Accurate phase diagram of tetravalent DNA nanostars

Nucleic acid liquids

The confluence of recent discoveries of the roles of biomolecular liquids in living systems and modern abilities to precisely synthesize and modify nucleic acids (NAs) has led to a surge of interest in liquid phases of NAs. These phases can be formed primarily from NAs, as driven by base-pairing interactions, or from the electrostatic combination (coacervation) of negatively charged NAs and positively charged molecules. Generally, the use of sequence-engineered NAs provides the means to tune microsopic particle properties, and thus imbue specific, customizable behaviors into the resulting liquids. In this way, researchers have used NA liquids to tackle fundamental problems in the physics of finite valence soft materials, and to create liquids with novel structured and/or multi-functional properties. Here, we review this growing field, discussing the theoretical background of NA liquid phase separation, quantitative understanding of liquid material properties, and the broad and growing array of functional demonstrations in these materials. We close with a few comments discussing remaining open questions and challenges in the field.

Competition between Self-Assembly and Phase Separation Governs High-Temperature Condensation of a DNA Liquid

In many biopolymer solutions, attractive interactions that stabilize finite-sized clusters at low concentrations also promote phase separation at high concentrations. Here we study a model biopolymer system that exhibits the opposite behavior, whereby self-assembly of DNA oligonucleotides into finite-sized, stoichiometric clusters tends to inhibit phase separation. We first use microfluidics-based experiments to map a novel phase transition in which the oligonucleotides condense as the temperature increases at high concentrations of divalent cations. We then show that a theoretical model of competition between self-assembly and phase separation quantitatively predicts changes in experimental phase diagrams arising from DNA sequence perturbations. Our results point to a general mechanism by which self-assembly shapes phase boundaries in complex biopolymer solutions.

Controlling the size and adhesion of DNA droplets using surface- enriched DNA molecules

Liquid droplets of biomolecules serve as organizers of the cellular interior and are of interest in biosensing and biomaterials applications. Here, we investigate means to tune the interfacial properties of a model biomolecular liquid consisting of multi-armed DNA 'nanostar' particles. We find that long DNA molecules that have binding affinity for the nanostars are preferentially enriched on the interface of nanostar droplets, thus acting as surfactants. Fluorescent measurements indicate that, in certain conditions, the interfacial density of the surfactant is around 20 per square micron, indicative of a sparse brush-like structure of the long, polymeric DNA. Increasing surfactant concentration leads to decreased droplet size, down to the sub-micron scale, consistent with droplet coalesence being impeded by the disjoining pressure created by the brush-like surfactant layer. Added DNA surfactant also keeps droplets from adhering to both hydrophobic and hydrophilic solid surfaces, apparently due to this same disjoining effect of the surfactant layer. We thus demonstrate control of the size and adhesive properties of droplets of a biomolecular liquid, with implications for basic biophysical understanding of such droplets, as well as for their applied use.

Interplay between self-assembly and phase separation in a polymer-complex model

We present a theoretical model for predicting the phase behavior of polymer solutions in which phase separation competes with oligomerization. Specifically, we consider scenarios in which the assembly of polymer chains into stoichiometric complexes prevents the chains from phase-separating via attractive polymer-polymer interactions. Combining statistical associating fluid theory with a two-state description of self-assembly, we find that this model exhibits rich phase behavior, including reentrance, and we show how system-specific phase diagrams can be derived graphically. Importantly, we discuss why these phase diagrams can resemble-and yet are qualitatively distinct from-phase diagrams of polymer solutions with lower critical solution temperatures.

Vacuole dynamics and popping-based motility in liquid droplets of DNA

Liquid droplets of biomolecules play key roles in organizing cellular behavior, and are also technologically relevant, yet physical studies of dynamic processes of such droplets have generally been lacking. Here, we investigate and quantify the dynamics of formation of dilute internal inclusions, i.e., vacuoles, within a model system consisting of liquid droplets of DNA 'nanostar' particles. When acted upon by DNA-cleaving restriction enzymes, these DNA droplets exhibit cycles of appearance, growth, and bursting of internal vacuoles. Analysis of vacuole growth shows their radius increases linearly in time. Further, vacuoles pop upon reaching the droplet interface, leading to droplet motion driven by the osmotic pressure of restriction fragments captured in the vacuole. We develop a model that accounts for the linear nature of vacuole growth, and the pressures associated with motility, by describing the dynamics of diffusing restriction fragments. The results illustrate the complex non-equilibrium dynamics possible in biomolecular condensates.

