Design principles for rapid folding of knotted DNA nanostructures

Comparative Simulative Analysis and Design of Single-Chain Self-Assembled Protein Cages

Coiled-coil protein origami (CCPO) is a modular strategy for the de novo design of polypeptide nanostructures. It represents a type of modular design based on pairwise-interacting coiled-coil (CC) units with a single-chain protein programmed to fold into a polyhedral cage. However, the mechanisms underlying the self-assembly of the protein tetrahedron are still not fully understood. In the present study, 18 CCPO cages with three different topologies were modeled in silico. Then, molecular dynamics simulations and CC parameters were calculated to characterize the dynamic properties of protein tetrahedral cages at both the local and global levels. Furthermore, a deformed CC unit was redesigned, and the stability of the new cage was significantly improved.

Encoding signal propagation on topology-programmed DNA origami

Biological systems often rely on topological transformation to reconfigure connectivity between nodes to guide the flux of molecular information. Here we develop a topology-programmed DNA origami system that encodes signal propagation at the nanoscale, analogous to topologically efficient information processing in cellular systems. We present a systematic molecular implementation of topological operations involving 'glue-cut' processes that can prompt global conformational change of DNA origami structures, with demonstrated major topological properties including genus, number of boundary components and orientability. By spatially arranging reactive DNA hairpins, we demonstrate signal propagation across transmission paths of varying lengths and orientations, and curvatures on the curved surfaces of three-dimensional origamis. These DNA origamis can also form dynamic scaffolds for regulating the spatial and temporal signal propagations whereby topological transformations spontaneously alter the location of nodes and boundary of signal propagation network. We anticipate that our strategy for topological operations will provide a general route to manufacture dynamic DNA origami nanostructures capable of performing global structural transformations under programmable control.

Crystal Structure of de Novo Designed Coiled-Coil Protein Origami Triangle

Coiled-coil protein origami (CCPO) uses modular coiled-coil building blocks and topological principles to design polyhedral structures distinct from those of natural globular proteins. While the CCPO strategy has proven successful in designing diverse protein topologies, no high-resolution structural information has been available about these novel protein folds. Here we report the crystal structure of a single-chain CCPO in the shape of a triangle. While neither cyclization nor the addition of nanobodies enabled crystallization, it was ultimately facilitated by the inclusion of a GCN2 homodimer. Triangle edges are formed by the orthogonal parallel coiled-coil dimers P1:P2, P3:P4, and GCN2 connected by short linkers. A triangle has a large central cavity and is additionally stabilized by side-chain interactions between neighboring segments at each vertex. The crystal lattice is densely packed and stabilized by a large number of contacts between triangles. Interestingly, the polypeptide chain folds into a trefoil-type protein knot topology, and AlphaFold2 fails to predict the correct fold. The structure validates the modular CC-based protein design strategy, providing molecular insight underlying CCPO stabilization and new opportunities for the design.

A tile model of circuit topology for self-entangled biopolymers

Building on the theory of circuit topology for intra-chain contacts in entangled proteins, we introduce tiles as a way to rigorously model local entanglements which are held in place by molecular forces. We develop operations that combine tiles so that entangled chains can be represented by algebraic expressions. Then we use our model to show that the only knot types that such entangled chains can have are [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and connected sums of these knots. This includes all proteins knots that have thus far been identified.

A single strand: A simplified approach to DNA origami

Just as a single polypeptide strand can self-fold into a complex 3D structure, a single strand of DNA can self-fold into DNA origami. Most DNA origami structures (i.e., the scaffold-staple and DNA tiling systems) utilize hundreds of short single-stranded DNA. As such, these structures come with challenges inherent to intermolecular construction. Many assembly challenges involving intermolecular interactions can be resolved if the origami structure is constructed from one DNA strand, where folding is not concentration dependent, the folded structure is more resistant to nuclease degradation, and the synthesis can be achieved at an industrial scale at a thousandth of the cost. This review discusses the design principles and considerations employed in single-stranded DNA origami and its potential benefits and drawbacks.

