Introduction: Self-organization in nonequilibrium chemical systems

Bifurcation and Transposition of the Wicking Front of Binary Solutions Infiltrating into Chromatography Paper Associated with Their Evaporation

Nonequilibrium fluid patterns, such as Marangoni contraction, coffee rings, and tears of wine, are generated in binary solutions spread on a substrate during their evaporation. In this study, we observed another type of nonequilibrium behavior exhibited by binary solutions as they infiltrate porous materials and undergo evaporation. A binary solution comprising hexane and ethanol was brought into contact with the chromatography paper to facilitate infiltration into the paper's pores. Because the experimental setup was in an open environment, infiltration and evaporation occurred simultaneously. The wicking front exhibited an initial rapid advancement, followed by subsequent receding and readvancing. Additionally, the bifurcation of the wicking front after the onset of its readvancement was confirmed by monitoring the temporal evolution of the spatial luminance distribution and temperature distribution on the surface of the chromatography paper. Chromatographic development of a hydrophilic dye was conducted in this experimental setup in an open environment. Additionally, it was confirmed that the receding and readvancing of the wicking front represented the transposition of the bifurcated wicking fronts.

An Approach to the De Novo Synthesis of Life

As the remit of chemistry expands beyond molecules to systems, new synthetic targets appear on the horizon. Among these, life represents perhaps the ultimate synthetic challenge. Building on an increasingly detailed understanding of the inner workings of living systems and advances in organic synthesis and supramolecular chemistry, the de novo synthesis of life (i.e., the construction of a new form of life based on completely synthetic components) is coming within reach. This Account presents our first steps in the journey toward this long-term goal. The synthesis of life requires the functional integration of different subsystems that harbor the different characteristics that are deemed essential to life. The most important of these are self-replication, metabolism, and compartmentalization. Integrating these features into a single system, maintaining this system out of equilibrium, and allowing it to undergo Darwinian evolution should ideally result in the emergence of life. Our journey toward de novo life started with the serendipitous discovery of a new mechanism of self-replication. We found that self-assembly in a mixture of interconverting oligomers is a general way of achieving self-replication, where the assembly process drives the synthesis of the very molecules that assemble. Mechanically induced breakage of the growing replicating assemblies resulted in their exponential growth, which is an important enabler for achieving Darwinian evolution. Through this mechanism, the self-replication of compounds containing peptides, nucleobases, and fully synthetic molecules was achieved. Several examples of evolutionary dynamics have been observed in these systems, including the spontaneous diversification of replicators allowing them to specialize on different food sets, history dependence of replicator composition, and the spontaneous emergence of parasitic behavior. Peptide-based replicator assemblies were found to organize their peptide units in space in a manner that, inadvertently, gives rise to microenvironments that are capable of catalysis of chemical reactions or binding-induced activation of cofactors. Among the reactions that can be catalyzed by the replicators are ones that produce the precursors from which these replicators grow, amounting to the first examples of the assimilation of a proto-metabolism. Operating these replicators in a chemically fueled out-of-equilibrium replication-destruction regime was found to promote an increase in their molecular complexity. Fueling counteracts the inherent tendency of replicators to evolve toward lower complexity (caused by the fact that smaller replicators tend to replicate faster). Among the remaining steps on the road to de novo life are now to assimilate compartmentalization and achieve open-ended evolution of the resulting system. Success in the synthesis of de novo life, once obtained, will have far-reaching implications for our understanding of what life is, for the search for extraterrestrial life, for how life may have originated on earth, and for every-day life by opening up new vistas in the form living technology and materials.

Friction Mechanism Features of the Nickel-Based Composite Antifriction Materials at High Temperatures