Theory and Simulation of Multiphase Coexistence in Biomolecular Mixtures

Biomolecular condensates constitute a newly recognized form of spatial organization in living cells. Although many condensates are believed to form as a result of phase separation, the physicochemical properties that determine the phase behavior of heterogeneous biomolecular mixtures are only beginning to be explored. Theory and simulation provide invaluable tools for probing the relationship between molecular determinants, such as protein and RNA sequences, and the emergence of phase-separated condensates in such complex environments. This review covers recent advances in the prediction and computational design of biomolecular mixtures that phase-separate into many coexisting phases. First, we review efforts to understand the phase behavior of mixtures with hundreds or thousands of species using theoretical models and statistical approaches. We then describe progress in developing analytical theories and coarse-grained simulation models to predict multiphase condensates with the molecular detail required to make contact with biophysical experiments. We conclude by summarizing the challenges ahead for modeling the inhomogeneous spatial organization of biomolecular mixtures in living cells.

DNA Droplets: Intelligent, Dynamic Fluid

Breathtaking advances in DNA nanotechnology have established DNA as a promising biomaterial for the fabrication of programmable higher-order nano/microstructures. In the context of developing artificial cells and tissues, DNA droplets have emerged as a powerful platform for creating intelligent, dynamic cell-like machinery. DNA droplets are a microscale membrane-free coacervate of DNA formed through phase separation. This new type of DNA system couples dynamic fluid-like property with long-established DNA programmability. This hybrid nature offers an advantageous route to facile and robust control over the structures, functions, and behaviors of DNA droplets. This review begins by describing programmable DNA condensation, commenting on the physical properties and fabrication strategies of DNA hydrogels and droplets. By presenting an overview of the development pathways leading to DNA droplets, it is shown that DNA technology has evolved from static, rigid systems to soft, dynamic systems. Next, the basic characteristics of DNA droplets are described as intelligent, dynamic fluid by showcasing the latest examples highlighting their distinctive features related to sequence-specific interactions and programmable mechanical properties. Finally, this review discusses the potential and challenges of numerical modeling able to connect a robust link between individual sequences and macroscopic mechanical properties of DNA droplets.

Emulsion imaging of a DNA nanostar condensate phase diagram reveals valence and electrostatic effects

Liquid-liquid phase separation (LLPS) in macromolecular solutions (e.g., coacervation) is relevant both to technology and to the process of mesoscale structure formation in cells. The LLPS process is characterized by a phase diagram, i.e., binodal lines in the temperature/concentration plane, which must be quantified to predict the system's behavior. Experimentally, this can be difficult due to complications in handling the dense macromolecular phase. Here, we develop a method for accurately quantifying the phase diagram without direct handling: We confine the sample within micron-scale, water-in-oil emulsion droplets and then use precision fluorescent imaging to measure the volume fraction of the condensate within the droplet. We find that this volume fraction grows linearly with macromolecule concentration; thus, by applying the lever rule, we can directly extract the dense and dilute binodal concentrations. We use this approach to study a model LLPS system of self-assembled, fixed-valence DNA particles termed nanostars (NSs). We find that temperature/concentration phase diagrams of NSs display, with certain exceptions, a larger co-existence regime upon increasing salt or valence, in line with expectations. Aspects of the measured phase behavior validate recent predictions that account for the role of valence in modulating the connectivity of the condensed phase. Generally, our results on NS phase diagrams give fundamental insight into limited-valence phase separation, while the method we have developed will likely be useful in the study of other LLPS systems.

Engineering DNA-based synthetic condensates with programmable material properties, compositions, and functionalities

Biomolecular condensates participate in diverse cellular processes, ranging from gene regulation to stress survival. Bottom-up engineering of synthetic condensates advances our understanding of the organizing principle of condensates. It also enables the synthesis of artificial systems with novel functions. However, building synthetic condensates with a predictable organization and function remains challenging. Here, we use DNA as a building block to create synthetic condensates that are assembled through phase separation. The programmability of intermolecular interactions between DNA molecules enables the control over various condensate properties including assembly, composition, and function. Similar to the way intracellular condensates are organized, DNA clients are selectively partitioned into cognate condensates. We demonstrate that the synthetic condensates can accelerate DNA strand displacement reactions and logic gate operation by concentrating specific reaction components. We envision that the DNA-based condensates could help the realization of the high-order functions required to build more life-like artificial systems.

