the pieces are too short for the shearing forces to break the chemical bonds. The flow rate of the fluid and the size of the constriction determine the final DNA fragment sizes. In one configuration of the device, size ranges of sheared DNA of from 650 base pairs to 40,000 base pairs are achievable. In a second configuration of the device, size ranges of 1,000 base pairs to 9,000 base pairs are achievable.

0060The target DNA may then be aliquoted (step 110) and combined with probe molecules (step 120). For example, a first aliquot may be combined with a solution containing molecules of probe specific for a first target subsequence (e.g., a 5 to 20 base pair subsequence) and a second aliquot may be combined with a probe that is specific for a second target subsequence. In a simple scheme, the number of aliquots is equal to the number of different probes to be used in the experiment. A single probe (i.e., a collection of probe molecules having the same or functionally equivalent sequence specificity) may then be added to each aliquot of the target DNA. Alternatively, the number of aliquots may be smaller or larger than the number of different probes; a mixture of probes may be added to each aliquot. The probes may be of either uniform or differing lengths. Various mixing procedures may be used to combine the target and probe, but if the procedure is performed at very low volumes (e.g., 0.1-10 nanoliter), diffusional mixing may suffice.

0061The aliquots are then incubated under stringent conditions (step 130) to allow the probe molecules to sample multiple subsequences and to approach equilibrium in finding energetically favored subsequences to bind to (i.e., the subsequences for which the probe is specific). In other words, each aliquot containing target DNA and a probe or a mixture of probes is incubated under conditions that result in greater hybridization of probes to matched recognition sequences than to sequences containing a mismatch. Taking into account the type of probe used, stringency may be adjusted through temperature, salt concentrations, addition of organic solvents, washing with solutions, electrophoretic washing, or other methods. Optionally, incubated aliquots may be combined prior to analysis, especially if tagged probes are used. The result is a formation of specific local probe-target complexes, which, as described below, may be modeled as a probe map (step 140). In specific embodiments, the probe map includes the relative positional information of the local ternary complexes along the double-stranded biopolymer, the absolute positional information of the local ternary complexes along the double-stranded biopolymer, and error of positional information of the local ternary complexes along the double-stranded biopolymer. In another embodiment, second probe specific for one or more second recognition sites of the target molecule is used to generate a second probe map. In yet another embodiment, two or more probes are used for the detection of local ternary complexes, and for the generation of two or more probe maps.

0062The collection of hybridized or otherwise bound probes and positions may be used to form a model probe map of the target DNA. The probe map may be used to reconstruct the target DNA sequence. For example, multiple probe maps from probes having a variety of sequence specificities may be aligned and assembled to reconstruct a sequence. In an embodiment, n-mer probes are used (e.g. polynucleotide probes), each probe having a specificity for one of 4ⁿ possible DNA sequence combinations. A complete library of 4ⁿ n-mer probes may be utilized to give complete target sequence coverage. In illustrative embodiments, n is from 3 to 10.

0063Since the target was fragmented, the complete probe map will be constructed from data derived from the multiple fragments. The probe map may be assembled by matching the pattern between overlapping regions of multiple fragments to arrive at an aggregated hybridization pattern for a given probe having a given target specificity. The pattern matching routine may include determining the 3'→5' orientation of each hybridization pattern, especially if this has not been determined previously, e.g. by comparison to a known sequence in a resequencing operation.

0064The sequence specificity of a probe, combined with its estimated probe map with respect to the target yields a partial sequence model of the target. In other words, if a probe-target complex is detected, it may be expected that the target sequence contains the subsequence for which a given probe is specific. For sufficiently short probes, this subsequence will likely be repeated multiple times in the target at positions corresponding to the positional information that should be available from detection of binding of that probe. The subsequences may be assigned relative positional information by making use of the distances of measured uncomplexed regions intervening between the probe binding sites. The positional information will likely contain some error however.

0065The model sequences derived from the probe map of multiple probes having multiple corresponding sequence specificities may be preliminarily aligned with respect to each other and/or with respect to other landmarks (step 150). For example, for resequencing operations, the sequences may be aligned based on a maximal overlap with a known sequence. Alternatively, the model sequences may be aligned based on maximal overlap with each other or with respect to bound proteins (e.g. zinc finger proteins) included in the mixture, or with respect to other sequence landmarks.

0066A starting model sequence is created (step 160). For example, a starting sequence may be created using the known sequence specificity of one of the probes for which a probe map has been determined. The chosen probe may be located at or near the 3' or 5' terminus of the preliminarily aligned spectrum map. A growing-end may be chosen for the starting sequence, on the internal side.