Topological principles of protein folding

What is the topology of a protein and what governs protein folding to a specific topology? This is a fundamental question in biology. The protein folding reaction is a critically important cellular process, which is failing in many prevalent diseases. Understanding protein folding is also key to the design of new proteins for applications. However, our ability to predict the folding of a protein chain is quite limited and much is still unknown about the topological principles of folding. Current predictors of folding kinetics, including the contact order and size, present a limited predictive power, suggesting that these models are fundamentally incomplete. Here, we use a newly developed mathematical framework to define and extract the topology of a native protein conformation beyond knot theory, and investigate the relationship between native topology and folding kinetics in experimentally characterized proteins. We show that not only the folding rate, but also the mechanistic insight into folding mechanisms can be inferred from topological parameters. We identify basic topological features that speed up or slow down the folding process. The approach enabled the decomposition of protein 3D conformation into topologically independent elementary folding units, called circuits. The number of circuits correlates significantly with the folding rate, offering not only an efficient kinetic predictor, but also a tool for a deeper understanding of theoretical folding models. This study contributes to recent work that reveals the critical relevance of topology to protein folding with a new, contact-based, mathematically rigorous perspective. We show that topology can predict folding kinetics when geometry-based predictors like contact order and size fail.

Genetically Encoding Ultrastable Virus-like Particles Encapsulating Functional DNA Nanostructures in Living Bacteria

DNA nanotechnology is leading the field of in vitro molecular-scale device engineering, accumulating to a dazzling array of applications. However, while DNA nanostructures' function is robust under in vitro settings, their implementation in real-world conditions requires overcoming their rapid degradation and subsequent loss of function. Viruses are sophisticated supramolecular assemblies, able to protect their nucleic acid content in inhospitable biological environments. Inspired by this natural ability, we engineered in vitro and in vivo technologies, enabling the encapsulation and protection of functional DNA nanostructures inside MS2 bacteriophage virus-like particles (VLPs). We demonstrate the ssDNA-VLPs nanocomposites' (NCs) abilities to encapsulate single-stranded-DNA (ssDNA) in a variety of sizes (200-1500 nucleotides (nt)), sequences, and structures while retaining their functionality. Moreover, by exposing these NCs to hostile biological conditions, such as human blood serum, we exhibit that the VLPs serve as an excellent protective shell. These engineered NCs pose critical properties that are yet unattainable by current fabrication methods.

OxDNA.org: a public webserver for coarse-grained simulations of DNA and RNA nanostructures

OxDNA and oxRNA are popular coarse-grained models used by the DNA/RNA nanotechnology community to prototype, analyze and rationalize designed DNA and RNA nanostructures. Here, we present oxDNA.org, a graphical web interface for running, visualizing and analyzing oxDNA and oxRNA molecular dynamics simulations on a GPU-enabled high performance computing server. OxDNA.org automatically generates simulation files, including a multi-step relaxation protocol for structures exported in non-physical states from DNA/RNA design tools. Once the simulation is complete, oxDNA.org provides an interactive visualization and analysis interface using the browser-based visualizer oxView to facilitate the understanding of simulation results for a user's specific structure. This online tool significantly lowers the entry barrier of integrating simulations in the nanostructure design pipeline for users who are not experts in the technical aspects of molecular simulation. The webserver is freely available at oxdna.org.

A Primer on the oxDNA Model of DNA: When to Use it, How to Simulate it and How to Interpret the Results

The oxDNA model of Deoxyribonucleic acid has been applied widely to systems in biology, biophysics and nanotechnology. It is currently available via two independent open source packages. Here we present a set of clearly documented exemplar simulations that simultaneously provide both an introduction to simulating the model, and a review of the model's fundamental properties. We outline how simulation results can be interpreted in terms of-and feed into our understanding of-less detailed models that operate at larger length scales, and provide guidance on whether simulating a system with oxDNA is worthwhile.

A nanobody toolbox targeting dimeric coiled-coil modules for functionalization of designed protein origami structures

Coiled-coil (CC) dimers are widely used in protein design because of their modularity and well-understood sequence-structure relationship. In CC protein origami design, a polypeptide chain is assembled from a defined sequence of CC building segments that determine the self-assembly of protein cages into polyhedral shapes, such as the tetrahedron, triangular prism, or four-sided pyramid. However, a targeted functionalization of the CC modules could significantly expand the versatility of protein origami scaffolds. Here, we describe a panel of single-chain camelid antibodies (nanobodies) directed against different CC modules of a de novo designed protein origami tetrahedron. We show that these nanobodies are able to recognize the same CC modules in different polyhedral contexts, such as isolated CC dimers, tetrahedra, triangular prisms, or trigonal bipyramids, thereby extending the ability to functionalize polyhedra with nanobodies in a desired stoichiometry. Crystal structures of five nanobody-CC complexes in combination with small-angle X-ray scattering show binding interactions between nanobodies and CC dimers forming the edges of a tetrahedron with the nanobody entering the tetrahedral cavity. Furthermore, we identified a pair of allosteric nanobodies in which the binding to the distant epitopes on the antiparallel homodimeric APH CC is coupled via a strong positive cooperativity. A toolbox of well-characterized nanobodies specific for CC modules provides a unique tool to target defined sites in the designed protein structures, thus opening numerous opportunities for the functionalization of CC protein origami polyhedra or CC-based bionanomaterials.

