Chemical composition from photos: Dried solution drops reveal a morphogenetic tree.

Under nonequilibrium conditions, inorganic systems can produce a wealth of life-like shapes and patterns which, compared to well-formed crystalline materials, remain widely unexplored. A seemingly simple example is the formation of salt deposits during the evaporation of sessile droplets. These evaporites show great variations in their specific patterns including single rings, creep, small crystals, fractals, and featureless disks. We have explored the patterns of 42 different salts at otherwise constant conditions. Based on 7,500 images, we show that distinct pattern families can be identified and that some salts (e.g., Na2SO4 and NH4NO3) are bifurcated creating two distinct motifs. Family affiliations cannot be predicted a priori from composition alone but rather emerge from the complex interplay of evaporation, crystallization, thermodynamics, capillarity, and fluid flow. Nonetheless, chemical composition can be predicted from the deposit pattern with surprisingly high accuracy even if the set of reference images is small. These findings suggest possible applications including smartphone-based analyses and lightweight tools for space missions.

A minimal physical model for curvotaxis driven by curved protein complexes at the cell's leading edge.

Cells often migrate on curved surfaces inside the body, such as curved tissues, blood vessels, or highly curved protrusions of other cells. Recent in vitro experiments provide clear evidence that motile cells are affected by the curvature of the substrate on which they migrate, preferring certain curvatures to others, termed "curvotaxis." The origin and underlying mechanism that gives rise to this curvature sensitivity are not well understood. Here, we employ a "minimal cell" model which is composed of a vesicle that contains curved membrane protein complexes, that exert protrusive forces on the membrane (representing the pressure due to actin polymerization). This minimal-cell model gives rise to spontaneous emergence of a motile phenotype, driven by a lamellipodia-like leading edge. By systematically screening the behavior of this model on different types of curved substrates (sinusoidal, cylinder, and tube), we show that minimal ingredients and energy terms capture the experimental data. The model recovers the observed migration on the sinusoidal substrate, where cells move along the grooves (minima), while avoiding motion along the ridges. In addition, the model predicts the tendency of cells to migrate circumferentially on convex substrates and axially on concave ones. Both of these predictions are verified experimentally, on several cell types. Altogether, our results identify the minimization of membrane-substrate adhesion energy and binding energy between the membrane protein complexes as key players of curvotaxis in cell migration.

Pattern selection by material aging: Modeling chemical gardens in two and three dimensions.

Chemical gardens are complex, often macroscopic, structures formed by precipitation reactions. Their thin walls compartmentalize the system and adjust in size and shape if the volume of the interior reactant solution is increased by osmosis or active injection. Spatial confinement to a thin layer is known to result in various patterns including self-extending filaments and flower-like patterns organized around a continuous, expanding front. Here, we describe a cellular automaton model for this type of self-organization, in which each lattice site is occupied by one of the two reactants or the precipitate. Reactant injection causes the random replacement of precipitate and generates an expanding near-circular precipitate front. If this process includes an age bias favoring the replacement of fresh precipitate, thin-walled filaments arise and grow-like in the experiments-at the leading tip. In addition, the inclusion of a buoyancy effect allows the model to capture various branched and unbranched chemical garden shapes in two and three dimensions. Our results provide a model of chemical garden structures and highlight the importance of temporal changes in the self-healing membrane material.

Bobbing chemical garden tubes: oscillatory self-motion from buoyancy and catalytic gas production.

Chemical reactions can induce self-propulsion by the production and ejection of gas bubbles from micro-rocket like cylindrical units. We describe related micro-submarines that change their depth in response to catalytic gas production. The structures consist of silica-supported CuO and are produced by utilizing the self-assembly rules of chemical gardens. In H2O2 solution, the tube cavity produces O2(g) and the resulting buoyancy lifts the tube to the air-solution interface, where it releases oxygen and sinks back down to the bottom of the container. In 5 cm deep solutions, the resulting bobbing cycles have a period of 20-30 s and repeat for several hours. The ascent is characterized by a vertical orientation of the tube and a constant acceleration. During the descent, the tubes are oriented horizontally and sink at a nearly constant speed. These striking features are quantitatively captured by an analysis of the involved mechanical forces and chemical kinetics. The results show that ascending tubes increase their oxygen-production rate by the motion-induced injection of fresh solution into the tube cavity.

Characteristic growth of chemical gardens from mixtures of two salts.

