Fluctuating Elasticity Mode in Transient Molecular Networks

Heterogeneous dynamics in aging phosphate-based geopolymer

The time-evolution of dynamics as well as microstructure and mechanical response of phosphate-based geopolymers was probed using x-ray photon correlation spectroscopy and rheological tests. The analyzed relaxation processes in the freshly prepared geopolymer mixes evidenced a q-independent mode of the autocorrelation function, ascribed to density fluctuations of the already established molecular network, undergoing reconfiguration without significant mass transport. Upon curing, the detected motions are localized and depict a system evolving toward structural arrest dominated by slower hyperdiffusive dynamics, characterized by a compressed exponential regime, pointing to a structural relaxation process subjected to internal stresses, in a context of marked dynamical and structural heterogeneity. The system ages through a "densification" process producing declining small angle scattered intensity, as two finely intermixed gel-like reaction products, namely, one hydrated aluminophosphate and one hydrated silica, form a percolated network possessing surface fractal scaling of progressively shorter average correlation length. In this scenario, the nominal Al/P molar ratio of the mix, being an index of network-forming ability, is positively correlated with the dynamic viscosity and the overall kinetics, whereas the contrary occurs for the fraction of water.

Reversible Self-Assembly of Nucleic Acids in a Diffusiophoretic Trap

The formation and dissociation of duplexes or higher order structures from nucleic acid strands is a fundamental process with widespread applications in biochemistry and nanotechnology. Here, we introduce a simple experimental system-a diffusiophoretic trap-for the non-equilibrium self-assembly of nucleic acid structures that uses an electrolyte gradient as the driving force. DNA strands can be concentrated up to hundredfold by a diffusiophoretic trapping force that is caused by the electric field generated by the electrolyte gradient. We present a simple equation for the field to guide selection of appropriate trapping electrolytes. Experiments with carboxylated silica particles demonstrate that the diffusiophoretic force is long-ranged, extending over hundreds of micrometers. As an application, we explore the reversible self-assembly of branched DNA nanostructures in the trap into a macroscopic gel. The structures assemble in the presence of an electrolyte gradient, and disassemble upon its removal, representing a prototypical adaptive response to a macroscopic non-equilibrium state.

Mesoscopic two-point collective dynamics of glass-forming liquids

The collective density-density and hydrostatic pressure-pressure correlations of glass-forming liquids are spatiotemporally mapped out using molecular dynamics simulations. It is shown that the sharp rise of structural relaxation time below the Arrhenius temperature coincides with the emergence of slow, nonhydrodynamic collective dynamics on mesoscopic scales. The observed long-range, nonhydrodynamic mode is independent of wave numbers and closely coupled to the local structural dynamics. Below the Arrhenius temperature, it dominates the slow collective dynamics on length scales immediately beyond the first structural peak in contrast to the well-known behavior at high temperatures. These results highlight a key connection between the qualitative change in mesoscopic two-point collective dynamics and the dynamic crossover phenomenon.

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.

"Shutter" Effects Enhance Protein Diffusion in Dynamic and Rigid Molecular Networks

Hydrogels have been widely applied to understand the fundamental functions and mechanism of a natural extracellular matrix (ECM). However, revealing the high permeability of ECM through synthetic hydrogels is still challenged by constructing analogue networks with rigid and dynamic properties. Here, in this study, taking advantage of the rigidity and dynamic binding of DNA building blocks, we have designed a model hydrogel system with structural similarity to ECM, leading to enhanced diffusion for proteins compared with a synthetic polyacrylamide (PAAm) hydrogel. The molecular diffusion behaviors in such a rigid and dynamic network have been investigated both in experiments and simulations, and the dependence of diffusion coefficients with respect to molecular size exhibits a unique transition from a power law to an exponential function. A "shutter" model based on the rigid and dynamic molecular network has been proposed, which has successfully revealed how the rigidity and dynamic bond exchange determine the diffusion mechanism, potentially providing a novel perspective to understand the possible mechanism of enhanced diffusion behaviors in ECM.

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.

Electrostatically Driven Topological Freezing of Polymer Diffusion at Intermediate Confinements

Breaking the paradigm that polymers in crowded aqueous media obey Einstein's law of diffusion, we report a localized nondiffusive hierarchical metastable state at intermediate confinements. Combining electrostatic and topological effects, we can tune the propensity of this new universality class in a quasicoacervate gel system consisting of guest polyamino acid chains inside an oppositely charged host hydrogel. Our observations offer strategies for controlled release and retention of macromolecules in aqueous crowded media, while opening a new direction for understanding topologically frustrated dynamics in polymers and other soft matter systems.

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.