The friction behavior of the formed antifriction films and their effect on the functional properties of the composite based on the powder nickel alloy EI929 with solid lubricant CaF2 at high temperatures was investigated. An antifriction film was formed on the contact surfaces during the friction process. Such a film was the result of the interaction of the contact surfaces with atmospheric oxygen at high temperatures. It contains oxides of alloying elements from materials of the frictional contact and solid lubricant calcium fluoride. The quantitative ratio of formed oxides depends on the temperature operating conditions of material. The data of thermodynamic simulation of the high-temperature interaction of the composite with oxygen coincide with the experimental data obtained by studying the fine structure of surface antifriction films. Antifriction films consist of oxide phases in combination with solid CaF2 lubricant. Anti-friction films provide high wear resistance of the self-lubricating composite in the range of temperatures 1073–1173 K due to the balance between the rate of their formation and wear. When the temperature exceeds 1200 K, the film loses its lubricating properties and acts as an abrasive substance due to the intense oxidation. Abrasive surfaces of materials were subjected also to microscopic examination, in which the mechanically mixed layer (MML) was described. The study of the friction surface roughness parameters confirmed the presence of the formed friction self-lubricating film and allowed to determine its parameters. The friction mechanism was the formation of an oxide layer combined with a solid lubricant, which provides high antifriction properties in the range of 1073–1273 K.

Self-organization across scales: from molecules to organisms

Creating ordered structures from chaotic environments is at the core of biological processes at the subcellular, cellular and organismic level. In this perspective, we explore the physical as well as biological features of two prominent concepts driving self-organization, namely phase transition and reaction-diffusion, before closing with a discussion on open questions and future challenges associated with studying self-organizing systems.This article is part of the theme issue 'Self-organization in cell biology'.

Self-assembling outside equilibrium: emergence of structures mediated by dissipation

Self-assembly under non-equilibrium conditions may give rise to the formation of structures not available at equilibrium.

A Synthetic Replicator Drives a Propagating Reaction-Diffusion Front

A simple synthetic autocatalytic replicator is capable of establishing and driving the propagation of a reaction-diffusion front within a 50 μL syringe. This replicator templates its own synthesis through a 1,3-dipolar cycloaddition reaction between a nitrone component, equipped with a 9-ethynylanthracene optical tag, and a maleimide. Kinetic studies using NMR and UV-vis spectroscopies confirm that the replicator forms efficiently and with high diastereoselectivity, and this replication process brings about a dramatic change in optical properties of the sample-a change in the color of the fluorescence in the sample from yellow to blue. The addition of a small amount of the preformed replicator at a specific location within a microsyringe, filled with the reaction building blocks, results in the initiation and propagation of a reaction-diffusion front. The realization of a replicator capable of initiating a reaction-diffusion front provides a platform for the examination of interconnected replicating networks under out-of-equilibrium conditions involving diffusion processes.

Exploiting recognition-mediated assembly and reactivity in [2]rotaxane formation

A small molecular reaction network exploits recognition-mediated reactive processes in order to drive the assembly and formation of both a self-replicating linear template (thread) and a [2]rotaxane, in which the linear template is encircled by a diamide macrocycle. Complementary recognition sites, placed at strategic positions on the reactive building blocks, drive these assembly and replication processes. Template-instructed experiments show that the thread is capable of efficient self-replication and that no cross-catalytic relationships exist between the thread and the [2]rotaxane. The rate of [2]rotaxane formation is insensitive to the addition of a preformed template, however, [2]rotaxane formation does show enhanced diastereoselectivity, most likely originating from its recognition-mediated formation through a ternary reactive complex.

Hysteresis and drift of spiral waves near heterogeneities: From chemical experiments to cardiac simulations

Dissipative patterns in excitable reaction-diffusion systems can be strongly affected by spatial heterogeneities. Using the photosensitive Belousov-Zhabotinsky reaction, we show a hysteresis effect in the transition between free and pinned spiral rotation. The latter state involves the rotation around a disk-shaped obstacle with an impermeable and inert boundary. The transition is controlled by changes in light intensity. For permeable heterogeneities of higher excitability, we observe spiral drift along both linear and circular boundaries. Our results confirm recent theoretical predictions and, in the case of spiral drift, are further reproduced by numerical simulations with a modified Oregonator model. Additional simulations with a cardiac model show that orbital motion can also exist in anisotropic and three-dimensional systems.

From chemical systems to systems chemistry: Patterns in space and time

We present a brief, idiosyncratic overview of the past quarter century of progress in nonlinear chemical dynamics and discuss what we view as the most exciting recent developments and some challenges and likely areas of progress in the next 25 years.

