Reaction-diffusion Processes Research Articles

The Impact of Membrane Protein Diffusion on GPCR Signaling.

Spatiotemporal signal shaping in G protein-coupled receptor (GPCR) signaling is now a well-established and accepted notion to explain how signaling specificity can be achieved by a superfamily sharing only a handful of downstream second messengers. Dozens of G-coupled GPCR signals ultimately converge on the production of cAMP, a ubiquitous second messenger. This idea is almost always framed in terms of local concentrations, the differences in which are maintained by means of spatial separation. However, given the dynamic nature of the reaction-diffusion processes at hand, the dynamics, in particular the local diffusional properties of the receptors and their cognate G proteins, are also important. By combining some first principle considerations, simulated data, and experimental data of the receptors diffusing on the membranes of living cells, we offer a short perspective on the modulatory role of local membrane diffusion in regulating GPCR-mediated cell signaling. Our analysis points to a diffusion-limited regime where the effective production rate of activated G protein scales linearly with the receptor–G protein complex’s relative diffusion rate and to an interesting role played by the membrane geometry in modulating the efficiency of coupling.

Spatial and Temporal Oscillations of Surface Tension Induced by an A + B → C Traveling Front

This work describes a new mechanism for the emergence of oscillatory dynamics driven by the interaction of hydrodynamic flows and reaction-diffusion processes with no autocatalytic feedback nor prescribed hydrodynamic instability involved. To do so, we study the dynamics of an A+ B → C reaction-diffusion front in the presence of chemically-driven Marangoni flows for arbitrary initial concentrations of reactants and diffusion coefficients of all species. All the species are assumed to affect the solution surface tension thereby inducing Marangoni flows at the air-liquid interface. The system dynamics is studied by numerically integrating the incompressible Navier-Stokes equations coupled to reaction-diffusion-convection equations for the three chemical species. We report spatial and temporal oscillations of surface tension triggered by differential diffusion effects of surfactant species coupled to the chemically-induced Marangoni effect. Such oscillations are related to the discontinuous traveling of the front along the surface leading to the progressive formation of local extrema in the surface tension profiles as time evolves.

Theoretical analysis of reaction-diffusion process in biocatalyst modified electrodes: Solutions derived via Akbari-Ganji method and Taylor’s series with Ancient Chinese algorithms

Theoretical analysis of reaction-diffusion process in biocatalyst modified electrodes: Solutions derived via Akbari-Ganji method and Taylor’s series with Ancient Chinese algorithms

Non-monotonous enzyme-assisted self-assembly profiles resulting from reaction-diffusion processes in host gels

Reaction–diffusion (RD) processes are responsible for surface and in-depth micropatterning in inanimate and living matter. Here we show that enzyme-assisted self-assembly (EASA) of peptides is a valuable tool to functionnalize host gels. By using a phosphatase distributed in a host hydrogel, the diffusion of phosphorylated peptides from a liquid/host gel interface leads to the spontaneous formation of a pattern of dephosphorylated peptide self-assembly presenting at least two self-assembly maxima. Variation of enzyme and peptide concentrations change the pattern characteristics. When a peptide drop is deposited on a phosphatase functionalized gel, a self-assembly pattern is also formed both along the gel-solution interface and perpendicular to the interface. This self-assembly pattern induces a local change of the gel mechanical properties measured by nanoindentation. Its appearance relies on the formation of self-assembled structures by nucleation and growth processes which are static in the hydrogel. This process presents great similarities with the Liesegang pattern formation and must be taken into account for the functionalization of hydrogels by EASA. A mechanism based on RD is proposed leading to an effective mathematical model accounting for the pattern formation. This work highlights EASA as a tool to design organic Liesegang-like microstructured materials with potential applications in biomaterials and artificial living systems design.

Computational modeling of the Balitsky–Kovchegov equation and its numerical solution using hybrid B-spline collocation technique

The dynamics of high-energy scattering of hadrons are governed by Quantum Chromodynamics (QCD). In the parton model of QCD, scattering can be represented as a kind of reaction–diffusion process and consequently can be included in the category of the Fisher–Kolmogorov–Petrovsky–Piscounov (FKPP) equation. We perform a numerical study in the mean-field approximation of QCD evolution given by the Balitsky–Kovchegov (BK) equation, using the hybrid B-spline (HB-spline) collocation technique. The Rubin–Graves type linearization process is used to linearize the nonlinear terms. The accuracy and efficiency of the method are checked by taking numerical examples. It is noticed that the present method gives more accurate results than existing methods. The von Neumann stability analysis is also discussed for the discretized system of the BK equation.

Cross-scale dynamic interactions in compacting porous media as a trigger to pattern formation

SUMMARYPatterns in nature are often interpreted as a product of reaction-diffusion processes which result in dissipative structures. Thermodynamic constraints allow prediction of the final state but the dynamic evolution of the microprocesses is hidden. We introduce a new microphysics-based approach that couples the microscale cross-constituent interactions to the large-scale dynamic behaviour, which leads to the discovery of a family of soliton-like excitation waves. These waves can appear in hydromechanically coupled porous media as a reaction to external stimuli. They arise, for instance, when mechanical forcing of the porous skeleton releases internal energy through a phase change, leading to tight coupling of the pressure in the solid matrix with the dissipation of the pore fluid pressure. In order to describe these complex multiscale interactions in a thermodynamic consistent framework, we consider a dual-continuum system, where the large-scale continuum properties of the matrix–fluid interaction are described by a reaction-self diffusion formulation, and the small-scale dissipation of internal energy by a reaction-cross diffusion formulation that spells out the macroscale reaction and relaxes the adiabatic constraint on the local reaction term in the conventional reaction-diffusion formalism. Using this approach, we recover the familiar Turing bifurcations (e.g. rhythmic metamorphic banding), Hopf bifurcations (e.g. Episodic Tremor and Slip) and present the new excitation wave phenomenon. The parametric space is investigated numerically and compared to serpentinite deformation in subduction zones.

Self-controlled wave solutions to the Tzitzeica-type nonlinear models in mathematical physics

Quantum field theory and solid-state physics phenomena are interpreted using the Tzitzeica-Dodd-Bullough model and nonlinear optics and electromagnetic waves are studied through the Dodd-Bullough-Mikhailov equation. The nonlinear Cahn-Allen model is important for describing the evolution of non-conserved order fields during anti-period sphere coarsening and the phase separation reaction–diffusion processes in multicomponent alloy structures. In this article, we have assessed the advanced and broad-spectrum solitary wave solutions to the stated models and studied the effects of wave speed as well as physical coordinates on the wave profiles and affirmed that waveform varies with the change of the free parameters associated to them. The soliton solutions are extracted by balancing the exponents of the highest-order linear and nonlinear terms. To thoroughly analyze the wave characteristic of the closed-form solutions, different standard wave profiles including kink, bell-shaped soliton, anti-peakon, periodic, quasi-periodic, complex singular, and several general solitons are depicted. Both Painlevé and traveling wave transformation play important roles in converting the equations into nonlinear differential equations. The solutions formulated in this probe are further generic, wide-spectral and some are distinctive which have not been established in the former studies.

VARIATIONAL PERSPECTIVE FOR THE FRACTAL THIN FILM EQUATION ARISING IN ELECTROANALYTICAL CHEMISTRY

The thin film equation is very important in electroanalytical chemistry arising in diffusion–reaction process. Considering the effort of the surface morphology on the diffusion process, the thin film equation is modified by using the fractal derivative, and its fractal variational principle is successfully established according to the semi-inverse method and two-scale transform method. It is very helpful to study the structure of the approximate solution.

