WO2013119784A1

WO2013119784A1 - Methods of sequencing nucleic acids using nanopores and active kinetic proofreading

Info

Publication number: WO2013119784A1
Application number: PCT/US2013/025106
Authority: WO
Inventors: Xinsheng Sean Ling
Original assignee: Brown University
Priority date: 2012-02-08
Filing date: 2013-02-07
Publication date: 2013-08-15

Abstract

Transient hybridization of di-nucleotides and/or tri-nucleotides to a template single stranded DNA is measured by passage of the complex through a nanopore, such that decreases in ionic current indicate the presence and locations of the bound di-nucleotide or tri-nucleotide to the single stranded DNA. Repeated analyses with all of the members of each di-nucleotides or tri-nucleotides set yield a sequence of the DNA.

Description

METHODS OF SEQUENCING NUCLEIC ACIDS USING NANOPORES AND ACTIVE KINETIC

PROOFREADING

Related applications

This application claims the benefit of provisional applications serial number 61/596,491 filed February 8, 2012 entitled, "Method of sequencing nucleic acids using nanopores and active kinetic proofreading", which is hereby incorporated herein by reference in its entirety.

Government funding

This invention was made with government support under grant R21HG004369 awarded by the National Human Genome Research Institute. The government has certain rights in this invention.

Technical Field

Methods of sequencing nucleic acids with di-nucleotide and tri-nucleotide hybridization using nanopores and active kinetic proofreading are provided.

Background

Sanger's dideoxy termination technique of sequencing DNA has revolutionized molecular biology. The technique has been improved and automated over the years and the cost of DNA sequencing has decreased significantly. However, further refinement of the method is unlikely to bring down the cost of DNA sequencing to the level that will make personalized molecular medicine affordable.

Therefore, there is a need to develop faster and more cost effective methods for DNA sequencing that do not rely on expensive polymerases and other reagents typically used in current DNA sequencing methods.

Summary

An embodiment of the invention is a method of sequencing DNA by hybridizing probes to a target single stranded DNA (ssDNA), the method including: hybridizing a plurality of oligonucleotide probes, each probe comprising two to three nucleotides of defined sequence, to the target ssDNA, such that the ssDNA is under tension, such that presence of the sequence in the target results in formation of at least one short double -stranded region; assessing presence of the probe sequence in the ssDNA target by determining probe locations on the target ssDNA, such that determining includes measuring time elapsed between nanopore ionic current fluctuations as the target ssDNA containing the short double stranded region translocates through a solid-state nanopore in the presence of the probe, such that hybridization of the probe decreases ionic current and the extent of the decrease is indicative of the sequence of the probe, and achieving resolution of probe locations, δχ, by satisfying the condition

5x²/2D > x/v (1) such that D is a diffusion constant measuring diffusion of the target ssDNA, v is drift velocity of the target ssDNA, and x is distance between two adjacent locations of a probe hybridized along the target ssDNA, and reiterating the determining of the probe locations on the target ssDNA by translocating the ssDNA back and forth through the nanopore by a plurality of translocations, thus obtaining a statistical distribution function for each probe location and fitting drift time to the statistical distribution function; and repeating the hybridizing and determining steps with each probe of a plurality of probes, such that each probe comprises a di-nucleotide or a tri- nucleotide, thereby sequencing the target ssDNA according to positions of the probe locations along the ssDNA target. The drift time is calculated from the known drift velocity v of the target ssDNA and the distance x between two adjacent locations of a probe. In a related embodiment of the method the probe is a single nucleotide. In other related embodiments the probe is four nucleotides in length.

Another embodiment of the method further includes a step of correcting errors that arise in the course of determining probe locations along the ssDNA target using a process of kinetic proofreading. Kinetic proofreading occurs in cells through actions of natural enzymes such as DNA polymerases during replication, and RNA polymerases during protein synthesis. The method of kinetic proofreading reduces or eliminates errors in sequencing caused by the binding of probes to incorrectly matched bases on the target ssDNA. In an embodiment of the method the target ssDNA is moved back and forth inside the nanopore by alternating voltage across the nanopore. In another embodiment, the back and forth movement of the target ssDNA during translocation through the solid-state nanopore is achieved by pulling or impelling the target ssDNA backward mechanically in an intermittent manner, for example, by tension applied to a bead attached to the DNA and affixed to a holding device such as a Pasteur pipette, a micropipette or a capillary. In translocation of the target ssDNA in a forward direction, the DNA moves such that the 3' end of the DNA is the leading end and the 5' end is the lagging end. Conversely during translocation in backward or reverse direction, the 5 ' end of the target ssDNA is the leading end and the 3' end the lagging end. Alternatively, in translocation in a forward direction, the 5' end of the DNA is the leading end, and the 3 'end the lagging end, and conversely in the backward direction of translocation, the 3'end is the leading end and the 5'end the lagging end.

According to another embodiment of the method, the target ssDNA with transiently bound probes is impelled or propelled or driven through an aperture in a solid-state nanopore large enough to allow double-stranded DNA segments or regions to pass through the nanopore. Upon detection of a region of double stranded DNA in which the ssDNA target is locally hybridized to an oligonucleotide, the target ssDNA is drawn backward after a wait time t_w such that a second reading can be carried out to determine if the probe is still bound to the ssDNA, where denotes waiting, such that the wait time is varied to control the error rate with waiting, R_w, of hybridization of the probes to the target ssDNA. This step is called an active kinetic proofreading. By applying the aforementioned step of kinetic proofreading, the error rate R_w is lowered compared to the error rate in the absence of kinetic proofreading, R₀, such that

R_w - R₀ exp(-(k_i2 - k_c2)t_w) ~ R₀ exp(-k_i2t_w) (2) where, R_{0 ,} the error rate absent a proofreading step is determined by a free energy difference in hybridization of correct and incorrect probes, and is expressed as

R_o ~ k_c2/k,₂ (3) where, k, and k_c2 are off rates for binding of incorrect and correct probes respectively to the target ssDNA during hybridization. The off rates are determined by probe binding energies, and

R₀ ~ k_c2lk_l2 = exp (-AG/k_BT) (4) where, AG is the free energy difference between correct and incorrect probe binding, k_B is Boltzman constant and T is temperature of operation.

