Catalytic nucleic acid system

Abstract

A complex for a toehold exchange system is provided. The complex comprised a substrate molecule and an output molecule. The substrate molecule and output molecule each comprise: a plurality of complementary regions where the substrate molecule and the output molecule are hybridised; and a non-complementary region where the substrate molecule and output molecule are not hybridised, the non-complementary region being located between complementary regions. The substrate molecule comprises a first exposed toehold region for hybridisation to a catalyst molecule and a second covered toehold region for hybridisation to a fuel molecule, and wherein the second covered toehold region comprises the region of non- complementarity. A toehold exchange system comprising the complex is also provided.

Description

[0001] Catalytic Nucleic Acid System

[0002] The present disclosure relates to a motif for toehold exchange, in particular for a catalytic nucleic acid system.

[0003] According to an aspect of the present disclosure, there is provided a complex for a toehold exchange system, the complex comprising a substrate molecule and an output molecule, the substrate molecule and output molecule each comprising: a plurality of complementary regions where the substrate molecule and the output molecule are hybridised; and a non-complementary region where the substrate molecule and output molecule are not hybridised, the non-complementary region being located between complementary regions; wherein the substrate molecule comprises a first exposed toehold region for hybridisation to a catalyst molecule and a second covered toehold region for hybridisation to a fuel molecule, and wherein the second covered toehold region comprises the region of non-complementarity.

[0004] The non-complementary region can permit irreversibility (or at least low reversibility) in a toehold exchange reaction where the catalyst molecule is hybridised to the substrate molecule via the first exposed toehold region for hybridisation and the output molecule is displaced from the substrate molecule to expose the second toehold region of the substrate. The irreversibility can enable high sensitivity to presence or absence of the catalyst.

[0005] The non-complementary region of the output molecule is non-complementary to the non- complementary region of the substrate molecule. The plurality of complementary regions of the output molecule are complementary to the plurality of complementary regions of the substrate molecule. The non-complementary region of the output molecule and the non- complementary region of the substrate molecule may jointly form a non-complementary region of the complex. The complementary regions of the output molecule and the complementary regions of the substrate molecule may jointly form a plurality of complementary regions of the complex.

[0006] At the complementary regions, hybridisation of the output molecule to the substrate molecule may be favoured. At the non-complementary region, hybridisation of the output molecule to the substrate molecule may not be favoured.

[0007] The second toehold region may be covered within the complex. The complex may expose the first toehold region.

[0008] The non-complementary region of the substrate molecule may comprise a part of the second toehold region. The non-complementary region of the substrate molecule may comprise the whole of the second toehold region.

[0009] For stability of the complex the second covered toehold region may comprise a complementary region. For stability of the complex the plurality of complementary regions may comprise a portion of the second covered toehold region. For selectivity a plurality of regions of the substrate may be for hybridisation to a catalyst molecule. Hybridisation of the catalyst to the substrate may cause displacement (optionally release) of the output. The output may be tethered to substrate. Displacement of the output may cause the second toehold region of the substrate to be exposed. Hybridisation of the fuel to the substrate can cause release of the catalyst. This can permit the catalyst to engage with a further instance of the complex, and hybridise to a further instance of the substrate molecule and cause displacement of a further instance of the output molecule. The substrate molecule may be configured to bind to the catalyst and cause the output to be displaced (optionally released) through competitive hybridisation.

[0010] The substrate molecule, the output molecule, the catalyst molecule and / or the fuel molecule are preferably nucleotide strands. The substrate molecule, the output molecule, the catalyst molecule and / or the fuel molecule may be formed of one or more of: DNA, RNA, modified DNA, modified RNA, DNA or RNA with modified nucleic acid backbone, modified sugar, modified linkage and / or modified base. The substrate molecule, the output molecule, the catalyst molecule and / or the fuel molecule may be formed of one or more of: 2’OMe or 2’MOE, 2’F, peptide nucleic acids, and locked nucleic acids. The output molecule, the catalyst molecule and / or the fuel molecule may comprise in full or in part a modified backbone, a modified sugar, a modified linkage and / or a modified nucleotide base.

[0011] The complementary regions may be formed of nucleotide bases that are complementary to one another.

[0012] The non-complementary region of the complex may comprise at least one nucleotide base of the substrate molecule that is not complementary to at least one nucleotide base of the output molecule. The non-complementary region of the complex may comprise at least one nucleotide base of the substrate molecule that is unmatched to a nucleotide base of the output molecule. The non-complementary region of the complex may comprise at least two or three nucleotide bases of the substrate molecule that are not complementary to at least two or three nucleotide bases of the output molecule.

[0013] The non-complementary region of the complex may be non-continuous. Portions of the non- complementary region may be located between portions of complementary regions of the complex. The non-complementary region of the complex may comprise a bulge and / or a hairpin. The non-complementary region of the complex may comprise a bulge and / or a hairpin in the substrate molecule. The non-complementary region of the complex may comprise a bulge and / or a hairpin in the output molecule. The non-complementary region of the complex may comprise a bulge and / or a hairpin in the output molecule; and a bulge and / or a hairpin in the substrate molecule.

[0014] The non-complementary region of the complex may be 1 or more nucleotide bases. The non- complementary region of the complex may be 2 or more nucleotide bases. The non- complementary region of the complex may be 3 or more nucleotide bases. The non- complementary region of the complex may be 5 or more nucleotide bases. The non- complementary region of one or both of the substrate molecule and the output molecule may be 1 or more nucleotide bases, optionally 2 or more nucleotide bases, optionally 4 or more nucleotide bases, optionally 5 or more nucleotide bases, optionally 7 or more nucleotide bases. For example where the non-complementary region comprises a bulge and / or a hairpin in the output molecule and / or in the substrate molecule, the non-complementary region may have an arbitrary number of nucleotide bases. In some examples there may be no particular upper limit to the number of nucleotide bases of the non-complementary region. The non- complementary region may be 30 or less nucleotide bases. The non-complementary region may be 25 or less nucleotide bases. The non-complementary region may be 20 or less nucleotide bases. The non-complementary region may be 15 or less nucleotide bases. The non-complementary region may be 10 or less nucleotide bases. The non-complementary region may be 5 or less nucleotide bases, or 2 or less. The non-complementary region of one or both of the substrate molecule and the output molecule may be 30 or less nucleotide bases, optionally 25 or less nucleotide bases, optionally 20 or less nucleotide bases, optionally 10 or less nucleotide bases, optionally 5 or less nucleotide bases. The non-complementary region may be 1-25 or 2- 18 or 4- 15 nucleotide bases.

[0015] The non-complementary region of the output molecule may be located at or near an end, optionally a 3’ end or a 5’ end, of the output molecule. The non-complementary region of the output molecule may be 1 or more nucleotide bases from the end of the output molecule, 2 or more nucleotide bases from the end of the output molecule, or 3 or more nucleotide bases from the end of the output molecule.

[0016] The first exposed toehold region of the substrate molecule may be at or near an end, optionally a 3’ end or a 5’ end of the substrate molecule. In the complex the second covered toehold region of the substrate molecule may be at or near an end, optionally a 5’ end or a 3’ end, of the output molecule.

[0017] The second covered toehold region of the substrate molecule may comprise 3 to 10 nucleotide bases, preferably 5, 6 or 7 nucleotide bases. The second covered toehold region may comprise 3 or more, 4 or more, 5 or more, 6 or more, 7 or more, 8 or more, 9 or more, 10 or more nucleotide bases. The second covered toehold region may comprise 20 or less, 15 or less, 12 or less, 10 or less, 9 or less, 8 or less, 7 or less, 6 or less, 5 or less nucleotide bases.

[0018] For improved signalling of the reaction, the complex may further comprise: a fluorophore at a region of the substrate molecule; and a quencher region of the output molecule that inactivates the fluorophore and displacement (optionally release) of the output molecule causes activation of the fluorophore; or a quencher molecule hybridised to the substrate molecule, wherein the quencher molecule inactivates the fluorophore, and displacement (optionally release) of the quencher molecule causes activation of the fluorophore.

[0019] For further strengthening of irreversibility and prevention of unintended crosstalk the output molecule may comprise at least two regions that are mutually complementary for hybridisation to form a hairpin loop. The output may form a hairpin loop when displaced (optionally released) from the substrate.

[0020] The complex may further comprise a second output molecule, the substrate molecule and the second output molecule each comprising: a plurality of complementary regions where the substrate molecule and the second output molecule are hybridised; and a non-complementary region where the substrate molecule and second output molecule are not hybridised, the non- complementary region being located between complementary regions. The second output molecule may have the same sequence as the output molecule or the second output molecule may include the sequence of the output molecule or the second output molecule may have at least two domains in common with the output molecule. Hybridisation of the fuel to the substrate may cause release of the second output.

[0021] The substrate molecule may comprise a tethered output region to which the second output molecule is at least partially hybridised. Hybridisation of the fuel to the substrate may further cause exposure of the tethered output. The tethered output may comprise or be the same sequence as the catalyst molecule.

[0022] The substrate molecule may comprise a tethered output region with at least two regions that are mutually complementary for hybridisation to form a hairpin loop. Hybridisation of the fuel to the substrate may cause opening of the hairpin loop to expose the tethered output.

[0023] The substrate molecule may comprise a first part of an associative output. Hybridisation of the fuel to the substrate may cause formation of an associative output. The associative output may comprise or be the same sequence as the catalyst molecule.

[0024] According to another aspect there is provided a complex for a toehold exchange system, the complex comprising a substrate molecule and an output molecule, the substrate molecule and output molecule each comprising: a plurality of complementary regions where the substrate molecule and the output molecule are hybridised; and a non-complementary region where the substrate molecule and output molecule are not hybridised, the non-complementary region being located between complementary regions; wherein the substrate molecule comprises a first exposed toehold region for hybridisation to a catalyst molecule and a second covered toehold region for hybridisation to a fuel molecule, and wherein the non-complementary region comprises at least a portion of the second toehold region. The complex may be as aforementioned. The substrate molecule may be as aforementioned. The output molecule may be as aforementioned.

[0025] According to another aspect there is provided a complex for a toehold exchange system. The complex may comprise a substrate molecule. The complex may comprise an output molecule. The substrate molecule and output molecule may each comprise a plurality of complementary regions where the substrate molecule and the output molecule are hybridised. The substrate molecule and output molecule may each comprise a non-complementary region where the substrate molecule and output molecule are not hybridised. The non-complementary region may be located between complementary regions. The substrate molecule may comprise a first exposed toehold region for hybridisation to a catalyst molecule. The substrate molecule may comprise a second covered toehold region for hybridisation to a fuel molecule. The second covered toehold region may comprise the region of non-complementarity of the substrate molecule. The complex may be as aforementioned. The substrate molecule may be as aforementioned. The output molecule may be as aforementioned.

[0026] According to another aspect there is provided a toehold exchange system comprising a complex as aforementioned. The system may comprise a fuel molecule.

