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In this paper, the impulsive conformable calculus approach is applied to the introduction of an M 1 oncolytic virotherapy neural network model. The proposed model extends some existing mathematical models that describe the dynamics of the concentrations of normal cells, tumor cells, nutrients, M 1 viruses and cytotoxic T lymphocyte (CTL) cells to the impulsive conformable setting. The conformable concept allows for flexibility in the modeling approach, as well as avoiding the complexity of using classical fractional derivatives. The impulsive generalization supports the application of a suitable impulsive control therapy. Reaction–diffusion terms are also considered. We analyze the stable behavior of sets of states, which extend the investigations of the dynamics of separate equilibrium points. By applying the impulsive conformable Lyapunov function technique, sufficient conditions for the uniform global exponential stability of sets of states are established. An example is also presented to illustrate our results. [ABSTRACT FROM AUTHOR]

Approximate analytical solutions to doubly degenerate reaction-diffusion models pertinent to population dynamics and chemical kinetics have been developed. The double integral-balance method applied to preliminary transformed models and by a direct integration approach has provided physically reasonable results. The model equation scaling has revealed the time and length scales, as well as the characteristic velocity of the process and the Fourier number as the controlling dimensionless group. [ABSTRACT FROM AUTHOR]

Artificial bio-nanocoatings, primarily composed of proteins, offer a broad range of applications across various fields thanks to their unique properties. Proteins, as major components of these structures, enable a high degree of customization, such as mutations, conjugation with other molecules or nanoparticles, or the inclusion of an enzymatic activity. Their ability to self-assembly simplifies the production of bio-nanocoatings, making this process efficient and environment-friendly. Despite these advantages, a comprehensive understanding of the underlying self-assembly mechanism is lacking, and the reaction rates governing this process have not been characterized. In this article, we introduce a novel method to determine the key parameters describing the self-assembly mechanism of bio-nanostructures. For the first time, this approach enables an accurate calculation of the autocatalytic and self-inhibitory parameters controlling the process. Through mathematical modeling, our method enhances the understanding of how the protein-based nanocoatings form and opens new avenues for their application in nanotechnology and synthetic biology. Improved control over the self-assembly processes may enable the development of nanomaterials optimized for specific functions, such as drug delivery, biosensing, and bioactive surface fabrication. [ABSTRACT FROM AUTHOR]

This paper aims to present a robust computational technique utilizing finite difference schemes for accurately solving time fractional reaction–diffusion models, which are prevalent in chemical and biological phenomena. The time-fractional derivative is treated in the Caputo sense, addressing both linear and nonlinear scenarios. The proposed schemes were rigorously evaluated for stability and convergence. Additionally, the effectiveness of the developed schemes was validated through various linear and nonlinear models, including the Allen–Cahn equation, the KPP–Fisher equation, and the Complex Ginzburg–Landau oscillatory problem. These models were tested in one-, two-, and three-dimensional spaces to investigate the diverse patterns and dynamics that emerge. Comprehensive numerical results were provided, showcasing different cases of the fractional order parameter, highlighting the schemes' versatility and reliability in capturing complex behaviors in fractional reaction–diffusion dynamics. [ABSTRACT FROM AUTHOR]

This article focuses on the analysis of dynamics emerging in a network of Hodgkin–Huxley reaction–diffusion equations. The network has three levels. The three neurons in level 1 receive a periodic input but do not receive inputs from other neurons. The three neurons in level 2 receive inputs from one specific neuron in level 1 and all neurons in level 3. The neurons in level 3 (all other neurons) receive inputs from all other neurons in levels 2 and 3. Furthermore, the right-hand side of pre-synaptic neurons is connected to the left-hand side of the post-synaptic neurons. The synchronization phenomenon is observed for neurons in level 3, even though the system is initiated with different functions. As far as we know, it is the first time that evidence of the synchronization phenomenon is provided for spatially extended Hodgkin–Huxley equations, which are periodically forced at three different sites and embedded in such a hierarchical network with space-dependent coupling interactions. [ABSTRACT FROM AUTHOR]

