Modeling the mechanical properties of DNA nanostructures

Mechanical properties of DNA and DNA nanostructures: comparison of atomistic, Martini and oxDNA models

The flexibility and stiffness of small DNA molecules play a fundamental role ranging from several biophysical processes to nano-technological applications. Here, we estimate the mechanical properties of short double-stranded DNA (dsDNA) with lengths ranging from 12 base-pairs (bp) to 56 bp, paranemic crossover (PX) DNA and hexagonal DNA nanotubes (DNTs) using two widely used coarse-grained models - Martini and oxDNA. To calculate the persistence length (Lp) and the stretch modulus (γ) of the dsDNA, we incorporate the worm-like chain and elastic rod model, while for the DNTs, we implement our previously developed theoretical framework. We compare and contrast all of the results with previously reported all-atom molecular dynamics (MD) simulations and experimental results. The mechanical properties of dsDNA (Lp ∼ 50 nm, γ ∼ 800-1500 pN), PX DNA (γ ∼ 1600-2000 pN) and DNTs (Lp ∼ 1-10 μm, γ ∼ 6000-8000 pN) estimated using the Martini soft elastic network and oxDNA are in very good agreement with the all-atom MD and experimental values, while the stiff elastic network Martini reproduces values of Lp and γ which are an order of magnitude higher. The high flexibility of small dsDNA is also depicted in our calculations. However, Martini models proved inadequate to capture the salt concentration effects on the mechanical properties with increasing salt molarity. oxDNA captures the salt concentration effect on the small dsDNA mechanics. But it is found to be ineffective for reproducing the salt-dependent mechanical properties of DNTs. Also, unlike Martini, the time evolved PX DNA and DNT structures from the oxDNA models are comparable to the all-atom MD simulated structures. Our findings provide a route to study the mechanical properties of DNA and DNA based nanostructures with increased time and length scales and has a remarkable implication in the context of DNA nanotechnology.

Absolute and arbitrary orientation of single-molecule shapes

DNA origami is a modular platform for the combination of molecular and colloidal components to create optical, electronic, and biological devices. Integration of such nanoscale devices with microfabricated connectors and circuits is challenging: Large numbers of freely diffusing devices must be fixed at desired locations with desired alignment. We present a DNA origami molecule whose energy landscape on lithographic binding sites has a unique maximum. This property enabled device alignment within 3.2° on silica surfaces. Orientation was absolute (all degrees of freedom were specified) and arbitrary (the orientation of every molecule was independently specified). The use of orientation to optimize device performance was shown by aligning fluorescent emission dipoles within microfabricated optical cavities. Large-scale integration was demonstrated with an array of 3456 DNA origami with 12 distinct orientations that indicated the polarization of excitation light.

Insights into the Structure and Energy of DNA Nanoassemblies

Since the pioneering work of Ned Seeman in the early 1980s, the use of the DNA molecule as a construction material experienced a rapid growth and led to the establishment of a new field of science, nowadays called structural DNA nanotechnology. Here, the self-recognition properties of DNA are employed to build micrometer-large molecular objects with nanometer-sized features, thus bridging the nano- to the microscopic world in a programmable fashion. Distinct design strategies and experimental procedures have been developed over the years, enabling the realization of extremely sophisticated structures with a level of control that approaches that of natural macromolecular assemblies. Nevertheless, our understanding of the building process, i.e., what defines the route that goes from the initial mixture of DNA strands to the final intertwined superstructure, is, in some cases, still limited. In this review, we describe the main structural and energetic features of DNA nanoconstructs, from the simple Holliday junction to more complicated DNA architectures, and present the theoretical frameworks that have been formulated until now to explain their self-assembly. Deeper insights into the underlying principles of DNA self-assembly may certainly help us to overcome current experimental challenges and foster the development of original strategies inspired to dissipative and evolutive assembly processes occurring in nature.

Coarse-grained modelling of the structural properties of DNA origami

We use the oxDNA coarse-grained model to provide a detailed characterization of the fundamental structural properties of DNA origami, focussing on archetypal 2D and 3D origami. The model reproduces well the characteristic pattern of helix bending in a 2D origami, showing that it stems from the intrinsic tendency of anti-parallel four-way junctions to splay apart, a tendency that is enhanced both by less screened electrostatic interactions and by increased thermal motion. We also compare to the structure of a 3D origami whose structure has been determined by cryo-electron microscopy. The oxDNA average structure has a root-mean-square deviation from the experimental structure of 8.4 Å, which is of the order of the experimental resolution. These results illustrate that the oxDNA model is capable of providing detailed and accurate insights into the structure of DNA origami, and has the potential to be used to routinely pre-screen putative origami designs and to investigate the molecular mechanisms that regulate the properties of DNA origami.

