Free energy landscape of salt-actuated reconfigurable DNA nanodevices

Models and simulations of structural DNA nanotechnology reveal fundamental principles of self-assembly

DNA is not only a centrally important molecule in biology: the specificity of bonding that allows it to be the primary information storage medium for life has also allowed it to become one of the most promising materials for designing intricate, self-assembling structures at the nanoscale. While the applications of these structures are both broad and highly promising, the self-assembly process itself has attracted interest not only for the practical applications of designing structures with more efficient assembly pathways, but also due to a desire to understand the principles underlying self-assembling systems more generally, of which DNA-based systems provide intriguing and unique examples. Here, we review the fundamental physical principles that underpin the self-assembly process in the field of DNA nanotechnology, with a specific focus on simulation and modelling and what we can learn from them. In particular, we compare and contrast DNA origami and bricks and briefly outline other approaches, with an overview of concepts such as cooperativity, nucleation and hysteresis; we also explain how nucleation barriers can be controlled and why they can be helpful in ensuring error-free assembly. While high-resolution models may be needed to obtain accurate system-specific properties, often very simple coarse-grained models are sufficient to extract the fundamentals of the underlying physics and can enable us to gain deep insight. By combining experimental and simulation approaches to understand the details of the self-assembly process, we can optimise its yields and fidelity, which may in turn facilitate its use in practical applications.

Engineering modular and tunable single-molecule sensors by decoupling sensing from signal output

Biosensors play key roles in medical research and diagnostics. However, the development of biosensors for new biomolecular targets of interest often involves tedious optimization steps to ensure a high signal response at the analyte concentration of interest. Here we show a modular nanosensor platform that facilitates these steps by offering ways to decouple and independently tune the signal output as well as the response window. Our approach utilizes a dynamic DNA origami nanostructure to engineer a high optical signal response based on fluorescence resonance energy transfer. We demonstrate mechanisms to tune the sensor's response window, specificity and cooperativity as well as highlight the modularity of the proposed platform by extending it to different biomolecular targets including more complex sensing schemes. This versatile nanosensor platform offers a promising starting point for the rapid development of biosensors with tailored properties.

Hairygami: Analysis of DNA Nanostructures' Conformational Change Driven by Functionalizable Overhangs

DNA origami is a widely used method to construct nanostructures by self-assembling designed DNA strands. These structures are often used as "pegboards" for templated assembly of proteins, gold nanoparticles, aptamers, and other molecules, with applications ranging from therapeutics and diagnostics to plasmonics and photonics. Imaging these structures using atomic force microscopy (AFM) or transmission electron microscope (TEM) does not capture their full conformation ensemble as they only show their shape flattened on a surface. However, certain conformations of the nanostructure can position guest molecules into distances unaccounted for in their intended design, thus leading to spurious interactions between guest molecules that are designed to be separated. Here, we use molecular dynamics simulations to capture a conformational ensemble of two-dimensional (2D) DNA origami tiles and show that introducing single-stranded overhangs, which are typically used for functionalization of the origami with guest molecules, induces a curvature of the tile structure in the bulk. We show that the shape deformation is of entropic origin, with implications for the design of robust DNA origami breadboards as well as a potential approach to modulate structure shape by introducing overhangs. We then verify experimentally that the DNA overhangs introduce curvature into the DNA origami tiles under divalent as well as monovalent salt buffer conditions. We further experimentally verify that DNA origami functionalized with attached proteins also experiences such induced curvature. We provide the developed simulation code implementing the enhanced sampling to characterize the conformational space of DNA origami as open source software.