Due to the facts that epidemic-related parameters vary significantly in different stages of infectious diseases and are relatively stable within the same stage, infectious disease models should be switch-type models. However, research on switch-type infectious disease models is scarce due to the complexity and intricate design of switching rules. This scarcity has motivated the writing of this paper. By assuming that switching instants and impulse times occur at different moments, this paper proposes switch rules suitable for impulse control and derives synchronization criteria for reaction–diffusion switch-type infectious disease systems under impulse control. The effectiveness of this method is validated through numerical simulations. It is important to mention that, based on the information available to us, this paper is currently the sole study focusing on switch-type reaction–diffusion models for infectious diseases. [ABSTRACT FROM AUTHOR]

An electrochemical photobioreactor with a packed bed containing transparent gel granules and immobilized photosynthetic bacterial cells is shown with a one-dimensional two-phase flow and transport model. We consider the biological/chemical events in the electrochemical photobioreactor, the intrinsically connected two-phase flow and mass transport, and other factors. This model is based on a system of nonlinear equations. This paper applies Akbari-Ganji's and Taylor series methods to find analytical solutions to nonlinear differential equations that arise in an immobilized-cell electrochemical photobioreactor. Approximate analytical expressions of the concentration of glucose and hydrogen are obtained in liquid and gas phases for different parameter values. Numerical simulations are presented to validate the theoretical investigations. [ABSTRACT FROM AUTHOR]

The current architecture practice is shifting towards Green Solutions designed, produced, and operated domestically in a self-sufficient decentralized fashion, following the UN sustainability goals. The current study proposes 3D-printed bioreceptive tiles for the passive immobilization of multi-scale-length algal strains from a mixed culture of Mougeotia sp., Oedogonium foveolatum, Zygnema sp., Microspora sp., Spirogyra sp., and Pyrocystis fusiformis. This customized passive immobilization of the chosen algal strains is designed to achieve bioremediation-integrated solutions in architectural applications. The two bioreceptive tiles following the reaction-diffusion, activator-inhibitor Grier–Meinhardt model have different patterns: P1: Polar periodic, and P2: Strip labyrinth, with niche sizes of 3000 µm and 500 µm, respectively. The results revealed that P2 has a higher immobilization capacity for the various strains, particularly Microspora sp., achieving a growth rate 1.65% higher than its activated culture density compared to a 1.08% growth rate on P1, followed by P. fusiformis with 1.53% on P2 and 1.3% on P1. These results prove the correspondence between the scale and morphology of the strip labyrinth pattern of P2 and the unbranched filamentous and fusiform large unicellular morphology of the immobilized algal strains cells, with an optimum ratio of 0.05% to 0.75% niche to the cell scale. Furthermore, The Mixed Culture method offered an intertwining net that facilitated the entrapment of the various algal strains into the bioreceptive tile. [ABSTRACT FROM AUTHOR]

The definition and description of the dynamics of a predator-prey system are some of the fundamental problems of population biology. Since 1925, several models have been introduced. Although they are highly effective, most of them neglect certain relevant criteria such as the spatial and temporal distribution of the studied species. We introduced these criteria by coupling two models designed initially for collective dynamics. The first is for predator mobility and is a Vicsek-type model, and the second is a Brownian particle (BP) model for prey. We observed, as occurs in the classical models, periodic cycles of the densities of predators and prey. In this case, the period of oscillations depends on the collective dynamics parameters. [ABSTRACT FROM AUTHOR]

The architecture of hydrogel composites results in not only synergistic property enhancement but also superior functionality. The reaction–diffusion (RD) process is acommon phenomenon throughout nature which induced ordered structure on a length scale from microscopic to macroscopic. Different from commonly used inorganic salts or oppositely charged nanoparticles for the RD process, a modified RD process was used for layered chitosan hydrogel (L-CH) and layered magnetic chitosan hydrogel (L-MCH). During the modified RD process reported in this paper, the protonated chitosan (CS-NH3+) with iron ions (Fe3+ and Fe2+) was used as an inner-reactant and hydroxide ion (-OH−) was used as an out-reactant. The protonated chitosan (CS-NH3+) not only played the role of an inner-reactant but also the reaction medium which controlled the diffusion behavior of the out-reactant (-OH−). A series of ordered layers were constructed and the ordered layers were parallel with the longitudinal axis. The layer width of L-CH and L-MCH can be tailored by varying interval time T. The mean layer width of L-MCH increased from 50 ± 5.8 μm to 90 ± 6.4 μm when the interval time T increased from 2 min to 5 min. The tailored layer structure of L-CH and L-MCH obeyed the time law and spacing law, which declared that the L-CH and L-MCH were constructed via the reaction–diffusion process. We also show that the tailored layer structure endows hydrogel with enhanced mechanical properties, especially toughness. The yield strength of magnetic chitosan hydrogel was improved significantly (from 95.1 ± 7.6 kPa to 401.7 ± 12.1 kPa, improved by about 4 times) when 10 wt. % magnetite nanoparticles were involved. The enhancement of the mechanical propertieswas due to a physical crosslinking effect of magnetite nanoparticles on chitosan. For L-MCH, the probe displacement reached 28.93 ± 2.6 mm when the rupture occurred, which was as high as 284.7% compared with that of the non-layered hydrogel. The tailor-made hydrogels might be possible for application as a tough implantable scaffold. [ABSTRACT FROM AUTHOR]