0067In certain embodiments, a spectrum map is generated from at least a first probe map and a second probe map. Determining the spectrum map may include using a combinatorial sequence reconstruction algorithm. Determining the spectrum map may also include determining a candidate sequence by ordering at least two probe sequences using positional information and error of positional information. If the first recognition site sequence and the second recognition site sequence overlap, determining the spectrum map may include aligning the recognition site sequences.

0068A weighted spectrum is chosen as a subset of the spectrum map with respect to the growing end (step 170). The probes encompassed in this subset of the spectrum are selected using positional information or some parameter related to positional information generated during the detection step. The various sequences corresponding to the probe-specificities for the probes for which binding events were detected within the weighted spectrum are then compared with a sequence of the growing end (in the initial stages of the process, this may be the entire starting sequence). If possible, a sequence is chosen that has maximal identity for the growing end yet extends at least one nucleotide beyond the growing end (step 180). At least one base of the non-overlapping sequence is then appended to the growing end (step 190). The weighted spectrum may then be changed. This process of selecting nucleotides, appending nucleotides, and changing the weighted spectrum is repeated until sufficient sequence is determined or the data set is exhausted (step 195). If more than one nucleotide choice is available for appending, this may be resolved by evaluating each possible choice in terms of maximal overlap for the next few sequence extensions.

0069Contrastingly, in standard SBH, the weighted spectrum of the target sequence from which probes are selected during each step of sequence reconstruction is exactly equal to the spectrum of the target. That is, every probe in the spectrum can be used at any step during reconstruction. In the case of positional hybridization detection, the weighted spectrum of the target sequence encompassing probes selected during each step of reconstruction may be smaller than the length of the target strand. The weighted spectrum may be as large as the spectrum of the target minus one probe. However, in most embodiments the weighted spectrum will be significantly smaller than the target spectrum. A consequence is that during reconstruction of the sequence, the weighted spectrum must change at least once in order to encompass all probes in the spectrum.

0070If there were no error in the probe maps with regard to the position of hybridization of the probe, the weighted spectrum could consist of only one probe. Some error is to be expected, however. At the other extreme, if there were no certainty regarding the position of probe locations in a probe map, then the next nucleotide to be appended would logically be selected from any probe binding to the target. This would correspond to standard SBH. Balancing these two extremes, an embodiment of the invention optimizes the weighted spectrum based on estimated error in the positional information contained in each probe map or in the spectrum map. For example, a standard deviation, variance or other quantitative measurement of the error in one or more probe locations may be calculated based on the detector output. The weighted spectrum may then be set to be a multiple of this estimated error. Accordingly, the number of probes encompassed by the weighted spectrum and the size of the error may be inversely proportional, or otherwise inversely correlated. Simply stated, a larger weighted spectrum may be used when a larger positional error is present. The weighted spectrum may be expressed in terms of probes that fall within a fixed number of nucleotides distance from the growing end. Alternatively, the range may vary based on the error in the positional information for each probe, or even based on the estimated error at each probe binding site.

0071Other alternative calculation methods may be employed including adaptive or genetic algorithms that adjust based on the quality of the sequence output. The output of multiple such methods may also be compared and the best one selected. The range or ranges may be calculated once, multiple times during the procedure, or after each nucleotide is appended.

0072A number of types of molecules are known to bind in a sequence-specific fashion to double-stranded DNA and may be used as probes in the current invention individually or in combination. The molecules may be composed of one or more moieties such as polyamides, a nucleic acid, and/or a peptide nucleic acid. In a specific embodiment, the molecule is a gapped polyamide molecule such as those described in the following Dervan references: <nplcit id="ncit0002" npl-type="s"><text>Dervan, P.B. Molecular Recognition of DNA by Small Molecules. Bioorg. Med. Chem. 2001, 9, 2215-2235</text></nplcit>; and<nplcit id="ncit0003" npl-type="s"><text> Dervan, P.B.; Edelson, B.S. Recognition of the DNA minor groove by pyrrole-imidazole polyamides. Curr. Op. Struc. Biol. 2003, 13, 284-299</text></nplcit>.