Self-Assembly of All-DNA Rods with Controlled Patchiness

Double-stranded DNA (dsDNA) fragments exhibit noncovalent attractive interactions between their tips. It is still unclear how DNA liquid crystal self-assembly is affected by such blunt-end attractions. It is demonstrated that stiff dsDNA fragments with moderate aspect ratio can specifically self-assemble in concentrated aqueous solutions into different types of smectic mesophases on the basis of selectively screening of blunt-end DNA stacking interactions. To this end, this type of attractions are engineered at the molecular level by constructing DNA duplexes where the attractions between one or both ends are screened by short hairpin caps. All-DNA bilayer and monolayer smectic-A type of phases, as well as a columnar phase, can be stabilized by controlling attractions strength. The results imply that the so far elusive smectic-A in DNA rod-like liquid crystals is a thermodynamically stable phase. The existence of the bilayer smectic phase is confirmed by Monte-Carlo simulations of hard cylinders decorated with one attractive terminal site. This work demonstrates that DNA blunt-ends behave as well-defined monovalent attractive patches whose strength and position can be potentially precisely tuned, highlighting unique opportunities concerning the stabilization of nonconventional DNA-based lyotropic liquid crystal phases assembled by all-DNA patchy particles with arbitrary geometry and composition.

Spatially uniform dynamics in equilibrium colloidal gels

Gels of DNA nanostars, besides providing a compatible scaffold for biomedical applications, are ideal model systems for testing the physics of equilibrium colloidal gels. Here, using dynamic light scattering and photon correlation imaging (a recent technique that, by blending light scattering and imaging, provides space-resolved quantification of the dynamics), we follow the process of gel formation over 10 orders of magnitude in time in a model system of tetravalent DNA nanostars in solution, a realization of limited-valence colloids. Such a system, depending on the nanostar concentration, can form either equilibrium or phase separation gels. In stark contrast to the heterogeneity of concentration and dynamics displayed by the phase separation gel, the equilibrium gel shows absence of aging and a remarkable spatially uniform dynamics.

Amphiphilic DNA nanostructures for bottom-up synthetic biology

DNA nanotechnology enables the construction of sophisticated biomimetic nanomachines that are increasingly central to the growing efforts of creating complex cell-like entities from the bottom-up. DNA nanostructures have been proposed as both structural and functional elements of these artificial cells, and in many instances are decorated with hydrophobic moieties to enable interfacing with synthetic lipid bilayers or regulating bulk self-organisation. In this feature article we review recent efforts to design biomimetic membrane-anchored DNA nanostructures capable of imparting complex functionalities to cell-like objects, such as regulated adhesion, tissue formation, communication and transport. We then discuss the ability of hydrophobic modifications to enable the self-assembly of DNA-based nanostructured frameworks with prescribed morphology and functionality, and explore the relevance of these novel materials for artificial cell science and beyond. Finally, we comment on the yet mostly unexpressed potential of amphiphilic DNA-nanotechnology as a complete toolbox for bottom-up synthetic biology - a figurative and literal scaffold upon which the next generation of synthetic cells could be built.

The flexibility-based modulation of DNA nanostar phase separation

Phase separation of biomolecules plays key roles in physiological compartmentalization as well as pathological aggregation. A deeper understanding of biomolecular phase separation requires dissection of a relation between intermolecular interactions and resulting phase behaviors. DNA nanostars, multivalent DNA assemblies of which sticky ends define attractive interactions, represent an ideal system to probe this fundamental relation governing phase separation processes. Here, we use DNA nanostars to systematically study how structural flexibility exhibited by interacting species impacts their phase behaviors. We design multiple nanostars with a varying degree of flexibility using single-stranded gaps of different lengths in the arm of each nanostar unit. We find that structural flexibility drastically alters the phase diagram of DNA nanostars in such a way that the phase separation of more flexible structures is strongly inhibited. This result is not due to self-inhibition from the loss of valency but rather ascribed to a generic flexibility-driven change in the thermodynamics of the system. Our work provides not only potential regulatory mechanisms cells may exploit to dynamically control intracellular phase separation but also a route to build synthetic systems of which assembly can be controlled in a signal dependent manner.

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.

Mechanical Properties of DNA Hydrogels: Towards Highly Programmable Biomaterials

DNA hydrogels are self-assembled biomaterials that rely on Watson–Crick base pairing to form large-scale programmable three-dimensional networks of nanostructured DNA components. The unique mechanical and biochemical properties of DNA, along with its biocompatibility, make it a suitable material for the assembly of hydrogels with controllable mechanical properties and composition that could be used in several biomedical applications, including the design of novel multifunctional biomaterials. Numerous studies that have recently emerged, demonstrate the assembly of functional DNA hydrogels that are responsive to stimuli such as pH, light, temperature, biomolecules, and programmable strand-displacement reaction cascades. Recent studies have investigated the role of different factors such as linker flexibility, functionality, and chemical crosslinking on the macroscale mechanical properties of DNA hydrogels. In this review, we present the existing data and methods regarding the mechanical design of pure DNA hydrogels and hybrid DNA hydrogels, and their use as hydrogels for cell culture. The aim of this review is to facilitate further study and development of DNA hydrogels towards utilizing their full potential as multifeatured and highly programmable biomaterials with controlled mechanical properties.