Two-phase binding of drug in a three-layered arterial wall following stent implantation

The present study explores the distribution and the binding of drug eluted from an embedded drug-eluting stent (DES), having struts of the circular cross-section. The arterial tissue is composed of three distinct layers, namely, the intima, the media and the adventitia, with varying diffusivity, and at the interfaces between different layers, a jump condition is imposed. The transport of free drug is modelled by the convection–diffusion-reaction process while the binding of drug is modelled by a nonlinear saturable reversible chemical reaction only. This model incorporates two types of binding mechanisms, namely, the specific binding caused by the interaction of drug and receptors, and the non-specific binding due to the gripping of drug in the extracellular medium (ECM). Furthermore, a constant as well as time-dependent release kinetics have been considered. All the governing equations along with suitable initial, boundary and jump interface conditions in cylindrical polar coordinate system are solved successfully by using the finite difference method. In this study, several clinical key factors like the degree of strut embedment, inter-strut distance (ISD), release mechanism are examined thoroughly. The study reveals that the inclusion of different layers along with jump interface conditions has a remarkable impact on stent-based delivery. Simulated results predict that a higher concentration profile for free drug and rapid saturation of binding sites take place for a half-embedded stent as compared to a quarterly and well-apposed stent. An intriguing feature is to be noted that the inter-strut distance through which the transmural plasma filtration takes place, plays a pivotal role in the distribution and retention of drug in the therapeutic domain considered. Furthermore, the steady-state simulation predicts the influence of strut dimension on the distributions of all drug forms.

Diffusive majority-vote model

We define a stochastic reaction-diffusion process that describes a consensus formation in a nonsedentary population. The process is a diffusive version of the majority-vote model, where the state update follows two stages: In the first stage, spins are allowed to jump to a random neighbor node with probabilities D_{+} and D_{-} for the respective spin orientations, and in the second stage, the spins in the same node can change its values according to the majority-vote update rule. The model presents a consensus formation phase when the concentration is greater than a threshold value and a paramagnetic phase on the converse for equal diffusion probabilities, i.e., maintaining the inversion symmetry. Setting unequal diffusion probabilities for the respective spin orientations is the same as applying an external magnetic field. The system undergoes a discontinuous phase transition for concentrations higher than the critical threshold on the external field. The individuals that diffuse more dominate the stationary collective opinion.

Green’s function for two absorbing boundaries in the reaction–diffusion system: Beyond Oster–Nishijima Model in barrierless reaction

We have derived the green’s function in the time domain for the presence of two localized sinks of finite strength on the potential energy surface in the barrierless reaction–diffusion processes. The previously proposed method (Saravanan and Chakraborty, 2020) has parametric limitations to find the time domain solution, whereas our present method gives the complete solution to the diffusion equation. Also experimentally observed nearly bi-exponential decay due to strong asymmetric placement of sinks has been observed.

Machine learning-based reduced-order modeling and predictive control of nonlinear processes

In this work, we develop a model predictive control scheme for nonlinear systems using autoencoder-based reduced-order machine learning models. First, an autoencoder is developed for model order reduction by projecting the process states onto a low-dimensional space using data generated from open-loop simulations of the nonlinear system in the original high-dimensional space. Subsequently, reduced-order recurrent neural networks (RNN) are developed to capture the dominant dynamics of the nonlinear system using the low-dimensional data. Lyapunov-based model predictive control (MPC) scheme using RNN models in low-dimensional space is developed to stabilize the nonlinear system. Finally, a diffusion-reaction process example is used to demonstrate the effectiveness of the proposed reduced-order RNN modeling approach and RNN-based predictive control method.