0073Alternatively, the probe molecules may be composed of native or modified DNA oligonucleotides that are capable of binding in a triple stranded fashion with double-stranded DNA. Alternatively, the probe molecules may be nucleic acid molecules that are combined with the target in the presence of a recombinational enzyme or a recombinational protein. A non-limiting example of a useful recombinational enzyme is recA. Further information about binding recA probes to DNA strands is provided in the following two references, <nplcit id="ncit0004" npl-type="s"><text>Bianco et al., Nucleic Acids Research Vol. 24, No. 24 (1996) 4933-4939</text></nplcit>; and <nplcit id="ncit0005" npl-type="s"><text>Cox, Nature Reviews - Molecular Cell Biology, Vol. 9 (February 2007) 127-138</text></nplcit>. Alternatively, the molecule may be a peptide nucleic acid capable of binding to double-stranded DNA. Other modified oligonucleotides, proteins, peptides, or other polymers are also capable of binding to double-stranded DNA in a sequence specific fashion and thus may be used.

0074As shown schematically in <figref idref="f0002">Fig. 2</figref>, probes 200 will bind to specific subsequences along a DNA strand 210 to create a probe map. In an embodiment, the DNA is double-stranded DNA and the probes may bind to both strands with comparable affinity or preferably to one strand, and may bind to the minor or major groove of helical dsDNA targets. Additionally, as shown in <figref idref="f0002">Fig. 3</figref>, the probes may invade and disrupt the base pairing of the dsDNA, as is known to occur with certain peptide nucleic acids. In an embodiment, the probes may contain moieties that do not have sequence specific binding behavior. The probe may contain two sequence-specific moieties separated by a relatively non-specific linker moiety. In the case of an oligonucleotide, the non-specific binding region may be composed of a universal base that is able to bind to all four cognate bases (see, e.g., Preparata <patcit id="pcit0007" dnum="US20010004728A" dnum-type="L"><text>U.S. Patent Application No. 20010004728</text></patcit>.) In the case that the target is double-stranded DNA, the probes may bind to both strands with comparable affinity or preferably to one strand, and may bind to the minor or major groove of helical dsDNA targets. Additionally, as shown in <figref idref="f0002">Fig. 3</figref>, the probes may invade and disrupt the base pairing of the dsDNA, as is known to occur with certain peptide nucleic acids. Non-specific linkers may also be included in probes that include binding regions composed of polyamides, peptide nucleic acids, peptides, or proteins. Probes may also be labeled to increase detection sensitivity, or to allow discrimination of different probes having different corresponding sequence specificities.

0075In an embodiment, the probes are polyamides that bind in a 2:1 complex with dsDNA in the minor groove of the DNA. Alternatively or in addition, the polyamide may bind to the DNA in a 1:1 complex or in a 2:1 or higher-order complex. In the case of a 2:1 complex, the two polyamides may be separate molecules or may be covalently joined at the ends or in the middle of the molecules to form hairpin polyamides, cyclic polyamides, H-pin motifs, or U-pin motifs. Charged groups may be placed at either end or in the middle of the polyamides in order to change their affinity for target or for other probe molecules. Linkers may be attached between heterocycles in the polyamide to modulate the curvature of the molecule. Curvature modulation may be used to increase the binding affinity of a polyamide to a longer DNA sequence by matching the curvature of the polyamide to the curvature of the DNA molecule. Other linkages and appendages may also be used.

0076Polyamide probes may consist of imidazole, pyrrole, hydroxy-pyrrole, benzimidazole, and hydroxybenzimidazole heterocycles. The heterocycles may be substituted with alkyl or functional groups in order to modulate their binding to DNA. Other heterocycles may also be used. Pairing rules of polyamides for minor groove recognition of DNA have been described by Dervan (see <nplcit id="ncit0006" npl-type="s"><text>Dervan, P.B.; Edelson, B.S. Recognition of the DNA minor groove by pyrrole-imidazole polyamides. Curr. Op. Struc. Biol. 2003, 13, 284-299</text></nplcit>).

0077Generally, each aliquot of target DNA is subsequently analyzed to detect binding of the probe to the target DNA. In a specific embodiment, a probe map is generated for each probe to give absolute or relative positional information of probe binding sites located on a longer stretch of dsDNA. The probe binding sites are separated by non-binding, uncomplexed regions of the target that have relatively low affinity for the probe. Accordingly, the probe map may include absolute or relative information related to the location and length (e.g., in base pairs) of the uncomplexed regions.