Chemical gardens formed from two metal salts (MCl2 or MSO4) have been investigated to understand the effects of mixing on the growth of precipitate tubes. The growth of tubes can be classified into three types, i.e., collaborative, inhibited, and individual growth, depending on the combination of the two metal salts. Characteristic features of tube growth are discussed in relation to the flow near the tip of the tube controlled by osmotic pressure and the solubility product, Ksp, for M(OH)2. The present study can be interpreted as an inanimate model system of symbiosis among different species, such as mixed cropping systems and survival among different kinds of microbial cells.

Nonclassical Crystallization Causes Dendritic and Band-Like Microscale Patterns in Inorganic Precipitates.

The self-organization of complex solids can create patterns extending hierarchically from the atomic to the macroscopic scale. A frequently studied model is the chemical garden system which consists of life-like precipitate shapes. In this study, we examine the thin walls of chemical gardens using microfluidic devices that yield linear Ni(OH)2 precipitate membranes. We observe distinct light-scattering patterns within the compositionally pure membranes, including disorganized spots, dendrites, and parallel bands. The bands are tilted with respect to the membrane axis and their spacing (20-100 µm) increases with increasing flow rates. Scanning electron microscopy reveals that the bands consist of submicron particles embedded in a denser material and these particles are also found in the reactant stream. We propose that dendrites and bands arise from the attachment of solution-borne nanoparticles. The bands are generated by particle-aggregation zones moving upstream along the slowly advancing membrane surface. The speed of the aggregation zones is proportional to the band distance and defines the system's dispersion relation. This speed-wavelength dependence and the flow-opposing motion of the aggregation zones are likely caused by low particle concentrations in the wake of the zones that only slowly recover due to Brownian motion and particle nucleation.

Front-like expansion and arrest of programmed cell death in brown banana spots.

The spot patterns on bananas are a striking case of biological pattern formation and-as a qualitative ripeness indicator-linked to 50 million tons of wasted food per year. Ripening bananas develop these senescent spots as phenolic compounds are enzymatically oxidized and cellular integrity is lost. We characterize the dynamics of the spot expansion and their nucleation rates based on time-lapse movies. Spots nucleate for about 2 days yielding a typical density of 8 spots/cm2. The expansion is initially diffusion controlled and the effective diffusion coefficient decreases with nucleation time from 1.3 to 0.4 mm2d-1. During and after expansion, the browning fronts maintain a steep and constant intensity gradient. We quantitatively reproduce these features by a reaction-diffusion model that considers the local oxygen concentration and browning degree of the peel. All model parameters are based on measurements and front stalling is explained by decreasing oxygen levels in the nucleation sites.

Collective motion of self-propelled chemical garden tubes.

In H2O2 solutions, manganese-containing chemical garden tubes can self-propel due to the catalytic production and ejection of oxygen bubbles. Here, we investigate the collective behavior of these self-assembled precipitate tubes. In thin solution layers, the tubes show definite autonomous dynamics with only weak interactions that result from fluid motion around the moving units and directional changes during collisions. In thick solution layers with convex menisci forcing spatial confinement, the tubes undergo cycles of self-assembly and dispersion. This collective motion results from the rhythmic creation of a large master bubble around which the tubes align tangentially.

Shape-preserving conversion of calcium carbonate tubes to self-propelled micromotors.

The self-assembly of inorganic structures beyond the euhedral shape repertoire is a powerful approach to grow hierarchically ordered materials and mesoscopic devices. The hollow precipitate tubes in chemical gardens are a classic example, which we produce on Nafion membranes separating a CaCl2-containing gel from a Na2CO3 solution. The resulting CaCO3 microtubes are conical and consist of either pure vaterite or calcite. The process also forms branched T- and Y-shaped structures. The metastable vaterite polymorph can be converted to Mn-based structures without loss of the macroscopic shape. In H2O2 solution, the resulting tubes self-propel by the release of O2 bubbles, which for branched structures causes rotation. The tubes can contain multiple bubbles which are ejected in a quasi-periodic fashion (e.g. in groups of four). The addition of surfactants causes the accumulation of bubble trails and bubble rafts that interact with the moving tubes and give rise to distinct motion patterns.

Coexistence of oscillatory and reduced states on a spherical field controlled by electrical potential.