Wave-Vector Dependence of the Dynamics in Supercooled Metallic Liquids

We present a detailed investigation of the wave-vector dependence of collective atomic motion in Au_{49}Cu_{26.9}Si_{16.3}Ag_{5.5}Pd_{2.3} and Pd_{42.5}Cu_{27}Ni_{9.5}P_{21} supercooled liquids close to the glass transition temperature. Using x-ray photon correlation spectroscopy in a previously uncovered spatial range of only a few interatomic distances, we show that the microscopic structural relaxation process mimics the structure and presents a marked slowing down at the main average interparticle distance. This behavior is accompanied by dramatic changes in the shape of the intermediate scattering functions, which suggest the presence of large dynamical heterogeneities at length scales corresponding to a few particle diameters. A ballisticlike mechanism of particle motion seems to govern the structural relaxation of the two systems in the highly viscous phase, likely associated with hopping of caged particles in agreement with theoretical studies.

On the role of flexibility in linker-mediated DNA hydrogels

Three-dimensional DNA networks, composed of tri- or higher valent nanostars with sticky, single-stranded DNA overhangs, have been previously studied in the context of designing thermally responsive, viscoelastic hydrogels. In this work, we use linker-mediated gels, where the sticky ends of two trivalent nanostars are connected through the complementary sticky ends of a linear DNA duplex. We can design this connection to be either rigid or flexible by introducing flexible, non-binding bases. The additional flexibility provided by these non-binding bases influences the effective elasticity of the percolating gel formed at low temperatures. Here we show that by choosing the right length of the linear duplex and non-binding flexible joints, we obtain a completely different phase behaviour to that observed for rigid linkers. In particular, we use dynamic light scattering as a microrheological tool to monitor the self-assembly of DNA nanostars with linear linkers as a function of temperature. While we observe classical gelation when using rigid linkers, the presence of flexible joints leads to a cluster fluid with a much-reduced viscosity. Using both the oxDNA model and a coarse-grained simulation to investigate the nanostar-linker topology, we hypothesise on the possible structure formed by the DNA clusters. Moreover, we present a systematic study of the strong viscosity increase of aqueous solutions in the presence of these DNA building blocks.

Uncovering the dynamic precursors to motor-driven contraction of active gels

Cells and tissues have the remarkable ability to actively generate the forces required to change their shape. This active mechanical behavior is largely mediated by the actin cytoskeleton, a crosslinked network of actin filaments that is contracted by myosin motors. Experiments and active gel theories have established that the length scale over which gel contraction occurs is governed by a balance between molecular motor activity and crosslink density. By contrast, the dynamics that govern the contractile activity of the cytoskeleton remain poorly understood. Here we investigate the microscopic dynamics of reconstituted actin-myosin networks using simultaneous real-space video microscopy and Fourier-space dynamic light scattering. Light scattering reveals different regimes of microscopic dynamics as a function of sample age. We uncover two dynamical precursors that precede macroscopic gel contraction. One is characterized by a progressive acceleration of stress-induced rearrangements, while the other consists of sudden, heterogeneous rearrangements. Intriguingly, our findings suggest a qualitative analogy between self-driven rupture and collapse of active gels and the delayed rupture of passive gels observed in earlier studies of colloidal gels under external loads.

Dynamics and reaction kinetics of coarse-grained bulk vitrimers: a molecular dynamics study

Vitrimers with dynamic covalent bonds make thermosetting materials plastic, recyclable and self-repairing, and have broad application prospects. However, due to the complex composition of vitrimers and the dynamic bond exchange reactions (BERs), the mechanism behind their unique dynamic behavior is not fully understood. We used the hybrid molecular dynamics-Monte Carlo (MD-MC) algorithm to establish a molecular dynamics model that can accurately reflect BERs, and reveal the intrinsic mechanism of the dynamic behavior of the vitrimer system. The simulation results show that BERs change the diffusion mode of the vitrimer's constituent molecules, which in turn affects the BER and other relaxation dynamics. This provides a theoretical basis and a specific method for the rational design of the rheological properties of vitrimers.

q-Independent Slow Dynamics in Atomic and Molecular Systems

Investigating million-atom systems for very long simulation times, we demonstrate that the collective density-density correlation time (τ_{α}) in simulated supercooled water and silica becomes wave-vector independent (q^{0}) when the probing wavelength is several times larger than the interparticle distance. The q independence of the collective density-density correlation functions, a feature clearly observed in light-scattering studies of some soft-matter systems, is thus a genuine feature of many (but not all) slow-dynamics systems, either atomic, molecular, or colloidal. Indeed, we show that when the dynamics of the density fluctuations includes particle-type diffusion, as in the case of the Lennard-Jones binary-mixture model, the q^{0} regime does not set in and the relaxation time continues to scale as τ_{α}∼q^{-2} even at small q.

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.