Hyperbranched DNA clusters

Taking advantage of the base-pairing specificity and tunability of DNA interactions, we investigate the spontaneous formation of hyperbranched clusters starting from purposely designed DNA tetravalent nanostar monomers, encoding in their four sticky ends the desired binding rules. Specifically, we combine molecular dynamics simulations and Dynamic Light Scattering experiments to follow the aggregation process of DNA nanostars at different concentrations and temperatures. At odds with the Flory-Stockmayer predictions, we find that, even when all possible bonds are formed, the system does not reach percolation due to the presence of intracluster bonds. We present an extension of the Flory-Stockmayer theory that properly describes the numerical and experimental results.

Gelling without Structuring: A SAXS Study of the Interactions among DNA Nanostars

We evaluate, by means of synchrotron small-angle X-ray scattering, the shape and mutual interactions of DNA tetravalent nanostars as a function of temperature in both the gas-like state and across the gel transition. To this end, we calculate the form factor from coarse-grained molecular dynamics simulations with a novel method that includes hydration effects; we approximate the radial interaction of DNA nanostars as a hard-sphere potential complemented by a repulsive and an attractive Yukawa term; and we predict the structure factors by exploiting the perturbative random phase approximation of the Percus-Yevick equation. Our approach enables us to fit all the data by selecting the particle radius and the width and amplitude of the attractive potential as free parameters. We determine the evolution of the structure factor across gelation and detect subtle changes of the effective interparticle interactions, that we associate to the temperature and concentration dependence of the particle size. Despite the approximations, the approach here adopted offers new detailed insights into the structure and interparticle interactions of this fascinating system.

DNA-GEL, Novel Nanomaterial for Biomedical Applications and Delivery of Bioactive Molecules

Novel DNA materials promise unpredictable perspectives for applications in cell biology. The realization of DNA-hydrogels built by a controlled association of DNA nanostars, whose binding can be tuned with minor changes in the nucleotide sequences, has been recently described. DNA hydrogels, with specific gelation properties that can be reassambled in desired culture media supplemented with drugs, RNA, DNA molecules and other bioactive compounds offer the opportunity to develop a novel nanomaterial for the delivery of single or multiple drugs in tumor tissues as an innovative and promising strategy. We provide here a comprehensive description of different, recently realized DNA-gels with the perspective of stimulating their biomedical application. Finally, we discuss the possibility to design sophisticated 3D tissue-like DNA-gels incorporating cell spheroids or single cells for the assembly of a novel kind of cellular matrix as a preclinical investigation for the implementation of tools for in vivo delivery of bioactive molecules.

Enzymatic degradation of liquid droplets of DNA is modulated near the phase boundary

Biomolecules can undergo liquid-liquid phase separation (LLPS), forming dense droplets that are increasingly understood to be important for cellular function. Analogous systems are studied as early-life compartmentalization mechanisms, for applications as protocells, or as drug-delivery vehicles. In many of these situations, interactions between the droplet and enzymatic solutes are important to achieve certain functions. To explore this, we carried out experiments in which a model LLPS system, formed from DNA "nanostar" particles, interacted with a DNA-cleaving restriction enzyme, SmaI, whose activity degraded the droplets, causing them to shrink with time. By controlling adhesion of the DNA droplet to a glass surface, we were able to carry out time-resolved imaging of this "active dissolution" process. We found that the scaling properties of droplet shrinking were sensitive to the proximity to the dissolution ("boiling") temperature of the dense liquid: For systems far from the boiling point, enzymes acted only on the droplet surface, while systems poised near the boiling point permitted enzyme penetration. This was corroborated by the observation of enzyme-induced vacuole-formation ("bubbling") events, which can only occur through enzyme internalization, and which occurred only in systems poised near the boiling point. Overall, our results demonstrate a mechanism through which the phase stability of a liquid affects its enzymatic degradation through modulation of enzyme transport properties.