Triangular in Vivo Self-Assembling Coiled-Coil Protein Origami

Coiled-coil protein origami (CCPO) polyhedra are designed self-assembling nanostructures constructed from coiled coil (CC)-forming modules connected into a single chain. For testing new CCPO building modules, simpler polyhedra could be used that should maintain most features relevant to larger scaffolds. We show the design and characterization of nanoscale single-chain triangles, composed of six concatenated parallel CC dimer-forming segments connected by flexible linker peptides. The polypeptides self-assembled in bacteria in agreement with the design, and the shape of the polypeptides was confirmed with small-angle X-ray scattering. Fusion with split-fluorescent protein domains was used as a functional assay in bacteria, based on the discrimination between the correctly folded and misfolded nanoscale triangles comprising correct, mismatched, or truncated modules. This strategy was used to evaluate the optimal size of linkers between CC segments which comprised eight amino acid residues.

Designed folding pathway of modular coiled-coil-based proteins

Natural proteins are characterised by a complex folding pathway defined uniquely for each fold. Designed coiled-coil protein origami (CCPO) cages are distinct from natural compact proteins, since their fold is prescribed by discrete long-range interactions between orthogonal pairwise-interacting coiled-coil (CC) modules within a single polypeptide chain. Here, we demonstrate that CCPO proteins fold in a stepwise sequential pathway. Molecular dynamics simulations and stopped-flow Förster resonance energy transfer (FRET) measurements reveal that CCPO folding is dominated by the effective intra-chain distance between CC modules in the primary sequence and subsequent folding intermediates, allowing identical CC modules to be employed for multiple cage edges and thus relaxing CCPO cage design requirements. The number of orthogonal modules required for constructing a CCPO tetrahedron can be reduced from six to as little as three different CC modules. The stepwise modular nature of the folding pathway offers insights into the folding of tandem repeat proteins and can be exploited for the design of modular protein structures based on a given set of orthogonal modules.

Understanding DNA interactions in crowded environments with a coarse-grained model

Nucleic acid interactions under crowded environments are of great importance for biological processes and nanotechnology. However, the kinetics and thermodynamics of nucleic acid interactions in a crowded environment remain poorly understood. We use a coarse-grained model of DNA to study the kinetics and thermodynamics of DNA duplex and hairpin formation in crowded environments. We find that crowders can increase the melting temperature of both an 8-mer DNA duplex and a hairpin with a stem of 6-nt depending on the excluded volume fraction of crowders in solution and the crowder size. The crowding induced stability originates from the entropic effect caused by the crowding particles in the system. Additionally, we study the hybridization kinetics of DNA duplex formation and the formation of hairpin stems, finding that the reaction rate k_on is increased by the crowding effect, while k_off is changed only moderately. The increase in k_on mostly comes from increasing the probability of reaching a transition state with one base pair formed. A DNA strand displacement reaction in a crowded environment is also studied with the model and we find that rate of toehold association is increased, with possible applications to speeding up strand displacement cascades in nucleic acid nanotechnology.

Design of novel protein building modules and modular architectures

Nature uses only a limited number of protein topologies and while several folds have evolved independently over time, there are clearly many possible topologies that have not been explored by evolution. With recent advances of protein design concepts, computational modeling tools, high resolution and high-throughput experimental methods it is now possible to design new protein architectures. The collection of building blocks and design principles widened both in size and complexity, offering an expanded toolset for building new modular folds and functional protein structures. Here we review and discuss recent achievements of protein design, focusing in particular on the use and prospects of modular approaches for assembling new protein folds.