0078In an embodiment of the invention, a single molecule detector is used to detect probe binding and thus arrive at a probe map. Unlike detectors typically used for SBH, the single molecule detector may determine the number of times that a given probe binds to a target molecule and the absolute or relative binding sites for that probe. For example, a nanopore based detector, a field effect transistor, Coulomb-charging based detector, or scanning-tunneling or force microscope may be used. Multiple such detectors may be used in parallel or in series. Data from multiple detectors may then be aggregated for analysis, including correlation analysis. Each mixture may be independently analyzed. In an embodiment of the technique, a nanopore is used to detect the position of local ternary complexes on the target DNA.

0079In certain embodiments, a nanopore-based detector detects temporal changes in current as probe-complexed and uncomplexed stretches of double-stranded DNA pass through the pore. As seen for single stranded DNA, the change in current may be positive or negative depending on the concentration of ions in the buffer on either side of the nanopore. The current may increase or decrease while a probe is passing through the pore due to blockade current, tunneling current or other mechanism.

0080<figref idref="f0002">Fig. 4a</figref> shows an idealized trace of a nanopore readout in terms of impedance as a function of time. Each time a probe molecule 200 passes through the nanopore detector, the impedance level increases (i.e., current blockade). Accordingly, the nanopore signal may be elevated or depressed for a period of time that reflects the length of the probe-target complex (item 400), or the length of the intervening non-binding regions (item 410). Relevant readout information may be recorded on computer media for future analysis.

0081A current signal, reflecting a change in impedance or current measured by the nanopore detector, may be monitored to gain information about the presence and spacings of hybridized probes. As an analyte moves through a volume monitored by the nanopore detector, the current signal changes. The signal may be elevated or depressed for a period of time that reflects the length of the analyte, e.g., a probe-target complex, or the length of the intervening regions without probes. A typical analyte will impede the flow of ions in the electrolyte and is non-conductive. Therefore, the current typically decreases as the analyte flows through the sensing volume. In some embodiments, e.g., a low salt electrolyte and a charge-carrying analyte, the current signal may increase as the analyte flows through the sensing volume. The current signal further changes when the portion of the analyte containing the hybridized probe moves through the volume between the sensing electrodes.

0082Referring to <figref idref="f0003">Fig. 4b</figref>, sample data is presented for a piece of double-stranded DNA with an attached probe passing through a pore. The x-axis is time in milliseconds and the vertical axis is current in picoamps. A negative current was run, so that the trace starts at about -3920 pA. That is the current when only buffer is present in the pore. As a DNA strand entered the pore, the current was reduced by almost 200 pA to about -3720 pA. When the section of DNA that had the probe attached passed through the nanopore, there was a further reduction in the current to a little less than -3420 pA. After the DNA and probe passed through, only DNA was in the nanopore, and the current returned to -3720 pA. When the DNA exited the pore, the current returned to the baseline of -3920 pA. <figref idref="f0003">Fig. 4b</figref> provides similar data, with the application of a baseline correction. Thus, the baseline appears at 0 pA and the peaks indicate the difference between the baseline and the chosen peak height.

0083A time interval between current signal changes may be recorded. The duration of the change in the current signal may indicate a presence of a hybridized probe. This duration may be used to determine a distance between two probes on the biopolymer. To determine the distance, one may calibrate the system with known standards and calculate an average speed for the analyte in the channel. Time would then be directly related to distance. In embodiments with multiple hybridized probes, multiple peaks may form, with each peak corresponding to a hybridized probe, with the time between peaks being indicative of the relative spacing of the hybridized probes.

0084Similarly, the duration of a change in the current signal may be used to determine a length of the analyte.

0085<figref idref="f0005 f0006 f0007">Figs. 5a-5c</figref> schematically show a nanopore detector in accordance with an embodiment of the invention. A cathode 500 and anode 510 (e.g., platinum terminals connected to an appropriate power supply) are positioned to create an electrophoretic field in a buffer solution. The solution is divided into two chambers by a nanopore 530. As a target-probe complex 520 is electrophoretically driven through the nanopore 530 by the electrophoretic field, a detection circuit 540 detects and records positional information related to the location of the bound probes along the length of the target to give a probe spectrum. The target-probe complex is shown as double-stranded, but could be the single stranded complex of <figref idref="f0002">Fig. 2</figref>. <figref idref="f0005">Fig 5a</figref> shows the complex 520 prior to entering the pore 530. <figref idref="f0006">Fig 5b</figref> shows the complex 520 within the pore 530; in this state the detection circuit 540 should detect the presence of a bound probe (through an increase or decrease of signal). <figref idref="f0007">Fig. 5c</figref> shows the complex in a configuration for which the detection circuit 540 should detect the absence of a bound probe. The orientation of the target as it passes through a nanopore may be determined from the probe map, e.g. by comparing the map to a known sequence in a resequencing procedure.