Liquid network connectivity regulates the stability and composition of biomolecular condensates with many components

One of the key mechanisms used by cells to control the spatiotemporal organization of their many components is the formation and dissolution of biomolecular condensates through liquid-liquid phase separation (LLPS). Using a minimal coarse-grained model that allows us to simulate thousands of interacting multivalent proteins, we investigate the physical parameters dictating the stability and composition of multicomponent biomolecular condensates. We demonstrate that the molecular connectivity of the condensed-liquid network-i.e., the number of weak attractive protein-protein interactions per unit of volume-determines the stability (e.g., in temperature, pH, salt concentration) of multicomponent condensates, where stability is positively correlated with connectivity. While the connectivity of scaffolds (biomolecules essential for LLPS) dominates the phase landscape, introduction of clients (species recruited via scaffold-client interactions) fine-tunes it by transforming the scaffold-scaffold bond network. Whereas low-valency clients that compete for scaffold-scaffold binding sites decrease connectivity and stability, those that bind to alternate scaffold sites not required for LLPS or that have higher-than-scaffold valencies form additional scaffold-client-scaffold bridges increasing stability. Proteins that establish more connections (via increased valencies, promiscuous binding, and topologies that enable multivalent interactions) support the stability of and are enriched within multicomponent condensates. Importantly, proteins that increase the connectivity of multicomponent condensates have higher critical points as pure systems or, if pure LLPS is unfeasible, as binary scaffold-client mixtures. Hence, critical points of accessible systems (i.e., with just a few components) might serve as a unified thermodynamic parameter to predict the composition of multicomponent condensates.

Cold-swappable DNA gels

We report an experimental investigation of an all-DNA gel composed by tetra-functional DNA nanoparticles acting as network nodes and bi-functional ones acting as links. The DNA binding sequence is designed to generate at room and lower temperatures a persistent long-lived network. Exploiting ideas from DNA-nanotechnology, we implement in the binding base sequences an appropriate exchange reaction which allows links to swap, constantly retaining the total number of network links. The DNA gel is thus able to rearrange its topology at low temperature while preserving its fully-bonded configuration.

Increasing valence pushes DNA nanostar networks to the isostatic point

The classic picture of soft material mechanics is that of rubber elasticity, in which material modulus is related to the entropic elasticity of flexible polymeric linkers. The rubber model, however, largely ignores the role of valence (i.e., the number of network chains emanating from a junction). Recent work predicts that valence, and particularly the Maxwell isostatic point, plays a key role in determining the mechanics of semiflexible polymer networks. Here, we report a series of experiments confirming the prominent role of valence in determining the mechanics of a model system. The system is based on DNA nanostars (DNAns): multiarmed, self-assembled nanostructures that form thermoreversible equilibrium gels through base pair-controlled cross-linking. We measure the linear and nonlinear elastic properties of these gels as a function of DNAns arm number, f, and concentration [DNAns]. We find that, as f increases from three to six, the gel's high-frequency plateau modulus strongly increases, and its dependence on [DNAns] transitions from nonlinear to linear. Additionally, higher-valence gels exhibit less strain hardening, indicating that they have less configurational freedom. Minimal strain hardening and linear dependence of shear modulus on concentration at high f are consistent with predictions for isostatic systems. Evident strain hardening and nonlinear concentration dependence of shear modulus suggest that the low-f networks are subisostatic and have a transient, potentially fractal percolated structure. Overall, our observations indicate that network elasticity is sensitive both to entropic elasticity of network chains and to junction valence, with an apparent isostatic point [Formula: see text] in agreement with the Maxwell prediction.

Flexibility defines structure in crystals of amphiphilic DNA nanostars

DNA nanostructures with programmable shape and interactions can be used as building blocks for the self-assembly of crystalline materials with prescribed nanoscale features, holding a vast technological potential. Structural rigidity and bond directionality have been recognised as key design features for DNA motifs to sustain long-range order in 3D, but the practical challenges associated with prescribing building-block geometry with sufficient accuracy have limited the variety of available designs. We have recently introduced a novel platform for the one-pot preparation of crystalline DNA frameworks supported by a combination of Watson-Crick base pairing and hydrophobic forces (Brady et al 2017 Nano Lett. 17 3276-81). Here we use small angle x-ray scattering and coarse-grained molecular simulations to demonstrate that, as opposed to available all-DNA approaches, amphiphilic motifs do not rely on structural rigidity to support long-range order. Instead, the flexibility of amphiphilic DNA building-blocks is a crucial feature for successful crystallisation.

Microrheology of DNA hydrogel gelling and melting on cooling

We present systematic characterisation by means of dynamic light scattering and particle tracking techniques of the viscosity and of the linear viscoelastic moduli, G'(ω) and G''(ω), for two different DNA hydrogels. These thermoreversible systems are composed of tetravalent DNA-made nanostars whose sticky sequence is designed to provide controlled interparticle bonding. While the first system forms a gel on cooling, the second one has been programmed to behave as a re-entrant gel, turning again to a fluid solution at low temperature. The frequency-dependent viscous and storage moduli and the viscosity reveal the different viscoelastic behavior of the two DNA hydrogels. Our results show how little variations in the design of the DNA sequences allow tuning of the mechanical response of these biocompatible all-DNA materials.

