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1.
Nat Commun ; 15(1): 1981, 2024 Mar 04.
Artigo em Inglês | MEDLINE | ID: mdl-38438391

RESUMO

Within a cell, synthetic and native genes compete for expression machinery, influencing cellular process dynamics through resource couplings. Models that simplify competitive resource binding kinetics can guide the design of strategies for countering these couplings. However, in bacteria resource availability and cell growth rate are interlinked, which complicates resource-aware biocircuit design. Capturing this interdependence requires coarse-grained bacterial cell models that balance accurate representation of metabolic regulation against simplicity and interpretability. We propose a coarse-grained E. coli cell model that combines the ease of simplified resource coupling analysis with appreciation of bacterial growth regulation mechanisms and the processes relevant for biocircuit design. Reliably capturing known growth phenomena, it provides a unifying explanation to disparate empirical relations between growth and synthetic gene expression. Considering a biomolecular controller that makes cell-wide ribosome availability robust to perturbations, we showcase our model's usefulness in numerically prototyping biocircuits and deriving analytical relations for design guidance.


Assuntos
Escherichia coli , Genes Sintéticos , Escherichia coli/genética , Conscientização , Ligação Competitiva , Ciclo Celular
2.
Biotechnol Adv ; 64: 108117, 2023.
Artigo em Inglês | MEDLINE | ID: mdl-36813010

RESUMO

Living organisms produce a wide range of metabolites. Because of their potential antibacterial, antifungal, antiviral, or cytostatic properties, such natural molecules are of high interest to the pharmaceutical industry. In nature, these metabolites are often synthesized via secondary metabolic biosynthetic gene clusters that are silent under the typical culturing conditions. Among different techniques used to activate these silent gene clusters, co-culturing of "producer" species with specific "inducer" microbes is a particularly appealing approach due to its simplicity. Although several "inducer-producer" microbial consortia have been reported in the literature and hundreds of different secondary metabolites with attractive biopharmaceutical properties have been described as a result of co-cultivating inducer-producer consortia, less attention has been devoted to the understanding of the mechanisms and possible means of induction for production of secondary metabolites in co-cultures. This lack of understanding of fundamental biological functions and inter-species interactions significantly limits the diversity and yield of valuable compounds using biological engineering tools. In this review, we summarize and categorize the known physiological mechanisms of production of secondary metabolites in inducer-producer consortia, and then discuss approaches that could be exploited to optimize the discovery and production of secondary metabolites.


Assuntos
Produtos Biológicos , Consórcios Microbianos , Metabolismo Secundário/genética , Produtos Biológicos/metabolismo , Bioengenharia , Biologia Sintética/métodos
3.
Front Bioeng Biotechnol ; 10: 957140, 2022.
Artigo em Inglês | MEDLINE | ID: mdl-36277404

RESUMO

The use of bacterial communities in bioproduction instead of monocultures has potential advantages including increased productivity through division of labour, ability to utilise cheaper substrates, and robustness against perturbations. A key challenge in the application of engineered bacterial communities is the ability to reliably control the composition of the community in terms of its constituent species. This is crucial to prevent faster growing species from outcompeting others with a lower relative fitness, and to ensure that all species are present at an optimal ratio during different steps in a biotechnological process. In contrast to purely biological approaches such as synthetic quorum sensing circuits or paired auxotrophies, cybergenetic control techniques - those in which computers interface with living cells-are emerging as an alternative approach with many advantages. The community composition is measured through methods such as fluorescence intensity or flow cytometry, with measured data fed real-time into a computer. A control action is computed using a variety of possible control algorithms and then applied to the system, with actuation taking the form of chemical (e.g., inducers, nutrients) or physical (e.g., optogenetic, mechanical) inputs. Subsequent changes in composition are then measured and the cycle repeated, maintaining or driving the system to a desired state. This review discusses recent and future developments in methods for implementing cybergenetic control systems, contrasts their capabilities with those of traditional biological methods of population control, and discusses future directions and outstanding challenges for the field.

4.
J R Soc Interface ; 19(189): 20210737, 2022 04.
Artigo em Inglês | MEDLINE | ID: mdl-35440202

RESUMO

We introduce a new design framework for implementing negative feedback regulation in synthetic biology, which we term 'dichotomous feedback'. Our approach is different from current methods, in that it sequesters existing fluxes in the process to be controlled, and in this way takes advantage of the process's architecture to design the control law. This signal sequestration mechanism appears in many natural biological systems and can potentially be easier to realize than 'molecular sequestration' and other comparison motifs that are nowadays common in biomolecular feedback control design. The loop is closed by linking the strength of signal sequestration to the process output. Our feedback regulation mechanism is motivated by two-component signalling systems, where a second response regulator could be competing with the natural response regulator thus sequestering kinase activity. Here, dichotomous feedback is established by increasing the concentration of the second response regulator as the level of the output of the natural process increases. Extensive analysis demonstrates how this type of feedback shapes the signal response, attenuates intrinsic noise while increasing robustness and reducing crosstalk.