Coacervation is a self-assembly strategy based on the complexation of polyelectrolytes, which is utilized in biomedicine and agriculture, as well as automotive and textile industries. In this paper, we developed a new approach to the on-demand periodic formation of polyelectrolyte complexes through a Liesegang-type hierarchical organization. Adjustment of reaction conditions allows us to assemble materials with a tunable spatiotemporal geometry and establish materials' production cycles with a regulated periodicity. The proposed methodology allows the membrane to self-assemble when striving to reach balance and self-heal after exposure to external stimuli, such as potential difference and high pH. Using chronopotentiometry, K+ ion permeability behavior of the PEI–PSS coacervate membranes was demonstrated. The periodically self-assembled polyelectrolyte nanomembranes could further be integrated into novel energy storage devices and intelligent biocompatible membranes for bionics, soft nanorobotics, biosensing, and biocomputing. [ABSTRACT FROM AUTHOR]

In this article, a new competitive neural network (CNN) with reaction-diffusion terms and mixed delays is proposed. Because this network system contains reaction-diffusion terms, it belongs to a partial differential system, which is different from the existing classic CNNs. First, taking into account the spatial diffusion effect, we introduce spatial diffusion for CNNs. Furthermore, since the time delay has an essential influence on the properties of the system, we introduce mixed delays including time-varying discrete delays and distributed delays for CNNs. By constructing suitable Lyapunov–Krasovskii functionals and virtue of the theories of delayed partial differential equations, we study the global asymptotic stability for the considered system. The effectiveness and correctness of the proposed CNN model with reaction-diffusion terms and mixed delays are verified by an example. Finally, some discussion and conclusions for recent developments of CNNs are given. [ABSTRACT FROM AUTHOR]

The present work aims at approximating the reduction of sulphate to sulphide caused by sulphate-reducing bacteria (SRB) inside the Canadian deep geological repository in order to calculate the expected lifetime of used nuclear fuel containers (UFCs). Previous studies have assumed a conservative constant concentration of sulphide at the host rock interface. The novelty of this study resides in the use of first-order kinetics to explicitly account for the SRB-induced sulphide production. This reaction term is developed following an empirical approach using published results on actual sulphate reduction by SRB and included in a coupled reaction-diffusion system. Lifetimes of UFCs are subsequently calculated following the conditions of two scenarios: having SRB active only at the region closest to the host rock and having SRB active at the host rock and throughout the bentonite clay. This study shows that the mean lifetimes of UFCs in both cases are above one million years. However, more accurate results would require the characterization of the host rock and groundwater of the prospective emplacement, as well as additional experiments on growth and sulphide production by the microbial communities from the site. [ABSTRACT FROM AUTHOR]

The lattice Boltzmann method is an efficient computational fluid dynamics technique that can accurately model a broad range of complex systems. As well as single-phase fluids, it can simulate thermohydrodynamic systems and passive scalar advection. In recent years, it also gained attention as a means of simulating chemical phenomena, as interest in self-organization processes increased. This paper will present a widely-used and versatile lattice Boltzmann model that can simultaneously incorporate fluid dynamics, heat transfer, buoyancy-driven convection, passive scalar advection, chemical reactions and enthalpy changes. All of these effects interact in a physically accurate framework that is simple to code and readily parallelizable. As well as a complete description of the model equations, several example systems will be presented in order to demonstrate the accuracy and versatility of the method. New simulations, which analyzed the effect of a reversible reaction on the transport properties of a convecting fluid, will also be described in detail. This extra chemical degree of freedom was utilized by the system to augment its net heat flux. The numerical method outlined in this paper can be readily deployed for a vast range of complex flow problems, spanning a variety of scientific disciplines. [ABSTRACT FROM AUTHOR]