The Belousov-Zhabotinsky (BZ) reaction was investigated to elucidate features of oscillations depending on the applied electrical potential, E. A cation-exchange resin bead loaded with the catalyst of the BZ reaction was placed on a platinum plate as a working electrode and then E was applied. We found that global oscillations (GO) and a reduced state coexisted on the bead at a negative value of E and that the source point of GO changed depending on E. The thickness of the reduced state was determined by a yellow colored region which corresponded to the distribution of Br2. The present studies suggest that the distribution of the inhibitor, Br-, which is produced from Br2, plays an important role in the existence of the reduced state and GO, and the source point of GO.

Chemical Garden Membranes in Temperature-Controlled Microfluidic Devices.

Thin-walled tubes that classically form when metal salts react with sodium silicate solution are known as chemical gardens. They share similarities with the porous, catalytic materials in hydrothermal vent chimneys, and both structures are exposed to steep pH gradients that, combined with thermal factors, might have provided the free energy for prebiotic chemistry on early Earth. We report temperature effects on the shape, composition, and opacity of chemical gardens. Tubes grown at high temperature are more opaque, indicating changes to the membrane structure or thickness. To study this dependence, we developed a temperature-controlled microfluidic device, which allows the formation of analogous membranes at the interface of two coflowing reactant solutions. For the case of Ni(OH)2, membranes thicken according to a diffusion-controlled mechanism. In the studied range of 10-40 °C, the effective diffusion coefficient is independent of temperature. This suggests that counteracting processes are at play (including an increased solubility) and that the opacity of chemical garden tubes arises from changes in internal morphology. The latter could be linked to experimentally observed dendritic structures within the membranes.

Hyperscroll dynamics: Vortices in four-dimensional networks.

We investigate a network of excitable nodes diffusively coupled to their neighbors along four orthogonal directions. This regular network effectively forms a four-dimensional reaction-diffusion system and has rotating wave solutions. We analyze some of the general features of these hyperscroll waves, which rotate around surfaces such as planes, spheres, or tori. The surfaces evolve according to local curvatures and a system-specific surface tension. They have associated local phases and phase gradients tend to decrease over time. We also discuss the robustness of these network states against the removal of random node connections and report an example of hyperscroll turbulence.

Flow-Assisted Self-Organization of Hybrid Membranes.

Microfluidic flows are a powerful tool to drive reactions far from equilibrium and, thus, induce chemical selforganization. Studies of membrane formation in microfluidic devices have been limited to non-redox and purely inorganic reactions. Here, the formation of hybrid membranes at the interface of AgNO3 and 3,3',5,5'-tetramethylbenzidine solutions, which are steadily co-injected into a microfluidic device, is reported. The membrane thickening occurs in both directions and reveals oscillatory dynamics. The hybrid membrane mainly consists of hair-like Ag microstructures, Ag nanowires, and unbranched TMB-TMB2+ microfibers. Branched dendrite-like fibers form on the TMB side when the flow is stopped. These components were characterized with techniques including micro-Raman and energy dispersive X-ray spectroscopy as well as scanning electron microscopy. The effects of initial concentration ratios on the membrane thickening speed and its opaqueness were also studied.

Microfluidic Production of Pyrophosphate Catalyzed by Mineral Membranes with Steep pH Gradients.

Pyrophosphate might have functioned as an energy storage/currency molecule on early Earth, essential for the emergence of life. Here we synthesized mineral membranes involving iron(II), iron(III), and other divalent metal cations (calcium, manganese, cobalt, copper, zinc, and nickel) and tested their ability to catalyze the formation of pyrophosphate from phosphate and acetyl phosphate across steep pH gradients in microfluidic devices. We studied the chemical compositions of the precipitate membranes (which included vivianite, goethite, and green rust) using in situ and ex situ micro-Raman spectroscopy. The yields of pyrophosphate were determined by aqueous 31 P NMR spectroscopy. We found that Fe2+ and Ca2+ were the best catalysts for pyrophosphate synthesis among investigated ions; Fe3+ and mixed-valence iron membranes were also able to promote pyrophosphate formation. In addition, the pH gradients across the membranes affected the pyrophosphate yields and the smallest pH gradient resulted in the highest yield. These results suggest a possible route of substrate phosphorylation in prebiotic hydrothermal systems.

Flow-Induced Precipitation in Thin Capillaries Creates Helices, Lamellae, and Tubes.