Coarse-Grained Molecular Simulation of Bolapolyphiles with a Multident Lateral Chain: Formation and Structural Analysis of Cubic Network Phases

Bolapolyphiles constitute a versatile class of materials with a demonstrated potential to form a wide variety of complex ordered mesophases. In particular, cubic network phases (like the gyroid, primitive, and diamond phases) have been a target of many studies for their ability to create percolating 3D nanosized channels. In this study, molecular simulations are used to explore the phase behavior of bolapolyphiles containing a rigid rodlike core, associating hydrophilic core ends and a hydrophobic side chain with a multident architecture, i.e., where the branching pattern can vary from bident (two branches) to hexadent (six branches). Upon network phase formation, its skeleton is made up of "nodes" populated by the core ends and "struts" populated by the cores. It is shown that, by varying the side chain length, branching pattern, and attachment point to the core, one can alter the crowding around the cores and hence tune the nodal size and nodal valence (i.e., number of connecting struts) which lead to different types of network morphologies. For example, for a fixed total side chain length, having more branches generates a stronger crowding around the molecular core, driving them to form bundlelike domains with curvier interfaces that result in thinner struts. Also, attaching the lateral chain closer to one core end breaks the symmetry between the environments around the two core ends, leading to networks with bimodal nodal sizes. Importantly, since the characterization of (ordered or partially ordered) network phases is challenging given the potential incompatibilities between the simulation box size with the structure's space group periodic symmetry and the effect of morphological defects, a detailed framework is presented to analyze and fully characterize the unit cell parameters and structure factor of such systems.

Prediction and Control in DNA Nanotechnology

DNA nanotechnology is a rapidly developing field that uses DNA as a building material for nanoscale structures. Key to the field's development has been the ability to accurately describe the behavior of DNA nanostructures using simulations and other modeling techniques. In this Review, we present various aspects of prediction and control in DNA nanotechnology, including the various scales of molecular simulation, statistical mechanics, kinetic modeling, continuum mechanics, and other prediction methods. We also address the current uses of artificial intelligence and machine learning in DNA nanotechnology. We discuss how experiments and modeling are synergistically combined to provide control over device behavior, allowing scientists to design molecular structures and dynamic devices with confidence that they will function as intended. Finally, we identify processes and scenarios where DNA nanotechnology lacks sufficient prediction ability and suggest possible solutions to these weak areas.

A computational model for structural dynamics and reconfiguration of DNA assemblies

Recent advances in constructing a structured DNA assembly whose configuration can be dynamically changed in response to external stimuli have demanded the development of an efficient computational modeling approach to expedite its design process. Here, we present a computational framework capable of analyzing both equilibrium and non-equilibrium dynamics of structured DNA assemblies at the molecular level. The framework employs Langevin dynamics with structural and hydrodynamic finite element models that describe mechanical, electrostatic, base stacking, and hydrodynamic interactions. Equilibrium dynamic analysis for various problems confirms the solution accuracy at a near-atomic resolution, comparable to molecular dynamics simulations and experimental measurements. Furthermore, our model successfully simulates a long-time-scale close-to-open-to-close dynamic reconfiguration of the switch structure in response to changes in ion concentration. We expect that the proposed model will offer a versatile way of designing responsive and reconfigurable DNA machines.

Steric Communication between Dynamic Components on DNA Nanodevices

Biomolecular nanotechnology has helped emulate basic robotic capabilities such as defined motion, sensing, and actuation in synthetic nanoscale systems. DNA origami is an attractive approach for nanorobotics, as it enables creation of devices with complex geometry, programmed motion, rapid actuation, force application, and various kinds of sensing modalities. Advanced robotic functions like feedback control, autonomy, or programmed routines also require the ability to transmit signals among subcomponents. Prior work in DNA nanotechnology has established approaches for signal transmission, for example through diffusing strands or structurally coupled motions. However, soluble communication is often slow and structural coupling of motions can limit the function of individual components, for example to respond to the environment. Here, we introduce an approach inspired by protein allostery to transmit signals between two distal dynamic components through steric interactions. These components undergo separate thermal fluctuations where certain conformations of one arm will sterically occlude conformations of the distal arm. We implement this approach in a DNA origami device consisting of two stiff arms each connected to a base platform via a flexible hinge joint. We demonstrate the ability for one arm to sterically regulate both the range of motion and the conformational state (latched or freely fluctuating) of the distal arm, results that are quantitatively captured by mesoscopic simulations using experimentally informed energy landscapes for hinge-angle fluctuations. We further demonstrate the ability to modulate signal transmission by mechanically tuning the range of thermal fluctuations and controlling the conformational states of the arms. Our results establish a communication mechanism well-suited to transmit signals between thermally fluctuating dynamic components and provide a path to transmitting signals where the input is a dynamic response to parameters like force or solution conditions.