Assuntos
Retroalimentação Fisiológica , Biologia Sintética , Retroalimentação , Retroalimentação Fisiológica/fisiologia , Fosforilação , Transdução de Sinais/fisiologia , Biologia Sintética/métodos
5.
EBioMedicine ; 76: 103868, 2022 Feb.
Artigo em Inglês | MEDLINE | ID: mdl-35172957

RESUMO

BACKGROUND: The manufacturing of any standard mechanical ventilator cannot rapidly be upscaled to several thousand units per week, largely due to supply chain limitations. The aim of this study was to design, verify and perform a pre-clinical evaluation of a mechanical ventilator based on components not required for standard ventilators, and that met the specifications provided by the Medicines and Healthcare Products Regulatory Agency (MHRA) for rapidly-manufactured ventilator systems (RMVS). METHODS: The design utilises closed-loop negative feedback control, with real-time monitoring and alarms. Using a standard test lung, we determined the difference between delivered and target tidal volume (VT) at respiratory rates between 20 and 29 breaths per minute, and the ventilator's ability to deliver consistent VT during continuous operation for >14 days (RMVS specification). Additionally, four anaesthetised domestic pigs (3 male-1 female) were studied before and after lung injury to provide evidence of the ventilator's functionality, and ability to support spontaneous breathing. FINDINGS: Continuous operation lasted 23 days, when the greatest difference between delivered and target VT was 10% at inspiratory flow rates >825 mL/s. In the pre-clinical evaluation, the VT difference was -1 (-90 to 88) mL [mean (LoA)], and positive end-expiratory pressure (PEEP) difference was -2 (-8 to 4) cmH2O. VT delivery being triggered by pressures below PEEP demonstrated spontaneous ventilation support. INTERPRETATION: The mechanical ventilator presented meets the MHRA therapy standards for RMVS and, being based on largely available components, can be manufactured at scale. FUNDING: Work supported by Wellcome/EPSRC Centre for Medical Engineering,King's Together Fund and Oxford University.


Assuntos
Desenho de Equipamento , Respiração Artificial/instrumentação , Animais , COVID-19/patologia , COVID-19/prevenção & controle , COVID-19/virologia , Feminino , Masculino , Taxa Respiratória , SARS-CoV-2/isolamento & purificação , Suínos , Volume de Ventilação Pulmonar
7.
Microb Biotechnol ; 14(6): 2481-2496, 2021 11.
Artigo em Inglês | MEDLINE | ID: mdl-33661573

RESUMO

SOS box of the recA promoter, PVRecA from Vibrio natriegens was characterized, cloned and expressed in a probiotic strain E. coli Nissle 1917. This promoter was then rationally engineered according to predicted interactions between LexA repressor and PVRecA . The redesigned PVRecA-AT promoter showed a sensitive and robust response to DNA damage induced by UV and genotoxic compounds. Rational design of PVRecA coupled to an amplification gene circuit increased circuit output amplitude 4.3-fold in response to a DNA damaging compound mitomycin C. A TetR-based negative feedback loop was added to the PVRecA-AT amplifier to achieve a robust SOS system, resistant to environmental fluctuations in parameters including pH, temperature, oxygen and nutrient conditions. We found that E. coli Nissle 1917 with optimized PVRecA-AT adapted to UV exposure and increased SOS response 128-fold over 40 h cultivation in turbidostat mini-reactor. We also showed the potential of this PVRecA-AT system as an optogenetic actuator, which can be controlled spatially through UV radiation. We demonstrated that the optimized SOS responding gene circuits were able to detect carcinogenic biomarker molecules with clinically relevant concentrations. The ultrasensitive SOS gene circuits in probiotic E. coli Nissle 1917 would be potentially useful for bacterial diagnosis.