In another related embodiment of the method, R₀, the error rate absent a proofreading step, is expressed as

R₀~ exp(-5) ~ 0.007 (5) for a free energy difference of about 3 kcal/mol ~ 5 k_BT, between the hybridization of correct and incorrect probes corresponding to one hydrogen bond. From equation (2), the factor in reducing error rate is introducing a waiting time t_w prior to carrying out a proof reading measurement.

A related embodiment of the method involves introducing the wait time by a time delay in reversing the target ssDNA translocation direction by changing the applied voltage. Another related embodiment involves introducing the wait time by applying mechanical tension, i.e., pulling DNA mechanically. For an incorrect 2-mer di-nucleotide probe, with a single A-T bond, the off-rate is estimated to be about k_i2~ lO³ Hz by applying Kramer's theory of reaction kinetics. Hynes, J. T. (1985) The theory of chemical reactions in solutions. In Theory of Chemical Reaction Dynamics Vol. IV (Baer, M., ed.). pp. 171 - 235, CRC, Boca Raton. A moderate wait time of t_w = 100 microseconds (μβ) achieves an additional factor of exp(-lO) in suppression of error. The achieved error rate is - (0.007)³ ~ 3x10^"7, which is equivalent to that of naturally occurring polymerases. Doubling the wait time to 200 μ5 further reduced the error rate to ~ lxlO^"1 ' , which is lower than that of the most accurate naturally occurring DNA

polymerases.

According to another embodiment of the method, holding the target ssDNA under tension includes attaching a first end of the ssDNA to a bead held by a micropipette, and attaching a second end by an applied electric field inside the solid-state nanopore. In a related embodiment, the bead is about one μηι (micrometer) in diameter. In another related embodiment of the method, the target ssDNA is attached to the bead by a biotin-streptavidin linkage.

In related embodiments of the method, the solid-state nanopore is a graphene nanopore.

For example, the graphene nanopore has a thickness less than about five nanometers. In another embodiment, the graphene nanopore has a thickness of one or a few atoms.

The hybridization of the probe is transient in another related embodiment of the method. Another embodiment of the invention is an apparatus for sequencing DNA by hybridizing probes to a ssDNA, the apparatus including: a micropipette mounted on a plate anchored to an micropositioning stage located inside a Faraday cage; a magnification device for obtaining visual feedback to locate and contact a bead attached to a first end of the target ssDNA by the micropipette, such that the micropipette is in physical contact with the bead; a nanopore assembly comprising a nanopore chip, a sealed sample holder, electrodes and a patch-clamp amplifier located inside the Faraday cage, such that the apparatus measures time elapsed between nanopore ionic current fluctuations during translocation of the target ssDNA through the nanopore chip to determine locations of probes hybridized to the target ssDNA. For example, the plate is a metal plate. For example, the micropositioning stage is automated. For example, the micropipette sucks the bead due to a pressure difference to make physical contact with the bead. In a related embodiment of the apparatus the micropositioning stage is controlled by two nanopositioning devices/motors having the capability of moving with multiple speeds with accuracy of about one nanometer. For example, the nanopositioning device is an inchworm motor. Inchworm motors are solid-state linear positioning devices that position objects without any loss of resolution at high speeds, or any loss of smoothness of motion at low speeds.

Inchworm motors rely on the highly precise positioning properties of piezoelectric materials which undergo dimensional change when voltage is applied. Inchworm motors are available commercially, for example Burleigh Inchworm motors from EXFO Burleigh Products Group, Victor, New York, USA.

According to another related embodiment of the apparatus, the micropipette is placed inside a large glass pipette and held in place with optical glue.

Another embodiment of the invention is a kit for determining a sequence of a DNA by hybridization of probes two to three nucleotides in length during translocation of the DNA through a solid-state nanopore, the kit including hybridization probes contained in labeled tubes, and instructions for correlating temporal traces of ionic current as the DNA translocates through the solid-state nanopore, with positions of probe binding sites on the DNA, of the probes contained in the respective tubes. In a related embodiment of the kit, the hybridization probes are contained in labeled tubes as individual probes. In another related embodiment of the kit, the hybridization probes are contained in labeled tubes as defined mixtures of probes.

Brief descriptions of the drawings

FIG. 1 panels A-D are schematic diagrams, a photograph and a line graph illustrating hybridization-assisted nanopore sequencing, HANS (Ling, X.S. et al. utility patent application publication number 2007/0190542).

FIG. 1 panel A (upper) is a schematic illustration of electric-field driven DNA translocation through a solid-state nanopore. The and "+" signs indicate electric field applied across the nanopore. The target single stranded DNA (ssDNA) is hybridized to two penta- nucleotides (5-mers) and is entering the nanopore. FIG. 1 panel A (lower) shows the method of HANS for obtaining a nucleotide sequence of a ssDNA based on the positions of the hybridizing 5-mers oligonucleotides as measured by the ionic current traces. Decreases or dips in an ionic current trace illustrated by the line above the DNA correspond to locations of hybridization of the probes on the ssDNA.

FIG. 1 panel B is a schematic diagram of the structure of a designed model DNA molecule formed by hybridization between three oligonucleotides (Balagurusamy, V. et al. 2010 Nanotechnology 21 : 335102). The model DNA molecule is a ternary complex (Oliver, J. et al. 2009 utility patent application publication number 2009/0099786), and consists of synthetic single-stranded poly-T (thymine) containing oligonucleotides: 3'-TGTGTGCTGTCG-(T

T)i3o-(Biotin)-5' (SEQ ID NO: 1 ); 3'-CGACAGCACACA-(T- - -T)i₂o-CGGCTATGTTGG-5' (SEQ ID NO: 2); and, 3'-(T- - -T)₁₃₀-CCAACATAGCCG-5 ' (SEQ ID NO: 3). The ternary complex structure is a result of hybridization of two oligonucleotides (at the two ends) to a third oligonucleotide (middle) and is characterized by the presence of two hybridized regions each 12 base pairs long.

FIG. 1 panel C is a photograph of a gel electrophoresis pattern of DNA molecules migrating under an applied voltage of 25 Volts (25 minutes) and then 75 Volts (200 minutes). Lanes marked A contains DNA samples that are monomers (m), dimers (d) and trimers (t) generated from oligonucleotides having SEQ ID NOs. 1-3. Lane L contains a 50bp increment DNA ladder as a marker of molecular weight. The monomers, dimers and trimers are well separated from one another after gel electrophoresis.