A mathematical model for the reaction-diffusion equation is developed to describe the nutrient release profiles and degradation of poly(lactic acid) (PLA)-coated controlled-release fertilizer. A multi-diffusion model that consists of coupled partial differential equations is used to study the diffusion and chemical reaction (autocatalytic degradation) simultaneously. The model is solved using an analytical-numerical method. Firstly, the model equation is transformed using the Laplace transformation as the Laplace transform cannot be inverted analytically. Numerical inversion of the Laplace transform is used by employing the Zakian method. The solution is useful in predicting the nutrient release profiles at various diffusivity, concentration of extraction medium, and reaction rates. It also helps in explaining the transformation of autocatalytic concentration in the coating material for various reaction rates, times of reaction, and reaction-multi diffusion. The solution is also applicable to the other biodegradable polymer-coated controlled-release fertilizers. [ABSTRACT FROM AUTHOR]

Human Immunodeficiency Virus (HIV) infection of humans represents a complex biological system and a great challenge to public health. Novel approaches for the analysis and prediction of the infection dynamics based on a multi-scale integration of virus ontogeny and immune reactions are needed to deal with the systems' complexity. The aim of our study is: (1) to formulate a multi-scale mathematical model of HIV infection; (2) to implement the model computationally following a hybrid approach; and (3) to calibrate the model by estimating the parameter values enabling one to reproduce the "standard"observed dynamics of HIV infection in blood during the acute phase of primary infection. The modeling approach integrates the processes of infection spread and immune responses in Lymph Nodes (LN) to that observed in blood. The spatio-temporal population dynamics of T lymphocytes in LN in response to HIV infection is governed by equations linking an intracellular regulation of the lymphocyte fate by intercellular cytokine fields. We describe the balance of proliferation, differentiation and death at a single cell level as a consequence of gene activation via multiple signaling pathways activated by IL-2, IFNa and FasL. Distinct activation thresholds are used in the model to relate different modes of cellular responses to the hierarchy of the relative levels of the cytokines. We specify a reference set of model parameter values for the fundamental processes in lymph nodes that ensures a reasonable agreement with viral load and CD4+ T cell dynamics in blood. [ABSTRACT FROM AUTHOR]

An information-theoretic perspective on coarse-graining is presented. It starts with an information characterization of configurations at the micro-level using a local information quantity that has a spatial average equal to a microscopic entropy. With a reversible micro dynamics, this entropy is conserved. In the micro-macro transition, it is shown how this local information quantity is transformed into a macroscopic entropy, as the local states are aggregated into macroscopic concentration variables. The information loss in this transition is identified, and the connection to the irreversibility of the macro dynamics and the second law of thermodynamics is discussed. This is then connected to a process of further coarse-graining towards higher characteristic length scales in the context of chemical reaction-diffusion dynamics capable of pattern formation. On these higher levels of coarse-graining, information flows across length scales and across space are defined. These flows obey a continuity equation for information, and they are connected to the thermodynamic constraints of the system, via an outflow of information from macroscopic to microscopic levels in the form of entropy production, as well as an inflow of information, from an external free energy source, if a spatial chemical pattern is to be maintained. [ABSTRACT FROM AUTHOR]

In this paper, an amperometric glucose biosensor is modeled numerically. The model is based on non-stationary reaction-diffusion type equations. The model consists of four layers. An enzyme layer lies directly on a working electrode surface. The enzyme layer is attached to an electrode by a polyvinyl alcohol (PVA) coated terylene membrane. This membrane is modeled as a PVA layer and a terylene layer, which have different diffusivities. The fourth layer of the model is the diffusion layer, which is modeled using the Nernst approach. The system of partial differential equations is solved numerically using the finite difference technique. The operation of the biosensor was analyzed computationally with special emphasis on the biosensor response sensitivity to oxygen when the experiment was carried out in aerobic conditions. Particularly, numerical experiments show that the overall biosensor response sensitivity to oxygen is insignificant. The simulation results qualitatively explain and confirm the experimentally observed biosensor behavior. [ABSTRACT FROM AUTHOR]