The role of effectiveness factor on the modeling of methanol steam reforming over CuO/ZnO/Al2O3 catalyst in a multi-tubular reactor

A pseudo-homogeneous model for the methanol steam reforming process was developed based on reaction kinetics over a CuO/ZnO/Al 2 O 3 catalyst and non-adiabatic heat and mass transfer performances in a co-current packed-bed reactor. A Thiele modulus method and an intraparticle distribution method were applied for predicting the effectiveness factors for main reactions and providing insights into the diffusion-reaction process in a cylindrical catalyst pellet. The results of both methods are validated and show good agreements with the experimental data, but the intraparticle distribution method provides better predictions. Results indicate that increases in catalyst size and bulk fluid temperature amplify the impact of intraparticle diffusion limitations, showing a decrease in effectiveness factors. To satisfy the requirements of a high temperature polymer electrolyte membrane fuel cell stack, the optimized operating conditions, which bring the methanol and CO concentrations to less than 1 % vol in the reformate stream, are determined based on the simulation results. • One-dimensional pseudo-homogeneous model of a packed-bed methanol steam reformer. • Two methods to obtain approximate solutions of the catalytic effectiveness factor. • Validation of reaction kinetics and effectiveness factors with experimental data. • Effects of main operating parameters on the intraparticle heat and mass transfer. • Optimized conditions to obtain less than 1% of CH 3 OH and CO in reformate gas.

Cooperative dynamics of curvature-sensing proteins control cytoskeletal assembly near the plasma membrane

The plasma membrane, demarcating the shape of a cell, works together with the cellular cytoskeleton to carry out many important functions such as mechanosensing. To study these phenomena, we have recently introduced a microscopic computational model, membrane-MEDYAN, which enables simulations of complex cytoskeleton-membrane dynamics. In the current work, we introduced a capability of treating stochastic reaction-diffusion processes on the membrane manifold, as well as adsorption and desorption exchange of proteins between the membrane and the enclosed cytosolic volume.

In Situ Characterization of the Reaction-Diffusion Behavior during the Gradient Interphase Formation of Polyetherimide with a High-Temperature Epoxy System.

This study presents two novel methods for in situ characterization of the reaction-diffusion process during the co-curing of a polyetherimide thermoplastic interlayer with an epoxy-amine thermoset. The first method was based on hot stage experiments using a computer vision point tracker algorithm to detect and trace diffusion fronts, and the second method used space- and time-resolved Raman spectroscopy. Both approaches provided essential information, e.g., type of transport phenomena and diffusion rate. They can also be combined and serve to elucidate phenomena occurring during diffusion up to phase separation of the gradient interphase between the epoxy system and the thermoplastic. Accordingly, it was possible to distinguish reaction-diffusion mechanisms, describe the diffusivity of the present system and evaluate the usability of the above-mentioned methods.

Chemical Tracking of Temperature by Concurrent Periodic Precipitation Pattern Formation in Polyacrylamide Gels.

In nature, nonequilibrium systems reflect environmental changes, and these changes are often “recorded” in their solid body as they develop. Periodic precipitation patterns, aka Liesegang patterns (LPs), are visual sums of complex events in nonequilibrium reaction–diffusion processes. Here we aim to achieve an artificial system that “records” the temperature changes in the environment with the concurrent LP formation. We first illustrate the differences in 1-D LPs developing at different temperatures in terms of band spacings, which can demonstrate the time, ramp steepness, and extent of a temperature change. These results are discussed and augmented by a mathematical model. Using scanning electron microscopy, we show that the average size of the CuCrO4 precipitate also reflects the temperature changes. Finally, we show that these changes can also be “recorded” in the 2-D and 3-D LPs, which can have applications in long-term temperature tracking and complex soft material design.

Emergence of a geometric pattern of cell fates from tissue-scale mechanics in the Drosophila eye.