Binary control of enzymatic cleavage of DNA origami by structural antideterminants

Controlling DNA nanostructure interaction with protein is essential in developing nanodevices with programmable function, reactivity, and stability for biological and medical applications. Here, we show that the sequence-specific action of restriction endonucleases towards sharp triangular or rectangular DNA origami exhibits a novel, binary ‘on/off’ behaviour, as canonical recognition sites are either essentially fully reactive, or strongly resistant to enzymatic cutting. Moreover, introduction of structural defects in the sharp triangle can activate an otherwise unreactive site, with a site-to-defect distance of ∼50 nm. We argue that site reactivity is dependent upon programmable, mechanical coupling in the two-dimensional DNA origami, with specific structural elements, including DNA nicks and branches proximal to the sites that can function as negative(anti) determinants of reactivity. Empirically modelling the constraints to DNA degrees of freedom associated with each recognition site in the sharp triangle can rationalize the pattern of suppressed reactivity towards nine restriction endonucleases, in substantial agreement with the experimental results. These results provide a basis for a predictive understanding of structure-reactivity correlates of specific DNA nanostructures, which will allow a better understanding of the behaviour of nucleic acids under nanoscale confinement, as well as in the rational design of functional nanodevices based on self-assembling nucleic acids.

Sites of high local frustration in DNA origami

The self-assembly of a DNA origami structure, although mostly feasible, represents indeed a rather complex folding problem. Entropy-driven folding and nucleation seeds formation may provide possible solutions; however, until now, a unified view of the energetic factors in play is missing. Here, by analyzing the self-assembly of origami domains with identical structure but different nucleobase composition, in function of variable design and experimental parameters, we identify the role played by sequence-dependent forces at the edges of the structure, where topological constraint is higher. Our data show that the degree of mechanical stress experienced by these regions during initial folding reshapes the energy landscape profile, defining the ratio between two possible global conformations. We thus propose a dynamic model of DNA origami assembly that relies on the capability of the system to escape high structural frustration at nucleation sites, eventually resulting in the emergence of a more favorable but previously hidden state.

Self-assembly of DNA origami is a complex folding problem without a unified view of the energetic factors involved. Here the authors analyse identical structures that differ by nucleotide sequence and identify how mechanical stress at nucleation sites shapes the energy landscape.

A coarse-grained model for DNA origami

Modeling tools provide a valuable support for DNA origami design. However, current solutions have limited application for conformational analysis of the designs. In this work we present a tool for a thorough study of DNA origami structure and dynamics. The tool is based on a novel coarse-grained model dedicated to geometry optimization and conformational analysis of DNA origami. We explored the ability of the model to predict dynamic behavior, global shapes, and fine details of two single-layer systems designed in hexagonal and square lattices using atomic force microscopy, Förster resonance energy transfer spectroscopy, and all-atom molecular dynamic simulations for validation of the results. We also examined the performance of the model for multilayer systems by simulation of DNA origami with published cryo-electron microscopy and atomic force microscopy structures. A good agreement between the simulated and experimental data makes the model suitable for conformational analysis of DNA origami objects. The tool is available at http://vsb.fbb.msu.ru/cosm as a web-service and as a standalone version.

Rhombic-Shaped Nanostructures and Mechanical Properties of 2D DNA Origami Constructed with Different Crossover/Nick Designs

DNA origami methods enable the fabrication of various nanostructures and nanodevices, but their effective use depends on an understanding of their structural and mechanical properties and the effects of basic structural features. Frequency-modulation atomic force microscopy is introduced to directly characterize, in aqueous solution, the crossover regions of sets of 2D DNA origami based on different crossover/nick designs. Rhombic-shaped nanostructures formed under the influence of flexible crossovers placed between DNA helices are observed in DNA origami incorporating crossovers every 3, 4, or 6 DNA turns. The bending rigidity of crossovers is determined to be only one-third of that of the DNA helix, based on interhelical electrostatic forces reported elsewhere, and the measured pitches of the 3-turn crossover design rhombic-shaped nanostructures undergoing negligible bending. To evaluate the robustness of their structural integrity, they are intentionally and simultaneously stressed using force-controlled atomic force microscopy. DNA crossovers are verified to have a stabilizing effect on the structural robustness, while the nicks have an opposite effect. The structural and mechanical properties of DNA origami and the effects of crossovers and nicks revealed in this paper can provide information essential for the design of versatile DNA origami structures that exhibit specified and desirable properties.

