Differences in enantiomeric diffusion can lead to selective chiral amplification.

A fundamental question associated with chirality is how mixtures containing equal amounts of interconverting enantiomers can spontaneously convert to systems enriched in only one of them. Enantiomers typically have similar chemical properties, but can exhibit distinct reactivity under specific conditions, and these differences can be used to bias the system's composition in favor of one enantiomer. Transport properties are also expected to differ for enantiomers in chiral solvents, but the role of such differences in chiral symmetry breaking has not been clarified yet. In this work, we develop a theoretical framework to show that asymmetry in diffusion properties can trigger a spontaneous and selective symmetry breaking in mixtures of enantiomers. We derive a generic evolution equation for the enantiomeric excess in a chiral solvent. This equation shows that the relative stability of homochiral domains is dictated by the difference of diffusion coefficients of the two enantiomers. Consequently, deracemization toward a specific enantiomeric excess can be achieved when this difference is large enough. These results hold significant implications for our understanding of chiral symmetry breaking.

Quantifying Catalysis at the Origin of Life.

The construction of hypothetical environments to produce organic molecules such as metabolic intermediates or amino acids is the subject of ongoing research into the emergence of life. Experiments specifically focused on an anabolic approach typically rely on a mineral catalyst to facilitate the supply of organics that may have produced prebiotic building blocks for life. Alternatively to a true catalytic system, a mineral could be sacrificially oxidized in the production of organics, necessitating the emergent 'life' to turn to virgin materials for each iteration of metabolic processes. The aim of this perspective is to view the current 'metabolism-first' literature through the lens of materials chemistry to evaluate the need for higher catalytic activity and materials analyses. While many elegant studies have detailed the production of chemical building blocks under geologically plausible and biologically relevant conditions, few appear to do so with sub-stoichiometric amounts of metals or minerals. Moving toward sub-stoichiometric metals with rigorous materials analyses is necessary to demonstrate the viability of an elusive cornerstone of the 'metabolism-first' hypotheses: catalysis. We emphasize that future work should aim to demonstrate decreased catalyst loading, increased productivity, and/or rigorous materials analyses for evidence of true catalysis.

Spontaneous mirror symmetry breaking in reaction-diffusion systems: ambivalent role of the achiral precursor.

The behaviour of a Frank-like chemical network model featuring autocatalytic production of chiral enantiomers from achiral reactants is studied numerically in 1D and 2D systems using fluctuating initial conditions and accounting for diffusion processes. Our results reveal that the achiral substrate concentration can play an ambivalent role. It is shown that when the achiral reactant concentration is maintained constant and homogeneous in 1D systems, global homochirality is not systematically reached when the size of the system or the achiral reactant concentration are increased. However, with a fixed concentration gradient, coexisting homochiral domains of opposite handedness are no longer observed and homogeneous homochirality, i.e. the presence of a single stable homochiral domain, is recovered. In 2D systems, reaching global homochirality is just a matter of time. This time is dramatically increased when insufficient or excessive amount of achiral reactant is used. An optimal amount of achiral material is observed to maximise the enantiomer production rates.

Initial source of heterogeneity in a model for cell fate decision in the early mammalian embryo.

During development, cells from a population of common progenitors evolve towards different fates characterized by distinct levels of specific transcription factors, a process known as cell differentiation. This evolution is governed by gene regulatory networks modulated by intercellular signalling. In order to evolve towards distinct fates, cells forming the population of common progenitors must display some heterogeneity. We applied a modelling approach to obtain insights into the possible sources of cell-to-cell variability initiating the specification of cells of the inner cell mass into epiblast or primitive endoderm cells in early mammalian embryo. At the single-cell level, these cell fates correspond to three possible steady states of the model. A combination of numerical simulations and bifurcation analyses predicts that the behaviour of the model is preserved with respect to the source of variability and that cell-cell coupling induces the emergence of multiple steady states associated with various cell fate configurations, and to a distribution of the levels of expression of key transcription factors. Statistical analysis of these time-dependent distributions reveals differences in the evolutions of the variance-to-mean ratios of key variables of the system, depending on the simulated source of variability, and, by comparison with experimental data, points to the rate of synthesis of the key transcription factor NANOG as a likely initial source of heterogeneity.