0086The target-probe complex 520 passes through multiple nanopore detectors in sequence. In this way, multiple data sets may be collected and analyzed to give a better signal to noise ratio. This may result in greater accuracy in the probe map. Alternatively, other single molecule detection systems may provide such correlative data.

0087If the biopolymer target molecule is single stranded DNA (ssDNA), double-stranded DNA may be generated from the single-stranded template by enzymatically synthesizing the second strand and thereby afford may of the aforementioned benefits of using dsDNA: a reduction in the amount of secondary structure present in the target, a more consistent transmission speed of the DNA through the nanopore, the ability to manipulate single molecules of target DNA prior to introduction into the nanopore, and a longer persistence length of the DNA. ssDNA can be stabilized using a plurality of single-stranded DNA binding agents to stabilize the single stranded DNA. The binding agent molecules may be nonspecific, or may be chosen to have specificity for various DNA target subsequences. For example, a mixture of tens, hundreds, or thousands of short (e.g., designed to bind to 6-mers) DNA, or DNA analogs designed to target particular target subsequences may be stringently incubated with a target ssDNA sample. One or more detection probes may then be added and the mixture incubated under stringent conditions. The mixture may be chosen so as to not preclude a detection probe from binding to its complementary subsequence. Different stabilizing agent mixtures may be used with additional aliquots containing target combined with additional detection probes having different subsequence specificity. The mixtures of stabilizing agents may be chosen to be non-overlapping in their sequence specificity. Using locked nucleic acid or peptide nucleic acid probes may allow the use of more stable probes, capable of binding in higher stringency conditions (e.g., high temperature or low-salt). As a result, the mixture may require fewer agents; e.g., a mixture may be sufficient that binds to only a third or less of the ssDNA sequence.

0088The reconstruction algorithm, in accordance with some embodiments of the invention, may include the following steps. The reconstruction algorithm proceeds iteratively, adding letters to the reconstructed DNA sequence from 5' to 3'. Progress along the sequence is measured by the variable <i>position,</i> which increases in increments of 1 from 0. The <i>set of available probes</i> is the population of probes whose annealing to the target strand is measured at a position within some distance Δ of <i>position.</i> Each element in the <i>set of available probes</i> is a <i>Record,</i> an object containing the probe's sequence and the position at which it was measured on the target strand. Let <i>Possibility</i> denote a structure consisting of a string denoting a DNA sequence, a real number <i>score</i> proportional to the logarithm of <i>Possibility's</i> probability, a boolean value <i>sentinel,</i> and a list of Records used by this sequence.

0089Referring to <figref idref="f0008">Figure 6</figref>, the algorithm 600 proceeds in three stages: initiation, elongation and termination.

<u>Initiation:</u>

0090<i>Position</i> is initialized to 0 and a list of <i>Possibilities</i> with one <i>Possibility</i> per <i>Record</i> in the <i>set of available probes</i> about 0 (step 610). The <i>Possibility</i> with <i>Record r is</i> given <i>score</i> of (<i>r.position - 0</i>)^2<i>.</i>

<u>Elongation:</u>

0091Increment <i>position</i> by 1 (step 620).

0092Trim the list of <i>Possibilities</i> as described below with reference to <figref idref="f0009">Fig. 7</figref> (step 630).

0093For each <i>Possibility p</i> in the list of <i>Possibilities</i> (step 640):