Inhibitory and excitatory pulse coupling of two frequency-different chemical oscillators with time delay

Dynamical regimes of two pulse coupled non-identical Belousov-Zhabotinsky oscillators have been studied experimentally as well as theoretically with the aid of ordinary differential equations and phase response curves both for pure inhibitory and pure excitatory coupling. Time delay τ between a spike in one oscillator and perturbing pulse in the other oscillator plays a significant role for the phase relations of synchronous regimes of the 1:1 and 1:2 resonances. Birhythmicity between anti-phase and in-phase oscillations for inhibitory pulse coupling as well as between 1:2 and 1:1 resonances for excitatory pulse coupling have also been found. Depending on the ratio of native periods of oscillations T2/T1, coupling strength, and time delay τ, such resonances as 1:1 (with different phase locking), 2:3, 1:2, 2:5, 1:3, 1:4, as well as complex oscillations and oscillatory death are observed.

Excitability Modulation of Oscillating Media in 3D-Printed Structures

Excitation and oscillation are central to living systems. For excitable systems, which can be brought into oscillation by an external stimulus, the excitation threshold is a crucial parameter. This is evident for neurons, which only generate an action potential when exposed to a sufficiently high concentration of excitatory neurotransmitters, which may only be achieved when multiple presynaptic axons deliver their action potential simultaneously to the synaptic cleft. Dynamic systems composed of relatively simple chemicals are of interest because they can serve as a model for physiological processes or can be exploited to implement chemical computing. With these applications in mind, we have studied the properties of the oscillatory Belousov-Zhabotinsky (BZ) reaction in 3D-printed reaction vessels with open channels of different dimensions. It is demonstrated that the channel geometry can be used to modulate the excitability of the BZ medium, switching a continuously oscillating medium to an excitable medium. Because large networks of channel-connected reaction wells of different depth can easily be fabricated by 3D printing, local excitability modulation could be built into the structure of the reaction vessel itself, opening the way to more extensive experimentation with networks of chemical oscillators.

Mixed mode and sequential oscillations in the cerium-bromate-4-aminophenol photoreaction

Cerium was introduced to the bromate-aminophenol photochemical oscillator to implement coupled autocatalytic feedbacks. Mixed mode and sequential oscillations emerged in the studied system, making it one of the few chemical oscillators known to support consecutive bifurcations in a batch system. The complex reaction behavior showed a strong dependence on the intensity of illumination supplied to the system. Removal of illumination during an oscillatory window affected both the frequency and amplitude of the oscillation but did not fully extinguish them, indicating that the cerium-bromate-4-aminophenol oscillator was photosensitive rather than photo-controlled. A moderate light intensity allowed for a slow evolution of the system, which proved to be critical for the emergence of transient complex oscillations. Variation of individual reaction parameters was carried out, which indicated that the development of complex oscillations occur in a narrow region and a phase diagram in the 4-aminophenol and sulfuric acid plane demonstrated this. Simulations provide strong support that transient complex oscillations observed experimentally arise from the coupling of two autocatalytic cycles.

Spiral defect drift in the wave fields of multiple excitation patterns

Spiral waves in excitable systems decay to drifting defects if forced by high-frequency wave trains. Using the Barkley model we analyze the drift velocity in planar wave trains as a function of wave frequency. Within two antiparallel, planar wave trains of equal frequency a defect is pushed into the collision region where it stops. Within two circular wave fields, however, it continues its drift in a direction perpendicular to the axis connecting the pacemakers. Depending on the forcing frequency and the initial position, this motion occurs either away from or toward the pacemaker axis. Three circular wave fields can be used to position the defect at a unique point close to the center of the pacemaker triangle. The results are also observed in experiments with the Belousov-Zhabotinsky reaction.

Elucidating the origin of diastereoselectivity in a self-replicating system: selfishness versus altruism

We have investigated a diastereoselective self-replicating system based on a cycloaddition of a fulvene derivative and a maleimide using a two-pronged approach of combining NMR spectroscopy with computational modelling. Two diastereomers are formed with identical rates in the absence of replication. When replication is enabled, one diastereomer takes over the resources as a "selfish" autocatalyst, while exploiting the competitor as a weak "altruist", resulting in a diastereoselectivity of 16:1. We applied 1D and 2D NMR spectroscopic techniques supported by ab initio chemical shifts as well as ab initio molecular dynamics simulations to study the structure and dynamics of the underlying network. This powerful combination allowed us to decipher the energetic and structural rationale behind the observed behaviour, while static computational methods currently used in the field did not.