Assuntos
Redes Reguladoras de Genes , Recombinases Rec A , Proteínas de Bactérias/genética , Dano ao DNA , Escherichia coli/genética , Recombinases Rec A/genética , Serina Endopeptidases/genética
8.
PLoS Genet ; 17(2): e1009099, 2021 02.
Artigo em Inglês | MEDLINE | ID: mdl-33539353

RESUMO

Regulation by oxygen (O2) in rhizobia is essential for their symbioses with plants and involves multiple O2 sensing proteins. Three sensors exist in the pea microsymbiont Rhizobium leguminosarum Rlv3841: hFixL, FnrN and NifA. At low O2 concentrations (1%) hFixL signals via FxkR to induce expression of the FixK transcription factor, which activates transcription of downstream genes. These include fixNOQP, encoding the high-affinity cbb3-type terminal oxidase used in symbiosis. In free-living Rlv3841, the hFixL-FxkR-FixK pathway was active at 1% O2, and confocal microscopy showed hFixL-FxkR-FixK activity in the earliest stages of Rlv3841 differentiation in nodules (zones I and II). Work on Rlv3841 inside and outside nodules showed that the hFixL-FxkR-FixK pathway also induces transcription of fnrN at 1% O2 and in the earliest stages of Rlv3841 differentiation in nodules. We confirmed past findings suggesting a role for FnrN in fixNOQP expression. However, unlike hFixL-FxkR-FixK, Rlv3841 FnrN was only active in the near-anaerobic zones III and IV of pea nodules. Quantification of fixNOQP expression in nodules showed this was driven primarily by FnrN, with minimal direct hFixL-FxkR-FixK induction. Thus, FnrN is key for full symbiotic expression of fixNOQP. Without FnrN, nitrogen fixation was reduced by 85% in Rlv3841, while eliminating hFixL only reduced fixation by 25%. The hFixL-FxkR-FixK pathway effectively primes the O2 response by increasing fnrN expression in early differentiation (zones I-II). In zone III of mature nodules, near-anaerobic conditions activate FnrN, which induces fixNOQP transcription to the level required for wild-type nitrogen fixation activity. Modelling and transcriptional analysis indicates that the different O2 sensitivities of hFixL and FnrN lead to a nuanced spatiotemporal pattern of gene regulation in different nodule zones in response to changing O2 concentration. Multi-sensor O2 regulation is prevalent in rhizobia, suggesting the fine-tuned control this enables is common and maximizes the effectiveness of the symbioses.


Assuntos
Proteínas de Bactérias/metabolismo , Histidina Quinase/metabolismo , Oxigênio/metabolismo , Rhizobium leguminosarum/metabolismo , Simbiose/genética , Fatores de Transcrição/metabolismo , Proteínas de Bactérias/genética , Fabaceae/genética , Fabaceae/metabolismo , Regulação Bacteriana da Expressão Gênica/genética , Histidina Quinase/genética , Mutação , Fixação de Nitrogênio/genética , Óperon/genética , Rhizobium leguminosarum/genética , Fatores de Transcrição/genética
9.
PLoS Biol ; 18(7): e3000794, 2020 07.
Artigo em Inglês | MEDLINE | ID: mdl-32730242

RESUMO

The precision and repeatability of in vivo biological studies is predicated upon methods for isolating a targeted subsystem from external sources of noise and variability. However, in many experimental frameworks, this is made challenging by nonstatic environments during host cell growth, as well as variability introduced by manual sampling and measurement protocols. To address these challenges, we developed Chi.Bio, a parallelised open-source platform that represents a new experimental paradigm in which all measurement and control actions can be applied to a bulk culture in situ. In addition to continuous-culturing capabilities, it incorporates tunable light outputs, spectrometry, and advanced automation features. We demonstrate its application to studies of cell growth and biofilm formation, automated in silico control of optogenetic systems, and readout of multiple orthogonal fluorescent proteins in situ. By integrating precise measurement and actuation hardware into a single low-cost platform, Chi.Bio facilitates novel experimental methods for synthetic, systems, and evolutionary biology and broadens access to cutting-edge research capabilities.


Assuntos
Reatores Biológicos , Técnicas de Cultura/instrumentação , Optogenética/instrumentação , Automação , Biofilmes , Proliferação de Células , Simulação por Computador , Software
10.
J Theor Biol ; 486: 110077, 2020 02 07.
Artigo em Inglês | MEDLINE | ID: mdl-31715181

RESUMO

Combating the evolution of widespread antibiotic resistance is one of the most pressing challenges facing modern medicine. Recent research has demonstrated that the evolution of pathogens with high levels of resistance can be accelerated by spatial and temporal inhomogeneities in antibiotic concentration, which frequently arise in patients and the environment. Strategies to predict and counteract the effects of such inhomogeneities will be critical in the fight against resistance. In this paper we develop a mechanistic framework for modelling the adaptive evolution of resistance in the presence of spatiotemporal antibiotic concentrations, which treats the adaptive process as an interaction between two mutually orthogonal forces; the first returns cells to their wild-type state in the absence of antibiotic selection, and the second selects for increased coping ability in the presence of an antibiotic. We apply our model to investigate laboratory adaptation experiments, and then extend it to consider the case in which multiple strategies for resistance undergo competitive evolution.