0094Let S denote the set of <i>Records r</i> in the <i>set of available probes</i> that satisfy the condition that, if <i>l</i> is the length of the probe indicated by <i>r,</i> the <i>l</i>-<i>1</i>-length suffix of the sequence denoted by <i>p</i> is equal to the <i>l-1-</i>length prefix of the probe indicated by <i>r</i> (step 650). (Note that it is not stipulated that all probes are of a length, as discussed in more detail below.) Such a probe sequence is called an <i>extension</i> of <i>p. r</i> is also preferably absent from <i>p</i>'s list of Records used, so that each <i>Possibility</i> uses each Record only once. If more than 1 Record in <i>S</i> denotes the same probe-sequence, remove all but the one with the lowest measured position. <ul id="ul0004" list-style="bullet" compact="compact"><li>If |<i>S</i>| = 1 (step 660), let the single <i>Record</i> in <i>S</i> be called <i>r.</i> Append the final character of <i>r</i>'s probe to <i>p</i>'s DNA sequence, add (<i>r.position - position</i>)^∧2 to <i>p.score,</i> set <i>p.sentinel</i> to false and add <i>r</i> to the set of <i>Records</i> used by <i>p</i> (step 665).</li><li>If |<i>S</i>| = 0 (step 670) and <i>p.sentinel</i> = true, remove <i>p</i> from the list of <i>Possibilities</i> and continue. If <i>p.sentinel</i> = false, remove <i>p</i> from the list of <i>Possibilities</i> and add 4 new <i>Possibilities</i> to the list with the DNA sequence and score of <i>p,</i> setting their <i>sentinels</i> to true. Increase the score of each new <i>Possibility</i> by some fixed amount (Δ^2 may be used). This action (extending a sequence without finding a <i>Record</i> to extend it) is called <i>a reach</i> (step 675).</li><li>If |<i>S</i>| > 1 (step 680), remove <i>p</i> from the list of <i>Possibilities.</i> For each Record <i>r</i> in <i>S</i>, add a new <i>Possibility q</i> which is a copy of <i>p.</i> Append the final character of <i>r</i>'s probe to <i>q</i>'s DNA sequence, add (<i>r.position - position</i>)^2 to <i>q.score,</i> set <i>q.sentinel</i> to true and add <i>r</i> to the set of <i>Records</i> used by <i>q.</i> This action (extending new sequences according to multiple found <i>Records</i> to extend it) is called a <i>branch</i> (step 685).</li></ul>

<u>Termination:</u>

0095Eventually, the end of the data set is reached and the <i>set of available probes</i> will be empty (step 690). At this point, the list of <i>Possibilities</i> will decrease in membership until there are no <i>Possibilities</i> left. As <i>Possibilities</i> are removed, a reference is kept to the <i>best Possibility. best</i> is the <i>Possibility</i> whose number of used probes is greatest, measured by <i>position</i> at which the <i>Possibility</i> is terminated minus the number of <i>reaches</i> the <i>Possibility</i> made. If more than one <i>Possibility</i> have used the same number of probes, <i>best</i> is the <i>Possibility</i> with the lowest score. The sequence stored in <i>best</i> is returned as the reconstructed sequence of the target strand (step 695).