FIG. 1 panel D is an exemplary ionic current trace with distinct signatures of the two double stranded segments (arrows in inset) corresponding to the two 12 base pair long hybridization regions in the model DNA molecule described in FIG. 1 B. Abscissa and ordinate represent time in milliseconds (ms) and current in nanoamperes (nA). The inset is an expanded view of the current trace between 0 ms and 1ms.

FIG. 2 is a schematic diagram of the methods, apparatus and kits provided herein entitled Dynamic Nanopore Southern Sequencing (DNSS) and a photograph of the apparatus for sequencing nucleic acids using DNSS.

FIG. 2 panel A is a schematic diagram of DNSS. One end of the target ssD A (201) is attached to a bead (202), and the other end extends through a nanopore composed of Si₃N₄ (203). The bead is held by a micropipette (204) and the ssDNA is and is held under tension by the electric field applied across the nanopore. Oligonucleotide probes that are di-nucleotides (2-mer) are illustrated either hybridized to the ssDNA (206) or free in solution (205).

FIG. 2 panel B is a photograph of the apparatus for carrying out DNSS. The

micropipette (204) is mounted on a stable aluminum plate (207) anchored on a movable stage (208) controlled by two Burleigh Inchworm motors (209, 210) that use piezoelectric actuators to move a shaft with nanometer accuracy at any of multiple moving speeds. The 50x magnification long working distance objective (211) provides visual feedback to facilitate locating and catching the bead to attach it to the micropipette. The micropipette is placed within a large glass pipette (212) to stabilize the system.

FIG. 3 is a schematic diagram of the steps involved in the method of kinetic

proofreading. The "on" and "off rates for probe binding and unbinding are indicated as k_c/ and k_C2 for correct probes, and ku and ka for incorrect probes, respectively. The "on" rates are a function of probe concentration, and are chosen such that k_ci = ku. The "off rates are a function of probe binding energies, thus k_c2 « k_i2. The wait time t_w, is the duration of time between detection of a bound probe in the forward translocation and again re-detection in the reverse translocation.

FIG. 4 is a bar graph of the number of the "ATG" sequences on the ordinate as a function of the number of nucleotides that separate one ATG sequence from another in a 1410 bp long nucleotide sequence of A/Poland/169/2009(H1N1) influenza virus. From these data it is observed that there are seven copies of ATG sequences spaced within 20 nt (nucleotides or base- pairs) of one another, or about 8nm.

Detailed description of embodiments

Reducing the cost of sequencing human DNA to the level of $1000 or less for a personal genome would substantially alter the way cancer and genetic diseases are diagnosed and treated. Even though the cost of polymerase-based Sanger DNA sequencing technology has steadily been reduced by improved automation systems, it is still significant enough to prevent Sanger sequencing from being used widely as a routine diagnostic tool for doctors.

Described herein are methods, apparatus, and kits for sequencing nucleic acids using a new approach, Dynamic Nanopore Southern Sequencing (DNSS). In this approach nucleic acid sequencing is performed using nanopores and active kinetic proofreading in which transient hybridization probes are used for reading the sequence of a target ssDNA as it is pulled through a solid-state nanopore. DNSS is a paradigm shift in the field of conventional Southern sequencing or sequencing-by-hybridization (SBH). All previously known hybridization-based approaches require hybridization probes capable of hybridizing stably to the target nucleic acid at room temperature. The stability requirement of the SBH approach demands long hybridization probes, which in turn requires a large library of probes, thereby increasing cost.

A brief consideration of the developments in the field of nucleic acid sequencing using nanopores provides a useful context for appreciating the methods, apparatus and kits described herein. Direct DNA sequencing using nanopores was first introduced by Church et al., U.S. patent number 5,795,782.

Direct DNA sequencing using a-hemolysin pores failed to detect individual nucleotides (Akeson, ML et al. 1999 Biophys. J. 77: 3227-3233; Meller, A. and Branton, D. 2002

Electrophoresis 23 : 2583). Spacing between nucleotides was about 0.4 nm, and the a-hemolysin channel length was about an order of magnitude longer, hence the ionic current blockade effect was an averaged signal from several nucleotides. Graphene nanopores with single atom or few atom thicknesses were proposed as a solution to this problem (Merchant C. et al. 2010 Nano Letters 10 (8): 2915-2921 ; Merchant C. et al. 2010 Nano Letters 10 (8): 2915-2921).

Clarke et al. proposed using α-hemolysin as a detector for single-base nucleotides as they are cleaved from an ssDNA molecule by exonucleases (Clarke J. et al. 2009 Nature

Nanotechnology 4: 265-270). A mutated a -hemolysin channel with a cyclodextrin covalently attached to the inside of the beta barrel part of the channel discriminates between nucleotides by their blockage signals in ionic current through the nanopore. This approach given the basic constraints imposed by the Second Law of thermodynamics allows sequence information to be scrambled by Brownian motion after the bases are cleaved. A biological pore prepared from porin A of Mycobacterium smegmatis referred to as "MspA" has a very short pore length which may avoid the intrinsic problem of the α-hemolysin pore (Derrington, I.M. et al. 2010 Proc. Nat. Acad. ScL USA 1 07: 16060-16065).

The physics of molecular transport through restricted spaces, for example, linearized transport of DNA through a nanopore is shown in Kasianowicz, J.J. et al. 1996 Proc. Nat. Acad. Sci. USA 93: 13770-13773; Akeson, M. et al. 1999 Biophys. J. 77: 3227-3233; and Meller, A. and Branton, D. 2002 Electrophoresis 23: 2583. Linearized transport of DNA through a nanopore was applied to sequencing-by-tunneling (Golovchenko, J.A. et al. U.S. patent application publication number 2004/0229386) and the hybridization-assisted-nanopore- sequencing (Ling X. S. et al. 2007 U.S. patent application publication number 2007/0190542). Developments in nanopore-based and other types of DNA sequenc ing methods are reviewed by Blow, N. 2008 Nature Methods 5: 267; and, Niedringhaus, T.P. et al. 2011 Anal. Chem. 83: 4327 and Branton, D. et al. 2008 Nature Biotechnology 26: 1 146.