Assuntos
Adaptação Fisiológica , Antibacterianos , Antibacterianos/farmacologia , Antibacterianos/uso terapêutico , Resistência Microbiana a Medicamentos/genética , Humanos
11.
ACS Synth Biol ; 8(10): 2212-2219, 2019 10 18.
Artigo em Inglês | MEDLINE | ID: mdl-31500408

RESUMO

The robustness and reliability of synthetic biological systems can be substantially improved by the introduction of feedback control architectures that parallel those employed in traditional engineering disciplines. One common control goal is adaptation (or disturbance rejection), which refers to a system's ability to maintain a constant output despite variation in some of its constituent processes (as frequently occurs in noisy cellular environments) or external perturbations. In this paper, we propose and analyze a control architecture that employs integrase and excisionase proteins to invert regions of DNA and an mRNA-mRNA annihilation reaction. Combined, these components approximate the functionality of a switching controller (as employed in classical control engineering) with three distinct operational modes. We demonstrate that this system is capable of near-perfect adaptation to variation in rates of both transcription and translation and can also operate without excessive consumption of cellular resources. The system's steady-state behavior is analyzed, and limits on its operating range are derived. Deterministic simulations of its dynamics are presented and are then extended to the stochastic case, which treats biochemical reactions as discrete events.


Assuntos
DNA/genética , Retroalimentação Fisiológica/fisiologia , RNA Mensageiro/genética , Biologia Sintética/métodos , Modelos Biológicos , Reprodutibilidade dos Testes
12.
Appl Environ Microbiol ; 85(6)2019 03 15.
Artigo em Inglês | MEDLINE | ID: mdl-30658983

RESUMO

A simple aspirin-inducible system has been developed and characterized in Escherichia coli by employing the Psal promoter and SalR regulation system originally from Acinetobacter baylyi ADP1. Mutagenesis at the DNA binding domain (DBD) and chemical recognition domain (CRD) of the SalR protein in A. baylyi ADP1 suggests that the effector-free form, SalRr, can compete with the effector-bound form, SalRa, binding the Psal promoter and repressing gene transcription. The induction of the Psal promoter was compared in two different gene circuit designs: a simple regulation system (SRS) and positive autoregulation (PAR). Both regulatory circuits were induced in a dose-dependent manner in the presence of 0.05 to 10 µM aspirin. Overexpression of SalR in the SRS circuit reduced both baseline leakiness and the strength of the Psal promoter. The PAR circuit forms a positive feedback loop that fine-tunes the level of SalR. A mathematical simulation based on the SalRr/SalRa competitive binding model not only fit the observed experimental results in SRS and PAR circuits but also predicted the performance of a new gene circuit design for which weak expression of SalR in the SRS circuit should significantly improve induction strength. The experimental result is in good agreement with this prediction, validating the SalRr/SalRa competitive binding model. The aspirin-inducible systems were also functional in probiotic strain E. coli Nissle 1917 and SimCells produced from E. coli MC1000 ΔminD These well-characterized and modularized aspirin-inducible gene circuits would be useful biobricks for synthetic biology.IMPORTANCE An aspirin-inducible SalR/Psal regulation system, originally from Acinetobacter baylyi ADP1, has been designed for E. coli strains. SalR is a typical LysR-type transcriptional regulator (LTTR) family protein and activates the Psal promoter in the presence of aspirin or salicylate in the range of 0.05 to 10 µM. The experimental results and mathematical simulations support the competitive binding model of the SalR/Psal regulation system in which SalRr competes with SalRa to bind the Psal promoter and affect gene transcription. The competitive binding model successfully predicted that weak SalR expression would significantly improve the inducible strength of the SalR/Psal regulation system, which is confirmed by the experimental results. This provides an important mechanism model to fine-tune transcriptional regulation of the LTTR family, which is the largest family of transcriptional regulators in the prokaryotic kingdom. In addition, the SalR/Psal regulation system was also functional in probiotic strain E. coli Nissle 1917 and minicell-derived SimCells, which would be a useful biobrick for environmental and medical applications.


Assuntos
Aspirina/metabolismo , Técnicas Biossensoriais/métodos , Escherichia coli/metabolismo , