WO2018129333A1 - Systems and methods for determining molecular motion - Google Patents

Abstract

The present invention generally relates to systems and methods for determining molecular motion, for example, using nanostructures such as DNA origami structures. In certain embodiments, a nanostructure, such as a DNA origami structure, may be used to amplify molecular motion of a species. For example, a species, such as a protein, may be used to move a DNA strand, or other component, which the nanostructure may be immobilized relative to. Rotation or other movement of the component by the species may be determined by determining movement of the nanostructure. Such movement may be determined, for instance, using a signaling entity attached to the nanostructure. Various other embodiments are generally directed to methods of preparing such systems, kits involving such systems or methods, or the like.

Description

SYSTEMS AND METHODS FOR DETERMINING MOLECULAR MOTION

RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Patent Application Serial No. 62/442,737, filed January 5, 2017, entitled "Systems and Methods for Determining Molecular Motion," by Zhuang, et ah , incorporated herein by reference in its entirety.

GOVERNMENT FUNDING

This invention was made with government support under Grant. Nos.

5R01GM105637-02, 1R01EB018659, and GM008313 awarded by the National Institutes of Health, Grant No. CCF1317291 awarded by the National Science Foundation, and Grant No. N000141310593 awarded by the Office of Naval Research. The government has certain rights in the invention.

FIELD

The present invention generally relates to systems and methods for determining molecular motion, for example, using nanostructures such as DNA origami structures.

BACKGROUND

Studies of Fl ATPase have shown that by directly observing biomolecular rotation, one could address fundamental yet previously inaccessible biological questions. The field of single molecule rotation has used assays using beads to mechanically amplify rotation or constrained fluorophores that report rotation via fluorescence polarization. However, the utility of single molecule rotation assays is limited by their experimental complexity and low throughput. Accordingly, improvements are needed.

SUMMARY

The present invention generally relates to systems and methods for determining molecular motion, for example, using nanostructures such as DNA origami structures. The subject matter of the present invention involves, in some cases, interrelated products, alternative solutions to a particular problem, and/or a plurality of different uses of one or more systems and/or articles.

In one aspect, the present invention is generally directed to a composition. In one set of embodiments, the composition comprises a surface, a DNA strand immobilized relative to and extending away from the surface, an arm attached to and extending away from the DNA strand, and a signaling entity attached to the arm.

In another set of embodiments, the composition comprises a surface, a molecular component immobilized relative to and extending away from the surface, an arm attached to and extending away from the molecular component, and a signaling entity attached to the arm.

In another set of embodiments, the composition comprises a DNA origami structure, a signaling entity attached to the DNA origami structure at a first point of attachment, and a component attached to the DNA origami structure at a second point of attachment at least 25 nm away from the first point of attachment. In some cases, the distance between the first point of attachment and the second point of attachment varies from the mean distance by no more than 20%. In certain embodiments, the component comprises a DNA strand.

The composition, in yet another set of embodiments, comprises a component attached to a DNA origami structure at a point of attachment. In some embodiments, the DNA origami structure comprises two or more arms extending away from the point of attachment. In certain cases, the component comprises a DNA strand. In one embodiment, the component is immobilized with respect to a surface.

According to still another set of embodiments, the composition comprises a component attached to a DNA origami structure at a point of attachment. In some cases, the DNA origami structure extends at least 25 nm away from the point of attachment and is substantially rotationally symmetric about the point of attachment. In certain embodiments, the component comprises a DNA strand. In some instances, the component is immobilized with respect to a surface.

In yet another set of embodiments, the composition comprises a surface, a component immobilized relative to the surface at a point of attachment, and a DNA origami structure attached to the component. In some cases, the component comprises a DNA strand.

The present invention is generally directed to a method in another aspect. In accordance with one set of embodiments, the method includes acts of exposing an agent to a component immobilized relative to a surface at a point of attachment and exhibiting a first molecular motion, and determining motion and/or a position of a nanostructure attached to and extending away from the component to determine the first molecular motion and the second molecular motion. In some cases, upon interaction of the agent with the component, the component exhibits a second molecular motion distinguishable from the first molecular motion.

In another set of embodiments, the method includes determining molecular motion of a nanostructure attached to a species immobilized relative to a surface. In some cases, the nanostructure amplifies molecular motion of the species to produce the molecular motion of a nanostructure. In yet another set of embodiments, the method comprises determining molecular motion of a species immobilized relative to a surface by determining motion of a rigid nanostructure attached to the species.

In another aspect, the present invention encompasses methods of making one or more of the embodiments described herein, for example, nanostructures such as those described herein. In still another aspect, the present invention encompasses methods of using one or more of the embodiments described herein, for example, nanostructures such as those described herein.

Other advantages and novel features of the present invention will become apparent from the following detailed description of various non-limiting embodiments of the invention when considered in conjunction with the accompanying figures.

BRIEF DESCRIPTION OF THE DRAWINGS

Non-limiting embodiments of the present invention will be described by way of example with reference to the accompanying figures, which are schematic and are not intended to be drawn to scale. In the figures, each identical or nearly identical component illustrated is typically represented by a single numeral. For purposes of clarity, not every component is labeled in every figure, nor is every component of each embodiment of the invention shown where illustration is not necessary to allow those of ordinary skill in the art to understand the invention. In the figures:

Figs. 1 A-1G illustrate the determination of rotation of DNA, in accordance with one embodiment of the invention;

Figs. 2A-2I illustrate analysis of pausing and backtracking, in another embodiment of the invention;

Fig. 3 illustrates an example schematic of a DNA origami nanostructure, in accordance with one embodiment of the invention;

Figs. 4A-4E illustrate various DNA origami nanostructures, in certain embodiments of the invention;

Fig. 5 illustrates an example schematic of a DNA origami nanostructure, in accordance with another embodiment of the invention;

Figs. 6A-6B illustrate certain DNA origami nanostructures, in some embodiments of the invention;

Fig. 7 illustrates an anchored DNA origami nanostructure, in yet another embodiment of the invention;

Fig. 8 is a schematic diagram illustrating another embodiment of the invention. Fig. 9 illustrates DNA oligomers used for a DNA origami rotor, in one embodiment of the invention;

Fig. 10 illustrates DNA oligomers used for a DNA origami base, in another embodiment of the invention;

Figs. 11A-11B illustrate additional DNA oligomers, used in certain embodiments of the invention;

Figs. 12A-12D illustrate Brownian dynamics of a protein, in some embodiments of the invention;

Figs. 13A-13E illustrate unwinding rates of molecules, in other embodiment of the invention;

Figs. 14A-14B illustrate unwinding pausing times of individual molecules, in some embodiments of the invention; and

DETAILED DESCRIPTION

The present invention generally relates to systems and methods for determining molecular motion, for example, using nanostructures such as DNA origami structures. In certain embodiments, a nanostructure, such as a DNA origami structure, may be used to amplify molecular motion of a species. For example, a species, such as a protein, may be used to move a DNA strand, or other component, which the nanostructure may be

immobilized relative to. Rotation or other movement of the component by the species may be determined by determining movement of the nanostructure. Such movement may be determined, for instance, using a signaling entity attached to the nanostructure. Various other embodiments are generally directed to methods of preparing such systems, kits involving such systems or methods, or the like.

In one aspect, the present invention is generally directed to systems and methods of amplifying the molecular motion of a species (e.g., rotational motion) to cause larger motion of a nanostructure that can be determined in some fashion. For instance, in one embodiment, a species, such as a protein, may cause a double- stranded DNA (or another suitable component) to rotate, for example, by acting on the DNA strand in some fashion. For example, a protein such as RecBCD may manipulate DNA by rotating and unwinding the strands of DNA. Typically, however, such rotations of DNA are of a length scale that are too small to be easily detected. For instance, a signaling entity, such as a fluorescent dye, attached to one of the DNA strands may be rotated as the DNA rotates, but the amplitude of rotation of the attached dye may be too small to be easily detected. In certain embodiments of the invention, however, a nanostructure may be used which is able to amplify the molecular motion of the species (e.g., the RecBCD protein). Referring now to Fig. 1 A as an illustrative non-limiting example, a component such as a DNA strand may be attached to a nanostructure that extends away from the DNA strand. For example, the nanostructure may comprise one or more arms (4 in this example), and movement of the nanostructure may be detected by movement of a signaling entity, such as a fluorescent dye, that is attached to the nanostructure. When the DNA strand rotates, as shown by the smaller arrows, the nanostructure also rotates, causing the signaling entity to rotate to a much larger degree. Such motions can then be determined. The DNA strand or other component may be immobilized relative to a surface, directly or indirectly, e.g., via a species able to cause the DNA to exhibit molecular motion, as is shown in Fig. 1A.

In some cases, the nanostructure comprises a relatively rigid portion, for example, such that the movement of the signaling entity can be attributed, at least in part, to the movement of the DNA strand or other component. There may be other components of movement that are determined (e.g., some flexing of the rigid portion, Brownian motion, etc.), although at least a statistically detectable degree of motion may nonetheless be attributable to movement of the DNA strand, e.g., by the species. This can be seen, for example, by directed movements of the signaling entity. In contrast, pure Brownian motion may occur randomly, and may not result in any systematic or directed motion in one direction over relatively long periods of time.

In some cases, the nanostructure may have a length of at least 10 nm, e.g., extending away from the DNA strand (or other component). Longer distances, e.g., at least 25 nm or at least 100 nm, are also possible in some cases. Relatively larger nanostructures may show additional resistance to motion (e.g. caused by drag force moving through a fluid) than relatively smaller nanostructures, but this difference is not significant for some embodiments. Without wishing to be bound by any theory, it is believed that the forces needed to rotate or otherwise move the DNA strand (e.g., from a species such as a RecBCD protein) may, in at least some cases, be much greater than the viscous drag force created by larger or more massive nanostructures. Accordingly, even relatively large nanostructures may be used in some embodiments without significantly affecting molecular motion of the nanostructure or the species.

In some cases, the nanostructure may comprise a DNA origami nanostructure, as is shown in Fig. 1A. In DNA origami, a DNA strand is folded arbitrarily to create suitable three-dimensional shapes at the nanoscale, for example, as is shown in this figure. In some cases, DNA origami structures may be formed using a long single strand of DNA and shorter, "staple" strands that are used to arbitrarily fold the DNA strand into a desired shape. The DNA origami nanostructure can be made relatively rigid in some cases, e.g., by using nanotubes or bundles of DNA double helixes arranged to form hollow tubes, e.g., using suitable crossovers between the bundles. These DNA double helixes are shown

schematically in Fig. 1A as rods.

As mentioned, in one set of embodiments, one or more signaling entities may be determined and used to determine motion of the nanostructure or the species. In some cases, more than one signaling entity may be used on the nanostructure, e.g., to allow different nanostructures to be distinguished from each other. For instance, two, three, four, or more signaling entities may be attached to nanostructures in different combinations, so as to allow the different nanostructures to be distinguished. (However, it should be noted that, due to rotational symmetry, not all combinations can be readily distinguished; for example, for a 2- rotor system, a first entity on a first arm and a second entity on a second arm may be indistinguishable from the first entity on the second arm and the second entity on the first arm.)

The discussion above assumes that the DNA strand is rotated; however, it should be understood that this is by way of example only, and that in other embodiments, other motions may be determined, e.g., in addition to and/or instead of DNA rotation. For instance, other molecular motions such as rocking, bending, twisting, swiveling, or linear motion may be determined. In addition in some embodiments, the exact molecular motion itself may be less important than determining a change in molecular motion, even if that change is a

combination of two or more types of motion. For example, in some cases, the DNA strand (or other component) and/or the species may be allowed to interact with an agent suspected of being able to interact with the DNA strand and/or the species. The interaction may cause a change in the general behavior of the molecular motion, which may be determinable as a change in the molecular motion of the signaling entity.

In some cases, DNA which is damaged or otherwise altered can be studied. These alterations may, for example, be based on damage that occurs naturally (biologically) or artificially, including damage which may be caused by a drug, small molecule, or other therapeutic agent. Non-limiting examples of DNA damage that may be analyzed include, but are not limited to nicks, gaps, methylation, based modifications, backbone modifications, covalent or non-covalent modification by drugs or other small molecules, etc. In addition, the physical properties of DNA or other molecules when damaged/altered (e.g. stiffness) as well as how the damage/alterations affect the interactions of small molecules, proteins, or other molecules with the DNA may be studied in certain embodiments.

In addition, the discussion above uses a DNA strand by way of example only. In other embodiments, other suitable components, such as RNA, PNA, proteins, other polymers, etc. may be determined, e.g., by determining the motion of a signaling entity attached to a nanostructure immobilized relative to the molecular entity. Other examples include unnatural nucleic acids, or other (bio)molecules can be studied, e.g., by using such molecules instead of, or in addition to, DNA, e.g., in a DNA origami structure such as those described herein. Such components may be immobilized relative to a species, which in some cases may be able to move the component in some fashion. In other cases, however, the component may not necessarily move in response to the species. The species may also be attached to a surface in some embodiments, e.g., such that molecular motion of the nanostructure can be determined relative to the surface.

The above discussion is a non-limiting example of one embodiment of the present invention generally directed to systems and methods for amplifying the molecular motion of a species to cause larger motion of a nanostructure. However, other embodiments are also possible. Accordingly, more generally, various aspects of the invention are directed to various systems and methods for determining molecular motion.

In one aspect, the present invention is generally directed to systems and methods for determining molecular motion of a component, such as a DNA strand. One schematic diagram of such a system may be seen in Fig. 8, as a non-limiting example. This figure illustrates a system 10 for determining molecular motion of a species. Species 15 is immobilized relative to a surface 20; for instance, species 15 may be directly or indirectly attached to surface 20. Extending from species 15 is a component 25; for example, component 25 may be DNA (single- or double- stranded), RNA, a protein or a peptide, a polymer, or the like. In some cases, the movement of component 25 caused by species 15 may be studied. However in some cases, movement due to species 15 is not necessarily required; for instance, species 15 may act as an "anchor" and the interaction between component 25 and an agent 30 that is able to interact in some fashion with component 25 (e.g., via specific or non-specific binding) may be determined.

Motion of component 25 may be determined using nanostructure 35. In this example, nanostructure 35 has two arms extending outwardly from a point of attachment between nanostructure 35 and component 25; although this is by way of example only. Nanostructure 35 in some embodiments may be relatively rigid, such that movement of component 25 (e.g., twisting motions) may cause larger motions to appear in nanostructure 35. In some cases, nanostructure 35 may be directly determined (e.g., imaged via microscopy); however, in certain cases, nanostructure 35 may contain one or more signaling entities 40 (for example, fluorescent entities) which can be determined, thereby determining the motion of

nanostructure 35 and component 25. In addition, in some cases, alteration of the motion may be determined, for example, upon interaction of agent 30 with nanostructure 35 and/or species 15.

A variety of different components may be studied, including DNA (which may be single- or double- stranded), RNA, PNA, peptides, proteins, polymers, or the like. In certain embodiments, as noted above, the component is attached to or immobilized relative to a surface. The component may be attached to a surface directly, or indirectly, e.g., via a species that itself is attached to or immobilized relative to a surface. The surface may be, for example, glass or silicon. In some cases, the component also extends away from the surface. For instance, the component may be immobilized relative to the surface at a single point of attachment. The component may extend away from the surface orthogonally, or at another angle.

Non-limiting examples of direct attachment of DNA to a surface include DNA modifications such as amination, succinylation, disulfides, or hydrazide groups, and may vary depending on the surface. As non-limiting examples of indirect attachment, the DNA strand may be attached to a surface via a suitable species, e.g., a protein such as an enzyme, that can interact with the DNA strand; for instance, the species may be an enzyme recognizes the DNA strand as a substrate.

In one set of embodiments, the species is able to manipulate the DNA strand, or other component, in some fashion. The species may also be attached to the surface, e.g., directly or indirectly, using techniques such as protein tags, physical adsorption, or covalent binding techniques. The species may cause the component to move in some fashion, which may be determined as discussed herein. Examples of molecular motions include, but are not limited to, rotation, rocking, bending, twisting, swiveling, linear motion, winding/unwinding, or separation of one strand from another (e.g., if the DNA is double- stranded). In some embodiments, the species is a protein, such as an enzyme, that is able to interact with the component. For instance, the component may be a substrate that an enzyme is able to specifically bind. In some cases, the species is a species able to manipulate DNA, e.g., a DNA-rotating enzyme, a helicase, a polymerase or a DNA packaging motor, a topoisomerase, a restriction enzyme, a ligase, a nuclease, or the like. In addition, in some embodiments, the species may not necessarily be able to move or manipulate the component, but may be able to immobilize the component with respect to a surface. In some cases, the species may be a protein such as an enzyme, or a DNA origami structure. A non-limiting example of such a structure can be seen in Fig. 7, where a DNA origami structure is constructed to immobilize a component with respect to a surface. In this figure, the structure is a tripod structure, although other structures are also possible in other embodiments.

In certain embodiments, the component is also attached, directly or indirectly, to a nanostructure that extends away from the component. For instance, the nanostructure may be connected to the component at a single point of attachment, such that the nanostructure extends for a distance beyond the component. The nanostructure may extend, in various embodiments, at least 5 nm, at least 10 nm, at least 15 nm, at least 20 nm, at least 25 nm, at least 30 nm, at least 40 nm, at least 50 nm, at least 75 nm, at least 100 nm, at least 150 nm, at least 200 nm, at least 250 nm, at least 300 nm, at least 400 nm, at least 500 nm, at least 750 nm, or at least 1000 nm away from the component, e.g., one or more points on the nanostructure are separated at least this distance away from the component, on average. In some cases, the nanostructure may extend relatively orthogonally away from the component, e.g., as is shown in Fig. 1, although this is not a requirement, and the nanostructure may extend from the component at other angles as well.

In one set of embodiments, the nanostructure may include one or more rods or arms that extend away from the point of attachment between the component and the nanostructure. For instance, in Fig. 1, four such arms are shown, although this is by way of example, and other arms may be present in other embodiments. For example, there may be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more arms radiating away from the point of attachment. In some cases, the arms may be generally rotationally symmetric about the point of attachment (e.g., as viewed using electron microscopy), although this is not required. In addition, the arms may independently be of the same, or different lengths, and may be identical or distinguishable, e.g., as viewed using electron microscopy. In addition, while straight arms are illustrated in Fig. 1, other shapes are also possible, e.g., curved or bent arms.

In some embodiments, the nanostructure is rigid. In some cases, the nanostructure may have sufficient rigidity such that a point on the nanostructure that is at least 5 nm, at least 10 nm, at least 15 nm, at least 20 nm, at least 25 nm, at least 30 nm, at least 40 nm, at least 50 nm, at least 75 nm, at least 100 nm, at least 150 nm, at least 200 nm, at least 250 nm, at least 300 nm, at least 400 nm, at least 500 nm, at least 750 nm, or at least 1000 nm away from the point of attachment has a variation in distance by no more than 50%, no more 40%, no more than 30%, no more than 25%, no more than 20%, no more than 15%, no more than 10%, or no more than 5% from the mean or average distance, e.g., as determined radially away from the component. It should be noted, that certain structures, structures such as single chains of carbon atoms (— C— C— C— C— ...), are inherently "floppy" and cannot maintain these distances of separation, on average. In addition, in some cases, the

nanostructure may have sufficient rigidity such that the movement of the nanostructure (or a signaling entity immobilized relative to the nanostructure) can be attributed, at least in part, to the movement of the component. It should be understood, however, that the entire nanostructure need not be rigid. For instance, only a portion of a nanostructure may have rigidities such as discussed above.

Examples of nanostructures that may be suitably rigid include, but are not limited to, silicon nanowires, carbon nanotubes, or DNA or RNA structures such as DNA or RNA origami structures. Those of ordinary skill in the art will be aware of techniques to produce branched silicon nanowires or carbon nanotubes. See, e.g., U.S. Pat. No. 8,058,640. In DNA origami, a DNA strand is folded arbitrarily to create suitable three-dimensional shapes at the nanoscale. See, e.g., U.S. Pat. No. 7,842,793. The folds may be designed based on knowledge of the interactions between complementary base pairs of DNA. In some embodiments, DNA origami uses a long single strand of DNA (e.g., viral DNA) aided by multiple smaller "staple" strands that are used to arbitrarily fold the DNA strand into a desired three-dimensional shape. For example, DNA strands may be used to form nanotubes using "bundles" of DNA double-helixes; examples include 6-helix and 10-helix bundles of DNA that form the nanotube. See, e.g., Mathieu, et ah, "Six-Helix Bundles Designed from DNA," Nano-Lett., 5(4):661-665, 2005, or Ke, et ah, "Three-Dimensional Structures Self- Assembled from DNA Bricks," Science, 338(6111): 1177-1183, 2012. The nanotubes, due to their repeated and intimate folding, are surprisingly rigid, and thus can be assembled into more complex structures, such as the 4-arm rotor seen in Fig. 1A. There are programs freely available on the Internet to design suitable 2-dimensional or 3 -dimensional DNA structures using DNA origami techniques, such as CADNano (Laboratory for Computational Biology & Biophysics, MIT).

The DNA strand may be attached to the nanostructure using various techniques. Non- limiting examples include chemical reaction, complementary interaction (e.g., a portion of the DNA strand may be complementary to a portion of the nanostructure, such as a DNA sequence), or through ligation of the DNA strand to the nanostructure (e.g., if the nanostructure comprises DNA). For complementary interactions, there may be at least 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, or more bases that are complementary (e.g., Watson-Crick pairing), and they may be sequential or include a small number of interspersed mismatches, e.g., 1, 2, 3, etc. mismatches. Non-limiting examples of ligases include DNA ligases such as DNA Ligase I, DNA Ligase II, DNA Ligase III, DNA Ligase IV, T4 DNA ligase, T7 DNA ligase, T3 DNA Ligase, E. coli DNA Ligase, Taq DNA Ligase, or the like. Many such ligases may be purchased commercially.

In one set of embodiments, the nanostructure includes one or more signaling entities. The signaling entity may include, but is not limited to, a fluorescent dye, a chemiluminescent entity, a radioactive label, a ligand which can serve as a specific binding partner to a labeled antibody, an enzyme, an antibody which can serve as a specific binding partner for a labeled ligand, an antigen, a group having a specific reactivity, or an electrochemically detectable moiety. Non-limiting examples of fluorescent signaling entities include Cy2, Cy3, Cy5, metal nanoparticles, semiconductor nanoparticles or "quantum dots," fluorescent proteins such as GFP (Green Fluorescent Protein), fluorescein, rhodamine, or hexachlorofluorescein. Those of ordinary skill in the art will be aware of other fluorescent entities that are readily commercially available.

The signaling entity may be directly attached to the nanostructure, or indirectly attached. For instance, in one set of embodiments, a signaling entity may be attached to a staple strand or a long single strand used within a DNA origami nanostructure, e.g., covalently. Those of ordinary skill in the art will know of various techniques for labeling DNA, e.g., with fluorescent dyes or other suitable signaling entities.

In one set of embodiments, the signaling entity may be attached to a position within the nanostructure such that movement of the nanostructure causes movement of the signaling entity. For example, in one embodiment, the signaling entity may be positioned on an arm of the nanostructure, such that movement of the arm (e.g., rotational movement) causes movement of the signaling entity, which can be determined in some fashion, as discussed herein. In some cases, the signaling entity may be positioned relatively far away from a single point of attachment, e.g., of a component to the nanostructure. This may allow relatively small movements to be amplified into relatively larger movements of the signaling entity, which may facilitate determination of such movements. For instance, the signaling entity may be attached to the nanostructure at a point that is at least 5 nm, at least 10 nm, at least 15 nm, at least 20 nm, at least 25 nm, at least 30 nm, at least 40 nm, at least 50 nm, at least 75 nm, at least 100 nm, at least 150 nm, at least 200 nm, at least 250 nm, at least 300 nm, at least 400 nm, at least 500 nm, at least 750 nm, or at least 1000 nm away from the point of attachment of the component.

In some cases, more than one signaling entity may be present attached to a

nanostructure, and they may be the same or distinguishable from each other, e.g., having different emissions. There may be 2 or more, 3 or more, 4 or more, 5 or more, 6 or more, 8 or more 10 or more, 12 or more, 15 or more, or more than 20 signaling entities attached to a nanostructure, in various embodiments. The signaling entities may each independently be positioned in the same location or in different locations. For example, more than one signaling entity may be attached in the same location (or attached relatively close to each other) to improve the signal from the nanostructure. For example, there may be 2 or more, 3 or more, 4 or more, 5 or more, 6 or more, 8 or more 10 or more, 12 or more, 15 or more, or more than 20 signaling entities attached to one arm of a nanostructure, in various

embodiments. In addition, in some cases, repeated transient binding of signaling entities to the nanostructure could be used to determine its position and movement. See, e.g.,

Jungmann, et ah, "Multiplexed 3D Cellular Super-resolution Imaging with DNA-PAINT and Exchange-PAINT," Nat. Methods, 11:313-318, 2014.

In addition, in some cases, e.g., if the nanostructure has more than one arm, then some or all of the arms may include signaling entities, e.g., to allow for easier determination of the various arms, or the movement thereof, etc. For instance, two, three, four, five, or more of the arms may each have a signaling entity (which may each independently be the same or distinguishable from each other). In certain cases, the signaling entities may be positioned to be rotationally symmetrically distributed on the arms. In addition, in some cases, two or more of the two signaling entities are substantially aligned relative to each other, e.g., by using similar attachment mechanisms.

In addition, in one set of embodiments, more than one signaling entity may be used as a "barcode" or identifier of one nanostructure from another nanostructure, e.g., to allow for coding of the nanostructures, e.g., having different DNA or other properties. For instance, a first nanostructure having a first pattern of signaling entities may be distinguishable from a second nanostructure having a second pattern of signaling entities on the basis of the different patterns of signaling entities. The patterns may differ by the use of different signaling entities (e.g., having different emissions), different positions of the signaling entities on an arm (e.g., closer or farther away from a point of attachment), different positions of the signaling entities on different arms (e.g., a first nanostructure may have a first signaling entity on one arm and a second signaling entity on another arm, while a second nanostructure may have the first and second signaling entities on the same arm, a third nanostructure may have two first signaling entities and no second signaling entities, etc.), or any combination of these. By using different signaling entities and/or different locations within a nanostructure, even a relatively small number of potential signaling entities may give rise to a relatively large number of distinguishable combinations. Non-limiting examples of techniques for using signaling entities as barcodes can be seen in Lin, et al., "Submicrometre geometrically encoded fluorescent barcodes self-assembled from DNA," Nat. Chem., 4:832-839, 2012.

Temporal readout of barcodes can also be used in some embodiments. For example, by attaching different nucleic acid oligomers to different nanostructures, the nanostructures can be distinguished by hybridization, for instance, with a fluorescent oligonucleotide in temporally separated imaging rounds. See, e.g., Chen, et al., "Spatially Resolved, Highly Multiplexed RNA Profiling in Single Cells," Science, 348(6233): aaa6090, 2015. See also Int. Pat. Apl. Pub. Nos. WO 2016/018960 and WO 2016/018963, each incorporated herein by reference.

The signaling entity (or entities) may be determined using a variety of techniques.

For example, fluorescent signaling entities may be determined using a variety of fluorescent microscopy techniques known to those of ordinary skill in the art. In some cases, super- resolution techniques may be used, such as STORM (stochastic optical reconstruction microscopy), STED, NSOM, 4Pi microscopy, SIM, SMI, RESOLFT, GSD, SSEVI, SPDM, PALM, FPALM, LIMON, SOFI, or the like. See also U.S. Pat. Nos. 7,838,302, or

8,564,792, Int. Pat. Apl. Pub. No. WO 2013/090360, each incorporated herein by reference in their entireties. However, it should be understood that super-resolution techniques are not necessarily required in all cases, and that in other cases, other microscopy techniques may be used.

In addition, in some embodiments, the signaling entity (or entities) may be determined as a function of time, e.g., to determine molecular motion of the signaling entity, which may be used to infer molecular motion of the nanostructure or of a species. Any suitable time resolution may be used e.g., frame rates of at least 1, at least 2, at least 3, at least 5, at least 10, at least 15, at least 20, at least 25, at least 30, at least 40, at least 50, at least 60, at least 75, at least 100, at least 120, at least 150, at least 200, at least 250, at least 300, at least 500, at least 1000, at least 1500, at least 2000, at least 3000, at least 4000, at least 5000, at least 6000, at least 7000, or at least 8000 per second.

Thus, in certain embodiments, movement of one or more signaling entities may be used to determine movement of the nanostructure, and thus movement of a species, such as a protein, that is able to move in some fashion. For example, the species may cause movement of a component, which may be immobilized relative to the nanostructure. Movement or action of the species on the component may thus be determined based on movement of the signaling entities, e.g., microscopically.

In some aspects, such movement may be modified through interaction of the system with other agents. For example, in one set of embodiments, a component, such as a DNA strand, positioned between a nanostructure and a species (e.g., immobilized with respect to a surface) may interact in some fashion with an agent. The agent may bind to the component and/or the species, which may cause the movement to be modified or altered in some fashion, e.g., from a first molecular motion to a second molecular motion. For example, the location where the nanostructure is positioned may change, or the periodicity or other characteristic of the motion may change. For instance, an agent binding to a DNA strand may warp or bend the DNA strand, or prevent or facilitate its movement. In such fashion, interaction of the agent to the DNA strand (or other component) may be determined.

In addition or instead of motion, static positions may be determined in certain embodiments of the invention. As a non-limiting example, by measuring the offset between the rotational angle of two nanostructures (e.g. above and below a piece of DNA), one can extract structural information about the linker (such as helicity, bending angle, etc.).

In some cases, the agent may interact with the species, e.g., to alter its ability to move the DNA strand or other component. In other embodiments, however, the species may be a species anchoring the component to a surface, and may not contribute to movement of the component (e.g. acting as an anchor), although binding of the agent to the component may still be determined as a change in movement of the nanostructure.

Examples of agents that may interact with DNA include, but are not limited, to enzymes that are able interact with DNA, such as a DNA-rotating enzyme, a helicase, a polymerase or a DNA packaging motor, a topoisomerase, a restriction enzyme, a ligase, a nuclease, a DNA unwinding enzyme (e.g., Cas9 or RecA), a transposon, a repressor, a transcriptional silencer, a DNA-binding compound (e.g., small molecules, for instance, with a molecular weight of less than 2000 Da), or the like. Other non-limiting examples of agents include transcription factors, DNA binding proteins, intercalating agents, suspected anticancer drugs that interact with DNA, or the like. In some cases, a variety of agents may be screened, for example, to determine agents that are able to bind to DNA (or otherwise interact with DNA, or other components), or agents that are able to bind to or otherwise interact with a specific sequence of DNA. In some embodiments, the motion and/or position of the nanostructure can be used to characterize the physical properties of a component (e.g., DNA structure, flexibility, etc.), and/or how these properties change upon interaction with agents such as small molecules, proteins, nucleic acids, or the like, e.g., as discussed herein. For instance, static properties such as the helical pitch of a DNA strand (or other component) can be determined relatively accurately. This could be performed, for example, by measuring the static offset in rotation between nanostructures flanking the DNA strand (or other component). In addition, in some embodiments, the flexibility of a DNA strand (or other component) can be determined relatively accurately, for example, by measuring the Brownian dynamics of a nanostructure attached to the DNA strand (or other component), and subsequently fitting a model to the power spectrum of the Brownian dynamics.

In addition, it should be understood that although DNA strands are discussed herein, this is by way of example only, and in other aspects, other components, such as other nucleic acids (e.g., RNA), or other polymers can be used instead of and/or in addition to a DNA strand, e.g., that a nanostructure can be attached to. For example, movement of such components may be determined by determining the movement of nanostructures that are attached to the component. As yet another example, other rotating or moveable components may be studied, for example, flagellar motors or F-type ATPases. Thus, for example, a nanostructure (e.g., containing one or more signaling entities) may be immobilized with respect to a component, and molecular motion of the component (e.g., rotation, rocking, bending, twisting, swiveling, linear motion, etc.) may be determined by determining motion of the nanostructure, such as discussed herein.

U.S. Provisional Patent Application Serial No. 62/442,737, filed January 5, 2017, entitled "Systems and Methods for Determining Molecular Motion," by Zhuang, et al. is incorporated herein by reference in its entirety.

The following examples are intended to illustrate certain embodiments of the present invention, but do not exemplify the full scope of the invention.

EXAMPLE 1

The following examples generally describe single molecule rotation measurements using DNA origami rotors reveal RecBCD dynamics. Single molecule methods have been indispensable for understanding motor proteins. This example introduces origami rotational beacon image tracking (ORBIT), a DNA-origami based method that allows rotational tracking of hundreds of single DNA molecules in parallel and with millisecond time resolution. Using ORBIT, the helicase activity of the RecBCD enzyme was studied. During RecBCD translocation and in the absence of any external force, backtracking and two distinct pause states was observed. The simplicity and customizable nature of this method makes high-resolution studies more accessible for a variety of motor proteins.

This example illustrates Origami Rotational Beacon Image Tracking (ORBIT), a single molecule method for high-resolution, high-throughput measurement of DNA rotation that can be used with a standard TIRF ((total internal reflection fluorescence) microscope. 3D DNA origami technology was used to assemble fluorescently labeled nanoscale rotors that amplify the rotation of a DNA duplex (Fig. 1A). The rotor design was used to reduce the timescale and magnitude of its Brownian fluctuations so as to maximize spatiotemporal resolution.

ORBIT was used to directly observe substrate binding followed by DNA unwinding activity by the DNA repair enzyme RecBCD. Origami movements were monitored in hundreds of individual complexes in parallel and with millisecond time resolution for up to several minutes. During translocation, RecBCD' s pausing and backtracking in the absence of an externally applied force was observed and quantified. Building on established approaches, DNA origami rotors were designed and prepared, each having two perpendicular 160 nm arms (See Figs. 3, 4, and 9). Six Cy3 dyes were incorporated at the tip of one of the rotor arms to allow for rotation tracking using fluorescence. AFM and gel electrophoresis of the origami samples revealed proper folding in high yield (Fig. IB). These origami structures were ligated to pieces of double stranded DNA that served as the substrate for RecBCD. The substrate-origami connection was designed to orient the DNA substrate orthogonally to the plane of the rotor, thus allowing it to function as a drive shaft. After ligation, the substrate- origami sample was purified by agarose gel electrophoresis.

To conduct ORBIT experiments, RecBCD was adsorbed onto the surface of a microscope flow chamber, free RecBCD was washed out, and then the substrate-origami was added to imaging buffer containing ATP. When presented with the double stranded break at the end of the DNA substrate, RecBCD was expected to bind and begin to unwind the duplex, resulting in a rotation of about 34.6°/bp. This rotation was amplified by the attached origami, resulting in the dyes moving along a generally circular path as the rotor spins. By tracking the movement of the fluorescent dyes, using standard fluorescence imaging methods (see below), the enzyme-driven DNA unwinding could be directly tracked.

An sCMOS camera was used to capture with sampling rates of 200-1000 Hz the binding and unwinding activity of many enzymes-substrate complexes in a single field of view. Analysis of individual fluorescence trajectories revealed many instances where the localizations displayed persistently unidirectional circular movements (Fig. 1C, D).

Processive movement was followed by a phase characterized by stalling or random

swiveling, likely due to steric hindrance or disruption of the torsionally rigid incorporation of the substrate into the origami, respectively. The diameter of these circular trajectories indicated that the origami was rotating about its center and thus that it was likely connected to the enzyme through the substrate DNA duplex (Fig. IE). The total amount of rotation of these unidirectional traces was consistent with the length of the substrate. It was found that the average rate of rotation per trace sampled a broad distribution, while the aggregate rate depended on ATP (Fig. IF). The unwinding rate under a wide range of ATP concentrations (25 to 300 micromolar) was measured, and 315 single molecule traces that met quality thresholds were obtained (see below). Fitting to Michaelis-Menten kinetic resulted in V_max = 325 +/- 7 bp/s and K_M = 155 +/- 7 micromolar.

Notably, the spatio temporal resolution of the measurements appeared to be limited not by the acquisition rate, but by the angular Brownian dynamics of the origami structure. The dynamics were theoretically estimated and experimentally measured, and the angular resolution was found to be 1.4 deg (Hz) 1/2. See also Example 4, below.

Fig. 1 illustrates that ORBIT reports on the rotation of DNA by RecBCD. Fig. 1 A is a schematic of ORBIT assay. After adding a motor protein to the microscope slide surface, the origami substrate is added. As the motor protein moves along the double stranded DNA extension, the small rotation of the duplex is amplified by the larger origami structure. The fluorescent dyes on one arm report the motion (not to scale). Fig. IB are AFM images of properly folded origami probes. Fig. 1C illustrates representative traces from three experiments, at 25 (lower curve), 75 (middle curve) and 300 (higher curve) micromolar ATP. Fig. ID illustrates traces from a single experiment, with 75 micromolar ATP and collected at 500 Hz. Traces are filtered as in Fig. 1C. Fig. IE illustrates localization positions of the fluorescent dyes during each frame of the translocation phase of an example trace. Time is indicated in the grayscale. Fig. IF illustrates the kinetics of RecBCD translocation at 23 °C. The average rate of translocation at each ATP concentration was fit to Michaelis-Menten kinetics. Error bars are standard error of the mean (s.e.m.).

Fig. 3 is a schematic of probe template and staple strands. The origami probe structure had two six -helix bundle arms. The intact arm (far left) passed through a break in the orthogonal arm (two half-length bundles). Additional helices stabilize the junction. The longer stabilizing bundle contains two staple strands that are extended beyond the origami structure (not shown here; see sequence table). The exterior portions included 14 nucleotide of complementary DNA and one staple has a 12 nucleotide overhang to allow ligation.

Fig. 4 shows a 3D rendering of the probe structure. Fig. 4A shows an origami with two six helix bundles. One of these is separated into two parts, connected with additional helices. The long arm passed through the created hole. Dyes are added using modified staple strands. Fig. 4B: the two extended staple strands (black) exit the origami structure at adjacent points in the structure, indicated here with arrows. In this image, one arm has been removed for clarity. Fig. 4C: after ligation, additional DNA extends away from the origami structure (not to scale).

Fig. 5 illustrates a different structure, having three arms, each made of a short six helix bundle motif. Some staple strands were extended with binding sites for biotin-labeled secondary oligomers for surface attachment. Figs. 6A and 6B are 3D-renderings of the base structure. Each arm is -20 nm. At the end of each arm, several staple strands are extended to create binding sites for biotin secondaries (not shown). The top black strand contains a 12 nucleotide overhang, allowing ligation to an additional DNA linker.

Fig. 7 illustrates anchored origami for characterization of Brownian dynamics fluctuations. In order to characterize the angular fluctuations of the origami probe, an origami base structure was constructed to attach the probe to the surface rigidly without an enzyme. The base was attached to a biotin-BSA coated coverslip surface using streptavidin and biotinylated secondary oligomers.

EXAMPLE 2

ORBIT, as discussed in Example 1, allowed the study the helicase activity of

RecBCD in greater detail than has been previously possible. In particular, pausing and backtracking of RecBCD have previously been reported only in the presence of the Chi sequence (pauses) or an opposing force from an optical trap. Here, frequent pausing (Fig.

2A) and backtracking (Fig. 2B) was observed during RecBCD translocation in the absence of an externally applied opposing force or regulatory sequence.

A pause finding algorithm (see below) was used to quantify the pausing and backtracking behavior of RecBCD during translocation. It was found that entry into the pause state depended on ATP concentration (Fig. 2C), but no effect of ATP was observed on the pause duration for pauses which did not show significant backtracking (Fig. 2D). While pauses became less common at high ATP values, they were observed even at 300 micromolar ATP. It was found that no effect of ATP concentration on the average backtracking distance (Fig. 2E). In contrast, after backtracking, RecBCD dwells in a paused state that showed an ATP-dependent recovery time (Fig. 2F). The ATP dependence of the post-backtracking pauses indicated that they represented a state different from the pre-backtracking pauses.

These results are summarized in the model of translocation shown in Fig. 2G, including explicitly consider only one motor domain. The ATP hydrolysis cycle can be interpreted as the leading motor or as a simplified model of both motors if coupling between motors is significant. Translocation occurs as a result of ATP binding, hydrolysis, and ADP release. While RecBCD is in the apo state, it can enter the pause state. While it is not known whether the pause entry rate is ATP dependent, competition of this transition with ATP binding can account for the apparent ATP dependence of pausing. From this pause, the enzyme may enter a backtracking state or return to the regular ATP hydrolysis cycle.

Backtracking is followed by a second pause; recovery from this pause is ATP-dependent. Two consecutive transitions are thus required to recover from backtracking: an ATP- independent transition followed by an ATP-dependent transition. Recently, large fluctuations were observed during RecBCD activity at very low ATP with an opposing force. These fluctuations are accounted for in the model: at low ATP, the enzyme more often enters a pause state, which in turn makes backtracking events more common. Additionally, application of an opposing force may make both pausing and backtracking more common.

Fig. 2 shows analysis of pausing and backtracking during RecBCD translocation. Figs. 2A and 2B are examples of pausing without and with backtracking during translocation. Pauses and backtracking events were determined using an automated algorithm (see below). Raw angle data (gray) as well as filtered (binomial filter, 40 Hz) data are shown. Fig. 2C shows the frequency of pauses per translocated base pairs is reduced at lower ATP. Fig. 2D shows the duration of pauses without backtracking does not depend on ATP concentration, indicating that recovery from this state does not require ATP. Fig. 2E shows that the backtracking distance also does not depend on ATP. Fig. 2F shows that after a backtracking event, the time required for recovery into forward translocation does depend on ATP. Fig. 2G shows a simple model of translocation. Forward translocation occurs during the ATP cycle. While in the apo state, the enzyme can enter a paused state, likely in an ATP- independent step. The observed ATP dependence can be explained by competition between entry into this state and ATP binding. The enzyme can backtrack, and, after backtracking, enter into a second pause state. This state is distinct from the first as recovery into forward translocation now requires ATP.

EXAMPLE 3

Following are various materials and methods used in the above examples. DNA Origami Preparation and Purification. DNA origami were designed using CADNano. All DNA oligomers, including origami staple strands and additional DNA linkers, were ordered from Integrated DNA Technologies (IDT). Oligomers containing dye or phosphorylation modifications and any strands being ligated were ordered with HPLC or PAGE purification. DNA staple strands and the M13mpl8 single stranded scaffold were mixed in folding buffer (10 mM Tris, pH 8.0, 1 mM EDTA, 18 mM MgCl₂ for the origami probe and 9 mM MgCl₂ for the base). 10 nM scaffold and 100 nM of most staple strands were used. A larger excess (1 micromolar) of Cy3 labeled staple strands was used. The mixtures were folded using a thermocycler. For the probe, these mixtures were held at 80 °C for 5 minutes, and annealed by cooling, first to 65 °C in 1 °C steps every 1 minute, then to 25 °C with 1 °C steps every 105 minutes.

For RecBCD experiments, the folded origami was first PEG precipitated to remove most of the free staple strands. The origami sample was mixed 1: 1 with 2x PEG precipitation buffer (15% PEG-8000, 5 mM Tris, pH 8.0, 1 mM EDTA, 500 mM NaCl), incubated 30 minutes at 4 °C, and centrifuged at 8000 g for at least 30 minutes (Stahl AngChemie 2014). The pellet was washed with lx PEG wash buffer (7.5% PEG, 10 mM Tris, pH 8.0, 1 mM EDTA, 18 mM MgCl₂). After being redissolved, the origami was ligated for 2 hours at room temperature to additional DNA extensions which served as the substrate for RecBCD using T4 DNA ligase (New England Biolabs). After treatment with Proteinase K (New England Biolabs) for 1 hour at room temperature to degrade the ligase, the origami sample was purified by agarose gel electrophoresis. Electrophoresis was performed in an ice bath with a 2% agarose gel in running buffer containing 89 mM Tris, 89 mM borate, 2 mM EDTA, and 10 mM MgCl₂. The origami band was excised from the gel and the origami extracted using a Freeze 'n' Squeeze spin column (Bio-Rad). Depending on the desired concentration, the sample was then used for single molecule imaging experiments or concentrated by PEG precipitation.

To characterize the origami dynamics, a DNA origami probe was prepared, attached via variable length linkers to the origami base. To remove excess origami extension strands, the origami were gel purified before ligation. The two origami structures and the linker were ligated together as described above. See also Example 5, below.

Origami folding was confirmed using AFM and TEM.

Single Molecule Imaging. Single molecule fluorescence imaging was conducted using a Nikon Eclipse Ti inverted microscopy body with a 60x 1.4 NA oil objective (Nikon) and a high speed scientific CMOS camera (Hamamatsu Orca- Flash 4.0 v2). The sCMOS field of view was cropped as needed to achieve high frame rates. The sample was illuminated using objective-type total internal reflection with a 1 W 532 nm laser

(CrystaLaser). Laser intensity was controlled using an acousto-optical tunable filter (Crystal Technologies). The microscope filter cube contained a dichroic (Chroma Technology Corp ZT532/640rpc-UF3) and an emission filter (Chroma Technology Corp ZET532/640m-TRF). The focus was maintained with an IR laser reflection focus lock system. An IR laser (ThorLabs) was reflected off the coverslip surface and the resulting reflections were imaged on USB camera (ThorLabs DCC 1545M). The position of the reflections depend on the focus; a z piezo stage (Prior Scientific) was used to maintain a steady focus. No x-y drift correction was applied. Each camera pixel corresponded to 160 nm in the sample plane. All experiments were done at room temperature (-23 °C). The microscope hardware was controlled with custom software written in Python.

Molecules were imaged with a flow chamber consisting of a glass coverslip (VWR, No. 1.5) attached to a slide with double sided tape. The coverslip was cleaned by sonication in 95% ethanol, rinsing in water, drying thoroughly with compressed nitrogen, and plasma cleaning under argon atmosphere (Harrick Plasma PDC-32G). Slides were drilled with two holes to facilitate buffer exchange. Between uses, slides were soaked in acetone and water, then scrubbed with a water-alconox slurry, sonicated in 1 M KOH, rinsed in water, burned with a propane torch, and plasma cleaned. After assembling the flow chambers with double sided tape and sealing the edges with epoxy, they were vacuum sealed and stored at -20 °C until use. Tubing was inserted into the slides and epoxied in place. A syringe pump (KD Scientific KDS210) was used to pull solution into the chamber.

Standard reaction buffer included 50 mM Tris at pH 7.5, 2 mM trolox, 5 mM protocatechuic acid (PCA), 10% glycerol, and 10 mM MgCl₂. Before imaging, 0.25 U/mL protocatechuate-dioxygenase (PCD; sold by OYC Americas as rPCO) was added. The

PCA/PCD system acted as an oxygen scavenger and trolox suppresses dye blinking. ATP was also added as indicated above. All imaging buffers were allowed to incubate for -10 minutes after adding PCD to allow the PCA/PCD system to remove oxygen.

RecBCD single molecule imaging. First, Cy3 labeled DNA oligomers in T50 buffer (10 mM Tris, pH 8.0, 50 mM NaCl) with 10 mM MgCl₂ added were flowed into the chamber to set the focus lock. Some slides show unusually high Cy3 spot density during this step; these were discarded. The chamber was washed with -100 microliters T50 twice. Next, RecBCD (New England Biolabs) was added to the chamber in reaction buffer. After -1 minute, the RecBCD was washed out twice with -100 microliters reaction buffer. The second wash contained PCD and the desired ATP concentration. Finally, origami was added to the slide in reaction buffer with PCD and the desired ATP concentration. Data acquisition was started immediately after the syringe pump was activated. Data was typically acquired for 3-4 minutes at 200 Hz to 1 kHz.

Image analysis. Single molecule imaging data was analyzed using a custom python code. Because each origami spot was present for only a short portion of the movie, both the position and approximate appearance and disappearance time of each spot was determined. Briefly, the movie was divided into 100-200 frame segments. Each segment was median filtered and peaks were found by looking for local maxima in intensity that were above an intensity threshold and well resolved from other peaks. Using a median filter allows origami which was diffusing in and out of the evanescent field to be ignored. Once a peak was found, it was considered active until the intensity dropped below 1.5 times the local background. Single molecule traces were extracted for each by integrating the intensity over the local region around each spot and by fitting the region to a 2D Gaussian.

The single molecule traces were further analyzed using custom Igor Pro code. In order to facilitate picking traces that show processive circular motion, a series of 2D x-y position histograms were generated for each trace. Traces which showed localizations predominantly along the rim of a circle for at least part of their duration were selected for further analysis. The x-y data was displayed as a movie to show the motion. Traces were fit to a circle and its center position was used to convert the data to polar coordinates. In order to track the circular motion, all angular steps were assumed to be less than 180°; 360° adjustments were made using an additional angular trace generated after 3 (199 and 498 Hz) or 5 (996 Hz) point median filtering the x-y data. This filtering prevents additional jumps due to a single bad fit or nearby diffusing origami.

RecBCD translocation analysis. Origami traces that showed processive motion were selected. Traces which showed no motion or rapid random fluctuations were not analyzed further; these likely were incorrectly attached to the surface (e.g. through binding of RecBCD directly to the origami), attached to inactive enzymes, or were not properly torsionally constrained due to, for example, a nick in the double stranded DNA connecting the origami to the RecBCD. In order to analyze the average kinetics, the start and stop frames of processive translocation were selected. Traces were only included in the analysis if they passed two quality filters. The radial uncertainty was largely determined by the intensity of the fluorescent spot. Only traces with a radial standard deviation below a threshold, generally 0.1 pixels or -16 nm, were considered. Second, traces were removed which showed signs of sticking to the surface during translocation by comparing the radial standard deviation (dominated by fit noise) to the angular standard deviation (dominated by Brownian dynamics). The angular standard deviation was calculated during a rolling 20 frame window and compared to the radial standard deviation over the translocation period. If the ratio between the angular and radial standard deviation was less than 1.3 for > 5% of windows during translocation, the trace was not analyzed. Typically, 10-15% of traces were removed due to possible sticking. The average rate during the translocation phase and the total angular motion were determined. Angular changes were converted to base pairs using the average DNA angular twist of 34.6°/bp. Translocation phases are shown after low pass filtering (binomial filtering with a half transmission frequency of 40 Hz).

Pausing Analysis. The traces selected for translocation analysis were subjected to an automated pause-finding algorithm. Briefly, the traces were subjected to a binomial smoothing filter using frames from a time window of 0.351 s, corresponding to a half- transmission frequency of 20 Hz, and differentiated to obtain the instantaneous velocity. Frames showing a velocity of below a threshold, kept constant for all ATP values at

498°/second (1° per frame at 498 Hz), were identified as pause frames and frames moving backwards faster than this rate were identified as backtracking. Because long pauses tended to get broken up due to short fluctuations, a second smoothing with a time window of 2 seconds (half transmission frequency 8.4 Hz) was applied; additional frames were called as pauses here using the same threshold. Smoothing tended to remove the edges of pausing so pauses were extended forward and backward until the angle moved outside of a 1 base pair window from the original pause location. Adjacent pauses at the same angular location were merged. Finally, because detection of short pauses was unreliable, any contiguous stretches of pause and backtracking frames which lasted less than 100 ms (2/half transmission frequency) were re-classified as runs. Except for calculations of the frequency of entry into the pause state, pauses were separated based on whether they contained significant backtracking, defined using a threshold of 100°. Results were similar using lower (70°) or higher (130°) thresholds.

Origami fluctuation analysis. Anchored origami traces that showed fluctuations along an arc were selected. The fluctuations of the origami were characterized under different conditions by fitting the power spectrum of the angular motion.

AFM. AFM images were obtained using an Asylum MFP-3D system (Asylum Research). A 2 microleter droplet (2 to 10 nM) of purified sample and then a 20 microliter drop of 0.5x TE + lOmM MgCl₂ + lOmM NiCl₂ solution was applied to a freshly cleaved mica surface and left for approximately 2 min. The images were taken under liquid tapping mode, with C-type triangular tips (resonant frequency, fo = 40-75 kHz; spring constant, k = 0.24 N m^"1) from the SNL-10 silicon nitride cantilever chip (Bruker Corporation).

TEM. For TEM imaging, the sample was adsorbed onto glow discharged carbon- coated TEM grids for 2 minutes and then stained for a few seconds using a 2% aqueous uranyl formate solution containing 25 mM NaOH. Imaging was performed using a JEOL JEM- 1400 TEM operated at 80 kV.

Fig. 9 illustrates DNA oligomers used for the origami rotor. DNA modifications (dye labels and phosphorylation) are included using their IDT codes. The final two strands extend outside of the origami.

Fig. 10 illustrates DNA oligomers used for the origami base. DNA modifications (dye labels and phosphorylation) are included using their IDT codes. The TTHr21 strands contain a 21 nucleotide binding site for the Hr21_5Bio biotinylated secondary strand. The final three strands form the extension from the origami for ligation and the connection for these strands to the main structure.

Fig. 11A illustrates additional DNA oligomers. The first two oligomers were used to form the standard blunt end 80 bp extension from origami after ligation. Additionally, another pairs of oligomers was used to construct the anchored origami complex to characterize the Brownian dynamics at 80 bp linker length. The strands were shorter than the corresponding final length in the complex because of the contribution of the origami extensions.

EXAMPLE 4

This example illustrates Origami-Rotor-Based Imaging and Tracking (ORBIT), which uses fluorescently labeled DNA origami rotors to track DNA rotation in real time at the single-molecule level, as an example of one embodiment of the present invention. This substantially improves spatiotemporal resolution and throughput of DNA rotation

measurements without applying a force or torque to the DNA. Using ORBIT, the rotation of DNA generated by the repair enzyme RecBCD was directly observed, providing new insights into the unwinding dynamics of the RecBCD-mediated DNA unwinding.

Because of the small width of double-stranded DNA (dsDNA), rotation-induced movements of the DNA are small, typically of a sub-nanometer scale, and easily obscured by Brownian motion. This can be overcome by attaching to the DNA molecule a fluorescently labeled amplifying rotor and then tracking the rotation of this rotor using, e.g., a light microscope. Ideally, this rotor should be sufficiently large in order to amplify the motion of the DNA, yet still display minimal hydrodynamic drag and torsional flexibility in order to minimize the obscuring effect of Brownian fluctuations. To meet these requirements, a rotor was prepared using DNA origami, a technology that allows custom 3D nanostructures to be designed and assembled with high precision, yield and reproducibility. The DNA origami approach also made it straightforward to functionalize the rotors with fluorescent dyes and to link them in a specific manner to any DNA of interest. In this design, the origami rotor had four rotor blades, each extending 80 nm perpendicular to the axis of rotation, and a short dsDNA segment emerging from the center of the rotor, which can be ligated to the dsDNA substrate of a DNA-interacting enzyme (Figs. 1A, 3, and 9). Due to the planar structure of the origami rotor, it generates a hydrodynamic drag that is substantially smaller than that of a spherically shaped bead of similar or larger radius as used in previous methods for tracking DNA rotation (see below); as a result, the origami rotor may give a substantially faster time resolution in rotation tracking. Meanwhile, the direct and rigid connection between the origami rotor and the dsDNA substrate minimizes torsional flexibility. The tip of one of the rotor blades was labeled with multiple fluorescent dye molecules (6 x Cy3), which allowed tracking of the rotor blade position with -10 nm precision at 1 ms time resolution. The assembly of the origami rotors was assessed using atomic force microscopy (AFM), which showed proper folding at high yield (Fig. IB).

The mechanical properties of the origami rotor-DNA constructs were characterized by anchoring them to a surface through a tripod-like origami-anchor structure (Figs. 5-7 and 10) and measuring the Brownian dynamics of the rotor at kHz frame rates on a scientific CMOS camera. The power spectrum of the angular movements of the rotors revealed a Lorentzian frequency response that is typical of Brownian dynamics in a harmonic potential (Fig. 12A). Based on such power spectra, the torsional stiffness of the constructs was determined as a function of DNA length (Fig. 12B) and the hydrodynamic drag of the rotors was determined as a function of solution viscosity (Fig. 12C). To estimate our rotation measurement accuracy, the measured hydrodynamic drag and torsional stiffness was used to calculate the expected angular uncertainty as a function of integration time for a DNA rotor connected to a 52-bp dsDNA (Fig. 12D). This estimate was in good agreement with the actual measurement of angular uncertainty on the same structure (Fig. 12D). These results indicated that an angular change due to a single base-pair (bp) rotation (34.6°) could be resolved with a signal- to-noise ratio of 3 using an integration time of only 20 ms (Fig. 12D). For comparison, other torque-free DNA rotation tracking methods would require an integration time of 80 ms to over an hour to achieve the same angular accuracy. To demonstrate the power of ORBIT, the activity of the DNA helicase RecBCD was studied, which was expected to generate DNA rotation as it unwinds DNA; however, due to the enzyme's extremely fast DNA unwinding rate, RecBCD-induced DNA rotation has not been directly observed, and such detection would require methods with very high temporal resolution. RecBCD is a processive helicase that detects double-stranded breaks and initiates homologous recombination in DNA. As RecBCD unwinds dsDNA, its two motors RecB and RecD should each track along one of the DNA strands, which is expected to generate a rotation of the DNA with respect to the enzyme of -34.6° per unwound base pair. To measure RecBCD-induced DNA rotation in real time, RecBCD was first anchored onto the surface of a microscope flow chamber, and then added origami rotor-dsDNA complexes in buffer containing ATP (Fig. 1A). As RecBCD binds to the double- stranded break at the end of the dsDNA substrate and begins to unwind the DNA duplex, the resulting DNA rotation should be amplified by the origami rotor and result in a persistent motion of the fluorescent dyes along a circular path. Using a TIRF microscope equipped with a scientific CMOS camera, the dye movement was captured and tracked at sampling rates of 500-1000 Hz.

As shown in the single-molecule ORBIT trajectories, the fluorescent dyes on the origami rotor indeed displayed unidirectional movements along a circle with a diameter similar to the diameter of the rotor (Fig. IE). Because of the wide-field imaging nature of ORBIT, tens to hundreds of single-molecule trajectories were collected in a single experiment. Examples of such trajectories acquired at different ATP concentrations are shown in Fig. 1G. The angular measurement can be converted into the position of RecBCD along the dsDNA substrate by using the average angular shift of 34.6° per bp, allowing measurement of the DNA unwinding rate. The unwinding rate was measured under a range of ATP concentrations (25 to 300 micromolar) at room temperature and the average rates of individual RecBCD molecules were found to exhibit a broad distribution even at the same ATP concentration (Fig. 13). This heterogeneity was consistent with previous single- molecule studies of RecBCD. Despite the heterogeneity, the ensemble-averaged unwinding rate derived from many molecules showed a clear ATP dependence (Fig. IF), which could be fitted to a Michaelis-Menten relation, yielding v_max = 325 +/- 7 bp/s and K_M = 155 +/- 7 micromolar at room temperature. These parameters were comparable to previously measured values from both bulk and single-molecule experiments, indicating that the measurement geometry did not perturb the enzyme activity.

Fig. 1 shows measurement of single-molecule DNA rotation using ORBIT, in accordance with one embodiment of the invention. Fig. 1A shows a schematic depiction of the ORBIT method. Rotation of a dsDNA segment is amplified by a DNA origami rotor and detected by tracking the position of fluorescent dyes attached to the tip of a rotor blade. To measure the rotation of DNA induced by an enzyme, the enzyme molecules are first attached to the surface of a microscope slide. DNA substrates with attached origami rotors are then added in a buffer containing ATP. Enzyme-substrate binding and subsequent DNA rotation is captured using a total internal reflection fluorescence (TIRF) microscope. Fig. IB shows AFM images of DNA origami rotors. Scale bar: 100 nm. Fig. IE shows localization trajectory of the fluorescent dyes from a single origami rotor connected to a dsDNA substrate being unwound by the RecBCD helicase. The rotation angle Θ (theta) was measured from the position of dyes along a circular path. Time is indicated by the shaded bar. Scale bar: 100 nm. Fig. 1G shows representative single-molecule DNA rotation trajectories (θ , theta vs. time) during processive unwinding by RecBCD, from three experiments at different ATP concentrations coded according to ATP concentration (25 μΜ, 75 μΜ, 300 μΜ, 3

experiments for each). The corresponding amount of DNA unwinding is given on the right axis. Fig. IF shows ATP dependence of DNA unwinding rate by RecBCD. The average rates were fit to Michaelis-Menten kinetics. Error bars indicate standard error of the mean.

Three distinct features in the processive DNA unwinding phase were observed in the single-molecule trajectories: unwinding, pausing, and backtracking (Figs. 2A and 2H).

RecBCD was previously observed to pause and backtrack under an opposing force. These results demonstrated that pausing and backtracking of RecBCD also occurs in the absence of an opposing force, but the pause durations and the backtracking distances were substantially smaller than those observed under opposing forces. Furthermore, it was observed that the pause frequency decreased with increasing ATP concentration and then plateaued at higher ATP (Fig. 2C). On the other hand, the average pause duration remained largely constant across all tested ATP concentrations (Figs. 2D and 14A), suggesting that exiting a pause requires an ATP-independent process. Pauses were followed either by resumed unwinding or by a backtracking event (i.e. rotation of DNA in the opposite direction), potentially due to rewinding of the substrate' s two DNA strands. The average backtracking distance did not appear to depend on the ATP concentration (Fig. 2E) but stayed constant at approximately 6 bp. Previous optical trap experiments have showed rapid RecBCD fluctuations on the DNA during the processive DNA unwinding phase, which may be related to the backtracking events that were observed here. The backtracking events were typically followed by a pause, which can be referred to as the recovery pause, before DNA unwinding was resumed. Interestingly, and in contrast to the above-described pauses that were not associated with backtracking, the recovery pause duration displayed a clear dependence on the ATP concentration (Figs. 2F and 14B), showing that these two types of pauses represent distinct states. Based on these result, it is suggested the following kinetic model of DNA unwinding by RecBCD (Fig. 21): During DNA unwinding, pausing occurs frequently and some of the pauses lead to enzyme backtracking; the enzyme can then exit the backtracking state and resume DNA unwinding through a recovery pause intermediate, which is distinct from the pause state entered by the enzyme during forward unwinding.

Fig. 2 shows pausing and backtracking during ATP-driven DNA unwinding by RecBCD. Figs. 2A and 2H show example single-molecule unwinding trajectories showing pausing and backtracking. Fig. 2C shows the dependence of the pause frequency on the ATP concentration. The pause frequency is determined both as the number of pauses per kilo base pairs (kbp) and the number of pauses per second (s). Fig. 2D shows the ATP dependence of the duration of pauses that were not associated with backtracking. Fig. 2E shows the ATP dependence of the backtracking distance. Fig. 2F shows the ATP dependence of the recovery pause duration after a backtracking event. Fig. 21 shows a schematic of a kinetic model of RecBCD-induced DNA unwinding.

To summarize, this example shows the development of ORBIT, a high-throughput, high-resolution method for tracking rotational motion at the single-molecule level, in accordance with one embodiment of the present invention. ORBIT was applied to track DNA rotation and study the processive helicase activities of RecBCD on DNA substrates. The unwinding, pausing and backtracking phases in real time during RecBCD-induced DNA unwinding was directly observed. The kinetics and ATP dependence of each phase was quantified, revealed two different types of pause states. Due to the flexibility of the origami design, the structural properties of the origami rotors can be designed and tuned to suit specific applications as needed, and the rotation tracking capabilities can be realized using a standard fluorescence microscope. Thus embodiments such as ORBIT may allow high- resolution single-molecule studies of a variety of DNA-processing enzymes.

EXAMPLE 5

Following are various materials and methods used in the above examples.

DNA origami preparation and purification. DNA origami rotors (Figs. 4, 5, and 10) and anchors (Figs. 6-8 and 11) were designed using CADNano. All DNA oligomers, including origami staple strands and additional DNA linkers, were ordered from Integrated DNA Technologies (IDT). All origami structures contained extension strands with single- stranded DNA (ssDNA) overhangs for ligation to additional DNA. Oligomers containing dye, phosphorylation, or biotinylation modifications and any strands being ligated were ordered with HPLC or PAGE purification. DNA staple strands (Figs. 10 and 11) and the M13mpl8 viral DNA (single-stranded, New England Biolabs) used as the scaffold were mixed in folding buffer (10 mM Tris, pH 8.0, 1 mM EDTA, 18 mM MgCl₂ for the origami rotor and 9 mM MgCl₂ for the anchor). The concentration of DNAs were 10 nM for the scaffold strand and 100 nM for the unlabeled staple strands, and 0.5 to 1 micromolar for the Cy3-labeled staple strands. The mixtures were incubated and annealed using a thermocycler. For the origami rotor, these mixtures were held at 80 °C for 5 minutes, and annealed by cooling, first to 65 °C in 1 °C steps every 5 minutes, then to 25 °C with 1 °C steps every 20 minutes. The origami anchor was folded by heating to 80 °C for 5 minutes, and annealed by cooling, first to 65 °C in 1 °C steps every 1 minute, then to 25 °C with 1 °C steps every 105 minutes.

For RecBCD experiments, the folded origami rotors were first PEG precipitated to remove most of the free staple strands. The origami sample was mixed 1: 1 with 2x PEG precipitation buffer (15% PEG-8000, 5mM Tris, pH 8.0, 1 mM EDTA, 500 mM NaCl), incubated 30 minutes at 4 °C, and centrifuged at 8000g for at least 30 minutes. The pellet was washed with lx PEG wash buffer (7.5% PEG, 10 mM Tris, pH 8.0, 1 mM EDTA, 18 mM MgCl₂). After being resuspended in T4 ligation buffer, the short extension strands were ligated to longer DNA oligomers (Table 1 IB) using T4 DNA ligase (New England Biolabs) for 2 hours at room temperature. This double- stranded DNA (dsDNA) served as the substrate for RecBCD unwinding activity. The reaction mixture was treated with Proteinase K (New England Biolabs) for 1 hour at room temperature to degrade the ligase and the origami sample was purified by agarose gel electrophoresis. Electrophoresis was performed with a 2% agarose gel in an ice bath in running buffer containing 89 mM Tris, 89 mM borate, 2 mM EDTA, and 10 mM MgCl₂. The origami band was excised from the gel and the origami extracted using a freeze 'n' squeeze spin column (Bio-Rad) by spinning at 1000 g for 60 minutes. Depending on the desired concentration, the sample was then directly used for single molecule imaging experiments or first concentrated by PEG precipitation as described above.

To characterize the angular resolution of the rotor due to the Brownian fluctuations, a complex was prepared with a DNA origami rotor attached to the origami anchor via variable length dsDNA linkers (Fig. 7). To remove excess origami extension strands, the origami structures were gel purified before ligation. The two origami structures were ligated together as described above. The length of the linker DNA between the two origami structures included the 14 base pairs (bp) extending from the origami rotor (Fig. 5D), 26 bp on the origami anchor (Figs. 5-7), 12 nucleotides (nt) of ssDNA overhang on both structures, and any additional DNA added between the two origami. For the shortest DNA linker length, 52 bp, the linker was entirely of DNA present on the rotor and anchor structures (Figs. 9-11). The two longer lengths used additional dsDNA linkers in the ligation reaction (Fig. 1 IB). These were either purchased from IDT (92 bp) and annealed prior to ligation or prepared by PCR and dU excision (163 bp). In the latter case, the DNA was prepared using PCR with PfuTurbo Cx Hotstart DNA Polymerase (Agilent) and primers with a dU base 12 nt from their 5' ends (Fig. 11B). Following purification on a column (Zymo DCC-100), the product's dU bases were excised with the USER enzyme system (New England Biolabs) to create 12 nt overhangs for ligation with the rotor and anchor structures and then the ligation products were again purified.

AFM imaging. AFM images were obtained using an Asylum MFP-3D system (Asylum Research) at the Center for Nanoscale Systems at Harvard University. A 2 microliter droplet of purified sample (low nM concentration) and then a 20 microliter drop of 0.5x TE + lOmM MgCl₂ + lOmM NiCl₂ solution was applied to a freshly cleaved mica surface and left for approximately 2 min. The images were taken under liquid tapping mode, with C-type triangular tips (resonant frequency, fo = 40-75 kHz; spring constant, k = 0.24 N m^"1) from the SNL-10 silicon nitride cantilever chip (Bruker Corporation).

TEM imaging. For TEM imaging, sample was adsorbed onto glow discharged carbon-coated TEM grids for 2 minutes and then stained for a few seconds using a 2% aqueous uranyl formate solution containing 25 mM NaOH. Imaging was performed at the Center for Nanoscale Systems at Harvard University using a JEOL JEM- 1400 TEM operated at 80 kV.

Single molecule imaging. Single molecule fluorescence imaging was conducted using a Nikon Eclipse Ti inverted microscopy body with a 60x 1.4 NA oil objective (Nikon) and a high speed scientific CMOS camera (Hamamatsu Orca- Flash 4.0 v2). The sCMOS field of view was cropped as needed to achieve high frame rates. The sample was illuminated using objective-type total internal reflection with a 1 W 532 nm laser (CrystaLaser). Laser intensity was controlled using an acousto-optical tunable filter (Crystal Technologies). The microscope filter cube contained a dichroic (Chroma Technology Corp ZT532/640rpc-UF3) and an emission filter (Chroma Technology Corp ZET532/640m-TRF). The focus was maintained with an IR laser reflection focus lock system. Each camera pixel corresponded to 160 nm in the sample plane. All experiments were done at room temperature (-23 ^C). The microscope hardware was controlled with custom software written in Python.

Molecules were imaged in a flow chamber consisting of a glass coverslip (VWR, No. 1.5) attached to a microscope slide with double sided tape. Slides were drilled with two holes to facilitate buffer exchange. The coverslip was cleaned by sonication in 95% ethanol, rinsing in water, drying thoroughly with compressed nitrogen, and plasma cleaning under argon atmosphere (Harrick Plasma PDC-32G). Between uses, slides were soaked in acetone and water to facilitate flow chamber disassembly, then scrubbed with a water-alconox slurry, sonicated in 1 M KOH, rinsed in water, burned with a propane torch, and plasma cleaned. After assembling the flow chambers with double sided tape and sealing the edges with epoxy, they were vacuum sealed until use to prevent dust accumulation. Tubing was inserted into the slides and epoxied in place. A syringe pump (KD Scientific KDS210) was used to pull solution into the chamber.

Standard reaction buffer included 50 mM Tris at pH 7.5, 2 mM trolox, 5 mM protocatechuic acid (PCA), 10% glycerol, and 10 mM MgCl₂. Before imaging, 0.25 U/mL protocatechuate-dioxygenase (PCD; sold by OYC Americas as rPCO) was added. The PCA/PCD system acts as an oxygen scavenger and trolox suppresses dye blinking. ATP (Affymetrix) was also added when indicated in the text. PCD was added -10 minutes before imaging to allow the PCA/PCD system to remove oxygen.

Single molecule imaging of RecBCD -induced DNA unwinding. After setting the microscope focus lock, 300 units/mL RecBCD (New England Biolabs) in reaction buffer was added to the chamber to attach some RecBCD molecules to the slide surface. After -1 minute, the unbound RecBCD was washed out twice with -100 microliters of reaction buffer. The second wash contained PCD and the desired ATP concentration. Finally, the origami- dsDNA substrate complex was added to the chamber in reaction buffer with PCD and the desired ATP concentration by pulling the buffer through the flow chamber using a syringe pump. Data acquisition was started immediately after the syringe pump was activated. Data was typically acquired for 3-4 minutes at 500 Hz - 1 kHz.

Image analysis Single molecule imaging data was analyzed using a custom Python code. Because each origami spot was present for only a short portion of the movie, both the position and approximate appearance and disappearance time of each spot was determined. Briefly, the movie was divided into 100-200 frame segments. Each segment was median filtered and peaks were found by looking for local maxima in intensity that were above an intensity threshold and well resolved from other peaks. Using a median filter allowed us to ignore origami which were diffusing in and out of the evanescent field. Once a peak was found, it was considered active until the intensity dropped below 1.5 times the local background. Single molecule trajectories were constructed by integrating the intensity over the local region around each spot and by fitting the region to a 2D Gaussian. The Python code is available at https://github.com/altheimerb/python-sma/.

The single molecule trajectories were further analyzed using custom code in Igor Pro. Because the single-molecule trajectories showed localizations predominantly along the rim of a circle, the localization positions were fit to a circle and the center position of the circle was used to convert the (x,y) positions to polar coordinates.

RecBCD unwinding analysis. Origami trajectories that showed processive unwinding motion were selected for further analyses. Trajectories which showed no motion (likely due to binding of RecBCD directly to the DNA origami rotor rather than the dsDNA linker) or rapid random fluctuations (likely due to nicked dsDNA linkers) were not analyzed further. High localization precision is required for high-accuracy rotational tracking. Radial variance (localization variance in the radial direction orthogonal to the circular path) was used, which was largely determined by the photon number from the fluorescent spot in each frame, as a measure of the localization precision and included only trajectories with a localization precision better than 16 nm (0.1 pixels) in the analysis of unwinding. In these traces, the angular noise of the origami rotor trajectories was dominated by the Brownian dynamics, which was substantially larger than the localization precision measured by the radial variance. A small fraction of traces (<10%) showed periods when the angular motion of the origami was comparable to the localization precision, likely due to interactions with the surface, and were excluded from further analysis. Pauses during DNA unwinding, on the other hand, showed angular fluctuations matching the expected Brownian dynamics. Angular changes were converted to base pairs using the average DNA angular twist of 34.6°/bp. It is noted that although the above selection criteria were applied to select high-quality traces for analysis, the biological results (e.g. the average DNA unwinding rate) that were obtained did not depend significantly on the selection criteria.

RecBCD pausing analysis. An automated pause-finding algorithm was used to identify pauses in the single-molecule unwinding trajectories. Briefly, the trajectories were subjected to a 20 Hz half-transmission frequency binomial smoothing filter, and time derivatives of the trajectory were than used to determine the instantaneous velocity. Frames showing a velocity of below a threshold (1° per frame at 500 Hz), were identified as pause frames and frames moving backwards faster than this rate were identified as potential backtracking frames. Because long pauses tended to get broken up due to short fluctuations, a second, 8.4 Hz, binomial smoothing was applied and additional frames were called as pauses here using the same threshold. Since smoothing tends to blur the edges of the pausing phase, pauses were extended forward and backward until the angle in the raw data moved outside of a 1 bp window from the pause location. Adjacent pauses at the same angular location were merged. Because of signal fluctuations, only pauses that lasted at least 100 ms as real pauses and backtracks that lasted at least 100 ms (including pre-backtracking pause and recovery pause) and exhibited a minimum of 100° (3 bp) backward motion as real backtracks were considered.

Brownian dynamics characterization. Origami rotor-anchor complexes (Fig. 7) were attached to cleaned glass coverslips using biotinylated BSA and streptavidin. These were imaged in RecBCD reaction buffer or a similar buffer without glycerol at 1500 Hz or 3000 Hz. Localization trajectories were determined in a similar fashion to the RecBCD analysis described above. Localization positions were fit to a circle and the center position was used to convert the (x,y) positions to polar coordinates A power spectrum was generated from each angular trajectory by determining the squared magnitude of the Fourier transform of the rotor angle. The power spectrum, P(f), was fit to a model of the observed Brownian noise taking into account motion blur and aliasing and the frequency-independent contribution of localization error,

where ke is Boltzmann' s constant, is the temperature, γ (gamma) is the rotor' s viscous drag, K (kappa) is the system's spring constant, /_s is the camera frame rate, and ε (epsilon) is the contribution of localization error. The contribution of localization error was fixed for each trajectory based on the trajectory' s radial variance. The radial variance was converted to an angular equivalent using the radius of the arc of localizations.

Figs 3 and 4 show origami rotor design. Fig. 4 shows a routing diagram. The origami rotor structure has two 160 nm arms. The intact arm (a six -helix bundle) passes through a break in the orthogonal arm (two half-length six-helix bundles). Additional helices stabilize the junction. Two of these helices contain staple strands (black) that are extended beyond the origami structure (extension not shown; see Figs. 5D and 10). The portion of these strands extending from the origami has 14 bp of complementary DNA and a single 12 nt overhang on one staple for ligation. Six staples within 14 nm of the end of the intact arm are labeled with Cy3 at their 3' ends. Fig. 4A shows a 3D rending of the rotor design. Fig. 4D shows two staple strands are extended from the center of the structure, forming a 14 bp double stranded region and a 12 nt overhang on one strand for ligation. Fig. 4E shows that the overhang is ligated to a longer piece of dsDNA, which serves as the substrate of RecBCD.

Figs. 5-7 show origami anchor design. Fig. 5 shows a routing diagram. The origami anchor structure has three 20 nm arms, each made of a short six-helix bundle motif. Several staple strands were extended with binding sites for biotin-labeled secondary oligomers for surface attachment (Fig. 11). From the center of the structure, three strands (black) were used to make an adaptor to allow ligation to additional DNA. Following the final strand crossover, the adaptor consists of 26 bp of dsDNA followed by a 12 nt ssDNA overhang. Figs. 6A and 6B show 3D renderings of the origami anchor structure. Fig. 7 shows a surface anchored origami structure used for characterizing the Brownian dynamics. The origami rotor, anchor, and a dsDNA linker (as needed), were ligated together. The origami anchor is attached to the microscope surface using multiple biotin tags (not shown).

Fig. 12 shows characterization of the Brownian dynamics of the origami rotor using the origami rotor-anchor complex. Fig. 12A shows a power spectrum showing the thermal Brownian noise in the angular position of the rotor attached to the anchor by 52 bp of dsDNA. Line shows the modified Lorentzian fit, as described above (Eq. S I). Fig. 12B shows the dependence of the inverse of the torsional stiffness on the length of DNA between the rotor and origami. Line shows linear fit. Fig. 12C shows the dependence of the hydrodynamic drag of the origami rotor on the viscosity of the buffer. The drag of the origami rotor connected by a 92-bp dsDNA to the anchor was determined in 0%, 10% and

25% glycerol. The buffer viscosity was determined from the glycerol concentration. Fig. 12D shows the standard deviation of the angular positions of the rotor as a function of integration time. Lines show the measurement of a single rotor connected to the anchor with a 52-bp dsDNA tracked at 3 kHz, and the predicted precision using the parameters (stiffness = 7.77 pN nm rad^"1, drag = 4.60 fN nm s) derived from the measurements of multiple rotors with 52- bp dsDNA connecting the rotor to the surface anchor. The upper and lower dashed lines correspond to the single base-pair rotation angle (34.6°) and 1/3 of single base-pair rotation angle, respectively, and the crossing points of these lines with the standard deviation vs. integration time curve give the integration times required for detection of single base-pair rotation with a signal-to-noise ratio of 1 and 3, respectively.

Fig. 13 shows histograms of the average unwinding rate of individual molecules at various ATP concentrations. (Fig. 13A) 25 micromolar ATP. (Fig. 13B) 50 micromolar ATP. (Fig. 13C) 75 micromolar ATP. (Fig. 13D) 150 micromolar ATP. (Fig. 13E) 300 micromolar ATP.

Fig. 14 shows pause duration characterization at various ATP concentrations. Fig. 14A shows the cumulative pause duration distributions for pauses not associated with backtracking. Fig. 14B shows the cumulative distributions of post-backtracking recovery pause durations.

Fig. 9 shows DNA oligomers used for the origami rotor. DNA modifications (Cy3 dye labels and phosphorylation) are included using their IDT codes. The final two strands extend outside of the origami. They have 14 nt of complementarity (underlined) followed by a 12 nt single stranded overhang (bold) for ligation to additional DNA (Fig. 11B).

Fig. 10 shows DNA oligomers used for the origami anchor. DNA modifications

(biotinylation and phosphorylation) are included using their IDT codes. The six strands ending in 'TTHr21' contain a 21 nt binding site (underlined) for the Hr21_5Bio biotinylated secondary strand. The final three strands form the adaptor for ligating additional DNA to the anchor using the 12 nt overhang (bold). Two regions of complementarity between these adaptor strands are indicated in italics and bold/underlined. Note Anchor_Ext0_oh by is replaced in Anchor_ExtO_oh_direct (Fig. 1 IB) for the anchor-rotor complex linker by a 52- bp dsDNA.

Fig. 11B shows additional DNA oligomers. DNA modifications (phosphorylation) are included using their IDT codes. Sample descriptions indicate the final linker duplex DNA length after ligation. This length includes contributions from one or both origami structures (14 bp for the origami rotor, 26 bp for the origami anchor, and a 12 nt overhang on each).. The strands for 80- and 92-bp duplexes are annealed prior to ligation to the origami structure(s). The primers used to generate the 163-bp DNA linker between the origami rotor and anchor contained dU bases. One strand of the PCR product for the 163-bp linker is shown prior to dU excision of the nucleotides shown in underlining, which created the 12-nt ssDNA overhang required for ligation to the origami structures. The other strand also contains a dU base to create ssDNA overhangs on each end. To generate the origami anchor- rotor complex with a 52-bp linker, strand Anchor_Ext0_oh (Fig. 10) in the anchor folding reaction was replaced with Anchor_ExtO_oh_direct. For this sample, no additional DNA was required to connect the rotor and anchor. Overhangs for ligation to the origami rotor or anchor are shown in italics and bases complementary to Anchor_Extl (Fig. 10) are in bold.

