Stability analysis and simulations of coupled bulk-surface reaction–diffusion systems

In this article, we formulate new models for coupled systems of bulk-surface reaction–diffusion equations on stationary volumes. The bulk reaction–diffusion equations are coupled to the surface reaction–diffusion equations through linear Robin-type boundary conditions. We then state and prove the necessary conditions for diffusion-driven instability for the coupled system. Owing to the nature of the coupling between bulk and surface dynamics, we are able to decouple the stability analysis of the bulk and surface dynamics. Under a suitable choice of model parameter values, the bulk reaction–diffusion system can induce patterning on the surface independent of whether the surface reaction–diffusion system produces or not, patterning. On the other hand, the surface reaction–diffusion system cannot generate patterns everywhere in the bulk in the absence of patterning from the bulk reaction–diffusion system. For this case, patterns can be induced only in regions close to the surface membrane. Various numerical experiments are presented to support our theoretical findings. Our most revealing numerical result is that, Robin-type boundary conditions seem to introduce a boundary layer coupling the bulk and surface dynamics

Non-equilibrium steady states as saddle points and EDP-convergence for slow-fast gradient systems

The theory of slow-fast gradient systems leads in a natural way to non-equilibrium steady states, because on the slow time scale the fast subsystem stays in steady states that are driven by the interaction with the slow system. Using the theory of convergence of gradient systems in the sense of the energy-dissipation principle shows that there is a natural characterization of these non-equilibrium steady states as saddle points of a Lagrangian where the slow variables are fixed. We give applications to slow-fast reaction-diffusion systems based on the so-called cosh-type gradient structure for reactions. It is shown that two binary reaction give rise to a ternary reaction with a state-dependent reaction coefficient. Moreover, we show that a reaction-diffusion equation with a thin membrane-like layer convergences to a transmission condition, where the formerly quadratic dissipation potential for diffusion convergences to a cosh-type dissipation potential for the transmission in the membrane limit

Solar-Driven Reduction of 1 atm of CO_2 to Formate at 10% Energy-Conversion Efficiency by Use of a TiO_2-Protected III–V Tandem Photoanode in Conjunction with a Bipolar Membrane and a Pd/C Cathode

A solar-driven CO_2 reduction (CO_2R) cell was constructed, consisting of a tandem GaAs/InGaP/TiO_2/Ni photoanode in 1.0 M KOH(aq) (pH = 13.7) to facilitate the oxygen-evolution reaction (OER), a Pd/C nanoparticle-coated Ti mesh cathode in 2.8 M KHCO_3(aq) (pH = 8.0) to perform the CO_2R reaction, and a bipolar membrane to allow for steady-state operation of the catholyte and anolyte at different bulk pH values. At the operational current density of 8.5 mA cm^(–2), in 2.8 M KHCO_3(aq), the cathode exhibited 94% Faradaic efficiency for the reduction of 1 atm of CO_2(g) to formate. The anode exhibited a 320 ± 7 mV overpotential for the OER in 1.0 M KOH(aq), and the bipolar membrane exhibited ∼480 mV voltage loss with minimal product crossovers and >90 and >95% selectivity for protons and hydroxide ions, respectively. The bipolar membrane facilitated coupling between two electrodes and electrolytes, one for the CO_2R reaction and one for the OER, that typically operate at mutually different pH values and produced a lower total cell overvoltage than known single-electrolyte CO_2R systems while exhibiting ∼10% solar-to-fuels energy-conversion efficiency

Non-Equilibrium Large-Scale Membrane Transformations Driven by MinDE Biochemical Reaction Cycles

The MinDE proteins from E. coli have received great attention as a paradigmatic biological pattern-forming system. Recently, it has surfaced that these proteins do not only generate oscillating concentration gradients driven by ATP hydrolysis, but that they can reversibly deform giant vesicles. In order to explore the potential of Min proteins to actually perform mechanical work, we introduce a new model membrane system, flat vesicle stacks on top of a supported lipid bilayer. MinDE oscillations can repeatedly deform these flat vesicles into tubules and promote progressive membrane spreading through membrane adhesion. Dependent on membrane and buffer compositions, Min oscillations further induce robust bud formation. Altogether, we demonstrate that under specific conditions, MinDE self-organization can result in work performed on biomimetic systems and achieve a straightforward mechanochemical coupling between the MinDE biochemical reaction cycle and membrane transformation.We thank MPI‐B Core Facility for assistance in protein purification

De novo vesicle formation and growth: an integrative approach to artificial cells.

The assembly of artificial cells provides a novel strategy to reconstruct life's functions and shed light on how life emerged on Earth and possibly elsewhere. A major challenge to the development of artificial cells is the establishment of simple methodologies to mimic native membrane generation. An ambitious strategy is the bottom-up approach, which aims to systematically control the assembly of highly ordered membrane architectures with defined functionality. This perspective will cover recent advances and the current state-of-the-art of minimal lipid architectures that can faithfully reconstruct the structure and function of living cells. Specifically, we will overview work related to the de novo formation and growth of biomimetic membranes. These studies give us a deeper understanding of the nature of living systems and bring new insights into the origin of cellular life