Nanopore technology was combined with the SBH to develop hybridization-assisted nanopore sequencing (HANS), based on using nanopore conductance as a nanopositioning device for detecting DNA probes used for hybridizing with the target DNA (Ling X. S. et al. 2007 U.S. patent application publication number 2007/0190542). In the HANS method, the probes hybridized to the template are chosen to have a length such that the hybrids are stable at room temperature, and therefore have a length that is at least six nucleotides in length (6-mer) or longer. Balagurusamy et al. used solid-state-nanopore and the HANS approach (FIG. 1 ) to resolve individual hybridization segments (or 'probes') on a DNA molecule. (Balagurusamy, V. et al. 2010 Nanotechnology 21 : 335102). Sample DNA, consisting of three oligonucleotides (FIG. 1 B), was translocated through solid-state-nanopores to detect the sequential arrangement of two double-stranded 12-mer hybridization segments on a single-stranded DNA molecule (FIG. 1 D). The translocated sample DNA contained two 12 base pair long stretches of hybridized regions (FIG. 1 B). An electrical signature of the translocation of the sample DNA molecule through the nanopore was identified in the temporal traces of ionic current (FIG. 1 D).

As shown in FIG. 1 panel A with 5-mers: HANS sequencing results from aligning the current blockade signals and their corresponding probe sequences as in SBH (Southern, E. M. 1975 Journal of Molecular Biology 98 (3): 503-517; Drmanac R. et al. 2002 Adv. Biochem. Eng. Biotechnol. 77:75-101). A difference between HANS and SBH is that the main framework of sequence information in HANS is formed by the locations of the DNA probes with known sequences, while SBH relies completely on whether a particular probe hybridizes to the DNA. If there are multiple hybridization sites on a single ssDNA for a given probe, the SBH construction of the DNA sequence gives erroneous result because human DNA is full of repeat sequences. Without the positional information of the probes, the SBH approach cannot be used for sequencing human DNA longer than approximately 1000 bases (Drmanac R. et al. 2002 Adv. Biochem. Eng. Biotechnol. 77:75-101). In a way, the HANS approach is a method of solving the "repeat problem" in SBH using solid-state nanopores. The major difference between the HANS approach and that of the direct nanopore sequencing of Church et al. (U.S. patent number 5,795,782) is that the HANS approach bypasses the harsh requirement of single-base spatial resolution (0.4nm). This advantage comes at the expense of a large number of samples needed to analyze DNA sequence. For a probe of length n, the library size N of the oligonucleotides needed is such that N=4".

Balagurusamy et al. demonstrated the capability of detecting 12-mer hybridization probes (see FIG. l panel D) using HANS. (Balagurusamy, V. et al. 2010 Nanotechnology 21 : 335102). For a probe of length n=12, the required library size, N is approximately 16,000,000, and one would need to scan through 16 million DNA samples, increasing the cost prohibitively. For n=6, N is 4096, a significantly smaller number. The necessary microfluidic system to handle more than four thousand samples adds to the prohibitively high cost of a large library of probes. A drastically new, simplified method remains needed.

In the methods, apparatus and kits for sequencing nucleic acids provided herein, the DNSS approach is used, and the hybridization probes are di-nucleotides (2-mers) and tri- nucleotides (3-mers). The 2-mer or 3-mer oligonucleotides exhibit transient binding to ssDNA at room temperature with a residence times for a 2-mer or a 3-mer probe long enough to give rise to a discernible signal in ionic current passing through a nanopore. The target ssDNA is held under tension such that self-hybridization and diffusion induced smearing effects are avoided. The size of the library of oligonucleotides needed in the DNSS approach is approximately 1/100 of that used in other approaches that require stable hybridization probes, thus greatly reducing the cost of DNA sequencing. By using 2-mer oligonucleotide probes, Southern sequencing is performed with only 16 probes. With 3-mer oligonucleotide probes, the library size is 64. At these library sizes, the cost of sequencing is drastically reduced compared to the at least 6-mer oligonucleotide probes and a library of 4096 oligonucleotides required in the HANS approach.

DNSS is made possible by recent advancements in the understanding of the physics of the DNA translocation process, and by the availability of new types of nanopores, for example grapheme nanopores.

A significant recent development related to nanopore sequencing is the understanding that Brownian motion of the translocating DNA places a fundamental limit on nanopore sequencing. See Lu, B., et al. 2011 Biophysical Journal 101 :70-79, and Ling, X.S. 2011

Nanopores: Sensing and Fundamental Biological Interactions p.177 S.M. Iqbal and R. Bashir (eds.), Springer Science. The DNA translocation time distribution can be described by the first- passage-time distribution function derived from a ID biased diffusion model (Li, J. and Talaga, D.S. 2010 J. Phys. : Condens. Matter 22: 454129; Ling, D.Y. and Ling, X.S. 2012 Bull. APS, vol.57, No. l ). In the DNA hybridization example, the time interval between the two dips in the ionic current trace exhibits a broad distribution (Balagurusamy, V. et al. 2010 Nanotechnology 21 :335102).

Certain of the considerations indicate that the conditions for nanopore DNA sequencing are similar to that for gel or capillary electrophoresis of the Sanger sequencing (Ling, X.S. 2011 Nanopores: Sensing and Fundamental Biological Interactions p.177 S.M. Iqbal and R. Bashir (eds.), Springer Science). In Sanger sequencing, to achieve singe-base resolution, the spatial spread in each band (for each fragment) should be less than the separation between the adjacent bands. Since the separation (due to drift) grows with time t linearly, and the band width scales as t¹'² (due to diffusion), the separation between adjacent bands (hence the single-base resolution) occurs after a sufficiently long time. In the context of DNA translocation through nanopores, the quantity measured is the time elapsed between probes or sequences (spaced x distance apart) as the DNA is driven through the pore. The condition equivalent to Sanger's condition for obtaining single base resolution is that diffusion time (over resolution δχ) be larger than the drift time (between two probes or two sequences, x),