<u>Reducing list size</u>

0096As described above, the algorithm 600 has exponential runtime because the list of <i>Possibilities</i> grows by a factor of at least one at each position. In practice, the base of this exponent is highly sequence and probe-length-dependent since a branch takes place when two probes with the same prefix are found within a distance of 2Δ. Since exponential runtimes are intractable, it is preferable to keep the size of the list of <i>Possibilities</i> from growing too much. Referring to <figref idref="f0009">Figure 7</figref>, at each step, before elongating the putative <i>Possibilities</i> (step 700), the following list-size reducing measures (step 630) are enacted: <ol id="ol0001" compact="compact" ol-style=""><li>A. Haircutting (step 710) Since a <i>Possibility's</i> score is proportional to the log-probability of the <i>Possibility,</i> one may impose a lowest probability that one is willing to entertain in a <i>Possibility.</i> All <i>Possibilities</i> in the list whose probabilities are worse than the best-scoring <i>Possibility</i> by a certain amount are removed from the list (step 720).</li><li>B. Parallel culling (step 730) A problem with traditional SBH using probes of length <i>k</i> are the so-called SBH failure modes. These modes arise in sequences of the form AbAcA or AcBdAeB, where A and B are sequences of length <i>k-1</i> and b,c,d and e are sequences of any length. In the first case, it is not possible to distinguish between AbAcA and AcAbA while in the second case, it is not possible to distinguish between AcBdAeB and AeBdAcB. These modes pose a challenge to the disclosed algorithm as well, because each SBH failure mode produces two <i>Possibilities</i> that have used exactly the same probes and now extend the same sequence. Therefore, each SBH failure mode doubles the number of <i>Possibilities</i> in the list. In parallel culling, the complete list of active <i>Possibilities</i> is examined. Any two <i>Possibilities</i> that have used exactly the same <i>Records</i> and are extending the same sequence (i.e. S will be identical when elongation is applied to these <i>Possibilities</i>), are a case of <i>parallel paths.</i> The future, including all <i>reaches</i> and <i>branches</i> of these paths are the same, with the exception that their scores differ by a constant amount. As such, one has all the information one is going to get about the difference in probability between these paths, and one preferably picks the better-scoring option (step 735) and discards the other (step 720). The code is also outfitted to search a reference human genome and eliminate the <i>Possibility</i> whose most recent sequence extensions are not found in the reference. This is effective because, while existing sequencing technologies make large-scale errors, they are generally accurate on the scale in which SBH failure-modes arise in algorithm 600.</li><li>C. Jump-forward culling (step 740) Consider two <i>Possibilities p</i> and <i>q</i> that diverged at a <i>branch.</i> Without loss of generality, assume that <i>p</i> is the correct path and that <i>q</i> has been extending incorrect sequence since this branch. Since the re-use of Records is not permitted, the first Record used by <i>q</i> and not by <i>p</i> preferably comes from later on in the sequence and not earlier on. As such, all branches away from the correct path are <i>jump-ahead errors.</i> Let the <i>position</i> at the branch be <i>t</i> and the true position of the first Record used by <i>q</i> after the <i>branch</i> be <i>t+u (true position</i> denotes the position at which the correct path would incorporate the Record). The <i>u</i> probes in between <i>t</i> and <i>t+u</i> remain untouched by <i>q unless q</i> enacts a jump backward to use them. Note that if <i>q</i> makes this jump back and a subsequent jump forward to use all the probes used by <i>p, q</i> and <i>p</i> will have used the same set of probes and one will be in an SBH-failure-mode situation, already handled above. Thus, assume that <i>q</i> does not jump back for these <i>u</i> Records. As such, at any <i>position, q</i> is using a probe whose true position is greater than that of the probe used by <i>p</i>. Once <i>position</i> increases to the point where all <i>u</i> of the Records skipped by <i>q</i> have <i>positions</i> too low to be in the <i>set of available probes,</i> the set of probes used by <i>q</i> that are in the <i>set of available probes</i> will be a superset of the probes used by <i>p</i> in the <i>set of available probes.</i> Another way of thinking about this is that because <i>q</i> has skipped over <i>u</i> Records and continues to extend the same number of probes as <i>p, q</i> has <i>u</i> fewer Records in its future. The set of Records in the future is the union of the Records whose positions are too high to be in the <i>set of available probes</i> and the set of unused Records in the <i>set of available probes.</i> So having a greater number of used Records inside the <i>set of available probes</i> is identical to having fewer Records available for future use. Since both <i>p</i> and <i>q</i> have used the same number of probes (they are both extending sequences <i>position</i> long) and <i>p</i> has more Records available for future use, <i>p</i> will use more Records in the total and extends a more correct sequence than does <i>q.</i> Therefore, it is safe to remove all <i>Possibilities q</i> from the list for which there exist a <i>Possibility p</i> in the list that uses a subset of the Records still in the <i>set of available possibilities</i> that <i>q</i> does. </li></ol>