Connecting gene expression to cellular movement: A transport model for cell migration.

The adhesion properties and the mobility of biological cells play key roles in the propagation of cancer. These properties are expected to depend on intracellular processes and on the concentrations of chemicals inside the cell. While most existing reaction-diffusion models for cell migration consider that cell mobility and proliferation rate are constant or depend on an external diffusing species, they do not include the gene expression dynamics taking place in moving cells that affect cellular transport. In this work, we propose a multiscale model where mobility and proliferation depend explicitly on the cell's internal state. We focus more specifically on the case of cellular mobility in epithelial tissues. Wound-healing experiments have demonstrated that the loss of a key protein, E-cadherin, results in a significant increase in both mobility and invasiveness of epithelial cells, with dramatic consequences on cancer progression. We can reproduce the results of these experiments under various genetic conditions with a single set of parameters.

Stochastic thermodynamics based on an Einstein-Boltzmann definition of fluctuating entropy.

Stochastic thermodynamics is an extension of classical nonequilibrium thermodynamics to small systems, where fluctuations are expected to play an important role. A central difficulty met when developing such an extension is how to define a nonequilibrium fluctuating entropy. Typically, the expression used is based on Gibbs' formula for entropy at equilibrium. In this work, we show that one can construct an alternative framework for stochastic thermodynamics based on an extension of Einstein's formula connecting the probability of fluctuations and entropy around equilibrium states. We compare the two approaches and discuss, in particular, how they lead to different interpretations of what a stochastic entropy and entropy production represent.

Reconstructing stochastic attractors from nanoscale experiments on a non-equilibrium reaction.

We studied the catalytic NO2(g) + H2(g)/Pt system on model platinum catalysts with nanoscale spatial resolution by means of field emission microscopy (FEM). While the surface of the catalyst is in a non-reactive state at low H2 partial pressure, bursts of activity are observed when increasing this parameter. These kinetic instabilities subsequently evolve towards self-sustained periodic oscillations for a wide range of pressures. Combining time series analyses and numerical simulations of a simple reaction model, we clarify how these observations fit in the traditional classification of dynamical systems. In particular, reconstructions of the probability density around oscillating trajectories show that the experimental system defines a crater-like structure in probability space. The experimental observations thus correspond to a noise-perturbed limit cycle emerging from a nanometric reactive system. This conclusion is further supported by comparison with stochastic simulations of the proposed chemical model. The obtained results and simulations pave the way towards a better understanding of reactive nanosystems.

Stochastic approach to irreversible thermodynamics.

An extension of classical irreversible thermodynamics pioneered by Ilya Prigogine is developed, in which fluctuations of macroscopic observables accounting for microscopic-scale processes are incorporated. The contribution of the fluctuations to the entropy production is derived from a generalized entropy balance equation and expressed in terms of the fluctuating variables, via an extended local equilibrium Ansatz and in terms of the probability distributions of these variables. The approach is illustrated on reactive systems involving linear and nonlinear steps, and the role of the distance from equilibrium and of the nonlinearities is assessed.

Modelling the propagation of a dynamical signature in gene expression mediated by the transport of extracellular microRNAs.

Extracellular microRNAs (miRNAs) carried by exosomes can play a key role in cell-to-cell communication. Deregulation of miRNA expression and exosome secretion have been related to pathological conditions such as cancer. While it is known that circulating miRNAs can alter gene expression in recipient cells, it remains unclear how significant the dynamical impact of these extracellular miRNAs is. To shed light on this issue, we propose a model for the spatio-temporal evolution of the protein expression in a cell tissue altered by abnormal miRNA expression in a donor cell. This results in a nonhomogeneous cellular response in the tissue, which we quantify by studying the range of action of the donor cell on the surrounding cells. Key model parameters that control the range of action are identified. Based on a model for a heterogeneous cell population, we show that the dynamics of gene expression in the tissue is robust to random changes of the parameter values. Furthermore, we study the propagation of gene expression oscillations in a tissue induced by extracellular miRNAs. In the donor cell, the miRNA inhibits its own transcription which can give rise to local oscillations in gene expression. The resulting oscillations of the concentration of extracellular miRNA induce oscillations of the protein concentration in recipient cells. We analyse the nonmonotonic spatial evolution of the oscillation amplitude of the protein concentration in the tissue which may have implications for the propagation of oscillations in biological rhythms such as the circadian clock.