Quadruplex knots as network nodes: nano-partitioning of guanosine derivates in supramolecular hydrogels

Aqueous solutions of guanosine-5'-monophosphates (GMP) - known to form G-quadruplexes and liquid crystal phases - can be induced to turn into high water content gels by the addition of guanosine (Gua). By a combination of Light Scattering (LS) and AFM we show that Gua/GMP hydrogels are microscopically heterogeneous, formed by Gua-rich disordered microcoils of intertwined filaments ("knots") connected by GMP-rich long linear threads. The different thermal stability of knots and threads controls the gel transition.

Single-Molecule Study of Peptide Gel Dynamics Reveals States of Prestress

De novo peptide surfactant (I₃K) gels provide an ideal system to study the complex dynamics of lightly cross-linked semiflexible fibers because of their large contour lengths, simple chemistry, and slow dynamics. We used single-molecule fluorescence microscopy to record individual fibers and Fourier decomposition of the fiber dynamics to separate thermal contributions to the persistence length from compressive states of prestress (SPS). Our results show that SPS in the network depend strongly on peptide concentration, buffer, and pH and that the fibril energies in SPS follow a Lévy distribution. The presence of SPS in the network imply that collective states of self-stress are also present. Therefore, semiflexible polymer gels need to be considered as complex load-bearing structures and the mean field models for polymer gel elasticity and dynamics often applied to them will not be fully representative of the behavior at the nanoscale. We quantify the impact of cross-links on reptation tube dynamics, which provides a second population of tube fluctuations in addition to those expected for uncross-linked entangled solutions.

Autonomous Actuation of Zero Modes in Mechanical Networks Far from Equilibrium

A zero mode, or floppy mode, is a nontrivial coupling of mechanical components yielding a degree of freedom with no resistance to deformation. Engineered zero modes have the potential to act as microscopic motors or memory devices, but this requires an internal actuation mechanism that can overcome unwanted fluctuations in other modes and the dissipation inherent in real systems. In this Letter, we show theoretically and experimentally that complex zero modes in mechanical networks can be selectively mobilized by nonequilibrium activity. We find that a correlated active bath actuates an infinitesimal zero mode while simultaneously suppressing fluctuations in higher modes compared to thermal fluctuations, which we experimentally mimic by high frequency shaking of a physical network. Furthermore, self-propulsive dynamics spontaneously mobilize finite mechanisms as exemplified by a self-propelled topological soliton. Nonequilibrium activity thus enables autonomous actuation of coordinated mechanisms engineered through network topology.

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.

Crack Initiation in Viscoelastic Materials

In viscoelastic materials, individually short-lived bonds collectively result in a mechanical resistance which is long lived but finite as, ultimately, cracks appear. Here, we provide a microscopic mechanism by which a critical crack length emerges from the nonlinear local bond dynamics. Because of this emerging length scale, macroscopic viscoelastic materials fracture in a fundamentally different manner from microscopically small systems considered in previous models. We provide and numerically verify analytical equations for the dependence of the critical crack length on the bond kinetics and applied stress.

Binding branched and linear DNA structures: From isolated clusters to fully bonded gels

The proper design of DNA sequences allows for the formation of well-defined supramolecular units with controlled interactions via a consecution of self-assembling processes. Here, we benefit from the controlled DNA self-assembly to experimentally realize particles with well-defined valence, namely, tetravalent nanostars (A) and bivalent chains (B). We specifically focus on the case in which A particles can only bind to B particles, via appropriately designed sticky-end sequences. Hence AA and BB bonds are not allowed. Such a binary mixture system reproduces with DNA-based particles the physics of poly-functional condensation, with an exquisite control over the bonding process, tuned by the ratio, r, between B and A units and by the temperature, T. We report dynamic light scattering experiments in a window of Ts ranging from 10 °C to 55 °C and an interval of r around the percolation transition to quantify the decay of the density correlation for the different cases. At low T, when all possible bonds are formed, the system behaves as a fully bonded network, as a percolating gel, and as a cluster fluid depending on the selected r.

Newtonian to non-newtonian fluid transition of a model transient network

The viscosity of gel-forming fluids is notoriously complex and its study can benefit from new model systems that enable a detailed control of the network features. Here we use a novel and simple microfluidic-based active microrheology approach to study the transition from Newtonian to non-Newtonian behavior in a DNA hydrogel whose structure, connectivity, density of bonds, bond energy and kinetics are strongly temperature dependent and well known. In a temperature range of 15 °C, the system reversibly and continuously transforms from a Newtonian dispersion of low-valence nanocolloids into a strongly shear-thinning fluid, passing through a set of intermediate states where it behaves as a power-law fluid. We demonstrate that the knowledge of network topology and bond free energy enables to quantitatively predict the observed behavior using established rheology models.