Engineering a DNAzyme-Based Operon System for the Production of DNA Nanoscaffolds in Living Bacteria

The ability to create nanoscaffolds within living cells using DNA has the potential to become a powerful tool in synthetic biology. However, to date, genetically encoded DNA nanostructures are limited to simple architecture due to the lack of genetic parts that can produce multiple ssDNAs in a single bacterium. Here, we develop a system that overcomes this challenge by using a single oligo gene mimicking operons. This was achieved by converting a noncoding RNA into a long ssDNA that self-cleaves into multiple ssDNAs using R3-DNAzymes (DNAzyme-based operon). We demonstrate the ability to apply the DNAzyme-based operon to produce a four-ssDNA crossover nanostructure (25 nm) that recruits split YFPs when properly assembled. This system enables the formation of more complex DNA nanostructures in vivo and thus paves the way to further integrate the field of DNA nanotechnology into living bacteria for basic biology, bioengineering, and medicine applications.

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.

Synthetic Biology for Multiscale Designed Biomimetic Assemblies: From Designed Self-Assembling Biopolymers to Bacterial Bioprinting

Nature is based on complex self-assembling systems that span from the nanoscale to the macroscale. We have already begun to design biomimetic systems with properties that have not evolved in nature, based on designed molecular interactions and regulation of biological systems. Synthetic biology is based on the principle of modularity, repurposing diverse building modules to design new types of molecular and cellular assemblies. While we are currently able to use techniques from synthetic biology to design self-assembling molecules and re-engineer functional cells, we still need to use guided assembly to construct biological assemblies at the macroscale. We review the recent strategies for designing biological systems ranging from molecular assemblies based on self-assembly of (poly)peptides to the guided assembly of patterned bacteria, spanning 7 orders of magnitude.

Triangulated Wireframe Structures Assembled Using Single-Stranded DNA Tiles

The field of structural DNA nanotechnology offers a wide range of design strategies with which to build structures with a desired aspect ratio, size, and shape. Compared with traditional close-packed DNA structures, triangulated wireframe structures require less material per surface or volume unit and improve the stability in biologically relevant conditions due to the reduced electrostatic repulsion. Herein, we expand the design space of the DNA single-stranded tile method to cover a range of anisotropic, finite, triangulated wireframe structures as well as a number of one-dimensional crystalline assemblies. These structures are composed of six-arm junctions with a single double helix as connecting edges that assemble in physiologically relevant salinities. For a reliable folding of the structures, single-stranded spacers 2-4 nucleotides long have to be introduced in the junction connecting neighboring arms. Coarse-grained molecular dynamics simulations using the oxDNA model suggests that the spacers prevent the stacking of DNA helices, thereby facilitating the assembly of planar geometries.

RNA nanostructures and scaffolds for biotechnology applications

RNA plays important roles in the regulation of gene expressions and other cellular functions. It functions as both as an informational carrier and a nanomachine due to its complementary base-pairing ability and complexed three-dimensional structure. Several nanostructures have been designed and constructed by exploiting these natural RNA properties. In this review, we will introduce the design principles of RNA nanostructures and their biotechnology applications as molecular scaffolds. RNA-based molecular scaffolds can control the accumulation and interaction of target proteins at nanometer-scale to regulate the function of bacterial and mammalian cells. Combining useful property of RNA as a nano-material and a molecular scaffold may provide us powerful tools in biological research, bioengineering, and future medicine.

Programming molecular topologies from single-stranded nucleic acids

Molecular knots represent one of the most extraordinary topological structures in biological polymers. Creating highly knotted nanostructures with well-defined and sophisticated geometries and topologies remains challenging. Here, we demonstrate a general strategy to design and construct highly knotted nucleic acid nanostructures, each weaved from a single-stranded DNA or RNA chain by hierarchical folding in a prescribed order. Sets of DNA and RNA knots of two- or three-dimensional shapes have been designed and constructed (ranging from 1700 to 7500 nucleotides), and they exhibit complex topological features, with high crossing numbers (from 9 up to 57). These single-stranded DNA/RNA knots can be replicated and amplified enzymatically in vitro and in vivo. This work establishes a general platform for constructing nucleic acid nanostructures with complex molecular topologies.