While several embodiments of the present invention have been described and illustrated herein, those of ordinary skill in the art will readily envision a variety of other means and/or structures for performing the functions and/or obtaining the results and/or one or more of the advantages described herein, and each of such variations and/or modifications is deemed to be within the scope of the present invention. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and/or configurations will depend upon the specific application or applications for which the teachings of the present invention is/are used. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific embodiments of the invention described herein. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, the invention may be practiced otherwise than as specifically described and claimed. The present invention is directed to each individual feature, system, article, material, kit, and/or method described herein. In addition, any combination of two or more such features, systems, articles, materials, kits, and/or methods, if such features, systems, articles, materials, kits, and/or methods are not mutually inconsistent, is included within the scope of the present invention.

In cases where the present specification and a document incorporated by reference include conflicting and/or inconsistent disclosure, the present specification shall control. If two or more documents incorporated by reference include conflicting and/or inconsistent disclosure with respect to each other, then the document having the later effective date shall control.

All definitions, as defined and used herein, should be understood to control over dictionary definitions, definitions in documents incorporated by reference, and/or ordinary meanings of the defined terms.

The indefinite articles "a" and "an," as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean "at least one."

The phrase "and/or," as used herein in the specification and in the claims, should be understood to mean "either or both" of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases. Multiple elements listed with "and/or" should be construed in the same fashion, i.e., "one or more" of the elements so conjoined. Other elements may optionally be present other than the elements specifically identified by the "and/or" clause, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, a reference to "A and/or B", when used in conjunction with open-ended language such as "comprising" can refer, in one embodiment, to A only (optionally including elements other than B); in another embodiment, to B only (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc.

As used herein in the specification and in the claims, "or" should be understood to have the same meaning as "and/or" as defined above. For example, when separating items in a list, "or" or "and/or" shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as "only one of or "exactly one of," or, when used in the claims, "consisting of," will refer to the inclusion of exactly one element of a number or list of elements. In general, the term "or" as used herein shall only be interpreted as indicating exclusive alternatives (i.e. "one or the other but not both") when preceded by terms of exclusivity, such as "either," "one of," "only one of," or "exactly one of."

As used herein in the specification and in the claims, the phrase "at least one," in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase "at least one" refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, "at least one of A and B" (or, equivalently, "at least one of A or B," or, equivalently "at least one of A and/or B") can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another

embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc. When the word "about" is used herein in reference to a number, it should be understood that still another embodiment of the invention includes that number not modified by the presence of the word "about."

It should also be understood that, unless clearly indicated to the contrary, in any methods claimed herein that include more than one step or act, the order of the steps or acts of the method is not necessarily limited to the order in which the steps or acts of the method are recited.

In the claims, as well as in the specification above, all transitional phrases such as "comprising," "including," "carrying," "having," "containing," "involving," "holding," "composed of," and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases "consisting of and "consisting essentially of shall be closed or semi-closed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03.

Claims

is claimed is:

A composition, comprising:

a surface;

a DNA strand immobilized relative to and extending away from the surface; an arm attached to and extending away from the DNA strand; and a signaling entity attached to the arm.

2. The composition of claim 1, wherein the DNA strand is double-stranded.

3. The composition of any one of claims 1 or 2, wherein the signaling entity is attached to the arm at a first point of attachment, and the DNA strand is attached to the arm at a second point of attachment at least 25 nm away from the first point of attachment.

4. The composition of claim 3, wherein the second point of attachment is at least 50 nm away from the first point of attachment.

5. The composition of any one of claims 3 or 4, wherein the second point of attachment is at least 100 nm away from the first point of attachment.

6. The composition of any one of claims 3-5, wherein the distance between the first point of attachment and the second point of attachment varies from the mean distance by no more than 20%.

7. The composition of any one of claims 3-6, wherein the distance between the first point of attachment and the second point of attachment varies from the mean distance by no more than 10%.

8. The composition of any one of claims 1-7, wherein the signaling entity is fluorescent.

9. The composition of any one of claims 1-8, wherein the composition comprises at least two signaling entities.

10. The composition of any one of claims 1-9, wherein the composition comprises at least five signaling entities.

11. The composition of any one of claims 9 or 10, wherein the at least two signaling

entities are substantially aligned relative to each other.

12. The composition of any one of claims 9-11, wherein at least two of the signaling

entities are distinguishable.

13. The composition of any one of claims 1-12, wherein the arm is rigid.

14. The composition of any one of claims 1-13, wherein the arm varies from the mean length of the arm by no more than 20%.

15. The composition of any one of claims 1-14, wherein the arm varies from the mean length of the arm by no more than 10%.

16. The composition of any one of claims 1-15, wherein the arm has a length of at least 25 nm.

17. The composition of any one of claims 1-16, wherein the arm has a length of at least 100 nm.

18. The composition of any one of claims 1-17, wherein the arm has a length of at least 500 nm.

19. The composition of any one of claims 1-18, wherein the arm comprises a DNA

origami structure.

20. The composition of claim 19, wherein the DNA origami structure is substantially rotationally symmetric.

21. The composition of any one of claims 19 or 20, wherein the DNA origami structures comprises a 6-helix bundle.

22. The composition of any one of claims 19-21, wherein the DNA origami structure comprises a plurality of arms extending away from the DNA strand.

23. The composition of claim 22, wherein the DNA origami structure comprises two arms extending away from the DNA strand.

24. The composition of any one of claims 22 or 23, wherein the DNA origami structure comprises four arms extending away from the DNA strand.

25. The composition of any one of claims 22-24, wherein the DNA origami structure comprises six arms extending away from the DNA strand.

26. The composition of any one of claims 22-25, wherein two or more of the arms each comprises a signaling entity attached thereto.

27. The composition of any one of claims 22-26, wherein at least some of the arms each comprises a signaling entity attached thereto.

28. The composition of claim 27, wherein the signaling entities are rotationally

symmetrically distributed on the arms.

29. The composition of any one of claims 1-28, wherein the DNA strand is attached

directly to the surface.

30. The composition of any one of claims 1-29, wherein the DNA strand is immobilized relative to the surface via a protein.

31. The composition of claim 30, wherein the protein is immobilized relative to the

surface, and the DNA strand is immobilized relative to the protein.

32. The composition of any one of claims 30 or 31, wherein the protein is an enzyme.

33. The composition of claim 32, wherein the enzyme recognizes the DNA strand as a substrate.

34. The composition of any one of claims 32 or 33, wherein the enzyme is able to rotate the DNA strand.

35. The composition of any one of claims 1-34, wherein the DNA strand is immobilized relative to the surface via a second DNA origami nano structure.

36. The composition of any one of claims 1-35, further comprising an agent bound to the DNA strand.

37. The composition of claim 36, wherein the agent is an enzyme.

38. The composition of claim 37, wherein the enzyme is Cas9.

39. The composition of claim 37, wherein the enzyme is RecA.

40. The composition of claim 36, wherein the agent is suspected to be an anticancer drug.

41. The composition of claim 36, wherein the agent is a DNA-binding protein.

42. The composition of claim 36, wherein the agent is a DNA-binding compound.

43. The composition of claim 36, wherein the agent has a molecular weight of less than 2000 Da.

44. The composition of claim 36, wherein the agent is a compound that alters a physical property of DNA.

45. The composition of claim 36, wherein the agent is an intercalating agent.

46. The composition of any one of claims 1-45, wherein the surface comprises glass.

47. A composition, comprising:

a surface;

a molecular component immobilized relative to and extending away from the surface;

an arm attached to and extending away from the molecular component; and a signaling entity attached to the arm.

48. A method, comprising:

exposing an agent to a component immobilized relative to a surface at a point of attachment and exhibiting a first molecular motion, wherein upon interaction of the agent with the component, the component exhibits a second molecular motion distinguishable from the first molecular motion; and

determining motion and/or a position of a nanostructure attached to and extending away from the component to determine the first molecular motion and the second molecular motion.

49. The method of claim 48, wherein the component comprises a DNA strand.

50. The method of any one of claims 48 or 49, wherein the component comprises an RNA strand.

51. The method of any one of claims 48-50, wherein the component comprises a PNA strand.

52. The method of any one of claims 48-51, wherein the agent is able to bind to the

component.

53. The method of any one of claims 48-52, wherein the nanostructure comprises a DNA origami structure.

54. The method of any one of claims 48-53, wherein the nanostructure extends away from the component by at least 25 nm.

55. The method of any one of claims 48-54, wherein the nanostructure is attached to the component at a point of attachment.

56. The method of claim 55, wherein the nanostructure is substantially rotationally

symmetric about the point of attachment.

57. The method of any one of claims 48-56, wherein the nanostructure comprises an arm attached to and extending away from the component.

58. The method of claim 57, wherein the nanostructure comprises a plurality of arms attached to and extending away from the component.

59. The method of any one of claims 57-58, wherein the nanostructure comprises at least two arms attached to and extending away from the component.

60. The method of any one of claims 48-59, comprising determining motion of the

nanostructure by determining motion of a signaling entity attached to the

nanostructure.

61. The method of claim 60, wherein the signaling entity is fluorescent

62. The method of any one of claims 60 or 61, comprising determining motion of the nanostructure by determining motion of a plurality of signaling entities attached to the nanostructure.

63. The method of claim 62, wherein at least some of the plurality of signaling entities are distinguishable.

64. The method of claim 63, comprising exposing the agent to a plurality of components immobilized relative to a surface and determining molecular motion of the plurality of components by determining motion of a plurality of signaling entities each attached to a nanostructure, the nanostructures attached to and extending away from the components.

65. The method of claim 64, wherein at least some of the nanostructures comprise distinguishable signaling entities.

66. The method of claim 65, further comprising determining a nanostructure of the plurality of nanostructures by determining the signaling entities attached to the nanostructure.

67. The method of any one of claims 48-66, wherein the first and second molecular motions are rotation of the component.

68. The method of any one of claims 48-67, wherein the first and second molecular motions are twisting of the component.

69. The method of any one of claims 48-68, wherein the first and second molecular motions are bending of the component.

70. The method of any one of claims 48-69, wherein the component is immobilized relative to the surface via a protein.

71. The method of claim 70, wherein the protein is immobilized relative to the surface, and the component is immobilized relative to the protein.

72. The method of any one of claims 70 or 71, wherein the protein is an enzyme.

73. The method of claim 72, wherein the enzyme recognizes the component as a

substrate.

74. The method of any one of claims 72 or 73, wherein the enzyme is able to rotate the component.

75. The method of any one of claims 48-74, wherein the component is immobilized relative to the surface via a second DNA origami nanostructure.

76. The method of any one of claims 48-74, wherein the agent is an enzyme.

77. The method of claim 76, wherein the enzyme is Cas9.

78. The method of claim 76, wherein the enzyme is RecA.

79. The method of any one of claims 48-78, wherein the agent is suspected to be an

anticancer drug.

80. The method of any one of claims 48-79, wherein the agent is a DNA-binding protein.

81. The method of any one of claims 48-80, wherein the agent is an intercalating agent.

82. The method of any one of claims 48-81, further comprising determining a

modification to the component based on the motion and/or position of the

nano structure.

83. The method of claim 82, wherein the modification comprises covalent modification.

84. The method of any one of claims 82 or 83, wherein the modification comprises non- covalent modification.

85. The method of any one of claims 82-84, wherein the modification is caused by the agent.

86. The method of any one of claims 48-85, further comprising determining damage to the component based on the motion and/or position of the nanostructure.

87. The method of claim 86, wherein the damage comprises a nick.

88. The method of claim 86, wherein the damage comprises a gap.

89. A method, comprising:

determining molecular motion of a nanostructure attached to a species immobilized relative to a surface, wherein the nanostructure amplifies molecular motion of the species to produce the molecular motion of a nanostructure.