scholarly journals Robust banded protoxylem pattern formation through microtubule-based directional ROP diffusion restriction

2019 ◽  
Author(s):  
Bas Jacobs ◽  
Jaap Molenaar ◽  
Eva E. Deinum
Keyword(s):  
Diffusion Barrier ◽  
Vascular Tissue ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Underlying Mechanism ◽  
Small Gtpase ◽  
Growth Stages ◽  
Vertical Diffusion ◽  
Directional Diffusion ◽  
Biological Realism

AbstractIn plant vascular tissue development, different cell wall patterns are formed, offering different mechanical properties optimised for different growth stages. Critical in these patterning processes are Rho of Plants (ROP) proteins, a class of evolutionarily conserved small GTPase proteins responsible for local membrane domain formation in many organisms. While the spotted metaxylem pattern can easily be understood as a result of a Turing-style reaction-diffusion mechanism, it remains an open question how the consistent orientation of evenly spaced bands and spirals as found in protoxylem is achieved. We hypothesise that this orientation results from an interaction between ROPs and an array of transversely oriented cortical microtubules that acts as a directional diffusion barrier. Here, we explore this hypothesis using partial differential equation models with anisotropic ROP diffusion and show that a horizontal microtubule array acting as a vertical diffusion barrier to active ROP can yield a horizontally banded ROP pattern. We then study the underlying mechanism in more detail, finding that it can only orient curved pattern features but not straight lines. This implies that, once formed, banded and spiral patterns cannot be reoriented by this mechanism. Finally, we observe that ROPs and microtubules together only form ultimately static patterns if the interaction is implemented with sufficient biological realism.

scholarly journals Theoretical aspects of antibiotic diffusion into microbial biofilms.

1996 ◽  
Vol 40 (11) ◽  
pp. 2517-2522 ◽  
Author(s):  
P S Stewart
Keyword(s):  
Diffusion Barrier ◽  
Initial Conditions ◽  
Diffusion Mechanism ◽  
Enzymatic Reaction ◽  
Reaction Diffusion ◽  
Solute Diffusion ◽  
Beta Lactam ◽  
Microbial Biofilms ◽  
Mathematical Equations ◽  
And Diffusion

Antibiotic penetration into microbial biofilm was investigated theoretically by the solution of mathematical equations describing various combinations of the processes of diffusion, sorption, and reaction. Unsteady material balances on the antibiotic and on a reactive or sorptive biomass constituent, along with associated boundary and initial conditions, constitute the mathematical formulations. Five cases were examined: diffusion of a noninteracting solute; diffusion of a reversibly sorbing, nonreacting solute; diffusion of an irreversibly sorbing, nonreacting solute; diffusion of a stoichiometrically reacting solute; and diffusion of a catalytically reacting solute. A noninteracting solute was predicted to penetrate biofilms of up to 1 mm in thickness relatively quickly, within a matter of seconds or minutes. In the case of a solute that does not sorb or react in the biofilm, therefore, the diffusion barrier is not nearly large enough to account for the reduced susceptibility of biofilms to antibiotics. Reversible and irreversible sorption retards antibiotic penetration. On the basis of data available in the literature at this point, the extent of retardation of antibiotic diffusion due to sorption does not appear to be sufficient to account for reduced biofilm susceptibility. A catalytic (e.g., enzymatic) reaction, provided it is sufficiently rapid, can lead to severe antibiotic penetration failure. For example, calculation of beta-lactam penetration indicated that the reaction-diffusion mechanism may be a viable explanation for failure of certain of these agents to control biofilm infections. The theory presented in this study provides a framework for the design and analysis of experiments to test these mechanisms of reduced biofilm susceptibility to antibiotics.

scholarly journals Travelling colourful patterns in self-organized cellulose-based liquid crystalline structures

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Pedro E. S. Silva ◽  
Ricardo Chagas ◽  
Susete N. Fernandes ◽  
Pawel Pieranski ◽  
Robin L. B. Selinger ◽  
...  
Keyword(s):  
Simple Model ◽  
Temporal Variation ◽  
Liquid Crystalline ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Self Organization ◽  
Spatial And Temporal Variation ◽  
Living Matter ◽  
Equilibrium Conditions ◽  
Self Organized

AbstractCellulose-based systems are useful for many applications. However, the issue of self-organization under non-equilibrium conditions, which is ubiquitous in living matter, has scarcely been addressed in cellulose-based materials. Here, we show that quasi-2D preparations of a lyotropic cellulose-based cholesteric mesophase display travelling colourful patterns, which are generated by a chemical reaction-diffusion mechanism being simultaneous with the evaporation of solvents at the boundaries. These patterns involve spatial and temporal variation in the amplitude and sign of the helix´s pitch. We propose a simple model, based on a reaction-diffusion mechanism, which simulates the observed spatiotemporal colour behaviour.