Thermally reversible pattern formation in arrays of molecular rotors

Control over the mesoscale to microscale patterning of materials is of great interest to the soft matter community. Inspired by DNA origami rotors, we introduce a 2D nearest-neighbor lattice of spinning rotors that exhibit discrete orientational states and interactions with their neighbors. Monte Carlo simulations of rotor lattices reveal that they exhibit a variety of interesting ordering behaviors and morphologies that can be modulated through rotor design parameters. The rotor arrays exhibit diverse patterns including closed loops, radiating loops, and bricklayer structures in their ordered states. They exhibit specific heat peaks at very low temperatures for small system sizes, and some systems exhibit multiple order-disorder transitions depending on inter-rotor interaction design. We devise an energy-based order parameter and show via umbrella sampling and histogram reweighting that this order parameter captures well the order-disorder transitions occurring in these systems. We fabricate real DNA origami rotors which themselves can order via programmable DNA base-pairing interactions and demonstrate both ordered and disordered phases, illustrating how rotor lattices may be realized experimentally and used for responsive organization. This work establishes the feasibility of realizing structural nanomaterials that exhibit locally mediated microscale patterns which could have applications in sensing and precision surface patterning.

The oxDNA Coarse-Grained Model as a Tool to Simulate DNA Origami

This chapter introduces how to run molecular dynamics simulations for DNA origami using the oxDNA coarse-grained model.

Probing the Mechanical Properties of DNA Nanostructures with Metadynamics

Molecular dynamics simulations are often used to provide feedback in the design workflow of DNA nanostructures. However, even with coarse-grained models, the convergence of distributions from unbiased simulation is slow, limiting applications to equilibrium structural properties. Given the increasing interest in dynamic, reconfigurable, and deformable devices, methods that enable efficient quantification of large ranges of motion, conformational transitions, and mechanical deformation are critically needed. Metadynamics is an automated biasing technique that enables the rapid acquisition of molecular conformational distributions by flattening free energy landscapes. Here we leveraged this approach to sample the free energy landscapes of DNA nanostructures whose unbiased dynamics are nonergodic, including bistable Holliday junctions and part of a bistable DNA origami structure. Taking a DNA origami-compliant joint as a case study, we further demonstrate that metadynamics can predict the mechanical response of a full DNA origami device to an applied force, showing good agreement with experiments. Our results exemplify the efficient computation of free energy landscapes and force response in DNA nanodevices, which could be applied for rapid feedback in iterative design workflows and generally facilitate the integration of simulation and experiments. Metadynamics will be particularly useful to guide the design of dynamic devices for nanorobotics, biosensing, or nanomanufacturing applications.

Probing the Mechanical Properties of DNA Nanostructures with Metadynamics

Molecular dynamics simulations are often used to provide feedback in the design workflow of DNA nanostructures. However, even with coarse-grained models, the convergence of distributions from unbiased simulation is slow, limiting applications to equilibrium structural properties. Given the increasing interest in dynamic, reconfigurable, and deformable devices, methods that enable efficient quantification of large ranges of motion, conformational transitions, and mechanical deformation are critically needed. Metadynamics is an automated biasing technique that enables the rapid acquisition of molecular conformational distributions by flattening free energy landscapes. Here we leveraged this approach to sample the free energy landscapes of DNA nanostructures whose unbiased dynamics are nonergodic, including bistable Holliday junctions and part of a bistable DNA origami structure. Taking a DNA origami-compliant joint as a case study, we further demonstrate that metadynamics can predict the mechanical response of a full DNA origami device to an applied force, showing good agreement with experiments. Our results exemplify the efficient computation of free energy landscapes and force response in DNA nanodevices, which could be applied for rapid feedback in iterative design workflows and generally facilitate the integration of simulation and experiments. Metadynamics will be particularly useful to guide the design of dynamic devices for nanorobotics, biosensing, or nanomanufacturing applications.