Shape and Interhelical Spacing of DNA Origami Nanostructures Studied by Small-Angle X-ray Scattering

Scaffolded DNA origami nanostructures enable the self-assembly of arbitrarily shaped objects with unprecedented accuracy. Yet, varying physiological conditions are prone to induce slight structural changes in the nanoscale architecture. Here, we report on high precision measurements of overall shape and interhelical distance of three prototypic DNA origami structures in solution using synchrotron small-angle X-ray scattering. Sheet-, brick-, and cylinder-shaped DNA constructs were assembled and the shape factors determined with angstrom resolution from fits to the scattering profiles. With decreasing MgCl2 concentration electrostatic swelling of both shape cross section and interhelical DNA spacing of the DNA origami structures is observed. The structures tolerate up to 10% interhelical expansion before they disintegrate. In contrast, with increasing temperature, the cylinder-shaped structures show no thermal expansion in a wide temperature window before they abruptly melt above 50 °C. Details on molecular structure of DNA origami can also be obtained using in-house X-ray scattering equipment and, hence, allow for routine folding and stability testing of DNA-based agents that are designed to operate under varying salt conditions.

Direct Simulation of the Self-Assembly of a Small DNA Origami

By using oxDNA, a coarse-grained nucleotide-level model of DNA, we are able to directly simulate the self-assembly of a small 384-base-pair origami from single-stranded scaffold and staple strands in solution. In general, we see attachment of new staple strands occurring in parallel, but with cooperativity evident for the binding of the second domain of a staple if the adjacent junction is already partially formed. For a system with exactly one copy of each staple strand, we observe a complete assembly pathway in an intermediate temperature window; at low temperatures successful assembly is prevented by misbonding while at higher temperature the free-energy barriers to assembly become too large for assembly on our simulation time scales. For high-concentration systems involving a large staple strand excess, we never see complete assembly because there are invariably instances where two copies of the same staple both bind to the scaffold, creating a kinetic trap that prevents the complete binding of either staple. This mutual staple blocking could also lead to aggregates of partially formed origamis in real systems, and helps to rationalize certain successful origami design strategies.

Multiscale modelling of DNA mechanics

Mechanical properties of DNA are important not only in a wide range of biological processes but also in the emerging field of DNA nanotechnology. We review some of the recent developments in modeling these properties, emphasizing the multiscale nature of the problem. Modern atomic resolution, explicit solvent molecular dynamics simulations have contributed to our understanding of DNA fine structure and conformational polymorphism. These simulations may serve as data sources to parameterize rigid base models which themselves have undergone major development. A consistent buildup of larger entities involving multiple rigid bases enables us to describe DNA at more global scales. Free energy methods to impose large strains on DNA, as well as bead models and other approaches, are also briefly discussed.

DNA nanostructures: a shift from assembly to applications

The specificity of DNA hybridization allows for the modular design of 2D and 3D shapes with wide-ranging applications including sensors, actuators, and even logic devices. The inherent biocompatibility of DNA and the ability to produce monodisperse structures of controlled shape and size make DNA nanostructures of interest as potential drug and gene delivery vehicles. In this review, we discuss several new approaches for the assembly of DNA nanostructures, advances in the modeling of these structures, and we highlight recent studies on the use of DNA nanotechnology for therapeutic applications such as drug delivery in tumor models.

Kinetics of DNA tile dimerization

Investigating how individual molecular components interact with one another within DNA nanoarchitectures, both in terms of their spatial and temporal interactions, is fundamentally important for a better understanding of their physical behaviors. This will provide researchers with valuable insight for designing more complex higher-order structures that can be assembled more efficiently. In this report, we examined several spatial factors that affect the kinetics of bivalent, double-helical (DH) tile dimerization, including the orientation and number of sticky ends (SEs), the flexibility of the double helical domains, and the size of the tiles. The rate constants we obtained confirm our hypothesis that increased nucleation opportunities and well-aligned SEs accelerate tile-tile dimerization. Increased flexibility in the tiles causes slower dimerization rates, an effect that can be reversed by introducing restrictions to the tile flexibility. The higher dimerization rates of more rigid tiles results from the opposing effects of higher activation energies and higher pre-exponential factors from the Arrhenius equation, where the pre-exponential factor dominates. We believe that the results presented here will assist in improved implementation of DNA tile based algorithmic self-assembly, DNA based molecular robotics, and other specific nucleic acid systems, and will provide guidance to design and assembly processes to improve overall yield and efficiency.