where D is the diffusion constant and v is the drift velocity of the DNA. The condition (1) is valid regardless of whether the method used is direct sequencing by ionic current using MspA (Derrington, I.M. et al. 2010 Proc. Nat. Acad. Sci. USA 14; 107(37): 16060-16065), tunneling (Golovchenko, J.A. et al. U.S. patent application publication number 2004/0229386), HANS (Ling, X.S. et al. 2007 U.S. patent application publication number 2007/0190542), or the new DNSS described herein. For free unrestricted DNA translocation, according to Stokes-Einstein relation, D=k_BT/y, where k_B is the Boltzmann constant, T the temperature, and γ the Stokes drag coefficient, and γ =6πηΙ , where η is the buffer viscosity and R the Stokes radius; and the DNA drift velocity is described by v=pV/ γ, where p is the effective linear charge density on the DNA, V the applied voltage. The condition (1) then becomes, pV > 2 k_BTx/5x², (7) and is independent of the Stokes drag coefficient. For direct nanopore sequencing (Derrington, I.M. et al. 2010 Proc. Nat. Acad. Sci. USA 14; 107, 37: 16060-16065; Golovchenko, J.A. et al. U.S. patent application publication number 2004/0229386), x ~ 0.4 nm, and if δχ ~ 0.5x= 0.2nm, at room temperature k_BT ~ 25 meV, p ~ 0.5 e/0.4 nm (Keyser, U. F. et al. 2006 Nature Phys. 2: 473-477), the sequencing condition (2) is satisfied if the required applied V > 400 mV.

A decreased resolution, for example, δχ ~ x = 0.4 nm, requires an applied voltage V such that V > 100 mV. At 100 mV, the typical DNA translocation velocity in solid-state nanopores is ~ 25 b /μs (Li, J. et al. 2003 Nature Mat. 2:61 1 ; Storm, A. J. et al. 2005 Nano Lett. 5(7): 1 193- 1 197), which is too fast for single-base reading using present electronics. Similarly demanding conditions apply also to the HANS approach even though detection of the probes is much easier with HANS. Thus, developing a technique to simultaneously reduce the diffusion constant D, and the drift velocity of the DNA are the major determinants of success for development of a working nanopore sequencing technology.

One approach is to increase the viscosity of the buffer (Fologea, D. et al. 2005, Nano Lett. 5: 1734). The amount of reduction in D obtained by increasing the viscosity of buffer is not adequate. A "reverse translocation" method in which the diffusion constant can be greatly suppressed makes it possible to slow down the translocation speed such that condition (1) is still satisfied (Peng, H. et al. 2009 Nanotechnology 20: 185101).

Considering hybridization of a 12-mer oligonucleotide, which is clearly discernible in gel data (see FIG. l panel C), yet only a minority of hybridization segments remain attached to the target DNA during translocation (Balagurusamy, V. et al. 2010 Nanotechnology 21 :

335102). The on-and-off processes take place constantly in equilibrium. A more efficient way to implement SBH is using unstable hybridizations by short oligonucleotide probes. For short oligonucleotides, off-state diffusion constant is large. With a high concentration of the short oligonucleotide probes, such that the probes have long enough "residence time" for their "on- state" or hybridized state, use of nanopores to perform sequencing is facilitated. This mechanism is analyzed herein by a first approximation with 1 -mer probes.

Considering only the hydrogen bonds between the bases of hybridized DNA, and using known parameters (Kool, E.T. 2001 Annu. Rev. Biophy. Biomol. Struc. 30: 1), the binding energy E₀ for an A-T bond is approximately - 12.1 kcal/mol, and for a G-C bond is approximately -21.0 kcal/mol. By applying Kramer's escape theory the "residence time" τ is estimated using the formula τ = (1/ω₀)εχρ(Ε₀ /k_flT), where ω₀ is the "attempt" frequency which is set by the stretching frequency of the N-H and O-H bonds in the bases, ω₀ ~ 10¹⁴ Hz. Using these parameters, it is estimated that τ A T ~ 1 .0 μ5, τ G-C ~ 58.2 s. This estimate indicates that it would be difficult to achieve single-base Southern sequencing, since the A-T bond is too shortlived.

Calculations herein determined that a 2-mer probe of two A-T bonds should have a strength ~ -20 kcal/mol, similar to a G-C bond. Residence time of the A-T di-nucleotide should be similar to that of a single G-C bond, or τ AA-TT ~ 60 s. Thus one should be able to use 2-mer probes for sequencing applications. With 2-mer probes, the double-stranded segments are transient in time. However, because of the long residence time of the di-nucleotides, there will be on average detectable signatures of hybridization in the nanopore ionic current traces if the concentration of probe oligonucleotides is high (such that probes are always be available for binding) and the probe's diffusion constant is large (so that the incoming probes are not diffusion-limited). It was determined from these calculations that probes that are 2-mers or 3- mers are to be used in the DNSS approach herein.

The DNSS method is illustrated in FIG. 2 panel A. One end of a single-stranded target DN A (201) is attached to a micron-sized (202) bead by a linker molecule, for example a standard biotin-streptavidin linker. The bead is held by a micropipette (204). The other end of the DNA is held inside a nanopore by the applied electric field. A concentrated solution of oligonucleotide probes is added to a chamber holding the bead and the DNA. The ssDNA is obtained by melting a complementary strand of double stranded template by using high pH at the beginning of the sequencing. The pH of the buffer is then lowered for optimal hybridization of the probes. Probe molecules that are unable to hybridize (205) with the target DNA go through the pore too quickly and are not detected due to electronic filtering. Probes that hybridize (206) with the DNA have long enough residence time to give a detectable signal in the ionic current through the pore.

For the sequencing step the ssDNA is flossed back and forth through the pore for repeated measurements of probe binding sites such that sufficient data is collected for building a statistical distribution function for each probe location. The same procedure is repeated for each probe. The probe is changed, for example, by flushing the preceding probes with a solution. At a fundamental level, the repeated measurements of a probe binding site is equivalent to the presence of many copies of the same DNA fragment in a single band in a sequencing gel in Sanger's gel electrophoresis method of sequencing. In Sanger's method single-base resolution is achieved during gel electrophoresis only because each gel band contains many copies of the same DNA fragment.