The Free-Energy Landscape of a Mechanically Bistable DNA Origami

Molecular simulations using coarse-grained models allow the structure, dynamics and mechanics of DNA origamis to be comprehensively characterized. Here, we focus on the free-energy landscape of a jointed DNA origami that has been designed to exhibit two mechanically stable states and for which a bistable landscape has been inferred from ensembles of structures visualized by electron microscopy. Surprisingly, simulations using the oxDNA model predict that the defect-free origami has a single free-energy minimum. The expected second state is not stable because the hinge joints do not simply allow free angular motion but instead lead to increasing free-energetic penalties as the joint angles relevant to the second state are approached. This raises interesting questions about the cause of this difference between simulations and experiment, such as how assembly defects might affect the ensemble of structures observed experimentally.

Characterizing the free-energy landscapes of DNA origamis

We show how coarse-grained modelling combined with umbrella sampling using distance-based order parameters can be applied to compute the free-energy landscapes associated with mechanical deformations of large DNA nanostructures. We illustrate this approach for the strong bending of DNA nanotubes and the potentially bistable landscape of twisted DNA origami sheets. The homogeneous bending of the DNA nanotubes is well described by the worm-like chain model; for more extreme bending the nanotubes reversibly buckle with the bending deformations localized at one or two "kinks". For a twisted one-layer DNA origami, the twist is coupled to the bending of the sheet giving rise to a free-energy landscape that has two nearly-degenerate minima that have opposite curvatures. By contrast, for a two-layer origami, the increased stiffness with respect to bending leads to a landscape with a single free-energy minimum that has a saddle-like geometry. The ability to compute such landscapes is likely to be particularly useful for DNA mechanotechnology and for understanding stress accumulation during the self-assembly of origamis into higher-order structures.

A quantitative model for a nanoscale switch accurately predicts thermal actuation behavior

Manipulation of temperature can be used to actuate DNA origami nano-hinges containing gold nanoparticles. We develop a physical model of this system that uses partition function analysis of the interaction between the nano-hinge and nanoparticle to predict the probability that the nano-hinge is open at a given temperature. The model agrees well with experimental data and predicts experimental conditions that allow the actuation temperature of the nano-hinge to be tuned over a range of temperatures from 30 °C to 45 °C. Additionally, the model identifies microscopic interactions that are important to the macroscopic behavior of the system, revealing surprising features of the system. This combination of physical insight and predictive potential is likely to inform future designs that integrate nanoparticles into dynamic DNA origami structures or use strand binding interactions to control dynamic DNA origami behavior. Furthermore, our modeling approach could be expanded to consider the incorporation, stability, and actuation of other types of functional elements or actuation mechanisms integrated into nucleic acid devices.

Multifunctional Clip Strand for the Regulation of DNA Strand Displacement and Construction of Complex DNA Nanodevices

Strand displacement reactions are important bricks for the construction of various DNA nanodevices, among which the toehold-mediated strand displacement reaction is the most prevalently adopted. However, only a limited number of tools could be used to finely regulate the toehold reaction, thus restricting DNA nanodevices from being more multifunctional and powerful. Herein, we developed a regulation tool, Clip, and achieved multiple regulatory functions, including subtle adjustment of the reaction rates, allosteric strand displacement, selective activation, and resetting of the reaction. Taking advantages of the multiple functions, we constructed Clip-toehold-based DNA walking machines. They showed behaviors of controllable walking, concatenation, and programmable pathways. Furthermore, we built Clip-toehold-based AND and OR logic gates and integrated those logic gates to construct multilayer circuits, which could be reset and reused to process different input signals. We believe that the proposed Clip tool has expanded the functionality of DNA strand displacement-based nanodevices to a much more complex and diverse level and anticipate that the tool will be widely adopted in DNA nanotechnology.