Wireframe and tensegrity DNA nanostructures

CONSPECTUS: Not only can triangulated wireframe network and tensegrity design be found in architecture, but it is also essential for the stability and organization of biological matter. Whether the scaffolding material is metal as in Buckminster Fuller's geodesic domes and Kenneth Snelson's floating compression sculptures or proteins like actin or spectrin making up the cytoskeleton of biological cells, wireframe and tensegrity construction can provide great stability while minimizing the material required. Given the mechanical properties of single- and double-stranded DNA, it is not surprising to find many variants of wireframe and tensegrity constructions in the emerging field of DNA nanotechnology, in which structures of almost arbitrary shape can be built with nanometer precision. The success of DNA self-assembly relies on the well-controlled hybridization of complementary DNA strands. Consequently, understanding the fundamental physical properties of these molecules is essential. Many experiments have shown that double-stranded DNA (in its most commonly occurring helical form, the B-form) behaves in a first approximation like a relatively stiff cylindrical beam with a persistence length of many times the length of its building blocks, the base pairs. However, it is harder to assign a persistence length to single-stranded DNA. Here, normally the Kuhn length is given, a measure that describes the length of individual rigid segments in a freely jointed chain. This length is on the order of a few nucleotides. Two immediate and important consequences arise from this high flexibility: single-stranded DNA is almost always present in a coiled conformation, and it behaves, just like all flexible polymers in solution, as an entropic spring. In this Account, we review the relation between the mechanical properties of DNA and design considerations for wireframe and tensegrity structures built from DNA. We illustrate various aspects of the successful evolution of DNA nanotechnology starting with the construction of four-way junctions and then allude to simple geometric objects such as the wireframe cube presented by Nadrian Seeman along with a variety of triangulated wireframe constructions. We examine DNA tensegrity triangles that self-assemble into crystals with sizes of several hundred micrometers as well as prestressed DNA origami tensegrity architecture, which uses single-stranded DNA with its entropic spring behavior as tension bearing components to organize stiff multihelix bundles in three dimensions. Finally, we discuss emerging applications of the aforementioned design principles in diverse fields such as diagnostics, drug delivery, or crystallography. Despite great advances in related research fields like protein and RNA engineering, DNA self-assembly is currently the most accessible technique to organize matter on the nanoscale, and we expect many more exciting applications to emerge.

Ionic permeability and mechanical properties of DNA origami nanoplates on solid-state nanopores

While DNA origami is a popular and versatile platform, its structural properties are still poorly understood. In this study we use solid-state nanopores to investigate the ionic permeability and mechanical properties of DNA origami nanoplates. DNA origami nanoplates of various designs are docked onto solid-state nanopores where we subsequently measure their ionic conductance. The ionic permeability is found to be high for all origami nanoplates. We observe the conductance of docked nanoplates, relative to the bare nanopore conductance, to increase as a function of pore diameter, as well as to increase upon lowering the ionic strength. The honeycomb lattice nanoplate is found to have slightly better overall performance over other plate designs. After docking, we often observe spontaneous discrete jumps in the current, a process which can be attributed to mechanical buckling. All nanoplates show a nonlinear current-voltage dependence with a lower conductance at higher applied voltages, which we attribute to a physical bending deformation of the nanoplates under the applied force. At sufficiently high voltage (force), the nanoplates are strongly deformed and can be pulled through the nanopore. These data show that DNA origami nanoplates are typically very permeable to ions and exhibit a number of unexpected mechanical properties, which are interesting in their own right, but also need to be considered in the future design of DNA origami nanostructures.

Coarse-graining DNA for simulations of DNA nanotechnology

To simulate long time and length scale processes involving DNA it is necessary to use a coarse-grained description. Here we provide an overview of different approaches to such coarse-graining, focussing on those at the nucleotide level that allow the self-assembly processes associated with DNA nanotechnology to be studied. OxDNA, our recently-developed coarse-grained DNA model, is particularly suited to this task, and has opened up this field to systematic study by simulations. We illustrate some of the range of DNA nanotechnology systems to which the model is being applied, as well as the insights it can provide into fundamental biophysical properties of DNA.

Cooperativity in the annealing of DNA origamis

DNA based nanostructures built on a long single stranded DNA scaffold, known as DNA origamis, offer the possibility to organize various molecules at the nanometer scale in one pot experiments. The folding of the scaffold is guaranteed by the presence of short, single stranded DNA sequences (staples), that hold together separate regions of the scaffold. In this paper, we modelize the annealing-melting properties of these DNA constructions. The model captures important features such as the hysteresis between melting and annealing, as well as the dependence upon the topology of the scaffold. We show that cooperativity between staples is critical to quantitatively explain the folding process of DNA origamis.