[0027] The substrate molecule may comprise a first part of an associative output and the fuel may comprise a second part of the associative output. Hybridisation of the fuel to the substrate may cause formation of the associative output. The second output may be hybridised to at least a part of the first part of the associative output. Release of the second output may cause exposure of at least a part of the first part of the associative output. The associative output may comprise or be the same sequence as the catalyst molecule.

[0028] According to another aspect there is provided a toehold exchange system comprising: a first complex as aforementioned or a first system as aforementioned; and a second, different complex as aforementioned or a second, different system as aforementioned; wherein the second complex or second system is configured to receive as catalyst a molecule provided from the first complex or first system.

[0029] This can enable cascading of catalytic circuits for increased sensitivity.

[0030] The output molecule of the first complex or first system may be a catalyst for the second complex or second system. The second output molecule of the first complex or first system may be a catalyst for the second complex or second system. The tethered output region of the first complex or first system may be a catalyst for the second complex or second system. The associative output of the first complex or first system may be a catalyst for the second complex or second system.

[0031] According to another aspect there is provided a method comprising incubating the complex as aforementioned or the toehold exchange system as aforementioned with a sample to determine whether the catalyst molecule is present. According to another aspect there is provided a kit of components for formation of a complex as aforementioned or the toehold exchange system as aforementioned, the kit comprising the substrate molecule and the output molecule for formation of the complex and optionally the fuel molecule.

[0032] Any feature in one aspect of the disclosure may be applied to other aspects of the invention, in any appropriate combination. In particular, method aspects may be applied to apparatus aspects, and vice versa.

[0033] Any apparatus feature as described herein may also be provided as a method feature, and vice versa. As used herein, means plus function features may be expressed alternatively in terms of their corresponding structure, such as a suitably programmed processor and associated memory.

[0034] It should also be appreciated that particular combinations of the various features described and defined in any aspects of the disclosure can be implemented and / or supplied and / or used independently.

[0035] The disclosure extends to methods and / or apparatus substantially as herein described with reference to the accompanying drawings.

[0036] As used herein, the term “region,” preferably connotes any of a domain, a portion of a domain, or a plurality of domains.

[0037] The disclosure will now be described, by way of example, with reference to the accompanying drawings.

[0038] Figure 1a shows a typical toehold exchange hybrid.

[0039] Figure 1 b shows a reaction of a catalyst with a typical toehold exchange hybrid.

[0040] Figure 2a shows a novel toehold exchange hybrid comprising a non-complementary region.

[0041] Figure 2b shows a reaction of a catalyst with the novel toehold exchange hybrid.

[0042] Figure 3 shows a typical toehold exchange catalysis cycle.

[0043] Figure 4 shows an irreversible toehold exchange catalysis cycle using the novel toehold exchange hybrid.

[0044] Figure 5 shows the reactants and outputs of the irreversible toehold exchange catalysis cycle.

[0045] Figure 6 shows a modified toehold exchange catalysis cycle comprising a hairpin output.

[0046] Figure 7 shows an overview of the reactants and outputs of the modified catalysis cycle of Figure 6.

[0047] Figure 8 shows couple irreversible catalysis cycles which use a first output as a catalyst in a second cycle. Figure 9 shows coupled irreversible catalysis cycles with two outputs in the first cycle.

[0048] Figure 10 shows coupled irreversible catalysis cycles with a tethered output in the first cycle.

[0049] Figure 11 shows coupled irreversible catalysis cycles with an unravelled hairpin output in the first cycle.

[0050] Figure 12 shows coupled irreversible catalysis cycles with an associative output in the first cycle.

[0051] Figure 13 shows coupled irreversible catalysis cycles with twin output strands and an associative output in the first cycle.

[0052] Figure 14 shows an autocatalytic irreversible catalysis cycle.

[0053] Figure 15 shows an autocatalytic irreversible catalysis cycle with twin output strands.

[0054] Figure 16 shows a number of exemplary non-complementary regions.

[0055] Figure 17 shows an example embodiment in which fluorescence is enabled by the reaction.

[0056] Figures 18a and 18b show experimental results of catalytic activity of a cycle using the novel toehold exchange motif.

[0057] Figures 19a and 19b show catalytic activity of different toehold exchange systems at the lower limit of detection.

[0058] Figures 20a, 20b, 20c and 20d show catalytic activity of a toehold exchange systems with different oligonucleotide backbones.

[0059] Figure 21 shows a toehold exchange complex in a toehold exchange cycle.

[0060] Figure 22a shows different non-complementary regions of a covered toehold with 5 base pairs in a toehold exchange complex.

[0061] Figure 22b shows different non-complementary regions of a covered toehold with 6 base pairs in a toehold exchange complex.

[0062] Figure 22c shows different non-complementary regions of a covered toehold with 7 base pairs in a toehold exchange complex.

[0063] Figure 23a shows experimental results of catalytic activity of a system using the novel toehold exchange motifs of Figure 22a.

[0064] Figure 23b shows experimental results of catalytic activity of a system using the novel toehold exchange motifs of Figure 22b.

[0065] Figure 23c shows experimental results of catalytic activity of a system using the novel toehold exchange motifs of Figure 22c.

[0066] Figure 24 shows a toehold exchange complex in a toehold exchange cycle. Figure 1a shows a typical toehold exchange complex 100 (also referred to as a motif, a hybrid, or in the case of two entities a duplex). The complex is made of two oligonucleotide strands - short, single stranded molecules of an oligonucleotide such as DNA - which are hybridised, forming double stranded sections in the complex. In the following figures, oligonucleotide strands are shown as lines, with the 3’ ends of the strands indicated with hooks or arrows. Groups of nucleotide bases, also referred to as domains, are represented as numbers or numbers and lowercase letters. Domains are represented as numbers and lowercase letters and may also be referred to as sub-domains, e.g. 3a. Starred domain labels indicate complementary domains and sub-domains - e.g. 3c* is complementary to 3c.

[0067] The typical toehold exchange complex 100 comprises a substrate strand S, with domains 1*, 2* and 3*. The substrate is hybridised to an output strand O at domains 2* and 3*, which hybridise with domains 2 and 3 of the output. This forms a double stranded section of the complex at these domains. This leaves domain 1* as initially exposed in a single-stranded configuration. Domain 1* therefore forms a region available for hybridisation, to which other strands can hybridise (and potentially begin branch migration). Therefore, domain 1* is referred to as a toehold domain or region.

[0068] Figure 1 b shows a reaction 150 of the typical toehold exchange complex 100 with a catalyst C via toehold-mediated strand displacement. The catalyst C comprises two domains, 1 and 2, which are complementary to domains 1* and 2* of the substrate S. At stage 110, domain 1 of the catalyst C attaches to the toehold region 1* of the substrate S via hybridisation.

[0069] Subsequently, at stage 120, the catalyst C undergoes branch migration and displaces domain 2 of the output strand O. Finally, at stage 130, the output O completely detaches from the substrate S, leaving the hybridised substrate-catalyst complex 102. Note that in the S-C complex 102 the domain 3* of substrate S has been exposed, thus revealing the secondary hidden toehold of the strand. Domain 3* is initially covered and in a double-strand configuration. However, at a later stage of a reaction, it may be uncovered. Therefore, it serves as a second toehold which is initially hidden.

[0070] The reaction 150 provides a useful displacement reaction which has found many uses in the detection of various ligands, which can bind to the substrate S as a catalyst C and cause the release of the output O. Release of the output O can subsequently be detected to provide give a signal of the presence of the catalyst C, for example through attachment to a fluorescent probe or other detector. The reaction also forms the basis of a toehold exchange catalysis cycle, as will be described later.

[0071] However, each stage of the reaction 150 is reversible, meaning that it is also possible for the output to displace the catalyst. This may occur via abortive detachment, in which at stage 120 domain 2 of the output re-binds to domain 2* of the substrate, or through reattachment of the output at stage 130, where the output re-attaches to the substrate at domain 3*. In both cases, this limits the rate of the complete reaction and reduces the effectiveness of the catalyst. This may be a particular issue if there is a high concentration of output strands, or a low concentration of catalyst. For example, if the concentration of toehold exchange complexes 100 is increased in an effort to increase the rate of reaction, this may have limiting results as the resulting concentration of the output becomes large compared to the concentration of the catalyst.

[0072] Figure 2a shows a novel toehold exchange complex 200. This complex comprises a substrate strand S, with domains (and sub-domains) 1*, 2*, 3a* and 3b*. It is hybridised to output strand O, which has domains 2, 3a and 3b. Domains 2* and 3b* of the substrate are complementary with domains 2 and 3b of the output, thus forming the double stranded sections of complex 200. However, (sub-) domain 3a* is not complementary with domain 3c. The complex comprises a region of non-complementarity (or a non-complementary region) at domains 3a* and 3c. The two strands are not fully hybridised together at these domains. The non- complementary region (3a*, 3c) of the complex is located between two complementary regions (3b*-3b; and 2*-2) of the complex, such that the end of output O (here the 3’ end) is hybridised to the substrate S at both ends of the output and does not fray.

[0073] The substrate S comprises two toehold regions. The first toehold region, 1* is exposed in the complex 200 and is not hybridised to the output O. The second toehold region comprises domains 3a* and 3b*, and is covered in the complex by domains 3c and 3b of the output O respectively. The second toehold region comprises domain 3a* of substrate S that has a noncomplementarity with sub-domain 3c of output O. The non-complementary region of the complex therefore comprises a portion of the second toehold region. The second toehold of the substrate includes the non-complementary region of the substrate. The second toehold is uncovered upon reaction of the complex 200 with a catalyst C in stage 220 shown in Figure 2b. Following this stage, the second toehold region may hybridise with other molecules, such as a fuel molecule.

[0074] The non-complementary region of the complex is a portion in which the corresponding sections of the molecules do not hybridise or do not hybridise well. This non-complementarity may be due to a chemical non-complementarity, in which sections of the two molecules contain functional groups between which bonds are not favoured. For oligonucleotides, this chemical non-complementarity may be due to a nucleotide base mismatch, in which the two strands feature nucleotide bases which do not match. The oligonucleotides are preferably DNA (or DNA-based, such as modified DNA), for which complementary combinations of bases are A- T and C-G, whilst the other combinations are not complementary. In an alternative embodiment, the oligonucleotides may be RNA (or RNA-based, such as modified RNA), for which complementary combinations of bases are A-U and C-G whilst the remaining combinations bases are not complementary.

[0075] The non-complementary region of the complex may comprise a plurality of base mismatches (either arranged consecutively or with intervening matching bases). The domains 3a* and 3c may comprise a plurality of nucleotide bases (for example, 5, 6 or 7 nucleotide bases). Some of the nucleotide bases of the output strand O at domain 3c may be non-complementary with the corresponding nucleotide bases of the substrate strand S in domain 3a*, whilst other bases of domain 3c are complementary with the corresponding bases of domain 3a*. For example, 1 , 2 or 3 of the nucleotide bases of the output may be non-complementary with 1 , 2 or 3 nucleotide bases of the second toehold of the substrate respectively.