Nonlinear behavior and fluctuation-induced dynamics in the photosensitive Belousov-Zhabotinsky reaction.

The photosensitive Belousov-Zhabotinsky (pBZ) reaction has been used extensively to study the properties of chemical oscillators. In particular, recent experiments revealed the existence of complex spatiotemporal dynamics for systems consisting of coupled micelles (V < 10-21 L) or droplets (V ≈ [10-8-10-11] L) in which the pBZ reaction takes place. These results have been mostly understood in terms of reaction-diffusion models. However, in view of the small size of the droplets and micelles, large fluctuations of concentrations are to be expected. In this work, we investigate the role of fluctuations on the dynamics of a single droplet with stochastic simulations of an extension of the Field-Körös-Noyes (FKN) model taking into account the photosensitivity. The birhythmicity and chaotic behaviors predicted by the FKN model in the absence of fluctuations become transient or intermittent regimes whose lifetime decreases with the size of the droplet. Simple oscillations are more robust and can be observed even in small systems (V > 10-12 L), which justifies the use of deterministic models in microfluidic systems of coupled oscillators. The simulations also reveal that fluctuations strongly affect the efficiency of inhibition by light, which is often used to control the kinetics of these systems: oscillations are found for parameter values for which they are supposed to be quenched according to deterministic predictions.

Comment on "Flow-induced arrest of spatiotemporal chaos and transition to a stationary pattern in the Gray-Scott model".

In this Comment, we review the results of pattern formation in a reaction-diffusion-advection system following the kinetics of the Gray-Scott model. A recent paper by Das [Phys. Rev. E 92, 052914 (2015)10.1103/PhysRevE.92.052914] shows that spatiotemporal chaos of the intermittency type can disappear as the advective flow is increased. This study, however, refers to a single point in the space of kinetic parameters of the original Gray-Scott model. Here we show that the wealth of patterns increases substantially as some of these parameters are changed. In addition to spatiotemporal intermittency, defect-mediated turbulence can also be found. In all cases, however, the chaotic behavior is seen to disappear as the advective flow is increased, following a scenario similar to what was reported in our earlier work [I. Berenstein and C. Beta, Phys. Rev. E 86, 056205 (2012)10.1103/PhysRevE.86.056205] as well as by Das. We also point out that a similar phenomenon can be found in other reaction-diffusion-advection models, such as the Oregonator model for the Belousov-Zhabotinsky reaction under flow conditions.

Emergence of Chemical Oscillations from Nanosized Target Patterns.

This work investigates experimentally the mechanism by which chemical oscillations emerge in a nanometric system. We monitor the spatiotemporal dynamics of an oscillating reaction on the surface of a nanosized three-dimensional Pt model catalyst. Using high-resolution field emission techniques, we are able to show that the oscillations are generated by nanoscale chemical target patterns of much shorter characteristic time than the period with which the oscillations occur. Our observations are made for a specific reaction system-NO_{2} reduction with hydrogen-and represent the first experimental evidence for the presence of target patterns at the nanoscale. They can be seen as an experimental demonstration of reaction-diffusion mechanisms to hold at the nanoscale as they do at the macroscale. These results shed new light on the emergence of complexity through different time and length scales.

Stochastic thermodynamics of reactive systems: An extended local equilibrium approach.

The recently developed extended local equilibrium approach to stochastic thermodynamics is applied to reactive systems. The properties of the fluctuating entropy and entropy production are analyzed for general linear and for prototypical nonlinear kinetic processes. It is shown that nonlinear kinetics typically induces deviations of the mean entropy production from its value in the deterministic (mean-field) limit. The probability distributions around the mean are derived and shown to qualitatively differ in thermodynamic equilibrium, under nonequilibrium conditions and in the vicinity of criticalities associated to the onset of multistability. In each case large deviation-type properties are shown to hold. The results are compared with those of alternative approaches developed in the literature.