We have developed a set of DNA circuits that execute during gel electrophoresis to yield immobile, fluorescent features in the gel. The parallel execution of orthogonal circuits led to the simultaneous production of different fluorescent lines at different positions in the gel. The positions of the lines could be rationally manipulated by changing the mobilities of the reactants. The ability to program at the nanoscale so as to produce patterns at the macroscale is a step towards programmable, synthetic chemical systems for generating defined spatiotemporal patterns [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model of carbon nanotubes-based mediatorless biosensor. The developed model is based on nonlinear non-stationary reaction-diffusion equations. The model involves four layers (compartments): a layer of enzyme solution entrapped on a terylene membrane, a layer of the single walled carbon nanotubes deposited on a perforated membrane, and an outer diffusion layer. The biosensor response and sensitivity are investigated by changing the model parameters with a special emphasis on the mediatorless transfer of the electrons in the layer of the enzyme-loaded carbon nanotubes. The numerical simulation at transient and steady state conditions was carried out using the finite difference technique. The mathematical model and the numerical solution were validated by experimental data. The obtained agreement between the simulation results and the experimental data was admissible at different concentrations of the substrate. [ABSTRACT FROM AUTHOR]

In this paper the operation of an amperometric biosensor producing a chemically amplified signal is modelled numerically. The chemical amplification is achieved by using synergistic substrates. The model is based on non-stationary reaction-diffusion equations. The model involves three layers (compartments): a layer of enzyme solution entrapped on the electrode surface, a dialysis membrane covering the enzyme layer and an outer diffusion layer which is modelled by the Nernst approach. The equation system is solved numerically by using the finite difference technique. The biosensor response and sensitivity are investigated by altering the model parameters influencing the enzyme kinetics as well as the mass transport by diffusion. The biosensor action was analyzed with a special emphasis to the effect of the chemical amplification. The simulation results qualitatively explain and confirm the experimentally observed effect of the synergistic substrates conversion on the biosensor response. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

By applying impulsive control, this work investigated the global stabilization of a single-species ecosystem with Markovian jumping, a time delay and a Neumann boundary condition. Variational methods, a fixed-point theorem, and Laplacian semigroup theory were employed to derive the unique existence of the global stable equilibrium point, which is a positive number. Numerical examples illuminate the feasibility of the proposed methods. [ABSTRACT FROM AUTHOR]

The Gray–Scott (GS) model is a non-linear system of equations generally adopted to describe reaction–diffusion dynamics. In this paper, we discuss a numerical scheme for solving the GS system. The diffusion coefficients of the model are on surfaces and they depend on space and time. In this regard, we first adopt an implicit difference stepping method to semi-discretize the model in the time direction. Then, we implement a hybrid advanced meshless method for model discretization. In this way, we solve the GS problem with a radial basis function–finite difference (RBF-FD) algorithm combined with the closest point method (CPM). Moreover, we design a predictor–corrector algorithm to deal with the non-linear terms of this dynamic. In a practical example, we show the spot and stripe patterns with a given initial condition. Finally, we experimentally prove that the presented method provides benefits in terms of accuracy and performance for the GS system's numerical solution. [ABSTRACT FROM AUTHOR]

The Liesegang phenomenon can be used for micro- and nanofabrication processes to yield materials with periodic precipitation of diverse types of materials. Although there have been several attempts to control the periodicity of the Liesegang patterns, it remains unclear whether the periodic precipitation of AgCl in gel medium causes regular- or revert-type patterns. To confirm the periodicity of the AgCl pattern, we conduct one-dimensional experiments under various ion concentration conditions. From microscopic observations, three different precipitation modes were observed, i.e., continuous precipitation with a sharp front, periodic precipitation and continuous precipitation with a gradual front. For these three modes, numerical analyses of the pattern geometry are performed for the periodic precipitation. It was confirmed that the regular-type pattern appeared for all concentration conditions conducted in the present experiments. Furthermore, the pattern was found to obey the spacing law and the Matalon–Packter law. From our experiments, we concluded that AgCl forms regular-type Liesegang patterns, regardless of the dimension of diffusion. [ABSTRACT FROM AUTHOR]

