Nucleation dynamics of a model biomolecular liquid.

Liquid-liquid phase separation in biology has recently been shown to play a major role in the spatial control of biomolecular components within the cell. However, as they are phase transitions, these processes also display nontrivial dynamics. A model phase-separating system of DNA nanostars provides unique access to nucleation physics in a biomolecular context, as phase separation is driven near room temperature by highly thermo-responsive DNA hybridization and at modest DNA concentrations. By measuring the delay time for phase-separated droplets to appear, we demonstrate that the dynamics of DNA nanostar phase separation reflect that of a metastable binary mixture of patchy particles. For sufficiently deep temperature quenches, droplets undergo spinodal decomposition and grow spontaneously, driven by Brownian motion and coalescence of phase-separated droplets, as confirmed by comparing experimental measurements to particle-based simulations. Near the coexistence boundary, droplet growth slows substantially, indicative of a nucleation process. The temperature dependence of droplet appearance times can be predicted by a classical nucleation picture with mean field exponents and demonstrates that a theory previously used to predict equilibrium phase diagrams can also distinguish spinodal and nucleation dynamical regimes. These dynamical principles are relevant to behaviors associated with liquid-liquid phase separating systems, such as their spatial patterning, reaction coupling, and biological function.

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.

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.

Dynamical Approach to the Jamming Problem.

A simple dynamical model, biased random organization (BRO), appears to produce configurations known as random close packing (RCP) as BRO's densest critical point in dimension d=3. We conjecture that BRO likewise produces RCP in any dimension; if so, then RCP does not exist in d=1-2 (where BRO dynamics lead to crystalline order). In d=3-5, BRO produces isostatic configurations and previously estimated RCP volume fractions 0.64, 0.46, and 0.30, respectively. For all investigated dimensions (d=2-5), we find that BRO belongs to the Manna universality class of dynamical phase transitions by measuring critical exponents associated with the steady-state activity and the long-range density fluctuations. Additionally, BRO's distribution of near contacts (gaps) displays behavior consistent with the infinite-dimensional theoretical treatment of RCP when d≥4. The association of BRO's densest critical configurations with random close packing implies that RCP's upper-critical dimension is consistent with the Manna class d_{uc}=4.

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.

Random Close Packing as a Dynamical Phase Transition.

Sphere packing is an ancient problem. The densest packing is known to be a face-centered cubic (FCC) crystal, with space-filling fraction ϕ_{FCC}=π/sqrt[18]≈0.74. The densest "random packing," random close packing (RCP), is yet ill defined, although many experiments and simulations agree on a value ϕ_{RCP}≈0.64. We introduce a simple absorbing-state model, biased random organization (BRO), which exhibits a Manna class dynamical phase transition between absorbing and active states that has as its densest critical point ϕ_{c_{max}}≈0.64≈ϕ_{RCP} and, like other Manna class models, is hyperuniform at criticality. The configurations we obtain from BRO appear to be structurally identical to RCP configurations from other protocols. This leads us to conjecture that the highest-density absorbing state for an isotropic biased random organization model produces an ensemble of configurations that characterizes the state conventionally known as RCP.

Hyperuniform Structures Formed by Shearing Colloidal Suspensions.

In periodically sheared suspensions there is a dynamical phase transition, characterized by a critical strain amplitude γ_{c}, between an absorbing state where particle trajectories are reversible and an active state where trajectories are chaotic and diffusive. Repulsive nonhydrodynamic interactions between "colliding" particles' surfaces have been proposed as a source of this broken time reversal symmetry. A simple toy model called random organization qualitatively reproduces the dynamical features of this transition. Random organization and other absorbing state models exhibit hyperuniformity, a strong suppression of density fluctuations on long length scales quantified by a structure factor S(q→0)∼q^{α} with α>0, at criticality. Here we show experimentally that the particles in periodically sheared suspensions organize into structures with anisotropic short-range order but isotropic, long-range hyperuniform order when oscillatory shear amplitudes approach γ_{c}.

Optimizing a reconfigurable material via evolutionary computation.

Rapid prototyping by combining evolutionary computation with simulations is becoming a powerful tool for solving complex design problems in materials science. This method of optimization operates in a virtual design space that simulates potential material behaviors and after completion needs to be validated by experiment. However, in principle an evolutionary optimizer can also operate on an actual physical structure or laboratory experiment directly, provided the relevant material parameters can be accessed by the optimizer and information about the material's performance can be updated by direct measurements. Here we provide a proof of concept of such direct, physical optimization by showing how a reconfigurable, highly nonlinear material can be tuned to respond to impact. We report on an entirely computer controlled laboratory experiment in which a 6×6 grid of electromagnets creates a magnetic field pattern that tunes the local rigidity of a concentrated suspension of ferrofluid and iron filings. A genetic algorithm is implemented and tasked to find field patterns that minimize the force transmitted through the suspension. Searching within a space of roughly 10^{10} possible configurations, after testing only 1500 independent trials the algorithm identifies an optimized configuration of layered rigid and compliant regions.

Dense suspension splat: monolayer spreading and hole formation after impact.

We use experiments and minimal numerical models to investigate the rapidly expanding monolayer formed by the impact of a dense suspension drop against a smooth solid surface. The expansion creates a lacelike pattern of particle clusters separated by particle-free regions. Both the expansion and the development of the spatial inhomogeneity are dominated by particle inertia and, therefore, are robust and insensitive to details of the surface wetting, capillarity, and viscous drag.

Fast imaging technique to study drop impact dynamics of non-Newtonian fluids.

In the field of fluid mechanics, many dynamical processes not only occur over a very short time interval but also require high spatial resolution for detailed observation, scenarios that make it challenging to observe with conventional imaging systems. One of these is the drop impact of liquids, which usually happens within one tenth of millisecond. To tackle this challenge, a fast imaging technique is introduced that combines a high-speed camera (capable of up to one million frames per second) with a macro lens with long working distance to bring the spatial resolution of the image down to 10 µm/pixel. The imaging technique enables precise measurement of relevant fluid dynamic quantities, such as the flow field, the spreading distance and the splashing speed, from analysis of the recorded video. To demonstrate the capabilities of this visualization system, the impact dynamics when droplets of non-Newtonian fluids impinge on a flat hard surface are characterized. Two situations are considered: for oxidized liquid metal droplets we focus on the spreading behavior, and for densely packed suspensions we determine the onset of splashing. More generally, the combination of high temporal and spatial imaging resolution introduced here offers advantages for studying fast dynamics across a wide range of microscale phenomena.