The DNSS approach is used in the methods, apparatus and kits herein in combination with the methods of kinetic proofreading for achieving accuracy in sequencing (See FIG. 3). It is expected that measurements of binding events include false positives and false negatives due to the thermodynamic processes of binding and unbinding of hydrogen bonds between the probe oligonucleotides and target ssDNA. Similar phenomena exist in natural processes of DNA and protein syntheses. Kinetic proofreading is described by Hopfield as occurring in Nature (Hopfield, J. J., 1974 Proc. Nat. Acad. Sci. USA, 71 : 4135-4139).

FIG. 2 panel B shows an apparatus for sequencing DNA using the DNSS approach described herein. The micropipette (204) that holds the bead (202) to which target DNA (201) is attached is mounted on a stable aluminum plate (207). The aluminum plate is anchored on an automated movable micropositioning stage (208) controlled by two Burleigh Inchworm motors (209, 210) that are capable of multiple moving speeds with nanometer accuracy. The micropipette is emplaced inside a Faraday cage in which the nanopore system (nanopore chip, sealed sample holder, electrodes, patch-clamp amplifier, etc.) is located. The 50x long magnification working distance objective (211) provides a visual feedback such that one can locate and catch the bead with the micropipette. This system is a significant improvement over the magnetic tweezers system previously described in which the magnetic field gradient is provided by a permanent magnet outside of the nanopore cell (Peng, H. et al. 2009

Nanotechnology 20: 185101). In the apparatus herein the bead is impelled into, i.e., sucked up by a pressure difference and is in physical contact with the tip of the micropipette. In this method, the diffusion of the bead is greatly suppressed as it is anchored onto the end of the micropipette which is significantly bulkier than the bead and has less Brownian motion.

As shown in FIG. 3 kinetic proofreading is accomplished in DNSS by simply using a forward-reverse-forward-reverse-... translocation procedure. The error rate in sequencing is reduced exponentially with the wait time i_w, the time duration between binding of a probe detected in the forward translocation and again re-detected in the reverse translocation. With incorporation of kinetic proofreading an estimate of the sequencing error within an order-of- magnitude, is determined as follows.

Using Michaelis- 4enten formulation, the error rate R₀ in determining probe binding without a proofreading step is detennined by the free energy difference in the hybridization of correct and incorrect probes (i.e. one hydrogen bond ~ 3 kcal/mol ~ 5 k_BT), or

R_a~ exp(-5) ~ 0.007 (5)

By reversing the translocation process after each probe binding event in the forward translocation process, with a delay time t_w, a new error rate R_w is obtained such that

R_w ~ R₀ exp(-(k,₂ - k_c2)t_w) ~ R₀ exp(-k_i2t_w) (2)

The last step of approximation is due to the fact that the "off rate of a correct probe is much smaller than that of an incorrect one.

A quantitative estimate of R_w requires knowledge of the "off rates of the binding of incorrect probe. This information is not known for a monomer, a 2-mer, or a 3-mer probe. However, the calculated single A-T bond lifetime of 12 μ$ is used as a starting point. For an incorrect 2-mer probe with only one A-T bond, it is estimated that A¾ is approximately 10^s Hz. With a moderate wait time of t_w of 100 μβ, an additional factor of exp(- 10) in suppressing the error is obtained. The new error rate becomes approximately (0.007)³ or approximately 3x10^"7, which is equivalent to that of the natural polymerases. By doubling the wait time to 200 μβ, the error rate is reduced to approximately 1 x10^"11, which is better than the best known DNA polymerases in Nature.

Existing nanopore devices with 20nm pore length are inadequate for sensing 2-mer and 3-mer hybridization probes since regions in the target DNA that hybridize with the 2-mer or 3-mer probes are too closely spaced. A standard fabrication method using transmission electron microscopy drilling (Storm, A. J. et al. 2003 Nature Materials 2:537-540) may be fine-tuned according to obtain nanopores of suitable pore length (Wanunu, M. et al.2010 Nature

Nanotechnology 5: 807-814). Alternatively, graphene nanopores drilled with a special focused ion beam system (Nanopore Solutions, Inc. Portugal) may be used. The data in FIG. 4 illustrate the need for having nanopores of sufficiently small pore length by taking the example of a histogram of the population of "ATG" segments within the 1410 bp length of the A/Poland/169/2009 H1N 1 influenza virus genome. It was observed that seven copies of ATG are spaced within 20 nucleotides or base-pairs of the adjacent ATG, i.e. within approximately 8 nm. These probes are resolved by graphene or ultra-thin Si3N4 nanopores.

There are significant advantages of the DNSS approach including suppression of diffusion of the DNA by holding DNA under tension through which the effective diffusion constant of the DNA becomes that of the bead (and thus the pipette). Multiple measurements of translocation times is another advantage. As described, the condition of equations indicates that the physics in translocation of DNA through a nanopore is the same as in the passage of DNA through a gel during gel electrophoresis. In resolving DNA fragments using gel electrophoresis, the measured signal from each band is derived from thousands of copies of the same DNA fragment present in each band. To achieve similar accuracy of measurement in translocating DNA through a nanopore, each translocation measurement has to be repeated to build a clear histogram. Fitting the translocation measurements to a first-passage time distribution function (Schrodinger, E. 1915 Physik. Z 16: 289-295) is equivalent to fitting intensities in the common gel electrophoresis data analysis. Suppression of self-hybridization of ssDNA is achieved by holding the single-stranded DNA (ssDNA) under tension, avoiding the problem of having self- hybridized segments going through the pore.

A "solid-state nanopore" as described herein, refers to any solid-state material having nanometer sized pore dimensions suitable for nanopore-based DNA analysis. Solid-state nanopores are distinguished from nanopores which are fluid in nature such as the biological nanopore made of the protein a-hemolysin incorporated into lipid bilayers. Nanopore membranes made from incorporation of a-hemolysin in lipid bilayers have a short lifetime due to fragility of the lipid bilayers. Solid-state nanopores described in the methods and apparatus herein include thin films or membranes made of Silicon nitride (SiN) e.g. S13N4; metals e Al and Cr; polymers such as PMAA (poly(methyl methylacrylate)), Kapton^® (polyimide); crystalline forms of Si, A1₂0₃, AIN, SiC, Si0₂; polycrystal line metals such as Ni. Al, Au; and amorphous C. See Healy K et al. 2007 Nanomedicine 2(6): 875-897.