Microrheology of DNA hydrogels

A key objective in DNA-based material science is understanding and precisely controlling the mechanical properties of DNA hydrogels. We perform microrheology measurements using diffusing wave spectroscopy (DWS) to investigate the viscoelastic behavior of a hydrogel made of Y-shaped DNA (Y-DNA) nanostars over a wide range of frequencies and temperatures. We observe a clear liquid-to-gel transition across the melting temperature region for which the Y-DNA bind to each other. Our measurements reveal a cross-over between the elastic [Formula: see text] and loss modulus [Formula: see text] around the melting temperature [Formula: see text] of the DNA building blocks, which coincides with the systems percolation transition. This transition can be easily shifted in temperature by changing the DNA bond length between the Y shapes. Using bulk rheology as well, we further show that, by reducing the flexibility between the Y-DNA bonds, we can go from a semiflexible transient network to a more energy-driven hydrogel with higher elasticity while keeping the microstructure the same. This level of control in mechanical properties will facilitate the design of more sensitive molecular sensing tools and controlled release systems.

The Proof Is in the Pidan: Generalizing Proteins as Patchy Particles

The Chinese century egg, or pidan, is a traditional preparation of duck eggs that can be stored for months at room temperature without degradation. Raw eggs are soaked in a strong alkaline and salt solution, and the albumin gradually forms a stable, transparent gel. Here, we show that pidan gels belong to the class of materials formed from "patchy particles". We found that the β-sheet structure of ovalbumin, the major protein constituent of egg white, is preserved during gelation, while α-helical regions undergo a degree of unfolding into unstructured random coils that may form attractive patches. Upon dilution in additional strong base, the phase behavior of pidan gels is consistent with patchy-particle thermodynamics. This protein gel is also physically and structurally similar to the protein gels that form the squid lens. Both systems exhibit patchy thermodynamics, and the constituent proteins share physical features including a structured, charged core, and polar, unstructured "arms" that form attractive patches. Our work provides a path toward rational design of proteins for precisely structured, volume-spanning materials.

Effect of oligonucleic acid (ONA) backbone features on assembly of ONA-star polymer conjugates: a coarse-grained molecular simulation study

Understanding the impact of incorporating new physical and chemical features in oligomeric DNA mimics, termed generally as "oligonucleic acids" (ONAs), on their structure and thermodynamics will be beneficial in designing novel materials for a variety of applications. In this work, we conduct coarse-grained molecular simulations of ONA-star polymer conjugates with varying ONA backbone flexibility, ONA backbone charge, and number of arms in the star polymer at a constant ONA strand volume fraction to elucidate the effect of these design parameters on the thermodynamics and assembly of multi-arm ONA-star polymer conjugates. We quantify the thermo-reversible behavior of the ONA-star polymer conjugates by quantifying the hybridization of the ONA strands in the system as a function of temperature (i.e. melting curve). Additionally, we characterize the assembly of the ONA-star polymer conjugates by tracking cluster formation and percolation as a function of temperature, as well as cluster size distribution at temperatures near the assembly transition region. The key results are as follows. The melting temperature (T_m) of the ONA strands decreases upon going from a neutral to a charged ONA backbone and upon increasing flexibility of the ONA backbone. Similar behavior is seen for the assembly transition temperature (T_a) with varying ONA backbone charge and flexibility. While the number of arms in the ONA-star polymer conjugate has a negligible effect on the ONA T_m in these systems, as the number of ONA-star polymer arms increase, the assembly temperature T_a increases and local ordering in the assembled state improves. By understanding how factors like ONA backbone charge, backbone flexibility, and ONA-star polymer conjugate architecture impact the behavior of ONA-star polymer conjugate systems, we can better inform how the selection of ONA chemistry will influence resulting ONA-star polymer assembly.

Conformational Dynamics of Mechanically Compliant DNA Nanostructures from Coarse-Grained Molecular Dynamics Simulations

Structural DNA nanotechnology, the assembly of rigid 3D structures of complex yet precise geometries, has recently been used to design dynamic, mechanically compliant nanostructures with tunable equilibrium conformations and conformational distributions. Here we use coarse-grained molecular dynamics simulations to provide insights into the conformational dynamics of a set of mechanically compliant DNA nanostructures-DNA hinges that use single-stranded DNA "springs" to tune the equilibrium conformation of a layered double-stranded DNA "joint" connecting two stiff "arms" constructed from DNA helix bundles. The simulations reproduce the experimentally measured equilibrium angles between hinge arms for a range of hinge designs. The hinges are found to be structurally stable, except for some fraying of the open ends of the DNA helices comprising the hinge arms and some loss of base-pairing interactions in the joint regions coinciding with the crossover junctions, especially in hinges designed to exhibit a small bending angle that exhibit large local stresses resulting in strong kinks in their joints. Principal component analysis reveals that while the hinge dynamics are dominated by bending motion, some twisting and sliding of hinge arms relative to each other also exists. Forced deformation of the hinges reveals distinct bending mechanisms for hinges with short, inextensible springs versus those with longer, more extensible springs. Lastly, we introduce an approach for rapidly predicting equilibrium hinge angles from individual force-deformation behaviors of its single- and double-stranded DNA components. Taken together, these results demonstrate that coarse-grained modeling is a promising approach for designing, predicting, and studying the dynamics of compliant DNA nanostructures, where conformational fluctuations become important, multiple deformation mechanisms exist, and continuum approaches may not yield accurate properties.

Condensation and Demixing in Solutions of DNA Nanostars and Their Mixtures

We present a numerical/theoretical approach to efficiently evaluate the phase diagram of self-assembling DNA nanostars. Combining input information based on a realistic coarse-grained DNA potential with the Wertheim association theory, we derive a parameter-free thermodynamic description of these systems. We apply this method to investigate the phase behavior of single components and mixtures of DNA nanostars with different numbers of sticky arms, elucidating the role of the system functionality and of salt concentration. Specifically, we evaluate the propensity to demix, the gas-liquid phase boundaries and the location of the critical points. The predicted critical parameters compare very well with existing experimental results for the available compositions. The approach developed here is very general, easily extensible to other all-DNA systems, and provides guidance for future experiments.

Small-angle neutron scattering and molecular dynamics structural study of gelling DNA nanostars

DNA oligomers with properly designed sequences self-assemble into well defined constructs. Here, we exploit this methodology to produce bulk quantities of tetravalent DNA nanostars (each one composed of 196 nucleotides) and to explore the structural signatures of their aggregation process. We report small-angle neutron scattering experiments focused on the evaluation of both the form factor and the temperature evolution of the scattered intensity at a nanostar concentration where the system forms a tetravalent equilibrium gel. We also perform molecular dynamics simulations of one isolated tetramer to evaluate the form factor numerically, without resorting to any approximate shape. The numerical form factor is found to be in very good agreement with the experimental one. Simulations predict an essentially temperature-independent form factor, offering the possibility to extract the effective structure factor and its evolution during the equilibrium gelation.

Limiting the valence: advancements and new perspectives on patchy colloids, soft functionalized nanoparticles and biomolecules

Artistic representation of limited valance units consisting of a soft core (in blue) and a small number of flexible bonding patches (in orange).

Smectic phase in suspensions of gapped DNA duplexes

Smectic ordering in aqueous solutions of monodisperse stiff double-stranded DNA fragments is known not to occur, despite the fact that these systems exhibit both chiral nematic and columnar mesophases. Here, we show, unambiguously, that a smectic-A type of phase is formed by increasing the DNA's flexibility through the introduction of an unpaired single-stranded DNA spacer in the middle of each duplex. This is unusual for a lyotropic system, where flexibility typically destabilizes the smectic phase. We also report on simulations suggesting that the gapped duplexes (resembling chain-sticks) attain a folded conformation in the smectic layers, and argue that this layer structure, which we designate as smectic-fA phase, is thermodynamically stabilized by both entropic and energetic contributions to the system's free energy. Our results demonstrate that DNA as a building block offers an exquisitely tunable means to engineer a potentially rich assortment of lyotropic liquid crystals.

A possible four-phase coexistence in a single-component system

For different phases to coexist in equilibrium at constant temperature T and pressure P, the condition of equal chemical potential μ must be satisfied. This condition dictates that, for a single-component system, the maximum number of phases that can coexist is three. Historically this is known as the Gibbs phase rule, and is one of the oldest and venerable rules of thermodynamics. Here we make use of the fact that, by varying model parameters, the Gibbs phase rule can be generalized so that four phases can coexist even in single-component systems. To systematically search for the quadruple point, we use a monoatomic system interacting with a Stillinger-Weber potential with variable tetrahedrality. Our study indicates that the quadruple point provides flexibility in controlling multiple equilibrium phases and may be realized in systems with tunable interactions, which are nowadays feasible in several soft matter systems such as patchy colloids.