[0076] Instead of or in addition to the chemical non-complementarity (such as non-matching nucleotide bases), there may be a physical non-complementarity which occurs due to the shape of the molecules. For example, the section between two complementary regions may be longer in one molecule than in the other molecule. This may cause the presence of a bulge or loop in one of the molecules that does not allow the regions comprised in the bulge or loop to hybridise to the corresponding regions on the other molecule. In some embodiments, both a chemical non-complementarity and a physical non-complementarity will be present. Examples of non-complementarity include a mismatch, multiple mismatches, a bulge or a loop.

[0077] The complex 200 may comprise further domains, for example a further domain 4* of the substrate and domain 4 of the output. These may comprise, for example, a fluorophore and a quencher respectively. The quencher may also form a separate strand of the complex, as shown in Figure 21.

[0078] Figure 2b shows a reaction 250 of the novel toehold exchange complex 200 with a catalyst C via toehold-mediated strand displacement. The catalyst C comprises two domains, 1 and 2, which are complementary with domains 1* and 2* of the substrate S. At stage 210, domain 1 of the catalyst C attaches to the first toehold (domain 1*) of the substrate S via hybridisation. Subsequently, at stage 220, the catalyst C undergoes branch migration and displaces domain 2 of the output strand O. This releases domain 2 of the output O from the substrate S.

[0079] Since domain 3c of the output O is not complementary with domain 3a* of the substrate, it is not hybridised to the substrate in the complex 200. Thus the disassociation of domain 2 of the output leaves the output attached to the substrate only at domains 3b and 3b*. Subsequently, at stage 230, the output O completely detaches from the substrate S, leaving the hybridised substrate-catalyst complex 202.

[0080] The non-complementary section between the substrate and output in the complex 200 helps to reduce the rate of the reverse reaction of 250. The non-complementary section reduces the risk of re-hybridisation of the output to the substrate. The non-complementary section enhances disassociation of the output from the substrate. The non-complementary section reduces the favourability of abortive detachment, where a portion of the output is detached but re-hybridises to the substrate. This can be seen at stage 220, where the noncomplementarity of sub-domains 3a* and 3c, together with competition from domain 2 of the catalyst, means re-hybridisation of the output is unfavourable. As a result, the reverse reaction between stages 210 and 220, where the output O reattaches to the substrate and / or undergoes branch migration such that the other domains of the output reattach to the substrate, is made unfavourable by this non-complementarity (and the non-complementarity can help make this part of the reaction irreversible). In addition, once the output is detached at stage 230 and the second toehold region comprising domains 3a* and 3b* is exposed, a portion of the second toehold is non-complementary to the output. This reduces the favourability of an initial re-binding between domain 3 of the catalyst and domain 3* of the substrate.

[0081] In the S-C complex 202, the secondary toehold region comprising domains 3a* and 3b* has been exposed. This toehold region allows the hybridisation of further molecules to the substrate, thus acts as a second toehold, which is initially hidden in the complex 200. However, unlike the reaction 150 of the typical toehold exchange complex 100, re-hybridisation of the output to the second toehold of the substrate is unfavourable due to the presence of the non- complementarity. Therefore, the non-complementarity both assists with dissociation of the output from the substrate and reduces the chance of the output re-hybridising with the substrate. This helps to prevent the reverse reaction of 250 from taking place, and can help to make the reaction irreversible. The region of non-complementarity significantly hinders key (undesirable) reverse reactions and enables viable coupling of catalytic systems.

[0082] The catalyst may be a target ligand and the reaction can be used to identify a particular target ligand (such as a biomarker oligonucleotide or nucleic acid). Biomarker oligonucleotides and nucleic acids that can be target ligands include oligonucleotides from biological samples (including miRNAs, mRNA, tRNA, IncRNA, circRNA, DNA). Target ligands may be synthetic and / or chemically modified oligonucleotides and nucleic acids (including RNA-based therapeutics such as ASOs, siRNA, gapmers, aptamers, antagomirs, agomirs, cell and gene therapy agents, vaccines). Target ligands may be from samples during manufacturing QA / QC, pre-clinical research, product development or general R&D.

[0083] The output O may be used to signal the presence of catalyst C, for example by a fluorophore / quencher separation mechanism.

[0084] Figure 3 shows a typical toehold exchange catalysis cycle 300, using the typical toehold exchange complex 100 shown in Figures 1a and 1 b. In the initial stages of the cycle (stages 310, 320 and 330), the toehold exchange complex 100 (O-S) reacts with catalyst C to form the substrate-catalyst hybrid 102 (S-C), as in the reaction shown in Figure 1 b. Output O is released during the reaction, and may further hybridise with a detector or form an input to a further reaction. At stage 330, the S-C hybrid 102 reacts with a fuel strand F. This fuel strand comprises domains 2, 3 and 5, 2 and 3 being complementary to domains 2* and 3* of the substrate. Domain 5 is different from domain 4 of the output to ensure that the fuel F does not interfere in any reactions involving O. At stage 340 domain 3 of the fuel F binds with the second toehold of the substrate S (domain 3*), which has been exposed by the reaction of the substrate S with the catalyst C. Subsequently, in stage 350, the fuel F undergoes branch migration and causes the release of the catalyst C through competitive hybridisation. This releases catalyst C to restart the cycle by reacting with another substrate-output hybrid O-S. The substrate-fuel hybrid is also output from the reaction and may also serve a signalling function.

[0085] In the initial stages 310, 320, 330, the cycle takes catalyst C as an input and releases output O. Then, in the intermediate and final stages 340, 350, a fuel strand F is taken into the reaction and the catalyst C is released. This allows the cycle to detect the presence of catalyst C by releasing the output O, before releasing the catalyst C to allow the catalyst to react with further substrate molecules and produce an increased level of output.

[0086] However, since the toehold 3* of substrate S is fully complementary with domain 3 of the output O, the output may easily re-attach to the substrate at stages 330 and 320. As a result, each of the steps in the cycle 300 may happen in both directions, and the cycle 300 is completely reversible. This includes the initial binding of the catalyst and the substrate, where the output may re-bind to the substrate. If increasing the rate of reaction is desired, then one way to do this would be to increase the number of toehold binding complexes, i.e. the number of substrate and output strands. However, whilst the increased number of substrates would allow an increased binding probability with the catalyst, there would also be an increase in the number of output strands. This may mean that at high concentrations of output strands, the conditions would not be favourable for the catalyst to hybridise with the initial duplex, and there may be a high rate of the reverse reaction.

[0087] Figure 4 shows how the novel toehold exchange complex 200 introduces an irreversible step in the toehold exchange cycle of Figure 3.

[0088] The toehold exchange catalysis cycle 400 inputs the substrate-output hybrid O-S and the fuel F and releases the output O and the substrate-fuel hybrid S-F. The catalyst C enables the reaction, but is not consumed during the cycle and is released to react with further substrateoutput hybrids.

[0089] The catalyst may be a target ligand and the cycle can be used to identify presence or absence of a particular target ligand (such as a biomarker oligonucleotide). The cycle can be used to produce and amplify a signal in response to the presence of the target ligand. With suitable calibration the cycle can be used to quantify how much of the target ligand is present. Biomarker oligonucleotides that can be target ligands include oligonucleotides from biological samples (including but not limited to miRNAs, mRNA, tRNA, IncRNA, circRNA, DNA). Biological samples can include but are not limited to human or non-human blood, tears, mucous, saliva, sputum, breath condensate, bronchoalveolar lavage fluid, sweat, cerebrospinal fluid, amniotic fluid, urine, faeces, sperm, breast milk, tissue swabs e.g. buccal swabs, nasopharyngeal swabs and skin swabs, tissue samples e.g. from skin, muscle, and organ tissue, cell cultures, cultures of microorganisms, soil samples, organisms including eukaryotes, prokaryotes and multicellular organisms such as plants and insects. Target ligands may also be synthetic oligonucleotides and / or chemically modified oligonucleotides (including oligonucleotides for RNA-based therapeutics such as ASOs, siRNA, gapmers, aptamers, antagomirs, agomirs, cell and gene therapy agents, vaccines). Target ligands may be from samples during manufacturing QA / QC, pre-clinical research, product development or general R&D. The output O and the substrate-fuel hybrids S-F may be used to signal the presence of catalyst C, for example by a fluorophore / quencher separation mechanism.

[0090] During a first stage 410 of the toehold exchange catalysis cycle, domain 1 of the catalyst C hybridises to the exposed toehold 1* of the substrate S. Then, in stage 420, the catalyst undergoes branch migration and hybridises with domain 2* of the substrate, displacing domain 2 of the output through competitive hybridisation. Following this reaction, in the next stage 430 the output completely detaches from the substrate, leaving the substrate and catalyst hybridised in intermediate duplex 202. This exposes the initially hidden second toehold comprising domains 3a* and 3b* of the substrate. The output may be involved further reactions, for example it may react with a fluorescent probe to trigger a signal showing the presence of the catalyst.

[0091] Once the catalyst undergoes branch migration and displaces the output, the probability of the output O re-hybridising with the substrate S in a reverse reaction is reduce due to the noncomplementarity between domains 3c and 3a*. This means that the output O is less likely to re-hybridise with the substrate at stage 430, and less likely to undergo branch migration and displace the catalyst C at stage 420. Therefore, there is a reduced affinity between the molecules and a decreased probability of re-binding. The mismatch therefore increases the thermodynamic drive of the cycle, increasing the rate of the initial reaction.

[0092] Following the initial reaction, which has a highly reduced rate of reverse reaction due to the non-complementary, in the next stage 440 a fuel strand F, which comprises domains 2, 3a and 3b, and is thus fully complementary with the substrate, is able to attach to the substrate via toehold 3a* and 3b*. The affinity of the fuel to the substrate is higher than the affinity of the output to the substrate due to complete complementarity of domains 3a and 3b of the fuel to the toehold region of S, compared to the incomplete complementarity of domains 3b and 3c of the output. This further enhances the forward drive of the reaction. In the next stage 450 the fuel strand F undergoes branch migration, subsequently releasing the catalyst and allowing it to participate in further toehold exchange cycles.

[0093] The cycle is a series of non-covalent reactions between molecular domains, with some the reactions more reversible and others less reversible. The initial stages 410, 420, 430 are poorly reversible. The intermediate and final stages 440, 450 are more reversible. By virtue of the poorly reversible steps in the cycle the presence of catalyst C can be detected (e.g. by release of the output O) more sensitively. As the catalyst C is released at the end of a cycle the catalyst can react with further substrate molecules and produce an increased level of output.