Reaction-Diffusion Modeling of Photopolymerization During Femtosecond Projection Two-Photon Lithography

2021 ◽  
Author(s):  
Rushil Pingali ◽  
Sourabh K. Saha
Keyword(s):  
Diffusion Mechanism ◽  
Chemical Properties ◽  
Reaction Diffusion ◽  
Element Model ◽  
Polymerization Process ◽  
Layer By Layer ◽  
Length Scales ◽  
Two Photon ◽  
Reaction Diffusion Model ◽  
Direct Laser

Abstract Two-photon lithography (TPL) is a polymerization-based direct laser writing process that is capable of fabricating arbitrarily complex three-dimensional (3D) structures with submicron features. Traditional TPL techniques have limited scalability due to the slow point-by-point serial writing scheme. The femtosecond projection TPL (FP-TPL) technique increases printing rate by a thousand times by enabling layer-by-layer parallelization. However, parallelization alters the time and the length scales of the underlying polymerization process. It is therefore challenging to apply the models of serial TPL to accurately predict process outcome during FP-TPL. To solve this problem, we have generated a finite element model of the polymerization process on the time and length scales relevant to FP-TPL. The model is based on the reaction-diffusion mechanism that underlies polymerization. We have applied this model to predict the geometry of nanowires printed under a variety of conditions and compared these predictions against empirical data. Our model accurately predicts the nanowire widths. However, accuracy of aspect ratio prediction is hindered by uncertain values of the chemical properties of the photopolymer. Nevertheless, our results demonstrate that the reaction-diffusion model can accurately capture the effect of controllable parameters on FP-TPL process outcome and can therefore be used for process control and optimization.

scholarly journals Reaction Diffusion and Chemotaxis for Decentralized Gathering on FPGAs

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Bernard Girau ◽  
César Torres-Huitzil ◽  
Nikolaos Vlassopoulos ◽  
José Hugo Barrón-Zambrano
Keyword(s):  
Large Scale ◽  
Complex Dynamics ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Fpga Implementation ◽  
Cellular Slime Mold ◽  
Reaction Diffusion Model ◽  
Cellular Slime ◽  
Computational Resources ◽  
Embedded Implementation

We consider here the feasibility of gathering multiple computational resources by means of decentralized and simple local rules. We study such decentralized gathering by means of a stochastic model inspired from biology: the aggregation of theDictyostelium discoideumcellular slime mold. The environment transmits information according to a reaction-diffusion mechanism and the agents move by following excitation fronts. Despite its simplicity this model exhibits interesting properties of self-organization and robustness to obstacles. We first describe the FPGA implementation of the environment alone, to perform large scale and rapid simulations of the complex dynamics of this reaction-diffusion model. Then we describe the FPGA implementation of the environment together with the agents, to study the major challenges that must be solved when designing a fast embedded implementation of the decentralized gathering model. We analyze the results according to the different goals of these hardware implementations.

Radiolaria: validating the Turing theory

2017 ◽  
Author(s):  
Bernard Richards
Keyword(s):  
Diffusion Mechanism ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Black And White ◽  
Alan Turing ◽  
School Sports ◽  
The University ◽  
University Of Manchester

In his 1952 paper ‘The chemical basis of morphogenesis’ Turing postulated his now famous Morphogenesis Equation. He claimed that his theory would explain why plants and animals took the shapes they did. When I joined him, Turing suggested that I might solve his equation in three dimensions, a new problem. After many manipulations using rather sophisticated mathematics and one of the first factory-produced computers in the UK, I derived a series of solutions to Turing’s equation. I showed that these solutions explained the shapes of specimens of the marine creatures known as Radiolaria, and that they corresponded very closely to the actual spiny shapes of real radiolarians. My work provided further evidence for Turing’s theory of morphogenesis, and in particular for his belief that the external shapes exhibited by Radiolaria can be explained by his reaction–diffusion mechanism. While working in the Computing Machine Laboratory at the University of Manchester in the early 1950s, Alan Turing reignited the interests he had had in both botany and biology from his early youth. During his school-days he was more interested in the structure of the flowers on the school sports field than in the games played there (see Fig. 1.3). It is known that during the Second World War he discussed the problem of phyllotaxis (the arrangement of leaves and florets in plants), and then at Manchester he had some conversations with Claude Wardlaw, the Professor of Botany in the University. Turing was keen to take forward the work that D’Arcy Thompson had published in On Growth and Form in 1917. In his now-famous paper of 1952 Turing solved his own ‘Equation of Morphogenesis’ in two dimensions, and demonstrated a solution that could explain the ‘dappling’—the black-and-white patterns—on cows. The next step was for me to solve Turing’s equation in three dimensions. The two-dimensional case concerns only surface features of organisms, such as dappling, spots, and stripes, whereas the three-dimensional version concerns the overall shape of an organism. In 1953 I joined Turing as a research student in the University of Manchester, and he set me the task of solving his equation in three dimensions. A remarkable journey of collaboration began. Turing chatted to me in a very friendly fashion.

Design and characterization of a biocompatible packaging concept for implantable electronic devices

2011 ◽  
Vol 2011 (1) ◽  
pp. 000152-000160 ◽  
Author(s):  
Maaike Op de Beeck ◽  
Karen Qian ◽  
Paolo Fiorini ◽  
Karl Malachowski ◽  
Chris Van Hoof
Keyword(s):  
Diffusion Barrier ◽  
Barrier Properties ◽  
The Body ◽  
Second Phase ◽  
Electronic Systems ◽  
Wafer Level ◽  
Packaging Process ◽  
Directional Diffusion ◽  
Chip Sealing

A biocompatible packaging process for implantable electronic systems is described, combining biocompatibility and hermeticity with extreme miniaturization. In a first phase of the total packaging sequence, all chips are encapsulated in order to realize a bi-directional diffusion barrier preventing body fluids to leach into the package causing corrosion, and preventing IC materials such as Cu to diffuse into the body, causing various adverse effects. For cost effectiveness, this hermetic chip sealing is performed as post-processing at wafer level, using modifications of standard clean room (CR) fabrication techniques. Well known conductive and insulating CR materials are investigated with respect to their biocompatibility, diffusion barrier properties and sensitivity to corrosion. In a second phase of the packaging process, all chips of the final device should be electrically connected, applying a biocompatible metallization scheme using eg. gold or platinum. For electrodes being in direct contact with the tissue after implantation, IrOx metallization is proposed. Device assembly is the final packaging step, during which all system components such as electronics, passives, a battery,… will be interconnected. To provide sufficient mechanical support, all these components are embedded using a biocompatible elastomer such as PDMS.

scholarly journals Prominin-1 Modulates Rho/ROCK-Mediated Membrane Morphology and Calcium-Dependent Intracellular Chloride Flux

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Akiko Hori ◽  
Kenji Nishide ◽  
Yuki Yasukuni ◽  
Kei Haga ◽  
Wataru Kakuta ◽  
...  
Keyword(s):  
Cell Morphology ◽  
Coiled Coil ◽  
Chloride Ion ◽  
Underlying Mechanism ◽  
Mouse Embryonic Fibroblast ◽  
Small Gtpase ◽  
Calcium Dependent ◽  
Membrane Morphology ◽  
Fibre Formation ◽  
Amino Acid Stretch

Abstract Membrane morphology is an important structural determinant as it reflects cellular functions. The pentaspan membrane protein Prominin-1 (Prom1/CD133) is known to be localised to protrusions and plays a pivotal role in migration and the determination of cellular morphology; however, the underlying mechanism of its action have been elusive. Here, we performed molecular characterisation of Prom1, focussing primarily on its effects on cell morphology. Overexpression of Prom1 in RPE-1 cells triggers multiple, long, cholesterol-enriched fibres, independently of actin and microtubule polymerisation. A five amino acid stretch located at the carboxyl cytosolic region is essential for fibre formation. The small GTPase Rho and its downstream Rho-associated coiled-coil-containing protein kinase (ROCK) are also essential for this process, and active Rho colocalises with Prom1 at the site of initialisation of fibre formation. In mouse embryonic fibroblast (MEF) cells we show that Prom1 is required for chloride ion efflux induced by calcium ion uptake, and demonstrate that fibre formation is closely associated with chloride efflux activity. Collectively, these findings suggest that Prom1 affects cell morphology and contributes to chloride conductance.