Pattern formation controlled by time-delayed feedback in bistable media

Effects of time-delayed feedback on pattern formation are studied both numerically and theoretically in a bistable reaction-diffusion model. The time-delayed feedback applied to the activator and/or the inhibitor alters the behavior of the nonequilibrium Ising-Bloch (NIB) bifurcation. If the intensities of the feedbacks applied to the two species are identical, only the velocities of Bloch fronts are changed. If the intensities are different, both the critical point of the NIB bifurcation and the threshold of stability of front to transverse perturbations are changed. The effect of time-delayed feedback on the activator opposes the effect of time-delayed feedback on the inhibitor. When the time-delayed feedback is applied individually to one of the species, positive and negative feedbacks make the bifurcation point shift to different directions. The time-delayed feedback provides a flexible way to control the NIB bifurcation and the pattern formation.

Inward propagating chemical waves in Taylor vortices

Advection-reaction-diffusion (ARD) waves in the Belousov-Zhabotinsky reaction in steady Taylor-Couette vortices have been visualized using magnetic-resonance imaging and simulated using an adapted Oregonator model. We show how propagating wave behavior depends on the ratio of advective, chemical and diffusive time scales. In simulations, inward propagating spiral flamelets are observed at high Damköhler number (Da). At low Da, the reaction distributes itself over several vortices and then propagates inwards as contracting ring pulses--also observed experimentally.

Propagating waves separate two states of actin organization in living cells

Propagating actin waves are dynamic supramolecular structures formed by the self-assembly of proteins within living cells. They are built from actin filaments together with single-headed myosin, the Arp23 complex, and coronin in a defined three-dimensional order. The function of these waves in structuring the cell cortex is studied on the substrate-attached surface of Dictyostelium cells by the use of total internal reflection fluorescence (TIRF) microscopy. Actin waves separate two areas of the cell cortex from each other, which are distinguished by the arrangement of actin filaments. The Arp23 complex dominates in the area enclosed by a wave, where it has the capacity of building dendritic structures, while the proteins prevailing in the external area, cortexillin I and myosin-II, bundle actin filaments and arrange them in antiparallel direction. Wave propagation is accompanied by transitions in the state of actin with a preferential period of 5 min. Wave generation is preceded by local fluctuations in actin assembly, some of the nuclei of polymerized actin emanating from clathrin-coated structures, others emerging independently. The dynamics of phase transitions has been analyzed to provide a basis for modeling the nonlinear interactions that produce spatio-temporal patterns in the actin system of living cells.

On propagation of excitation waves in moving media: the FitzHugh-Nagumo model

Background

Existence of flows and convection is an essential and integral feature of many excitable media with wave propagation modes, such as blood coagulation or bioreactors.

Methods/Results

Here, propagation of two-dimensional waves is studied in parabolic channel flow of excitable medium of the FitzHugh-Nagumo type. Even if the stream velocity is hundreds of times higher that the wave velocity in motionless medium (), steady propagation of an excitation wave is eventually established. At high stream velocities, the wave does not span the channel from wall to wall, forming isolated excited regions, which we called “restrictons”. They are especially easy to observe when the model parameters are close to critical ones, at which waves disappear in still medium. In the subcritical region of parameters, a sufficiently fast stream can result in the survival of excitation moving, as a rule, in the form of “restrictons”. For downstream excitation waves, the axial portion of the channel is the most important one in determining their behavior. For upstream waves, the most important region of the channel is the near-wall boundary layers. The roles of transversal diffusion, and of approximate similarity with respect to stream velocity are discussed.

Conclusions

These findings clarify mechanisms of wave propagation and survival in flow.

Spontaneous oscillations and waves during chemical vapor deposition of InN

We report observations of self-sustaining spatiotemporal chemical oscillations during metal-organic chemical vapor deposition of InN onto GaN. Under constant supply of vapor precursors trimethylindium and NH3, the condensed-phase cycles between crystalline islands of InN and elemental In droplets. Propagating fronts between regions of InN and In occur with linear, circular, and spiral geometries. The results are described by a model in which the nitrogen activity produced by surface-catalyzed NH3 decomposition varies with the exposed surface areas of GaN, InN, and In.