Soft self-assembled nanoparticles with temperature-dependent properties

The fabrication of versatile building blocks that reliably self-assemble into desired ordered and disordered phases is amongst the hottest topics in contemporary materials science. To this end, microscopic units of varying complexity, aimed at assembling the target phases, have been thought, designed, investigated and built. Such a path usually requires laborious fabrication techniques, especially when specific functionalisation of the building blocks is required. Telechelic star polymers, i.e., star polymers made of a number of f di-block copolymers consisting of solvophobic and solvophilic monomers grafted on a central anchoring point, spontaneously self-assemble into soft patchy particles featuring attractive spots (patches) on the surface. Here we show that the tunability of such a system can be widely extended by controlling the physical and chemical parameters of the solution. Indeed, under fixed external conditions the self-assembly behaviour depends only on the number of arms and on the ratio of solvophobic to solvophilic monomers. However, changes in temperature and/or solvent quality make it possible to reliably change the number and size of the attractive patches. This allows the steering of the mesoscopic self-assembly behaviour without modifying the microscopic constituents. Interestingly, we also demonstrate that diverse combinations of the parameters can generate stars with the same number of patches but different radial and angular stiffness. This mechanism could provide a neat way of further fine-tuning the elastic properties of the supramolecular network without changing its topology.

Liquid-Liquid Phase Transitions in Tetrahedrally Coordinated Fluids via Wertheim Theory

Network interpenetration has been proposed as a mechanism for generating liquid-liquid phase transitions in one component systems. We introduce a model of four coordinated particles, which explicitly treats the system as a mixture of two interacting interpenetrating networks that can freely exchange particles. This model can be solved within Wertheim's theory for associating fluids and shows liquid-liquid phase separations (in addition to the gas-liquid) for a wide range of model parameters. We find that originating a liquid-liquid transition requires a small degree of interpenetrability and a preference for intranetwork bonding. Physically, these requirements can be seen as controlling the softness of the particle-particle interaction and the bond flexibility, in full agreement with recent findings [Smallenburg, F.; Filion, L.; Sciortino, F. Nat. Phys. 2014, 10, 653].

Equilibrium gels of trivalent DNA-nanostars: Effect of the ionic strength on the dynamics

Self-assembling DNA-nanostars are ideal candidates to explore equilibrium gelation in systems composed of limited-valence particles. We present here a light scattering study of the dynamics in a trivalent DNA-nanostars equilibrium gel and of its dependence on ionic strength and concentration. Reversible bonds between different nanostars, whose formation is sensitively dependent on temperature, concentration and ionic strength, are provided by complementary DNA sticky ends. We find that the decay of the density correlations is described by a two-step relaxation process characterised by: i) a slow time scale that varies over nearly four orders of magnitude in a temperature window of less than 30 degrees; ii) an increase of the amplitude (the so-called non-ergodicity factor) of the slow relaxation. The slow process follows an Arrhenius law with temperature. We observe that the activation enthalpy does not depend on the ionic strength and that the dependence of the relaxation time on the ionic strength can be rationalized in terms of the free-energy cost of forming a sticky-end duplex. Finally, we observe that dynamics is insensitive to nanostar concentration, in full agreement with the predicted behaviour in equilibrium gels.

Coarse-grained simulation study of sequence effects on DNA hybridization in a concentrated environment

A novel coarse-grained model is developed to elucidate thermodynamics and kinetic mechanisms of DNA self-assembly. It accounts for sequence and solvent conditions to capture key experimental results such as sequence-dependent thermal property and salt-dependent persistence length of ssDNA and dsDNA. Moreover, constant-temperature simulations on two single strands of a homogeneous sequence show two main mechanisms of hybridization: a slow slithering mechanism and a one-order faster zippering mechanism. Furthermore, large-scale simulations at a high DNA strand concentration demonstrate that DNA self-assembly is a robust and enthalpically driven process in which the formation of double helices is deciphered to occur via multiple self-assembly pathways including the strand displacement mechanism. However, sequence plays an important role in shifting the majority of one pathway over the others and controlling size distribution of self-assembled aggregates. This study yields a complex picture on the role of sequence on programmable self-assembly and demonstrates a promising simulation tool that is suitable for studies in DNA nanotechnology.

Soft-patchy nanoparticles: modeling and self-organization

We consider a novel class of patchy particles inspired by polymer-based complex units where the limited valence in bonding is accompanied by soft interactions and incessant fluctuations of the patch positions, possibly leading to reversible modifications of the patch number and size. We introduce a simple model that takes into account the aforementioned features and we focus on the role played by the patch flexibility on the self-organization of our patchy units in the bulk, with particular attention to the connectivity properties and the morphology of the aggregated networks.