Pyrolysis behaviors dominated by the reaction–diffusion mechanism in the fluorine-free metal–organic decomposition process

2020 ◽  
Vol 8 (48) ◽  
pp. 17417-17428
Author(s):  
Jiangtao Shi ◽  
Yue Zhao ◽  
Yue Wu ◽  
Jingyuan Chu ◽  
Xiao Tang ◽  
...  
Keyword(s):  
Diffusion Model ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Decomposition Process ◽  
One Dimensional ◽  
Reaction Diffusion Model ◽  
Metal Organic ◽  
Free Metal ◽  
Organic Decomposition

In this work, pyrolysis behaviors dominated by the reaction–diffusion mechanism were investigated. And one-dimensional reaction–diffusion model is proposed.

scholarly journals Myoblast Migration and Directional Persistence Affected by Syndecan-4-Mediated Tiam-1 Expression and Distribution

2020 ◽  
Vol 21 (3) ◽  
pp. 823 ◽  
Author(s):  
Daniel Becsky ◽  
Szuzina Gyulai-Nagy ◽  
Arpad Balind ◽  
Peter Horvath ◽  
Laszlo Dux ◽  
...  
Keyword(s):  
Skeletal Muscle ◽  
Underlying Mechanism ◽  
Small Gtpase ◽  
Asymmetric Distribution ◽  
Nucleotide Exchange ◽  
Muscle Stem Cells ◽  
Guanine Nucleotide Exchange ◽  
Nucleotide Exchange Factor ◽  
T Lymphoma ◽  
Migration Capacity

Skeletal muscle is constantly renewed in response to injury, exercise, or muscle diseases. Muscle stem cells, also known as satellite cells, are stimulated by local damage to proliferate extensively and form myoblasts that then migrate, differentiate, and fuse to form muscle fibers. The transmembrane heparan sulfate proteoglycan syndecan-4 plays multiple roles in signal transduction processes, such as regulating the activity of the small GTPase Rac1 (Ras-related C3 botulinum toxin substrate 1) by binding and inhibiting the activity of Tiam1 (T-lymphoma invasion and metastasis-1), a guanine nucleotide exchange factor for Rac1. The Rac1-mediated actin remodeling is required for cell migration. Syndecan-4 knockout mice cannot regenerate injured muscle; however, the detailed underlying mechanism is unknown. Here, we demonstrate that shRNA-mediated knockdown of syndecan-4 decreases the random migration of mouse myoblasts during live-cell microscopy. Treatment with the Rac1 inhibitor NSC23766 did not restore the migration capacity of syndecan-4 silenced cells; in fact, it was further reduced. Syndecan-4 knockdown decreased the directional persistence of migration, abrogated the polarized, asymmetric distribution of Tiam1, and reduced the total Tiam1 level of the cells. Syndecan-4 affects myoblast migration via its role in expression and localization of Tiam1; this finding may facilitate greater understanding of the essential role of syndecan-4 in the development and regeneration of skeletal muscle.

Turing's model and branching tip growth: relation of time and spatial scales in morphogenesis, with application to Micrasterias

1987 ◽  
Vol 65 (7) ◽  
pp. 1308-1319 ◽  
Author(s):  
Thurston C. Lacalli ◽  
Lionel G. Harrison
Keyword(s):  
Diffusion Theory ◽  
Spatial Scales ◽  
Diffusion Mechanism ◽  
Effective Diffusivity ◽  
Reaction Diffusion ◽  
Time And Space ◽  
Branch Formation ◽  
Simplifying Assumptions ◽  
Growth Activity ◽  
Probable Site

Morphogenesis following cell division in Micrasterias rotata is by outgrowth and repeated branching of a series of semicell lobes. Though successive branching events are qualitatively similar, they display changes in time and space scales, and these can be quantitated with the aid of autoradiographic patterns of labelled wall precursors that appear late in morphogenesis but which seem to represent its history. This enables us to consider branching as the conversion of a single centre of growth activity into two and to attempt to locate these centres precisely, in terms of both position and time of establishment. Temporal and spatial scales both decrease, by 75%, through a sequence of five branching events, in linear functional relationship to each other. This correlation points toward kinetic control of morphogenesis, i.e., the involvement of something like a reaction–diffusion mechanism. We analyse this possibility in terms of available reaction–diffusion theory to show how, after various simplifying assumptions, and if the time and space scales of branch formation are known, an effective diffusivity, [Formula: see text], for the patterning mechanism can be estimated. For M. rotata we obtain orders of magnitude: [Formula: see text], with an upper limit on the diffusivity of the faster diffusing of the two morphogenetic substances in the mechanism of ca. 1 × 10−7 cm2/s. These values implicate the cell membrane as the most probable site of pattern formation.

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