Pattern formation of biological structures involves the arrangement of different types of cells in an ordered spatial configuration. In this study, we investigate the mechanism of patterning the Drosophila eye epithelium into a precise triangular grid of photoreceptor clusters called ommatidia. Previous studies had led to a long-standing biochemical model whereby a reaction-diffusion process is templated by recently formed ommatidia to propagate a molecular prepattern across the eye. Here, we find that the templating mechanism is instead, mechanochemical in origin; newly born columns of differentiating ommatidia serve as a template to spatially pattern flows that move epithelial cells into position to form each new column of ommatidia. Cell flow is generated by a source and sink, corresponding to narrow zones of cell dilation and contraction respectively, that straddle the growing wavefront of ommatidia. The newly formed lattice grid of ommatidia cells are immobile, deflecting, and focusing the flow of other cells. Thus, the self-organization of a regular pattern of cell fates in an epithelium is mechanically driven.

An effectiveness factor model for slurry phase olefin polymerizations

The multigrain model (MGM) is the most widely used single-particle model, giving a detailed description of phenomena during olefin polymerization. However, the detailed modeling of the diffusion–reaction process inside the catalyst particles requires solving a large number of ordinary differential equations, which is unsuitable for coupling with multiphase CFD tools. That is the reason why the current CFD simulation studies of olefin polymerization reactors rarely consider intraparticle transport. To fill this gap, an effectiveness factor model (EFM) is developed from MGM for slurry olefin polymerizations. It maintains the multilevel framework of MGM and is suitable for use in multiphase CFD simulations. The MGM and EFM are first implemented into OpenFOAM. Moreover, the EFM has been validated by comparison with literature data. Detailed comparisons between MGM and EFM show that the EFM can produce similar results as the MGM with a much lower computation cost for olefin slurry polymerization when αi,mp < 2.0.

Interrelation between swelling, mechanical constraints and reaction-diffusion processes in molecular responsive hydrogels.

The net swelling dynamics in molecular responsive hydrogels can be viewed as an integrated effect of discernible processes involving transport of actuating species, reaction with network components like destabilization of physical crosslinks or cleavage of network strands and concomitant network relaxation. Here, we describe a finite element modeling approach coupling these interdependent, underlying processes in hydrogels including oligonucleotide duplexes as physical crosslinks that can be destabilized by a particular molecule. These molecular responsive hydrogels based on acrylamide including either DNA or oligomorpholinos (MO), a DNA analogue, as functional elements can be made with various content of dsDNA or dsMO supported cross-links. The dsDNA or dsMO integrated in the hydrogel can be fabricated with ssDNA designed to competitively displace the connectivity of the dsDNA supported crosslinks, and similar for the MO hydrogels. The overall processes can be framed in a diffusion-reaction scheme. This process is dependent on the concentration of the diffusing species, their diffusion coefficients and their location. Thus, the reaction taking place in particular molecular responsive hydrogels is coupled with the deformations due to swelling and mechanical constraints undergone by the gel. Numerical examples show the importance of coupling reaction-diffusion with mechanical deformations for such gels. Finally, our model is compared to swelling experiments of hemi-spheroidal molecular responsive hydrogels bound to an optical fiber. Parameters of the reaction-diffusion model were obtained by fitting the model to reported experimental data where molecular stimuli designed with different molecular parameters for the competitive displacement reaction were employed in the swelling experiments.

Vector field techniques for the detection of neuronal dynamics in the presence of mercury

Abstract. The role of mercury in the development of various neuropathologies is well known. The biogeochemical cycles of mercury indicate the possibility of its introduction into various organisms (including humans) through the corresponding trophic chains. However, as it turns out from the literature analysis, until recent years, there have been almost no works on the dynamic microscopic study (either in situ or in vivo) of the processes of connectome involution in aquatic organisms (including fishes, marine mammals, etc.) under the action of mercury. In this regard, we attempted to study the dynamics of morphogenesis and breakdown of the emerging connectome under the mercury exposure. A dynamic study of frames with the dynamics of the axonal path search was carried out in a series with an address-time code, on which it is possible to track the vector fields of displacements and reaction-diffusion processes in the cell culture immediately after the introduction of a drop of mercury or a mercury-containing liquid using capillary pipettes. This paper describes the observed effects and the possible mechanisms underlying them.