[0094] As previously mentioned, the complex 200 may be used as a probe and the catalyst C may be a target, such as a ligand. The full cycle 400 therefore takes as an input the catalyst C and produces an output signal, either by operation of the output strand (which may undergo further reactions), or by activation of a fluorophore, as shown in Figures 17 and 21 . The full cycle also releases the catalyst C, allowing it to participate in further reactions 400 and further increase the output signal. Fewer reverse reactions occurring that reduce the rate of the forward reaction help increase the rate of the forward reaction. The irreversibility (or low reversibility) of the initial reaction between the complex 200 and the catalyst C resulting from the noncomplementarity helps to reduce the prevent the occurrence of the reverse cycle of 400 (or reverse reactions of steps within the cycle), further increasing the rate of the cycle 400 and the production of the output signal. This increases the sensitivity of the probe as the cycle proceeds at a greater rate and a larger signal is produced in response to the same amount of catalyst. This is shown, for example, in Figures 18a-b, 19a-b and 23a-c.

[0095] The S-F duplex formed in this reaction of the hybridised substrate and fuel strand may also be used as a signalling element, for instance with a fluorescent probe that can produce a signal indicating the formation of the S-F duplex due to the presence of the catalyst.

[0096] The length and sequence of the toeholds and branch regions can be selected to give an enthalpic gain to help drive forward the reaction, in particular in the stages 440 and 450. Chaining displacement of multiple substrate strands may also be used to create favourable entropically driven reactions by release of multiple species. There can be multiple secondary / hidden toeholds.

[0097] The region of non-complementarity can give significant enhancement to the rate of catalysis. By virtue of the toehold exchange catalysis cycle quantification of modified oligonucleotides can be enabled at the very low concentration levels, e.g. pM quantities or fM quantities or below. This can be of interest for example for commercial applications in drug discovery / development and in manufacturing and quality assurance. Figure 5 shows the initial and final states of the catalytic circuit in Figure 4. The reaction converts the substrate-output hybrid S-0 into the substrate-fuel hybrid S-F, in the process releasing output O and taking in fuel F. The catalyst C is involved in the reaction but is ultimately released, so is not consumed by the reaction.

[0098] The catalytic circuit is enthalpically favourable due to the hybridisation of domains 3a-3a* in the fuel-substrate product, which has a higher affinity than the non-complementary pairing 3a*-3c in the substrate-output duplex. The circuit is also kinetically favourable due to the branch migration step 420, which significantly reduces the rate of reverse reaction. The catalytic circuit is entropically neutral.

[0099] A modified catalytic circuit 600 where the output O forms a hairpin loop is shown in Figure 6. This circuit differs from the circuit 400 through the presence of an additional domain (3c*) in the output O that is complementary to another domain of the output (domain 3c). The output is therefore capable of forming a hairpin loop 608, in which domains 3c and 3c* hybridise. Another domain (2) is located between these two domains to form part of the length of the hairpin.

[0100] To hybridise with the output, the substrate also has an additional domain (3c) that is complementary to the additional domain (3c*) of the output. The catalyst C and fuel F correspondingly each have an additional domain 3c* so that they are capable of fully hybridising to the substrate at later stages of the cycle.

[0101] The substrate-output duplex 602 undergoes an irreversible toehold exchange cycle, as described previously. At stage 610, the catalyst binds to the first toehold of the substrate. At stage 620, the catalyst displaces multiple domains (including the non-complementary region 3c) of the output through branch migration. It is at this stage that the hairpin 608 is formed - domains 3c* and 3c of the output are released and so are capable of hybridising with one another to form the hairpin 608. This further increases the unfavorability of the reverse reaction at this stage, since to re-hybridise with the substrate, the hairpin loop of the output would have to disassociate first. Together with the previously described non-complementarity which also works to prevent re-hybridisation, this further increases the forward drive of the reaction.

[0102] This hairpin loop detaches from the substrate at stage 630, exposing the secondary toehold 3a* and 3b* (wherein the non-complementarity 3c reduces the risk of the output re-hybridising with this toehold, as before). At stage 640, the fuel strand F is able to hybridise to the substrate via the exposed secondary toehold. At stage 650, the fuel strand undergoes branch migration to displace the catalyst, and at stage 660 the catalyst is released, forming substrate-fuel hybrid 606.

[0103] In addition to the thermodynamic and kinetic favourability provided by the mismatched domains 3a*-3c of the substrate and output respectively, cycle 600 further increases the favourability of the forward reaction through formation of the hairpin 608 at stage 620. The complementarity between domains 3c* and 3c of the output increases the favourability of domains 3c* and 2 detaching from the substrate, and reduces the favourability of the same domains re-hybridising to the substrate, since they are already hybridised in the hairpin loop.

[0104] This is further shown in Figure 7, which shows the initial and final states of the modified toehold exchange reaction. The enthalpic favourability of the reaction is increased not just by the formation of complementary domain 3a in the substrate-fuel hybrid to replace the non- complementary pair 3a*-3c in the substrate-output hybrid, but also by the formation of the hairpin 608, which forms additional domain 3c. Thus two additional domains are hybridised in reaction 600, compared to one additional domain hybridised in reaction 400.

[0105] Figure 8 shows the coupling 800 of two catalytic circuits in which the output 01 of the first circuit 802 catalyses the second circuit 804. The first circuit 802 is similar to the catalytic cycle 400 described with reference to Figure 4, except the first output 01 comprises an additional domain 4 at the 3’ end of the strand, which is not hybridised in the substrate-output S1-O1 complex 806. First substrate S1 comprises the same domains as substrate S of S-0 hybrid 200, including the domain 3a* for non-complementary pairing 3a*-3c located between two complementary domains 2* and 3b*. In a first stage 808 the output 01 is displaced from substrate S1 by catalyst C by competitive hybridisation to form S1-C hybrid. In the next stage 810 the catalyst is displaced from the substrate by a first fuel F1 , forming S1-F1 hybrid and releasing the catalyst.

[0106] The output 01 is used in a second reaction 804 together with a S2-O2 hybrid 812. The S2-O2 hybrid 812 performs a similar function as the substrate-output S1-O1 complex 806 of the first circuit, but takes as catalyst the output 01. The second substrate S2 comprises an initially exposed first toehold comprising domains 3c* and 3b*, a second hidden toehold comprising domains 5a* and 5b*, and a domain 4* located between the two toeholds. The second output 02 comprises domains 4 and 5b complementary to domains 4* and 5b* of S2, and a domain 5c which is non-complementary to domain 5a* and forms a concealed non-complementary section of the S2-O2 duplex.

[0107] The output 02 hybridises with the toehold region comprising domains 3c* and 3b* of S2 through its domains 3b and 3c. Domains 3b and 3c of the output 01 thus not only contribute to the non-reversibility of the disassociation of S1-O1 (through the non-complementary region in domain 3c), but also are used to attach to the toehold of S2. Domain 4 of 01 is used to facilitate branch migration and displace 02, which is released from S2. This forms S2-01 complex 814, where the displacement is made more favourable by the non-complementary region (5a*-5c) between S2 and 02. Output 02 may subsequently be used as a signalling molecule or otherwise. The non-complementarity between S1 and 01 thus serves multiple functions: in addition to providing irreversible disassociation between S1 and 01 , domains 3b and 3c of 01 attach to the toehold 3b*-3c* of S2. The domain 3c also ensures noncomplementarity between F1 and S2 as the toehold region 3b*-3c* of S2 is not fully complementary to domains 3a and 3b of the fuel F 1 , thus reducing the risk that the first circuit 802 interferes with the second circuit 804.

[0108] The second toehold 5a*, 5b* of S2 is exposed by the dissociation of 02. The second fuel F2 (comprising domains 5a, 5b and 4) is then able to bind to the second toehold of S2 and displace 01 through branch migration. Domains 5a and 5b of the second fuel F2 are complementary to the second toehold of S2, whereas domain 5c of the second output 02 is not complementary to domain 5a* of the substrate S2. This reduces the probability of 02 reassociating with the substrate S2 and helps to drive the second reaction 804 forward. This releases the final products of the second reaction circuit, the S2-F2 hybrid 816 and first output 01 . The first output 01 therefore acts as a second catalyst, enabling the second reaction 804 under consumption of the second fuel and being recycled at the end of the reaction.

[0109] The coupled circuits 802 and 804 show how catalytic circuits can be coupled. A single occurrence of a catalyst input can generate a large number of 01 outputs to be released, provided a large reservoir of S1-01 hybrids and F1 fuel is available. Each 01 output can generate a large number of 02 outputs provided a large reservoir of S2-O2 hybrids and F2 fuel is available. This allows the production of many output strands 01 from a single catalyst input. Since the first output 01 is capable of catalysing multiple cycles of the second reaction circuit 804, multiple outputs 02 (and hybrids S2-F2) can be produced from a single output 01 .

[0110] Due to the inclusion of the region of non-complementarity the two circuits can be designed to reduce crosstalk and undesired interference. In the illustrated example, the domain 3b, 3c of the output 01 is distinct from the domain 3b, 3a of the fuel F1 . The second circuit can take the output 01 as catalyst without being inadvertently activated by the fuel F1 . The region of noncomplementarity can therefore permit effective coupling of circuits for more powerful catalytic response to occurrence of an initial catalyst or target.

[0111] It will be appreciated that further catalytic circuits can be coupled (third, fourth, fifth, n-th circuit). For instance in the example illustrated in Figure 8 a third catalytic circuit of the same type can take as catalyst the output 02 of the second circuit. The output of each circuit is only limited by the number of instances of initial source-output complex and fuel. For high sensitivity a greater number of circuits can be coupled, such that a very small number of initial catalyst molecules can produce a very large number of outputs at the n-th circuit. For a fast signal a smaller number of circuits may be more convenient to permit rapid matching of the entities in a circuit and rapid formation of outputs.

[0112] A number of variants of the catalytic circuits described with reference to Figure 8 are described with reference to Figures 9-15. The catalytic circuits including those described below can be readily coupled with one another, including by coupling two or more like circuits and / or by coupling different variants together.

[0113] The embodiment shown in Figure 9 provides a coupled reaction 900 between two catalytic circuits 902 and 904 with dual output strands from the first circuit. First circuit 902 comprises substrate S1 with two outputs 01 and 02, each of outputs 01 , 02 couples to the substrate S1 to form S1-01 ,02 hybrid 906. The substrate S1 has two sets of domains 3a*-3b* and each of the outputs 01 , 02 has corresponding domains 3c and 3b, thus providing incomplete complementarity of each output 01 , 02 with the substrate S1 . The substrate S1 comprises a toehold 1* to allow catalyst C to bind and subsequently undergo branch migration, releasing first output 01 and producing S1-02 hybrid 908. This exposes second hidden toehold 3a* and 3b*, allowing first fuel F1 to hybridise, whilst non-complementarity between this toehold and 01 reduces the favourability of the reverse reaction. First fuel F1 comprises domains 3a and 3b complementary to the toehold at its centre, between domains 2 and 5 that are complementary to adjacent domains of the substrate S1. In this way, the first fuel F1 enables the disassociation of both catalyst C and second output 02, where the re-association of 02 is made unfavourable by the non-complementarity with the substrate S2 at domain 3c. This produces S1-F1 hybrid 910.