Multi-scale coarse-graining for the study of assembly pathways in DNA-brick self-assembly

Inspired by recent successes using single-stranded DNA tiles to produce complex structures, we develop a two-step coarse-graining approach that uses detailed thermodynamic calculations with oxDNA, a nucleotide-based model of DNA, to parametrize a coarser kinetic model that can reach the time and length scales needed to study the assembly mechanisms of these structures. We test the model by performing a detailed study of the assembly pathways for a two-dimensional target structure made up of 334 unique strands each of which are 42 nucleotides long. Without adjustable parameters, the model reproduces a critical temperature for the formation of the assembly that is close to the temperature at which assembly first occurs in experiments. Furthermore, the model allows us to investigate in detail the nucleation barriers and the distribution of critical nucleus shapes for the assembly of a single target structure. The assembly intermediates are compact and highly connected (although not maximally so), and classical nucleation theory provides a good fit to the height and shape of the nucleation barrier at temperatures close to where assembly first occurs.

Coiled coil protein origami: from modular design principles towards biotechnological applications

This review illustrates the current state in designing coiled-coil-based proteins with an emphasis on coiled coil protein origami structures and their potential.

Characterizing the Motion of Jointed DNA Nanostructures Using a Coarse-Grained Model

As detailed structural characterizations of large complex DNA nanostructures are hard to obtain experimentally, particularly if they have substantial flexibility, coarse-grained modeling can potentially provide an important complementary role. Such modeling can provide a detailed view of both the average structure and the structural fluctuations, as well as providing insight into how the nanostructure's design determines its structural properties. Here, we present a case study of jointed DNA nanostructures using the oxDNA model. In particular, we consider archetypal hinge and sliding joints, as well as more complex structures involving a number of such coupled joints. Our results highlight how the nature of the motion in these structures can sensitively depend on the precise details of the joints. Furthermore, the generally good agreement with experiments illustrates the power of this approach and suggests the use of such modeling to prescreen the properties of putative designs.

Designed Protein Origami

Proteins are highly perfected natural molecular machines, owing their properties to the complex tertiary structures with precise spatial positioning of different functional groups that have been honed through millennia of evolutionary selection. The prospects of designing new molecular machines and structural scaffolds beyond the limits of natural proteins make design of new protein folds a very attractive prospect. However, de novo design of new protein folds based on optimization of multiple cooperative interactions is very demanding. As a new alternative approach to design new protein folds unseen in nature, folds can be designed as a mathematical graph, by the self-assembly of interacting polypeptide modules within the single chain. Orthogonal coiled-coil dimers seem like an ideal building module due to their shape, adjustable length, and above all their designability. Similar to the approach of DNA nanotechnology, where complex tertiary structures are designed from complementary nucleotide segments, a polypeptide chain composed of a precisely specified sequence of coiled-coil forming segments can be designed to self-assemble into polyhedral scaffolds. This modular approach encompasses long-range interactions that define complex tertiary structures. We envision that by expansion of the toolkit of building blocks and design strategies of the folding pathways protein origami technology will be able to construct diverse molecular machines.

Universal interrelation between measures of particle and polymer size

The characterization of many objects involves the determination of a basic set of particle size measures derived mainly from scattering and transport property measurements. For polymers, these basic properties include the radius of gyration Rg, hydrodynamic radius Rh, intrinsic viscosity [η], and sedimentation coefficient S, and for conductive particles, the electric polarizability tensor αE and self-capacity C. It is often found that hydrodynamic measurements of size deviate from each other and from geometric estimates of particle size when the particle or polymer shape is complex, a phenomenon that greatly complicates both nanoparticle and polymer characterizations. The present work explores a general quantitative relation between αE, C, and Rg for nanoparticles and polymers of general shape and the corresponding properties η, Rh, and Rg using a hydrodynamic-electrostatic property interrelation.

Intrinsic Dynamics Analysis of a DNA Octahedron by Elastic Network Model

DNA is a fundamental component of living systems where it plays a crucial role at both functional and structural level. The programmable properties of DNA make it an interesting building block for the construction of nanostructures. However, molecular mechanisms for the arrangement of these well-defined DNA assemblies are not fully understood. In this paper, the intrinsic dynamics of a DNA octahedron has been investigated by using two types of Elastic Network Models (ENMs). The application of ENMs to DNA nanocages include the analysis of the intrinsic flexibilities of DNA double-helices and hinge sites through the calculation of the square fluctuations, as well as the intrinsic collective dynamics in terms of cross-collective map calculation coupled with global motions analysis. The dynamics profiles derived from ENMs have then been evaluated and compared with previous classical molecular dynamics simulation trajectories. The results presented here revealed that ENMs can provide useful insights into the intrinsic dynamics of large DNA nanocages and represent a useful tool in the field of structural DNA nanotechnology.