<u>Variable Probe-lengths</u>

0097In traditional SBH, all probes are of a common length, usually called <i>k</i>. Here, this constraint has been removed as a result of observations about the nature of human DNA. Simulations of DNA sequencing algorithms on random DNA (data strings in which each letter has an independent probability of being "a," "c," "g," or "t") are inevitably more favorable than simulations done on sequences drawn from human DNA. In the case of the disclosed algorithm, this is because short sequences are found repeated in very short stretches. In classical SBH, a repeated element of length <i>k-1</i> produces a branch-point. In the disclosed approach, this increases the computational burden by doubling the number of <i>Possibilities</i> in the list. It also exposes one to the chance of making incorrect decisions in cutting down the size of the list by Haircutting or Parallel-culling. In random DNA, the probability of finding two Records in the <i>set of available probes</i> with the same <i>k</i>-<i>1</i>-length prefix is equal for all <i>k-1-</i>length prefix strings. In human DNA, however, certain strings are enormously more common. To avoid these ambiguities, longer probes are used for all sequences exhibiting higher frequency. <ol id="ol0002" compact="compact" ol-style=""><li>A. Non-repeated prefixes Consider the case where the input string has the following form: acat<u>agtctga</u>t ... gtat<u>agtctga</u>a (where ... is a sequence of DNA no longer than Δ). One may wish to sequence this string by classical SBH with <i>k</i>=8. The underlined prefix agtctga is found twice, which would introduce a branch in the reconstruction. To avoid this ambiguity, one may extend the probe prefix back until the two are different: (agtctga, agtctga) -> (tagtctga, tagtctga) -> (atagtctga, atagtctga)-> (catagtctga, tatagtctga). Using a probe of length 11 instead of 8 eliminates this branch point and restores unambiguous reconstruction of this sequence. By analyzing existing versions of the human genome, one can develop a collection of proximally-repeated short elements ("ccctccct" is an identified example, as are all of the homo-polymer strings) for which to recommend longer probes.</li><li>B. Information content Another approach for probe set design is an examination of the information content of certain probes. In the human genome, there are functionally-relevant regions of reduced alphabet, i.e., regions in which only 2 or 3 of the DNA bases are found. These regions are generally either structural DNA (centromeres, telomeres, constitutive heterochromatin) or DNA that codes for functional RNA. In such regions, all probes exhibit the reduced alphabet of the region, which makes for greater ambiguity. For example, there are 4^∧7 = 16,384 prefixes of length 7 in a region in which the alphabet is all four letters of the DNA alphabet but only 2^∧7 = 128 prefixes of length 7 for a region with alphabet reduced to size 2. Therefore in a region of alphabet of size 2, there are only 128 possible prefixes and a <i>branch</i> event is 128 times as likely as in a A- alphabet region. To increase the number of prefixes, it is proposed that probes with reduced alphabet be longer. Specifically, if full-alphabet probes of length 8 were used (prefix of length 7), 3-letter-alphabet probes of length 10 would be used (3^∧9 = 19,683 -16,384) and 2-letter- alphabet probes of length 15 would be used (2^∧14 = 16,384).</li><li>C. Non-redundant prefixes Using probes of variable lengths opens the door for considerable redundancy. Redundancy is desirable because it permits multiple measurements to cross-check, but it may complicate matters by altering the probability model surrounding a single Record. Specifically, if a single Record represents two probe-landings (one of "aaaaaaaa" and another of "aaaaaaaaa") it should be treated as though it has less error than would a single probe-landing. To avoid these complications and keep the number of reactions down, the following condition may be imposed on any probe set: Let <i>T</i> denote the set of all infinitely-long strings over the alphabet {"a," "c," "g," "t"}. For all strings <i>str</i> in <i>T,</i> there exists exactly one probe <i>p</i> of length <i>l</i> in our probe set such that the <i>l</i>-<i>l</i> -length prefix of <i>p</i> is a suffix of <i>str.</i> This is identical to the condition that no probe in our probe set is the suffix of another.</li></ol>

0098The disclosed methods for biopolymer sequencing can be implemented as a computer program product for use with a computer system. Such implementations may include a series of computer instructions fixed either on a tangible medium, such as a computer readable medium (<i>e.g</i>., a diskette, CD-ROM, ROM, or fixed disk) or transmittable to a computer system, via a modem or other interface device, such as a communications adapter connected to a network over a medium. The medium may be either a tangible medium (<i>e.g</i>., optical or analog communications lines) or a medium implemented with wireless techniques (<i>e.g</i>., microwave, infrared or other transmission techniques). The series of computer instructions embodies all or part of the functionality previously described herein with respect to the system. Such computer instructions can be written in a number of programming languages for use with many computer architectures or operating systems.

0099Furthermore, such instructions may be stored in any memory device, such as semiconductor, magnetic, optical or other memory devices, and may be transmitted using any communications technology, such as optical, infrared, microwave, or other transmission technologies. It is expected that such a computer program product may be distributed as a removable medium with accompanying printed or electronic documentation (<i>e.g</i>., shrink wrapped software), preloaded with a computer system (<i>e.g</i>., on system ROM or fixed disk), or distributed from a server or electronic bulletin board over the network (<i>e.g</i>., the Internet or World Wide Web). Some embodiments of the invention may be implemented as a combination of both software (<i>e.g</i>., a computer program product) and hardware. Still other embodiments of the invention are implemented as entirely hardware, or entirely software (<i>e.g.,</i> a computer program product).

0100The steps described above are used to determine a whole or partial sequence of a target biopolymer. The method may include providing a double- stranded biopolymer target molecule. Then, the target molecule or fragment thereof may be contacted with a plurality of <i>n</i> probes each having specificity for one or more recognition sites of the target molecule, thereby forming local ternary complexes along the double- stranded biopolymer target molecule or fragment thereof, each of the recognition sites having a known sequence. At least a subset of the local ternary complexes along the double- stranded biopolymer target molecule or fragment thereof may be detected to determine one or more probe maps. A whole or partial sequence of the target biopolymer may be determined using at least one or more probe maps.

0101Detection may include passing the double-stranded biopolymer target molecule or fragment thereof through a nanopore and detecting an electrical signal indicative of locations of the local ternary complexes along a length of the double- stranded biopolymer target molecule, thereby determining the one or more probe maps. This detection step may be repeated for each of the <i>n</i> probes.