Fluctuating Dynamics of Nanoscale Chemical Oscillations: Theory and Experiments.

Chemical oscillations are observed in a variety of reactive systems, including biological cells, for the functionality of which they play a central role. However, at such scales, molecular fluctuations are expected to endanger the regularity of these behaviors. The question of the mechanism by which robust oscillations can nevertheless emerge is still open. In this work, we report on the experimental investigation of nanoscale chemical oscillations observed during the NO2 + H2 reaction on platinum, using field electron microscopy. We show that the correlation time and the variance of the period of oscillations are connected by a universal constraint, as predicted theoretically for systems subjected to a phenomenon called phase diffusion. These results open the way to a better understanding, modeling, and control of nanoscale oscillators.

Spatiotemporal chaos from bursting dynamics.

In this paper, we study the emergence of spatiotemporal chaos from mixed-mode oscillations, by using an extended Oregonator model. We show that bursting dynamics consisting of fast/slow mixed mode oscillations along a single attractor can lead to spatiotemporal chaotic dynamics, although the spatially homogeneous solution is itself non-chaotic. This behavior is observed far from the Hopf bifurcation and takes the form of a spatiotemporal intermittency where the system locally alternates between the fast and the slow phases of the mixed mode oscillations. We expect this form of spatiotemporal chaos to be generic for models in which one or several slow variables are coupled to activator-inhibitor type of oscillators.

Reconstructing the micrometeorological dynamics of the southern Amazonian transitional forest.

In this work, we reconstruct and analyze the micrometeorological dynamics of the transitional forest located south of the Amazon basin. For this, we use time series of micrometeorological variables collected over five years in the transitional forest of Mato Grosso (Brazil). We employ local feature analysis, a recently proposed extension of principal component analysis, to extract the most relevant physical variables from this set. We show in this way that temperature records contain most of the dynamical information in all seasons. Based on this result, the dimensionality of the space spanned by the system's dynamics and the properties of the so defined attractors are obtained. In the dry season, the system presents a robust oscillatory character described by a well-defined limit cycle. In the wet season, the dynamics becomes more irregular but can still be seen as a periodic behavior affected by external noise. These results can help to develop accurate models for the meteorology of the Amazonian transitional forest and can thus lead to a better understanding of this important ecosystem.

Stationary spots and stationary arcs induced by advection in a one-activator, two-inhibitor reactive system.

This paper studies the spatiotemporal dynamics of a reaction-diffusion-advection system corresponding to an extension of the Oregonator model, which includes two inhibitors instead of one. We show that when the reaction-diffusion, two-dimensional problem displays stationary patterns the addition of a plug flow can induce the emergence of new types of stationary structures. These patterns take the form of spots or arcs, the size and the spacing of which can be controlled by the flow.

Defect-mediated turbulence and transition to spatiotemporal intermittency in the Gray-Scott model.

In this paper, we show that the Gray-Scott model is able to produce defect-mediated turbulence. This regime emerges from the limit cycle, close or far from the Hopf bifurcation, but always right before the Andronov homoclinic bifurcation of the homogeneous system. After this bifurcation, as the control parameter is further changed, the system starts visiting more and more frequently the stable node of the model. Consequently, the defect-mediated turbulence gradually turns into spatiotemporal intermittency.

Towards an efficient multiscale modeling of low-dimensional reactive systems: study of numerical closure procedures.

We study a numerical closure approach for systems of chemically reacting systems [corrected] on lattices with low-dimensional support, for which a mean-field approximation is insufficiently accurate because of lateral interaction on the lattice. We introduce a hierarchy of macroscopic state variables, taking particle clusters into account, whose time evolution is obtained via microscopic (kinetic Monte Carlo) simulation. The macroscopic state variables are chosen such that they can be [corrected] straightforwardly conserved during reconstruction of a microscopic configuration (the so-called lifting step). We present and compare the effects of different alternatives to initialize the remaining degrees of freedom. We illustrate the strong interplay between the number of macroscopic state variables and the specifics of the lifting and that, for a given lifting operator, accuracy of the macroscopic dynamics does not necessarily improve monotonically when adding macroscopic state variables.