Precipitation reactions under flow in confined media are relevant to the control of pathological biomineralization, processes affecting aquifers, and challenges in the petroleum industry. Here we show that for a simple geometry, such conditions create macroscopic structures including helices, tubes, lamellae, slugs, and disordered patterns. All structures emerge when salt solution is slowly injected into thin capillaries filled with hydroxide solution. For the helices, the pitch is proportional to the pump rate revealing a constant period of 0.63 s. Different morphologies of the insoluble metal hydroxide can co-exist causing random transitions along the capillary. On average, 15 % of the final system contains residual hydroxide solution. While mechanically stable for flow speeds above 25 mm min-1 , structures collapse and sediment for slower injection speeds. Some of the observed features share similarities with precipitate tubes in chemical gardens and the dynamics of liquid-liquid pipe flow.

Filiform corrosion as a pressure-driven delamination process.

Filiform corrosion produces long and narrow trails on various coated metals through the detachment of the coating layer from the substrate. In this work, we present a combined experimental and theoretical analysis of this process with the aim to describe quantitatively the shape of the cross-section, perpendicular to the direction of propagation, of the filaments produced. For this purpose, we introduce a delamination model of filiform corrosion dynamics and show its compatibility with experimental data where the coating thickness has been varied systematically.

Chemical Wave Propagation in the Belousov-Zhabotinsky Reaction Controlled by Electrical Potential.

The Belousov-Zhabotinsky (BZ) reaction is an important experimental model for the study of chemical oscillations and waves far from the thermodynamic equilibrium. Earlier studies had observed that individual BZ microbeads can show both global oscillations and traveling waves, but failed to select these different dynamic states. Here, we report experiments, in which this control was achieved by an externally applied electrical potential. The spherical microbeads were first loaded with the catalyst, then immersed into a catalyst-free BZ solution, and finally placed onto a planar platinum electrode. For positive electrical potentials, we observed global oscillations, whereas negative potentials resulted in traveling waves. The spatio-temporal characteristics of these phenomena are discussed in relation to the activator, HBrO2, which is produced by an electrochemical reaction.

Wavy membranes and the growth rate of a planar chemical garden: Enhanced diffusion and bioenergetics.

To model ion transport across protocell membranes in Hadean hydrothermal vents, we consider both theoretically and experimentally the planar growth of a precipitate membrane formed at the interface between two parallel fluid streams in a 2D microfluidic reactor. The growth rate of the precipitate is found to be proportional to the square root of time, which is characteristic of diffusive transport. However, the dependence of the growth rate on the concentrations of hydroxide and metal ions is approximately linear and quadratic, respectively. We show that such a difference in ionic transport dynamics arises from the enhanced transport of metal ions across a thin gel layer present at the surface of the precipitate. The fluctuations in transverse velocity in this wavy porous gel layer allow an enhanced transport of the cation, so that the effective diffusivity is about one order of magnitude higher than that expected from molecular diffusion alone. Our theoretical predictions are in excellent agreement with our laboratory measurements of the growth of a manganese hydroxide membrane in a microfluidic channel, and this enhanced transport is thought to have been needed to account for the bioenergetics of the first single-celled organisms.

From nonlinear reaction-diffusion processes to permanent microscale structures.

Biomorphs are polycrystalline aggregates that self-assemble during inorganic precipitation reactions. The shape repertoire of these microstructures include hemispherical objects with complicated internal features such as radial spikes and cones as well as folded sheets reminiscent of corals. We propose that at the microscale, some of these patterns are caused by nonlinear reaction-diffusion processes and present a simple model for this unconventional type of precipitation. The model consists of three reaction steps that convert a reactant species autocatalytically into an intermediate and eventually into a solid, immobile product. Numerical simulations of the model in three space dimensions reveal product structures that are similar to the experimentally observed biomorphs.

Polyelectrolyte complex films influence the formation of polycrystalline micro-structures.

Silica-carbonate biomorphs are inorganic materials composed of thousands of crystalline nanorods that assemble complex morphologies such as helices, vessels, and sheets. We investigate the effect on biomorph crystallization of polyelectrolyte complex films that are prepared using the layer-by-layer deposition technique and post-processed to obtain three stable, chemically distinct films. Biomorph growth on poly(diallyldimethylammonium)-dominated substrates (cationic) shows polycrystalline helical and sheet structures bounded by large witherite prisms. Crystallization on poly(styrenesulfonate)-dominated (anionic) and stoichiometric substrates follows a qualitatively different pathway. We observe islands of radial mineral films that over several days extend at a remarkably constant velocity of 0.48 µm h-1 and eventually mineralize the whole substrate. Our work opens exciting avenues for the use of polyelectrolyte films as tunable substrates for biomimetic crystallization.