A "graphene" nanopore is a solid-state nanopore made with graphene, which is a two- dimensional layer of carbon atoms packed into a honeycomb lattice with a thickness of one atomic layer (0.3 nm). Despite its thickness, graphene is as strong as a free-standing membrane and a good conductor of electric current. The distance between two adjacent bases in DNA is 0.4 nm. Signals of ionic current fluctuations as each base of the DNA translocates through a nanopore are observed if the thickness of the nanopore is close to 0.4 nm, and averaging of signals is not needed. Measurement of ionic current fluctuations through nanopores of greater thickness is accomplished by averaging signals of current fluctuations from several nucleotides. Therefore, the thickness of graphene is suitable as a solid-state nanopore for DNA sequencing.

As used herein the phrase an "oligonucleotide probe" shall mean a single stranded DNA of two to four nucleotides in length, such as a di-nucleotide, a tri-nucleotide or a tetra- nucleotide.

As used herein "translocating the DNA^"' refers to linear transport of DNA through a nanopore. For, example DNA is transported through a solid-state nanopore under the driving force of an applied electric field across the nanopore. in translocating the target ssDNA in a forward direction, the DNA moves such that the 3' end of the DNA is the leading end and the 5' end is the lagging end. Conversely during translocation in backward direction, the 5' end of the target ssDNA is the leading end and the 3' end the lagging end. Alternatively, in translocation in a forward direction, the 5' end of the DNA is the leading end, and the 3'end the lagging end, and conversely in the backward direction of translocation, the 3 'end is the leading end and the 5 'end the lagging end.

The term "target" as used in the methods and apparatus herein refers to the DNA molecule which is to be sequenced. A double stranded DNA molecule is converted to a single stranded DNA molecule by treatment such as raising the pH of buffer or heating or adding a denaturant such as formaldehyde, and removing the complementary strand to obtain target single stranded DNA. Removal of the complementary strand is achieved by separating the bead attached ssDNA from the complementary strand which is in solution.

As used herein the phrase "holding the target ssDNA under tension" means controlling the movement of the target ssDNA to suppress diffusion and self-hybridization as the DNA translocates through a solid-state nanopore. By attaching DNA to a bulky object such as a bead, and by further attaching the bead to a bulkier micropipette, as in methods and apparatus herein, the effective diffusion constant of the DNA is that of the bulky object to which it is attached, resulting in suppression of diffusion of the DNA. Holding the target ssDNA under tension also prevents self-hybridization by preventing folding back of the DNA onto itself.

The phrase "kinetic proofreading" as used herein means a process included in embodiments of the method herein to reduce error rates in determining probe locations along the target ssDNA that result from binding of probes to the target ssDNA at locations of incorrectly matched bases. Kinetic proofreading is used during natural processes of DNA and protein biosynthesis for reducing errors that arise due to a mismatch between an amino acid or nucleotide building block and the corresponding template. Hopfield, J. J. 1974 Proc. Nat. Acad. Sci. USA 71 :4135-4139. Kinetic proofreading is accomplished in embodiments of the method herein by using alternating forward and reverse movements of the target ssDNA through the solid-state nanopore during translocation. The error rate in sequencing is decreased substantially, e.g., exponentially by introducing a wait time t_w, between detection of probe binding in a forward direction and the subsequent detection of probe binding in the reverse direction during translocation of the ssDNA target through the solid-state nanopore.

A skilled person will recognize many suitable variations of the methods to be substituted for or used in addition to those described above and in the claims. It should be understood that the implementation of other variations and modifications of the embodiments of the invention and its various aspects will be apparent to one skilled in the art, and that the invention is not limited by the specific embodiments described herein and in the claims. Therefore, it is contemplated to cover the present embodiments of the invention and any and all modifications, variations, or equivalents that fall within the true spirit and scope of the basic underlying principles disclosed and claimed herein.

The invention now having been fully described above, additional embodiments are found in the claims herein which are exemplary and not to be construed as further limiting. The contents of all literature and patent documents cited herein are hereby incorporated herein by reference.

Examples

Example 1. The DNSS approach

The design of the DNSS approach is shown in FIG. 2 panel A. A single-stranded target

DNA (ssDNA) is held on one end by a standard biotin-streptavidin linker to a micron-sized bead, which in turn is held by a micropipette. The other end of the DNA is held inside a nanopore by an applied electric field. The ssDNA is obtained by melting and flushing away the complementary strand by using high pH at the beginning of the experiment. The ssDNA is held under tension inside the nanopore by the applied electric field, which prevents the ssDNA from self-hybridization. A concentrated solution of oligonucleotides probes is introduced into the chamber having bead end of the ssDNA, the cis-chamber. The pH of the buffer is re-adjusted to a lower value such that the hybridization condition is optimal for the probes.

Probes that do not hybridize with the target DNA go through the pore too quickly to be detected (due to electronic filtering). The probes that hybridize with the DNA have sufficiently long residence time to give a detectable signal to the ionic current through the pore.

The sequencing step is carried out by flossing the ssDNA back and forth through the pore to measure the probe binding sites repeatedly such that sufficient data is obtained to build a statistical distribution function for the probe location. The same procedure is repeated for each probe. In this manner full scale sequencing of a full length bacteriophage lambda DNA is carried out. The probe change is achieved by simply flushing out the previous probes. The repeated measurements of each probe location are equivalent to the many copies of the same DNA fragments that are present in a single band in Sanger's gel electrophoresis method of sequencing. In Sanger's method single-base resolution is achieved in gel electrophoresis only because each gel band contains many copies of the same DNA fragment.