Antiparallel d-stable traces and a stronger version of ore problem

In 2013 a novel self-assembly strategy for polypeptide nanostructure design which could lead to significant developments in biotechnology was presented in Gradišar et al. (Nat Chem Bio 9:362-366, 2013). It was since observed that a polyhedron P can be realized by interlocking pairs of polypeptide chains if its corresponding graph G(P) admits a strong trace. It was since also demonstrated that a similar strategy can also be expanded to self-assembly of designed DNA (Kočar, Nat commun 7:1-8, 2016). In this direction, in the present paper we characterize graphs which admit closed walk which traverses every edge exactly once in each direction and for every vertex v, there is no subset N of its neighbors, with [Formula: see text], such that every time the walk enters v from N, it also exits to a vertex in N. This extends Thomassen's characterization (Thomassen, J Combin Theory Ser B 50:198-207, 1990) for the case [Formula: see text].

Upgrading biomaterials with synthetic biological modules for advanced medical applications

One key aspect of synthetic biology is the development and characterization of modular biological building blocks that can be assembled to construct integrated cell-based circuits performing computational functions. Likewise, the idea of extracting biological modules from the cellular context has led to the development of in vitro operating systems. This principle has attracted substantial interest to extend the repertoire of functional materials by connecting them with modules derived from synthetic biology. In this respect, synthetic biological switches and sensors, as well as biological targeting or structure modules, have been employed to upgrade functions of polymers and solid inorganic material. The resulting systems hold great promise for a variety of applications in diagnosis, tissue engineering, and drug delivery. This review reflects on the most recent developments and critically discusses challenges concerning in vivo functionality and tolerance that must be addressed to allow the future translation of such synthetic biology-upgraded materials from the bench to the bedside.

Characterizing DNA Star-Tile-Based Nanostructures Using a Coarse-Grained Model

We use oxDNA, a coarse-grained model of DNA at the nucleotide level, to simulate large nanoprisms that are composed of multi-arm star tiles, in which the size of bulge loops that have been incorporated into the tile design is used to control the flexibility of the tiles. The oxDNA model predicts equilibrium structures for several different nanoprism designs that are in excellent agreement with the experimental structures as measured by cryoTEM. In particular we reproduce the chiral twisting of the top and bottom faces of the nanoprisms, as the bulge sizes in these structures are varied due to the greater flexibility of larger bulges. We are also able to follow how the properties of the star tiles evolve as the prisms are assembled. Individual star tiles are very flexible, but their structures become increasingly well-defined and rigid as they are incorporated into larger assemblies. oxDNA also finds that the experimentally observed prisms are more stable than their inverted counterparts, but interestingly this preference for the arms of the tiles to bend in a given direction only emerges after they are part of larger assemblies. These results show the potential for oxDNA to provide detailed structural insight as well as to predict the properties of DNA nanostructures and hence to aid rational design in DNA nanotechnology.

Designing the structure and folding pathway of modular topological bionanostructures

Polypeptides and polynucleotides are programmable natural polymers whose linear sequence can be easily designed and synthesized by the cellular transcription/translation machinery. Nature primarily uses proteins as the molecular machines and nucleic acids as the medium for the manipulation of heritable information. A protein's tertiary structure and function is defined by multiple cooperative weak long-range interactions that have been optimized through evolution. DNA nanotechnology uses orthogonal pairwise interacting modules of complementary nucleic acids as a strategy to construct defined complex 3D structures. A similar approach has recently been applied to protein design, using orthogonal dimerizing coiled-coil segments as interacting modules. When concatenated into a single polypeptide chain, they self-assemble into the 3D structure defined by the topology of interacting modules within the chain. This approach allows the construction of geometric polypeptide scaffolds, bypassing the folding problem of compact proteins by relying on decoupled pairwise interactions. However, the folding pathway still needs to be optimized in order to allow rapid self-assembly under physiological conditions. Again the modularity of designed topological structures can be used to define the rules that guide the folding pathway of long polymers, such as DNA, based on the stability and topology of connected building modules. This approach opens the way towards incorporation of designed foldamers in biological systems and their functionalization.

Knot theory in modern chemistry

This tutorial review provides an introduction to the mathematics of knots and topological concepts in the context of the chemical sciences.