DNA nanotechnology offers a fine control over biochemistry by programming chemical reactions in DNA templates. Coupled to microfluidics, it has enabled DNA-based reaction-diffusion microsystems with advanced spatio-temporal dynamics such as traveling waves. The Finite Element Method (FEM) is a standard tool to simulate the physics of such systems where boundary conditions play a crucial role. However, a fine discretization in time and space is required for complex geometries (like sharp corners) and highly nonlinear chemistry. Graphical Processing Units (GPUs) are increasingly used to speed up scientific computing, but their application to accelerate simulations of reaction-diffusion in DNA nanotechnology has been little investigated. Here we study reaction-diffusion equations (a DNA-based predator-prey system) in a tortuous geometry (a maze), which was shown experimentally to generate subtle geometric effects. We solve the partial differential equations on a GPU, demonstrating a speedup of ∼100 over the same resolution on a 20 cores CPU. [ABSTRACT FROM AUTHOR]

Across metazoans, animal body structures and tissues exist in robust patterns that arise seemingly out of stochasticity of a few early cells in the embryo. These patterns ensure proper tissue form and function during early embryogenesis, development, homeostasis, and regeneration. Fundamental questions are how these patterns are generated and maintained during tissue homeostasis and regeneration. Though fascinating scientists for generations, these ideas remain poorly understood. Today, it is apparent that the Wnt/β-catenin pathway plays a central role in tissue patterning. Wnt proteins are small diffusible morphogens which are essential for cell type specification and patterning of tissues. In this review, we highlight several mechanisms described where the spatial properties of Wnt/β-catenin signaling are controlled, allowing them to work in combination with other diffusible molecules to control tissue patterning. We discuss examples of this self-patterning behavior during development and adult tissues' maintenance. The combination of new physiological culture systems, mathematical approaches, and synthetic biology will continue to fuel discoveries about how tissues are patterned. These insights are critical for understanding the intricate interplay of core patterning signals and how they become disrupted in disease. [ABSTRACT FROM AUTHOR]

The development of multicellular organisms proceeds through a series of morphogenetic and cell-state transitions, transforming homogeneous zygotes into complex adults by a process of self-organisation. Many of these transitions are achieved by spontaneous symmetry breaking mechanisms, allowing cells and tissues to acquire pattern and polarity by virtue of local interactions without an upstream supply of information. The combined work of theory and experiment has elucidated how these systems break symmetry during developmental transitions. Given that such transitions are multiple and their temporal ordering is crucial, an equally important question is how these developmental transitions are coordinated in time. Using a minimal mass-conserved substrate-depletion model for symmetry breaking as our case study, we elucidate mechanisms by which cells and tissues can couple reaction–diffusion-driven symmetry breaking to the timing of developmental transitions, arguing that the dependence of patterning mode on system size may be a generic principle by which developing organisms measure time. By analysing different regimes of our model, simulated on growing domains, we elaborate three distinct behaviours, allowing for clock-, timer- or switch-like dynamics. Relating these behaviours to experimentally documented case studies of developmental timing, we provide a minimal conceptual framework to interrogate how developing organisms coordinate developmental transitions. [ABSTRACT FROM AUTHOR]

Movement of cells and tissues is essential at various stages during the lifetime of an organism, including morphogenesis in early development, in the immune response to pathogens, and during wound-healing and tissue regeneration. Individual cells are able to move in a variety of microenvironments (MEs) (A glossary of the acronyms used herein is given at the end) by suitably adapting both their shape and how they transmit force to the ME, but how cells translate environmental signals into the forces that shape them and enable them to move is poorly understood. While many of the networks involved in signal detection, transduction and movement have been characterized, how intracellular signals control re-building of the cyctoskeleton to enable movement is not understood. In this review we discuss recent advances in our understanding of signal transduction networks related to direction-sensing and movement, and some of the problems that remain to be solved. [ABSTRACT FROM AUTHOR]