[0114] The first output 01 and second output 02 are then used in a second reaction circuit 904 (the inputs of which are shown). The second reaction 904 is similar to the second circuit 804 described with reference to Figure 8, with the difference that each of output 01 and 02 can initiate the second reaction 904. Both output 01 and 02 comprise the same domains 3c, 3b and 4 at their 3’ end, and differ only by a single domain at their 5’ end, 2 for 01 and 5 for 02. The domains 3b and 3c allow either output to hybridise with a second substrate S2 in the second reaction circuit 904, where the substrate S2 has toehold 3c*-3b*. The second substrate S2 is hybridised with a third output 03 via complementary domains 4-4* and 6b-6b*, between which is located a non-complementary section comprising non-complementary regions 6a* on S2 and 6c on 03. Domain 4 of 01 and 02 facilitates branch migration along S2, whilst the non-complementarity between S2 and 03 reduces the favourability of abortive disassociation of 03 from S2 or reassociation of 03 with S2. This disassociation exposes a second toehold 6a*-6b* of S2.

[0115] Subsequently, a second fuel F2, complementary to the second toehold of S2, is able to hybridise to S2 and displace 01 or 02 through branch migration. The second fuel F2 is fully complementary to the second toehold of S2, unlike third output 03, which has a region of non- complementarity to S2. This helps to drive the second reaction 904 forward and can help make the second reaction irreversible. This recycles the output 01 or 02, which is thus a catalyst for reaction 904. The second reaction circuit 904 produces S2-F2 hybrid 912 and output 03 as its products. The non-complementary region (3c) present in the first and second outputs 01 , 02 thus serves multiple functions: it reduces the favourability of the reverse reaction where 01 and 02 re-hybridise to S1 ; it provides complementarity between outputs 01 and 02 and the first toehold of the second substrate S2; and it reduces the risk of first fuel F1 reaction with the first toehold of S2.

[0116] The coupled reaction 900 provides a further increase in production of outputs. Similar to coupled reaction 800, the output of the first reaction 902 is capable of catalysing second reaction 904. Thus one occurrence of catalyst C in the first cycle 902 can produce two outputs 01 , 02 per circuit; and each output 01 , 02 is capable of enabling multiple cycles of the second circuit 904. The coupled reaction 900 is even more sensitive as the first cycle 902 produces two outputs 01 and 02, which are each capable of catalysing reaction in the second cycle 904, further increasing production of 03 from a single catalyst C. The coupled reaction 900 allows a large signal to be produced from a small amount of catalyst C, provided a large reservoir of S1-01 , 02 hybrids, S2-O3 hybrids, fuel F1 and fuel F2 is available.

[0117] Figure 10 shows a reaction 1000 of two coupled catalytic cycles 1002 and 1004. The first cycle comprises a first substrate S1 hybridised to two outputs 01 and 02 in a S1-01 ,02 hybrid 1006. Both outputs 01 , 02 have a region of non-complementary with the substrate (3c and 5c respectively) located between two regions that are complementary to the substrate. The substrate S1 comprises a first exposed toehold 1* and two initially hidden toeholds, second toehold 3a*-3b* and third toehold 5a*-5b* (which comprise the regions non-complementary with the respective outputs). The substrate also comprises an additional domain 6*.

[0118] The SI-01 ,02 hybrid reacts with a catalyst C via toehold-mediated strand exchange to displace 01 and produce S1-O2,C hybrid 1008. Subsequently, this S1-O2,C hybrid reacts with a first fuel F1 (which comprises a region complementary to the second toehold 3a*-3b* of S2), which displaces C and 02 through branch migration, producing S1-F1 hybrid 1010. Therefore, during this cycle, outputs 01 and 02 are irreversibly released, and catalyst C is recycled and able to catalyse another cycle.

[0119] S1-F1 hybrid 1010 comprises a tethered output region T, comprising third toehold 5a* and 5b* and domain 6*. This tethered output region is able to act as a catalyst to a second circuit 1004. Second circuit 1004 comprises a second substrate-third output hybrid 1012 (S2-O3) with a first toehold 5a-5b and a region of non-complementarity 7a-7c*. The tethered output T is able to hybridise with the first toehold 5a-5b, then undergo branch migration (via domain 6*) to displace output 03. A second fuel F2 then binds to a second initially hidden toehold (7b, 7a) of S2 and releases T (and the S1-F1 hybrid) to catalyse further reactions. The region of noncomplementarity present between S2 and 03 helps with the dissociation of S2-O3 complex 1012 and provides a forward thermodynamic drive to second reaction 1004. The coupled reaction 1000 is similar to the coupled reaction 900, except instead of the first and second outputs 01 and 02 being used to catalyse a further reaction, tethered output T of the S1-F1 complex is used instead. This can free up 01 and 02 to provide other functions, including as catalysts in a separate third reaction circuit similar to the second circuit 904 described with reference to Figure 9. This also allows the productive further use of the S1-F1 hybrid, which may otherwise not have any further function. As in reactions 800 and 900, the non-complementary regions 3c-3a* and 5c-5a* present in S1-O1 ,02 hybrid 1006 take multiple functions, facilitating hybridisation of the catalyst and first fuel to the first substrate, facilitating hybridisation of the tethered output region of the first substrate to the first toehold of the second substrate, preventing the risk of any products of first reaction 1002 from interfering with second reaction 1004, and preventing re-hybridisation of 02. In this reaction, the two hidden toeholds (3a*-3b* and 5a*-5b*) of S1 comprise different domains, so fuel F1 is not capable of binding to the first toehold 5a-5b of second substrate S2 as the domains are entirely non- complementary (rather than one domain being complementary and a second being non- complementary).

[0120] Figure 11 shows a reaction 1100 comprising a pair of coupled catalytic reactions 1002 and 1004 through an unravelled output U. Initial S1-O1 hybrid 1106 is another example of an irreversible toehold exchange complex with features corresponding to the complex 200 described with reference to Figure 2. The first substrate S1 further comprises additional domains 4*, 5a, 5b, and 4* at its 5’ end. Domains 4 and 4* are complementary, so are initially hybridised, forming a hairpin loop H at the 5’ end of S1. S1-O1 hybrid 1106 undergoes an irreversible toehold exchange cycle 400, releasing output 01 through interaction with catalyst C and exposing previously hidden second toehold 3b*, 3a*. Hybridisation of the first fuel F1 onto S1 (via hidden toehold 3a*-3b*) and branch migration of domain 4 of F1 onto domain 4* of S1 causes the unfolding of hairpin H domains 5a, 5b and 6 of S1 , exposing the unravelled output U.

[0121] The unravelled output U is subsequently able to act as a catalyst in a second irreversible toehold exchange reaction 1104, similar to the second circuit 1004 described with reference to Figure 10, with the difference that unravelled output U is formed from a hairpin loop rather than from release of an output 02. The unravelled output U binds to toehold 5a*-5b* of second substrate - second output S2-O2 hybrid 1112 of second catalytic circuit 1104. The S2-O2 hybrid 1112 is similar to the substrate-output hybrid O-S described with reference to Figure 4. The unravelled output U then triggers a further catalytic exchange cycle (as described for cycle 400), involving hybridisation of a second fuel F2 and release of output 02. The region of noncomplementarity between S2 and 02 assists with the dissociation of 02 from S2 and the association of F2 onto the second toehold of S2. This provides a forward thermodynamic drive to the reaction 1104 and reduces the favourability of a reverse reaction. Coupled reactions 1100 provide an alternative embodiment allowing the release of additional outputs through a product of an initial reaction catalysing a second reaction cycle. The non- complementary regions 3c-3a* in hybrid 1106 enable irreversible disassociation of 01 and S1 , whilst interaction with the second reaction cycle happens through a separate pair of domains 5a and 5b, reducing the risk of a product of first reaction 1102 interfering in second reaction 1104.

[0122] Figure 12 shows a reaction 1200 in which an associative output A of a first reaction 1202 catalyses a second reaction 1204. The initial reaction 1202 is an irreversible toehold exchange reaction, modified from reaction 400 by the presence of an additional domain 4 on one end of the first substrate S1 and an additional domain 5 at one end of the first fuel F1. In the S1-F1 hybrid 1210 produced in the reaction, associative output A is formed of domain 4 of S1 and domain 5 of F1.

[0123] The associative output A is capable of catalysing a further irreversible toehold exchange cycle 1204. Domain 4 of associative output A can hybridise with a first toehold 4* of irreversible toehold exchange complex 1212 of second catalytic circuit 1104. The second substrate - second output S2-O2 hybrid 1112 is similar to the substrate-output hybrid O-S described with reference to Figure 4. The associative output A triggers the second toehold exchange reaction 1204, in which second output 02 is released, second fuel F2 is hybridised and associative output A (and S1-F1 hybrid) is released.

[0124] The non-complementary region 3c-3a* in the first substrate S1 facilitates irreversible toehold exchange and allows formation of the associative output A, as well as enabling the reaction of first substrate S1 with the first fuel F1 . Non-interaction of the first fuel with the second toehold exchange complex 1212 is enabled by a different toehold 4* on S2, which is not complementary to F1 . The region of non-complementarity between S2 and 02 assists with the dissociation of 02 from S2 and the association of F2 onto the second toehold of S2. This provides a forward thermodynamic drive to the reaction 1204 and reduces the favourability of a reverse reaction.

[0125] Figure 13 shows a reaction 1300 in which an associative output A of first reaction 1302 catalyses a second reaction 1304, similar to reaction 1200. The embodiment is modified from the previous embodiment 1200 by the presence of an additional output 02 on the initial toehold exchange complex 1306, which comprises a region of non-complementarity 6c-6a*. Irreversible toehold exchange cycle 1302 releases outputs 01 and 02 through interaction with C and F1 , as described previously (wherein the reverse reaction is made unfavourable through the presence of non-complementarity of regions 3c-3a* and 6c-6a* respectively). An associative output A is formed from domains 6a*, 6b* and 7* of S1 and domain 8* of F1 , which are exposed in a single-stranded state. The associative output A catalyses a second reaction 1304. Domain 7* hybridises to a first toehold 7 of second substrate - second output S2-O2 hybrid (another irreversible toehold exchange complex) and hybridises to subsequent domains via branch migration. This releases the third output 03. Fuel strand F2 binds to a second previously hidden toehold of S2, causing the release of associative output A. The region of non-complementarity between S2 and 03 assists with the dissociation of 03 from S2 and the association of F2 onto the second toehold of S2. This provides a forward thermodynamic drive to the reaction 1304 and reduces the favourability of a reverse reaction.

