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.

Marangoni- vs. buoyancy-driven flows: competition for spatio-temporal oscillations in A + B → C systems.

The emergence of self-organized behaviors such as spatio-temporal oscillations is well-known for complex reactions involving nonlinear chemical or thermal feedback. Recently, it was shown that local oscillations of the chemical species concentration can be induced under isothermal batch conditions for simple bimolecular A + B → C reactions, provided they are actively coupled with hydrodynamics. When two reactants A and B, initially separated in space, react upon diffusive contact, damped spatio-temporal oscillations could develop when the surface tension increases sufficiently in the reaction zone. Additionally, if the density decreases, the coupling of both surface tension- and buoyancy-driven contributions to the flow can further sustain this oscillatory instability. Here, we investigate the opposite case of a reaction inducing a localized decrease in surface tension and an increase in density in the reacting zones. In this case, the competition arising from the two antagonistic flows is needed to create oscillatory dynamics, i.e., no oscillations are observed for pure chemically driven Marangoni flows. We study numerically these scenarios in a 2-dimensional system and show how they are controlled by the following key parameters: (i) ΔM and ΔR governing the surface tension and density variation during the reaction, respectively, (ii) the layer thickness of the system, and (iii) its lateral length. This work is a further step toward inducing and controlling chemical oscillations in simple reactions.

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.

Critical Role of Layer Thickness in Frontal Polymerization.

Thermal frontal polymerization (FP) is a chemical process during which a cold monomer-initiator mixture is converted into a hot polymer as a polymerization front propagates in the system due to the interplay between heat diffusion and the exothermicity of the reaction. The theoretical description of FP generally focuses on one-dimensional (1D) reaction-diffusion (RD) models where the effect of heat losses is encoded into an effective parameter in the heat equation. We show here the limits of such 1D models to describe FP under nonadiabatic conditions. To do so, the propagation of a polymerization front is analyzed both analytically and numerically in a rectangular two-dimensional (2D) layer. The layer thickness is shown to control the dynamics of the front and to determine its very existence. We find that for given heat losses, a minimum thickness is required for front propagation as recently observed in FP experiments of 2D thin films on wood. Moreover, when the thickness exceeds a critical value, the front is observed to survive independently of the rate of heat losses. This result cannot be predicted with 1D models where front extinction is always possible. A scaling analysis is proposed to highlight the physical interpretation of such a front survival. The influence of dimensionality on thermal instabilities is also analyzed, with a focus on the differences with the 1D predictions.

Chemo-hydrodynamic pulsations in simple batch A + B → C systems.

Spatio-temporal oscillations can be induced under batch conditions with ubiquitous bimolecular reactions in the absence of any nonlinear chemical feedback, thanks to an active interplay between the chemical process and chemically driven hydrodynamic flows. When two reactants A and B, initially separated in space, react upon diffusive contact, they can power convective flows by inducing a localized variation of surface tension and density at the mixing interface. These flows feedback with the reaction-diffusion dynamics, bearing damped or sustained spatio-temporal oscillations of the concentrations and flow field. By means of numerical simulations, we detail the mechanism underlying these chemohydrodynamic oscillations and classify the main dynamical scenarios in the relevant space drawn by parameters ΔM and ΔR, which rule the surface tension- and buoyancy-driven contributions to convection, respectively. The reactor height is found to play a critical role in the control of the dynamics. The analysis reveals the intimate nature of these oscillatory phenomena and the hierarchy among the different phenomena at play: oscillations are essentially hydrodynamic and the chemical process features the localized trigger for Marangoni flows unstable toward oscillatory instabilities. The characteristic size of Marangoni convective rolls mainly determines the critical conditions and properties of the oscillations, which can be further tuned or suppressed by the buoyancy competition. We finally discuss the possible experimental implementation of such a class of chemo-hydrodynamic oscillator and its implications in fundamental and applied terms.

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.

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.

Convective dynamics of traveling autocatalytic fronts in a modulated gravity field.

When traveling in thin solution layers, autocatalytic chemical fronts may be deformed and accelerated by convective currents that develop because of density and surface tension gradients related to concentration and thermal gradients across the front. On earth, both buoyancy and Marangoni related flows can act in solution layers open to the air while only buoyancy effects operate in covered liquid layers. The respective effects of density and surface tension induced convective motions are analysed here by studying experimentally the propagation of autocatalytic fronts in uncovered and covered liquid layers during parabolic flights in which the gravity field is modulated periodically. We find that the velocity and deformation of the front are increased during hyper-gravity phases and reduced in the micro-gravity phase. The experimental results compare well with numerical simulations of the evolution of the concentration of the autocatalytic product coupled to the flow field dynamics described by Navier-Stokes equations.

A + B → C reaction fronts in Hele-Shaw cells under modulated gravitational acceleration.

The dynamics of A + B → C reaction fronts is studied under modulated gravitational acceleration by means of a combination of parabolic flight experiments and numerical simulations. During modulated gravity the front position undergoes periodic modulation with an accelerated front propagation under hyper-gravity together with a slowing down under low gravity. The underlying reason for this is an amplification and a decay, respectively, of the buoyancy-driven double vortex associated with the front propagation under standard gravitational acceleration, as explained by reaction-diffusion-convection simulations of convection around an A + B → C front. Deeper insights into the correlation between grey-value changes in the experimental shadowgraph images and characteristic changes in the concentration profiles are obtained by a numerical simulation of the imaging process.