In this article, we study how the rates of diffusion in a reaction-diffusion model for a stage structured population in a heterogeneous environment affect the model's predictions of persistence or extinction for the population. In the case of a population without stage structure, faster diffusion is typically detrimental. In contrast to that, we find that, in a stage structured population, it can be either detrimental or helpful. If the regions where adults can reproduce are the same as those where juveniles can mature, typically slower diffusion will be favored, but if those regions are separated, then faster diffusion may be favored. Our analysis consists primarily of estimates of principal eigenvalues of the linearized system around (0 , 0) and results on their asymptotic behavior for large or small diffusion rates. The model we study is not in general a cooperative system, but if adults only compete with other adults and juveniles with other juveniles, then it is. In that case, the general theory of cooperative systems implies that, when the model predicts persistence, it has a unique positive equilibrium. We derive some results on the asymptotic behavior of the positive equilibrium for small diffusion and for large adult reproductive rates in that case. [ABSTRACT FROM AUTHOR]

The liquid milieu in which enzymes operate when they are immobilized in solid materials can be quite different from the milieu in bulk solution. Important differences are in the substrate and product concentration but also in pH and ionic strength. The internal milieu for immobilized enzymes is affected by the chemical properties of the solid material and by the interplay of reaction and diffusion. Enzyme performance is influenced by the internal milieu in terms of catalytic rate ("activity") and stability. Elucidation, through direct measurement of differences in the internal as compared to the bulk milieu is, therefore, fundamentally important in the mechanistic characterization of immobilized enzymes. The deepened understanding thus acquired is critical for the rational development of immobilized enzyme preparations with optimized properties. Herein we review approaches by opto-chemical sensing to determine the internal milieu of enzymes immobilized in porous particles. We describe analytical principles applied to immobilized enzymes and focus on the determination of pH and the O2 concentration. We show measurements of pH and [O2] with spatiotemporal resolution, using in operando analysis for immobilized preparations of industrially important enzymes. The effect of concentration gradients between solid particle and liquid bulk on enzyme performance is made evident and quantified. Besides its use in enzyme characterization, the method can be applied to the development of process control strategies. [ABSTRACT FROM AUTHOR]

We propose an approximate analytical approach to a (1 + 1) dimensional two-component system consisting of a nonlocal generalization of the well-known Fisher–Kolmogorov–Petrovskii– Piskunov (KPP) population equation and a diffusion equation for the density of the active substance solution surrounding the population. Both equations of the system have terms that describe the interaction effects between the population and the active substance. The first order perturbation theory is applied to the system assuming that the interaction parameter is small. The Wentzel–Kramers–Brillouin (WKB)–Maslov semiclassical approximation is applied to the generalized nonlocal Fisher–KPP equation with the diffusion parameter assumed to be small, which corresponds to population dynamics under certain conditions. In the framework of the approach proposed, we consider symmetry operators which can be used to construct families of special approximate solutions to the system of model equations, and the procedure for constructing the solutions is illustrated by an example. The approximate solutions are discussed in the context of the released activity effect variously debated in the literature. [ABSTRACT FROM AUTHOR]

We study the power spectrum of a space-time dependent neural field which describes the average membrane potential of neurons in a single layer. This neural field is modelled by a dissipative integro-differential equation, the so-called Amari equation. By considering a small perturbation with respect to a stationary and uniform configuration of the neural field we derive a linearized equation which is solved for a generic external stimulus by using the Fourier transform into wavevector-freqency domain, finding an analytical formula for the power spectrum of the neural field. In addition, after proving that for large wavelengths the linearized Amari equation is equivalent to a diffusion equation which admits space-time dependent analytical solutions, we take into account the nonlinearity of the Amari equation. We find that for large wavelengths a weak nonlinearity in the Amari equation gives rise to a reaction-diffusion equation which can be formally derived from a neural action functional by introducing a dual neural field. For some initial conditions, we discuss analytical solutions of this reaction-diffusion equation. [ABSTRACT FROM AUTHOR]

This paper presents a method for synthetic aperture radar (SAR) image segmentation by draing upon a reaction–diffusion (RD) level set evolution (LSE) equation. The well-known RD theory consists of two main parts: reaction and diffusion terms. We first constructed the reaction term using an energy functional, which integrates the gamma statistical distribution with region–edge information from SAR images that can simultaneously suppress speckle noise and drive the active contour toward the object boundaries. Then, we used partial differential equation-based LSE to solve the proposed energy functional. Finally, a diffusion term was introduced into the LSE to ensure stability of the level set function and regularize the segmented region. The experimental results of both simulated and real SAR images showed that the proposed model has good robustness against a speckle noise as well as higher segmentation efficiency and accuracy than some existing models. [ABSTRACT FROM AUTHOR]