[0126] Figure 14 shows an autocatalytic toehold exchange circuit 1400 with additional features compared to the toehold exchange circuit described with reference to Figure 4. The autocatalytic toehold exchange circuit is modified through the presence of additional domain 1 on an end of the substrate S and an additional domain 2 at the end of fuel F. In the final stage of the irreversible toehold exchange cycle, these two domains form autocatalytic output C2 as part of S-F complex. This autocatalytic output C2 is complementary to the toehold 1* and domain 2* of a substrate of a further S-0 hybrid. Therefore, the autocatalytic output C2 is capable of hybridising with a toehold of a further S-0 hybrid and undergoing branch migration, thereby triggering a further cycle 1400. Therefore, the autocatalytic output C2 is capable of catalysing further cycles 1400. This can increase the rate of the reaction from the input of C1 as each circuit produces further catalytic outputs capable of catalysing the same circuit.

[0127] Figure 15 shows an autocatalytic toehold exchange circuit with two catalyst outputs C1 , C2. The first toehold exchange complex is formed of a substrate - first output - second output hybrid S-O1 ,O2. The first output 01 and the second output 02 each comprises a region of non-complementarity to the substrate S (2a-2d* and 3a-3c*), allowing the release of both outputs to be irreversible. As described with reference to Figure 14, the substrate S and the fuel F include domains that form an autocatalytic output C2 as part of the S-F complex. The autocatalytic output C2 is capable of hybridising with a toehold of a further S-O1 ,O2 hybrid and undergoing branch migration, thereby triggering a further cycle.

[0128] Figure 16 shows a number of possible embodiments of the non-complementary region of the novel toehold exchange complex 200, as used in the reactions described above. The complex can vary with regards to the number, placement, spacing and length of non-complementary regions. The complex may comprise a non-complementary region with a plurality of portions of non-complementarity, each separated by a portion of complementarity. For example, as shown in Figure 16, domain 3 of complex 200 (corresponding to the second, hidden toehold of the substrate) may comprise one continuous non-complementary region (1601 and 1602), or a non-continuous non-complementary region e.g. with two non-complementary portions (1603 and 1604), three non-complementary portions (1605 and 1606), or more non- complementary portions. If the non-complementary region is non-continuous the plurality of portions of non-complementarity are separated by portions of complementary regions. The end of the complex (corresponding to the 5’ end of the output O and 3’ end of the substrate S) advantageously comprises a portion of a complementary region, which can prevent the ends of the strands from fraying. The sub-domain adjacent to domain 2 may also be a complementary portion (as shown in 1602, 1604, 1606) or may be a non-complementary portion (1601 , 1603, 1606).

[0129] The subdivision of the non-complementary region can include irregular or regular portions of non-complementarity. Each complementary portion or region may be of a similar length or a different length. The non-complementary portions or region may be of a different length to the complementary portions or region, or they may be of the same length.

[0130] Each non-complementary portion or region may comprise a single mismatched nucleotide base, or a plurality of mismatched nucleotide bases, such as 2, 3 or 4, or more mismatched nucleotide bases.

[0131] The non-complementary region may be formed of a greater number of nucleotides in one strand than in its counterpart, as illustrated in examples 1610,1620 and 1630.

[0132] In the examples 1610 and 1612 the non-complementary region comprises a hairpin motif 1610, 1612. Here, one of the strands comprises two complementary sub-domains 3c, 3c* which hybridise to form a hairpin loop whilst the strands are hybridised in the complex. The hairpin may be on the output as illustrated in example 1610, but may also be on the substrate as illustrated in example 1612.

[0133] In examples 1620 and 1630, the non-complementary region comprises a bulge, wherein one of the strands (either the output or the substrate) comprises an additional sub-domain not present in the counterpart strand. Example 1620 shows the presence of a bulge in the form of an additional sub-domain 3c on the output strand. Example 1630 shows the presence of a bulge in the form of an additional sub-domain 3c* on the substrate strand. The sub-domain 3c* may form part of the secondary hidden toehold of the substrate after dissociation of the output from the substrate.

[0134] A combination of any number of mismatches, hairpins and bulges may be provided in the output, in the substrate or in both the output and the substrate.

[0135] The total length of the non-complementary region, whether or not continuous, whether at the substrate or the output or both, may be 1 nucleotide base or more, 2 nucleotide bases or more, 3 nucleotide bases or more, 4 nucleotide bases or more, 5 nucleotide bases or more, 6 nucleotide bases or more, 7 nucleotide bases or more, 8 nucleotide bases or more, 9 nucleotide bases or more, or 10 nucleotide bases or more. In particular in examples where the non-complementary region comprises a bulge and / or a hairpin in the output molecule and / or in the substrate molecule, the non-complementary region may have a large number of nucleotide bases, including significantly higher than e.g. 10 nucleotide bases. There is generally no particular upper limit to the number of nucleotide bases of the non- complementary region. In addition, the total length of the non-complementary region, whether or not continuous, whether at the substrate or the output or both, may be 40 nucleotide bases or less, 30 nucleotide bases or less, 25 nucleotide bases or less, 20 nucleotide bases or less, 15 nucleotide bases or less, 10 nucleotide bases or less, 8 nucleotide bases or less, 6 nucleotide bases or less, 5 nucleotide bases or less, 4 nucleotide bases or less or 3 nucleotide bases or less. In some examples, the total length of the non-complementary region, whether or not continuous, whether at the substrate or the output or both, is 1-30 nucleotide bases or 1-25 nucleotide bases or 1-20 nucleotide bases or 1-15 nucleotide bases or 1-10 nucleotide bases or 1-8 nucleotide bases or 1-5 nucleotide bases or 2-30 nucleotide bases or 2-25 nucleotide bases or 2-20 nucleotide bases or 2-15 nucleotide bases or 2-10 nucleotide bases or 2-8 nucleotide bases or 2-5 nucleotide bases or 4-30 nucleotide bases or 4-25 nucleotide bases or 4-20 nucleotide bases or 4-15 nucleotide bases or 4-10 nucleotide bases or 4-8 nucleotide bases or 4-6 nucleotide bases or 5-30 nucleotide bases or 5-25 nucleotide bases or 5-20 nucleotide bases or 5-15 nucleotide bases or 5-10 nucleotide bases or 5-8 nucleotide bases or 8-30 nucleotide bases or 8=25 nucleotide bases or 8-20 nucleotide bases or 8-15 nucleotide bases or 8-12 nucleotide bases or 8-10 nucleotide bases or 10-30 nucleotide bases or 10-25 nucleotide bases or 10-20 nucleotide bases or 10-15 nucleotide bases. The length of the non-complementary region can vary for different reaction designs and can be adjusted to suit a particular requirement e.g. for reaction speed, reaction specificity, reaction environment, or any other factors that may be dictated by a desired outcome.

[0136] It will be understood that the domain lengths may be selected to suit a desired target, a desired reaction dynamic and other factors. Typical domain lengths are between 4 and 20 base pairs, but shorter or longer domains can occur. The non-complementary region in the novel toehold exchange complex 200 is typically shorter than an entire domain.

[0137] Figure 17 shows an example embodiment in which fluorescence is generated by the reaction. The substrate S of the novel toehold exchange complex 200 comprises a fluorophore (indicated with a lightning bolt symbol), and the output O comprises a quencher (indicated with a prohibition symbol). The quencher is arranged to be in the proximity of the fluorophore in the substrate-output complex. The fluorophore may be any suitable fluorophore, including FAM, HEX, TET, JOE, ROX, TAMRA, Cy3, or Cy5 fluorophores. The quencher may be any suitable for preventing activity of the fluorophore, including BHQ1 , BHQ2, BHQ3. In the complex 200, the proximity of the quencher to the fluorophore prevents activity of the fluorophore. However, if the output is released from the substrate, for example to form the substrate-fuel complex 404 as part of any of the reactions previously described, the quencher is no longer present in the complex to prevent activity of the fluorophore and the fluorophore produces a fluorescent signal. This can be used to provide a signal of the activity of the reaction. Alternatively, the fluorophore may be located on the output strand and the quencher on the substrate; this provides a similar signalling effect, except the fluorescent signal is produced by the dissociated output rather than the substrate-fuel complex 404.

[0138] In another example FRET (fluorescence resonance energy transfer) is employed for signalling occurrence of the reaction; proximity of an acceptor and donor fluorophore (e.g. at the substrate molecule and the fuel molecule) can cause output of a fluorescent signal. A variety of approaches (e.g. electrochemical, colorimetric, gel-electrophoresis, and atomic force microscopy) are widely used in detection of toehold meditated strand displacements, and can be used in the presently described system.

[0139] Figures 18a and 18b shows experimental data obtained from the novel toehold exchange complex as illustrated in Figure 4. A toehold exchange cycle comprising irreversible toehold exchange is facilitated by non-complementary region in the secondary toehold. A fluorescent tag is attached to output O, with the fluorescence quenched when output O is hybridised to substrate S. Release of output O from substrate S causes fluorescence. In the experiment an abundance of S-0 hybrid and fuel F is provided and between 0-100 pM of catalyst C is added.

[0140] Figure 18a shows normalised fluorescence activity of the toehold exchange reaction over 4 hours. Activity is shown for concentrations of 10pM, 20pM, 30pM, 40pM, 50pM, and 100pM of catalyst, as well as without a catalyst (OpM). Figure 18b shows a plot of the concentration of catalyst against normalised fluorescence after 4 hours. A linear relation can be seen between normalised fluorescence activity and catalyst concentration. With calibration an unknown sample can be analysed and the strength of the fluorescent signal can permit determination of not only presence or absence of a target catalyst in the sample, but quantitation of the catalyst.

[0141] Figures 19a and 19b show catalytic activity of the novel toehold exchange complex as illustrated in Figure 4 and classic toehold exchange complex as illustrated in Figure 3. A fluorescent tag is attached to output O, with the fluorescence quenched when output O is hybridised to substrate S. Release of output O from substrate S causes fluorescence. In the experiment an abundance of S-0 hybrid and fuel is provided and between 0-500 pM of catalyst C is added.

[0142] Figure 19a shows normalised fluorescence at 0-4 hours of the toehold exchange reaction comprising the novel toehold exchange complex as illustrated in Figure 4. Normalised fluorescence is shown at OpM, 1 pM, 2pM and 5pM of catalyst. Figure 17b shows normalised fluorescence over 24 hours of catalytic activity of a toehold exchange reaction comprising the classical toehold exchange complex of Figure 1 . This is performed at concentrations of OpM, 100pM, 200pM and 500pM of catalyst. It can be seen that a stronger signal is provided with the novel toehold exchange complex as illustrated in Figure 4, with less noise. The stronger signal can permit detection of smaller quantities of catalyst (down to 1 pM) more quickly (e.g. after 60 or 120 minutes). The novel toehold exchange complex yields a lower limit of detection of 1 pM in 240 mins (4 h) compared to 100 pM for the classical toehold exchange complex in 1440 mins (24 h). The system with irreversible toehold exchange is 100 times more sensitive and 6 times quicker.