Example 2. Construction and calibration of the nanopore micropipette system

A version of the nanopore micropipette system using two Burleigh Inchworm motors (209, 210) that use piezoelectric actuators for nanopositioning was constructed (FIG. 2 panel B). Because of its small bending modulus the long micropipette (204) is quite easy to disturb laterally. This potential source of instability was solved by placing the micropipette inside a large glass pipette (212) and holding the micropipette with optical glues (Norland 88). With these modifications the DNA-coated beads are accurately moved using the micropipette. Example 3. Preparation of target DNA and oligonucleotides for sequencing using DNSS

The 2-mer and 3-mer oligonucleotides are obtained commercially. Target DNA, for example, lambda-DNA (bacteriophage lambda DNA) with specific digestion are prepared and characterized. Once the double stranded DNA (dsDNA) is located inside the nanopore, the matching strand is removed by raising the pH of the buffer. After the matching strand is melted and flushed out, the pH is lowered back to a desired value for probe binding. Self-hybridization effects are avoided since the DNA is held under tension. Graphene nanopores with thickness less than 5nm are commercially available from Nanopore Solutions, Inc. Portugal.

Claims

What is claimed is:

1. A method of sequencing DN A by hybridizing probes to a target single stranded DNA (ssDNA), the method comprising:

hybridizing a plurality of oligonucleotide probes each probe comprising two to three nucleotides of defined sequence to the target ssDN A, wherein the ssDNA is under tension, wherein presence of the sequence in the target results in formation of at least one short double-stranded region;

assessing presence of the probe sequence in the ssDNA target by determining probe locations on the target ssDNA, wherein determining comprises measuring time elapsed between nanopore ionic current fluctuations as the target ssDNA containing the short double stranded region translocates through a solid-state nanopore in the presence of the probe, wherein hybridization of the probe decreases ionic current and the extent of the decrease is indicative of the sequence of the probe, and achieving resolution of probe locations, δχ by satisfying the condition

5x²/2D > x/v, wherein D is a diffusion constant measuring diffusion of the target ssDNA, v is drift velocity of the target ssDNA, and x is distance between two adjacent locations of a probe hybridized along the target ssDNA, and reiterating the determining of the probe locations on the target ssDNA by translocating the ssDNA back and forth through the nanopore by a plurality of translocations, thereby obtaining a statistical distribution function for each probe location and fitting drift time to the statistical distribution function; and

repeating the hybridizing and determining steps with each probe of a plurality of probes, wherein each probe comprises a di-nucleotide or a tri-nucleotide, thereby sequencing the target ssDNA according to positions of the probe locations along the ssDNA target.

2. The method according to claim 1, wherein the target ssDNA is moved back and forth inside the nanopore by applying alternating voltages across the solid-state nanopore.

3. The method according to claim 1, wherein the target ssDNA is moved back and forth inside the nanopore by pulling the target ssDNA mechanically in an intermittent manner.

4. The method according to claim 1 wherein, the back and forth translocation is separated by a wait time t_w, wherein the wait time is varied to control the error rate R_w of hybridization of the probes to the target ssDNA through a calculation of mechanism of kinetic proofreading, wherein

R_w ~ R_o exp(-(k_i2 - k_c )t_w) ~ R₀ exp(-k_i2t_w) wherein, R₀ is the error rate absent a proofreading step determined by a free energy difference in hybridization of correct and incorrect probes, and is expressed as

wherein, k_i2 and k_c2 are off rates for binding of incorrect and correct probes respectively to the target ssDNA during hybridization, the off rates are determined by probe binding energies, and wherein k_c2 « k_i2.

5. The method according to claim 4, wherein R₀, the error rate absent a proofreading step is expressed as,

R₀~ exp(-5) ~ 0.007, for a free energy difference of about 3 kcal/mol ~ 5 k_BT, between the hybridization of correct and incorrect probes corresponding to one hydrogen bond, wherein k_B is the Boitzman constant and T the temperature.

6. The method according to claim 4, wherein the wait time t_w is about 50 microseconds (μβ), about 100 μβ, about 200 μβ, about 300 μ$ or about 400 μβ.

7. The method according to claim 1, wherein holding the target ssDNA under tension comprises attaching a first end of the ssDNA to a bead held by a micropipette, and attaching a second end by an applied electric field inside the solid-state nanopore.

8. The method according to claim 7, wherein the bead is about one μτη (micrometer) in diameter.

9. The method according to claim 7 wherein the target ssDNA is attached to the bead by a biotin-streptavidin linkage.

10. The method according to claim 1, wherein the solid-state nanopore is a graphene nanopore.

1 1. The method according to claim 10, wherein the graphene nanopore has a thickness less than about five nanometers.

12. The method according to claim 10, wherein the graphene nanopore has a thickness of one or a few atoms.

13. The method according to claim 1, wherein hybridization of the probe is transient.

14. An apparatus for sequencing DNA by hybridizing probes to a target single-stranded DNA (ssDNA), the apparatus comprising:

a micropipette mounted on a plate anchored to an micropositioning stage located inside a

Faraday cage;

a magnification device for obtaining visual feedback to locate and contact a bead attached to a first end of the target ssDNA by the micropipette, wherein the micropipette is in physical contact with the bead;

a nanopore assembly comprising a nanopore chip, a sealed sample holder, electrodes and a patch-clamp amplifier located inside the Faraday cage, wherein the apparatus measures time elapsed between nanopore ionic current fluctuations during translocation of the target ssDNA through the nanopore chip to determine locations of probes hybridized to the target ssDNA.

15. The apparatus according to claim 14, wherein the plate is a metal plate.

16. The apparatus according to claim 14, wherein the micropositioning stage is automated.

17. The apparatus according to claim 14, wherein the micropipette sucks the bead due to a pressure difference to make physical contact with the bead;

18. The apparatus according to claim 14, wherein the micropositioning stage is controlled by two nanopositioning devices having the capability of moving with multiple speeds with accuracy of about one nanometer.

19. The apparatus according to claim 14, wherein the micropipette is placed inside a large glass pipette and held in place with optical glue.

20. A kit for determining a sequence of a DNA by hybridization of probes two to three nucleotides in length as the DNA translocates through a solid-state nanopore, the kit comprising hybridization probes contained in labeled tubes, and instructions for correlating temporal traces of ionic current as the DNA translocates through the solid-state nanopore, with positions of probe binding sites on the DNA of the probes contained in the respective tubes.

21. The kit according to claim 20, wherein the hybridization probes are contained in labeled tubes as individual probes.

22. The kit according to claim 20, wherein hybridization probes are contained in labeled tubes as defined mixtures of probes.

23. The method according to claim 18, wherein a nanopositioning device comprises an inchworm motor having a piezoelectric actuator that undergoes a dimensional change when voltage is applied.