[0143] The molecules (e.g. substrate, output(s), catalyst, fuel(s)) participating in the toehold exchange reactions described above are generally nucleotides (also referred to as oligonucleotides). The nucleotides may be DNA or RNA, or modified DNA or RNA. The nucleotides may be natural DNA or RNA, synthetic DNA or RNA, and / or chemically modified DNA or RNA. Examples of chemically modified RNA are 2’oMe (2'-O-methyl RNA) or 2’MOE (2'-0-methoxyethyl RNA). Modified DNA or RNA may be present in any of the substrate, output, catalyst, and fuel strands described above. One, some or all of a set of interacting nucleotides may include modified DNA or RNA. Modified DNA or RNA may be present in the non-target (non-catalyst) strands, in the target (catalyst) strand, or in a combination of both. A nucleotide may be completely of a modified DNA or RNA, or partially of a modified DNA or RNA, e.g. with a region of modified DNA or RNA or a single instance of modified DNA or RNA. The nucleotides may comprise modifications of DNA or RNA in the nucleic acid backbone, sugar, linkage and / or base.

[0144] Backbone modifications may include modifications at the 1 ’, 2’, 3’ or 4’ position in the ribose cyclopentane ring and / or modifications substituting other molecules for the oxygen in the ribose cyclopentane ring. Backbone modifications may include 2’-0 methyl (2’-OMe), 2’-O- methoxy-ethyl (2’-MOE), 2’-Fluoro (2’-F), 2’-arabino-fluoro (2’-Ara-F), 2’-O-benzyl (2’-benzyl), phosphorodiamidate (PMO), thiophosphoramidate (TMO), phosphoramidate (MO), locked nucleic acids (LNA), peptide nucleic acids (PNA). Backbone modifications may include enantiomers (e.g. L-DNA, L-RNA). Backbone modifications may include those with uncharged backbones, positively charged backbones, and hydrogen bonding groups that allow for preorganisation.

[0145] Linkage modifications may include phosphorothioate, phosphorodithioate, methyl phosphonate, methoxypropyl-phosphonate, methyl phosphorothioate, or mesyl phosphoramidate.

[0146] Base modifications may include C5-propyne T, C5-propyne C, G-clamp, C5-thiazoles, C5’- methyl C, 2-thio T, Hachimoji DNA, Hachimoji RNA.

[0147] Any combination of these or any other modifications may be utilised in any of the strands shown.

[0148] Figures 20a, 20b, 20c and 20d show catalytic activity of the novel toehold exchange complex as illustrated in Figure 4 similar to Figure 18b, but for different types of oligonucleotides. Concentration of catalyst (pM) against normalised fluorescence after 4 hours is shown for concentrations of 10pM, 20pM, 30pM, 40pM, 50pM, and 100pM of catalyst, as well as without a catalyst (OpM). Figure 20a shows catalytic activity of the novel toehold exchange complex with the oligonucleotides having DNA backbones. Figure 20b shows catalytic activity of the novel toehold exchange complex with the oligonucleotides having RNA backbones. Figure 20c shows catalytic activity of the novel toehold exchange complex with the oligonucleotides having 2’oMe backbones. Figure 20d shows catalytic activity of the novel toehold exchange complex with the oligonucleotides having 2’MOE backbones. For all investigated oligonucleotides a linear relation can be seen between normalised fluorescence activity and catalyst concentration.

[0149] Figure 21 shows an embodiment of the novel toehold exchange complex in a toehold exchange cycle. The novel toehold exchange complex (or probe complex) 1810 comprises a substrate strand S with domains cF, p? y^7and 6" (from the 3’ end to the 5’ end respectively). Of particular interest are domains a? which forms the first, exposed, toehold, and domain y^7, which forms the second hidden or covered toehold. Hybridised to the substrate strand S is the output strand O (also referred to as the incumbent strand or the protector strand), which comprises, starting from the 3’ end, domainsmys-7(which comprises a region of noncomplementarity with covered toehold domain y^.7of the protector strand P) and p (which is complementary to domain p" of the substrate strand S). In addition to the output strand O, a quencher strand Q, comprising domain 5, is hybridised to domain CFof the substrate S.

[0150] The probe complex 1810 reacts with catalyst strand C to form intermediate complex 1820. The catalyst strand C comprises domains p and a. Domain a of the catalyst strand C hybridises with the exposed toehold cF of the substrate S. Through branch migration, domain p of the catalyst strand C displaces domain p of the output strand O and the output strand O is released from the substrate strand S. Due to the region of non-complementarity in the output strand O with respect to the corresponding region of the substrate strand S, the forward reaction, which proceeds at rate kimy5-7, is favoured over the reverse reaction, which proceeds at a lower rate k-imys-7. This provides the necessary irreversibility (i.e. a low rate of reverse reaction) for the cycle.

[0151] The intermediate complex 1820 subsequently reacts with a fuel strand F to form the signal complex 1830 and release the quencher strand Q and the catalyst strand C. Domain ys-7of the fuel strand F hybridises with the second toehold region y^.7of the substrate strand S. Since there is no mismatch between these respective domains of the fuel and substrate strands, the rate of association of the fuel strand F to the second toehold is higher than that of the output strand O to the same toehold. Through branch migration, domains p and 5 of the fuel strand F displace the catalyst strand C and quencher strand Q respectively.

[0152] The quencher strand Q comprises a quencher molecule or portion, for example BHQ1 . Other quenchers such as BHQ2, BHQ3 may also be used. The substrate strand S comprises a fluorophore, for example a FAM fluorophore. Other fluorophores such as HEX, TET, JOE, ROX, TAMRA, Cy3, or Cy5 may be used. As a result, disassociation of the quencher strand Q from the substrate strand S causes activity of the fluorophore, which produces a signal. This way, the rate of the reaction may be observed.

[0153] Figures 22a-22c show possible arrangements of the non-complementary regions Ys-7andmys-7 forming the second covered toehold. Figure 22a shows an embodiment in which the second toehold region yl of the substrate strand S consists of 5 nucleotide bases (ys). A corresponding domain y5of the output strand O having 5 nucleotide bases which match the bases of domain Ys is shown at the top of the figure. The length of the other domains in the strands is also shown at the top of the figure; note that domain 5 is preferably part of a separate quencher strand Q, although it may also be part of the output strand O. Domain ys is the second, hidden toehold region of the substrate strand S. Two domainsm1y5andm2y5of the output strand O are shown. Domainm1y5has a single mismatched nucleotide base at the first nucleotide position of the domain (measured in the direction from the 5’ end of the strand) so the nucleotide base is not complementary to the nucleotide base at the corresponding position of domain ys of the substrate strand S, whilst all of the other nucleotide bases in the domain are complementary the corresponding bases on domain ys. Domainm2y5, meanwhile, has a single mismatched nucleotide base at the second nucleotide position of ys, whilst the others are all matched.

[0154] Figure 22b shows the second toehold region ye consisting of 6 nucleotide bases. The corresponding domain of the output strand O also consists of 6 nucleotide bases. Four possible domains of the output strand O are shown:m1y6, having a mismatch at the first nucleotide position;m2y6, having a mismatch at the second nucleotide position;m3y6, having a mismatch at the third nucleotide position; andm12ye, which has mismatched bases at both the first and second positions.

[0155] Figure 22c shows the second toehold region y? consisting of 7 nucleotide bases. The corresponding domain of the output strand O also consists of 7 nucleotide bases. Four possible domains of the strand O are shown:m1y7, having a mismatch at the first nucleotide position;m2y7, having a mismatch at the second nucleotide position;m3y7, having a mismatch at the third nucleotide position;m12y7, having mismatches at the first and second nucleotide positions;m23y7, having mismatches at the second and third nucleotide positions;m14y7, having mismatches at the first and fourth nucleotide positions; andm123y7, having mismatches at the first, second and third nucleotide positions.

[0156] Table 1 below shows example DNA sequences for the domains shown in Figures 21 and 22 and described above, with mismatched nucleotide bases of domainsmy5-7from domains ys-7shown in bold:

[0157]

[0158] Table 1

[0159] Table 2 shows example DNA sequences for the catalyst, substrate, fuel, protector (which may also be referred to as the output or the incumbent) and quencher strands. The strands are formed of the domains shown above in Table 1. Mismatches in the protector strands from the corresponding substrate sequences are shown in bold.

[0160] Table 2

[0161] Figures 23a to 23c show experimental results of catalytic systems comprising the strands described above. Figure 23a shows the fluorescent signal over time for a y5catalytic system comprising the y5strands shown in Figure 22a. Results for systems comprisingm1y5andm2y5domains are shown, as well as a y5domain with no mismatches as a control. Figure 23b shows the fluorescent signal over time for a y6catalytic system comprising the y6strands shown in Figure 22b. Results for systems comprisingm1y6,m2ye,m3ye andm12y6domains are shown, as well as a y6domain with no mismatches as a control. Figure 23c shows the fluorescent signal over time for a y6catalytic system comprising the y7strands shown in Figure 22c. Results for systems comprisingm1y7,m2y7,m3y7,m12y7,m23y7,m14y7, andm123y7domains are shown, as well as a y7domain with no mismatches as a control. In all three cases, 1 nM catalyst was used.

[0162] As can be seen in all of Figures 23a to 23c, the domains comprising mismatched bases show increased fluorescence over time compared to the control without mismatched bases, for all three domain lengths (5, 6, and 7 base pairs) for the covered toehold investigated. For the y6and y7systems, further heightened fluorescence is shown in the systems having more than one mismatched base.

[0163] Figure 23a shows responses for different 5 base pair covered toehold domains. Fluorescent signal saturation is achieved after approximately 200 minutes for either probe with a 1-base pair mismatch. After 200 minutes no further signal amplification is observed, and instead the signal remains at the same level until around 1200 minutes. For the control probe with no mismatch at 200 minutes a significantly weaker signal is observed at less than half the signal strength as the probes with a mismatch. For the control probe after 200 minutes the signal continues to increase gradually, remaining below the signal strength of the probes with a mismatch even after 1200 minutes. The graph suggests that for a 5 base pair domain a single base pair mismatch results in significantly faster and stronger signal amplification than without a mismatch. The graph suggests that location of a single base pair mismatch in either the second or first position in the domain does not noticeably affect strength or speed of signal amplification.

[0164] Figure 23b shows responses for different 6 base pair toehold domains. For a probe with a 2- base pair mismatch fluorescent signal saturation is achieved after approximately 160 minutes, and more gradually for the probes with a 1-base pair mismatch. For the control probe with no mismatch at 160 minutes a comparatively weak signal is observed at a fraction of the signal strength of the probes with one or two mismatches. For the control probe the signal increases gradually over time, remaining at a fraction the signal strength of the probes with one or two mismatches after 1200 minutes. The graph suggests that for a 6 base pair domain a 2-base pair mismatch results in faster signal amplification than with a single base pair mismatch, with comparable signal amplification strength achieved for both over time. The graph suggests that location of a single base pair mismatch in either the third, second or first position in the 6 base pair toehold domain may have a slight effect on strength and speed of signal amplification.

[0165] Figure 23c shows responses for different 7 base pair toehold domains. For a probe with a 3- base pair mismatch fluorescent signal saturation is achieved after approximately 200 minutes, similar to probes with a 2-base pair mismatch. More gradual signal increase is observed for probes with a 1-base pair mismatch. For the control probe with no mismatch comparatively little amplification is observed, even after 1200 minutes. The graph suggests that a 7 base pair toehold domain with a 3-base pair mismatch or a 2-base pair mismatch results in faster and stronger signal amplification than with a single base pair mismatch. The graph suggests that location of a two base pair mismatch in either consecutive base pairs in the domain (e.g. positions 1 and 2, or positions 2 or 3) or in non-consecutive base pairs in the domain (e.g. positions 1 and 4) does not have more than a marginal effect on strength or speed of signal amplification.

[0166] The foregoing examples have shown the toehold exchange complex with the first exposed toehold region (e.g. cF in Figure 21) at the 3’ end of the substrate strand, and the second covered toehold region (e.g. ys-7 in Figure 21) nearer the 5’ end of the substrate strand. The toehold sequence can be swapped such that the first exposed toehold region is at the 5’ end of the substrate strand, and the second covered toehold region nearer the 3’ end of the substrate strand. Generally other arrangements of the domains in the strands can be provided.

[0167] Figure 24 illustrates an example of a toehold exchange system and complex 1910 similar to that of Figure 21 , but with the first exposed toehold region cF at the 5’ end of the substrate strand S, and the second covered toehold region y" nearer the 3’ end of the substrate strand S. The output strand O (referred to elsewhere as the incumbent strand or the protector strand), quencher strand Q, catalyst strand C and fuel strand F as illustrated in Figure 24 interact with the substrate strand S analogous to the strands shown in Figure 21 .

[0168] In some examples the catalyst strand C is a longer strand, and only an end portion of the catalyst strand engages in interactions with the toehold exchange system and complex as described. In some examples it may be advantageous to target the 3’ end of the longer catalyst strand for interaction with the toehold exchange system and complex as described. In other examples it may be advantageous to target the 5’ end of the longer catalyst strand for interaction with the toehold exchange system and complex as described.

[0169] The catalytic reactions described above are typically performed at ambient pressure and room temperature, e.g. at 18°C or at 20°C or at 22°C or at 25°C, but can generally be adapted for performance in a wide range of temperatures, e.g. including the range from 15°C to 55°C. The reaction is typically performed in a pH-buffered aqueous salt solution (of which many are well- known for use with toehold mediated strand displacement reactions) but may be performed in a wide range of media, including non-aqueous media, deionised water, unbuffered media, and media with a wide range of salt concentration, e.g. from 10mM to 150,000mM. The buffer may include enzymes required for the inhibition of RNases and / or DNases. The buffer may include surfactants e.g. for lysis of biological components or for lysis of drug delivery vehicles which may be employed alongside nucleic acid therapeutics.

[0170] The novel toehold exchange complex may be provided as part of a kit of components. In an example the kit comprises an output and a substrate separately, such that the complex of output and substrate can be formed by a user prior to exposure to a sample. In another example the kit comprises a complex of output and substrate, such that the user need not take steps for formation of the complex prior to use. The kit may further comprise the fuel strands. The kit may further comprise (for example for reactions with coupled circuits as described with reference to Figures 8-15):

[0171] • a second or further substrate for formation of a second or further complex;

[0172] • a second or further output for hybridisation to the substrate, to the second substrate or to the further substrate;

[0173] • a second or further complex;

[0174] • second or further fuel strands.

[0175] The kit can be used in the reactions described above for detecting a target, which would catalyse the reaction.

[0176] In an example a sample is brought into contact with a mixture that includes complexes of substrate and output and fuel strands as described above. The substrate, output and fuel strands are such that in the presence of a specific catalyst one of the reactions described with reference to figures 4-15 can occur, producing outputs that can be detected as described above. If the sample contains the target catalyst, then the reaction is catalysed and outputs can be detected. If the sample does not contain the target catalyst, then the reaction is not catalysed and the outputs are not affected.

[0177] Where certain reactions are referred to as irreversible, it should be understood that this encompasses reactions that are poorly reversible. Where certain features are referred to as irreversible, it should be understood that this encompasses features that promote irreversible or poorly reversible reactions.

[0178] It will be understood that the present invention has been described above purely by way of example, and modifications of detail can be made within the scope of the invention. Reference numerals appearing in the claims are by way of illustration only and shall have no limiting effect on the scope of the claims.

Claims

Claims1. A complex for a toehold exchange system, the complex comprising a substrate molecule and an output molecule, the substrate molecule and output molecule each comprising: a plurality of complementary regions where the substrate molecule and the output molecule are hybridised; and a non-complementary region where the substrate molecule and output molecule are not hybridised, the non-complementary region being located between complementary regions; wherein the substrate molecule comprises a first exposed toehold region for hybridisation to a catalyst molecule and a second covered toehold region for hybridisation to a fuel molecule, and wherein the second covered toehold region comprises the region of non-complementarity.

2. A complex according to claim 1 , wherein the second covered toehold region comprises a complementary region.

3. A complex according to claim 1 or 2, wherein a plurality of regions of the substrate are for hybridisation to a catalyst molecule.

4. A complex according to any preceding claim, wherein hybridisation of the catalyst to the substrate causes displacement (optionally release) of the output.

5. A complex according to claim 4, wherein displacement of the output causes the second toehold region of the substrate to be exposed.

6. A complex according to claim 5, wherein hybridisation of the fuel to the substrate causes release of the catalyst.

7. A complex according to any preceding claim, wherein the substrate molecule is configured to bind to the catalyst and cause the output to be displaced (optionally released) through competitive hybridisation.

8. A complex according to any preceding claim, wherein the substrate molecule, the output molecule, the catalyst molecule and / or the fuel molecule are nucleotide strands, optionally formed of one or more of: DNA, RNA, modified DNA, modified RNA, DNA or RNA with modified nucleic acid backbone, modified sugar, modified linkage and / or modified base.

9. A complex according to any preceding claim, wherein the non-complementary region of the substrate molecule comprises at least one nucleotide base (optionally at least two or at least three nucleotide bases) that is not complementary to at least one nucleotide base of the non- complementary region of the output molecule (optionally at least two or at least three nucleotide bases).

10. A complex according to claim 9, wherein the non-complementary region of the substrate molecule comprises at least one nucleotide base (optionally at least two or at least three nucleotide bases) that is complementary to at least one nucleotide base of the non- complementary region of the output molecule (optionally at least two or at least three nucleotide bases).11 . A complex according to any of claims 9 or 10, wherein the first nucleotide base or bases of the substrate molecule are comprised in the second toehold region.

12. A complex according to any preceding claim, wherein the non-complementary region is non-continuous with portions of the non-complementary region located between portions of complementary regions; and / or wherein the non-complementary region comprises a bulge and / or a hairpin.

13. A complex according to any preceding claim, wherein the output molecule comprises at least two regions that are mutually complementary for hybridisation to form a hairpin loop.

14. A complex according to any preceding claim, wherein the second covered toehold region of the substrate molecule comprises 3 to 10 nucleotide bases, preferably 5, 6 or 7 nucleotide bases.

15. A complex according to any preceding claim, further comprising: a fluorophore at a region of the substrate molecule; and a quencher region of the output molecule that inactivates the fluorophore and displacement (optionally release) of the output molecule causes activation of the fluorophore; or a quencher molecule hybridised to the substrate molecule, wherein the quencher molecule inactivates the fluorophore, and displacement (optionally release) of the quencher molecule causes activation of the fluorophore.

16. Acomplex according to any preceding claim, further comprising a second output molecule, the substrate molecule and the second output molecule each comprising: a plurality of complementary regions where the substrate molecule and the second output molecule are hybridised; and a non-complementary region where the substrate molecule and second output molecule are not hybridised, the non-complementary region being located between complementary regions.

17. A complex according to claim 16, wherein the second output molecule has the same sequence as the output molecule or wherein the second output molecule includes the sequence of the output molecule or wherein the second output molecule has at least two domains in common with the output molecule.

18. A complex according to claim 16 or 17, wherein hybridisation of the fuel to the substrate causes release of the second output.

19. A complex according to claim 18, wherein the substrate molecule comprises a tethered output region to which the second output molecule is at least partially hybridised, optionally wherein hybridisation of the fuel to the substrate further causes exposure of the tethered output.

20. A complex according to any preceding claim, wherein the substrate molecule comprises a tethered output region with at least two regions that are mutually complementary for hybridisation to form a hairpin loop, optionally wherein hybridisation of the fuel to the substrate causes opening of the hairpin loop to expose the tethered output.21 . A complex according to any preceding claim, wherein the substrate molecule comprises a first part of an associative output, wherein hybridisation of the fuel to the substrate causes formation of an associative output.

22. A toehold exchange system comprising a complex according to any preceding claim and a fuel molecule.

23. A toehold exchange system according to claim 22, wherein the substrate molecule comprises a first part of an associative output and the fuel comprises a second part of the associative output, wherein hybridisation of the fuel to the substrate causes formation of the associative output, optionally wherein the associative output comprises or is the same sequence as the catalyst molecule.

24. A toehold exchange system according to claim 23 when dependent on claim 16, wherein the second output is hybridised to at least a part of the first part of the associative output, and release of the second output causes exposure of at least a part of the first part of the associative output.

25. A toehold exchange system comprising: a first complex according to any one of claims 1 to 21 or a first system according to any one of claims 22 to 24; and a second, different complex according to any one of claims 1 to 21 or a second, different system according to any one of claims 22 to 24; wherein the second complex or second system is configured to receive as catalyst a molecule provided from the first complex or first system.

26. A toehold exchange system according to claim 25, wherein the output molecule of the first complex or first system is a catalyst for the second complex or second system.

27. A toehold exchange system according to claim 25 or 26 when dependent on claim 16, wherein the second output molecule of the first complex or first system is a catalyst for the second complex or second system.

28. A toehold exchange system according to any one of claims 25 to 27 when dependent on claim 19 or 20, wherein the tethered output region of the first complex or first system is a catalyst for the second complex or second system.

29. A toehold exchange system according to claim 25 when dependent on claim 21 or 23, wherein the associative output of the first complex or first system is a catalyst for the second complex or second system.

30. A method comprising incubating the toehold exchange complex according to any of claims 1 to 21 or the toehold exchange system according to any of claims 22 to 29 with a sample to determine whether the catalyst molecule is present.31 . A kit of components for formation of a toehold exchange complex according to any of claims 1 to 21 or a toehold exchange system according to any of claims 22 to 29, the kit comprising the substrate molecule and the output molecule for formation of the complex and optionally the fuel molecule.

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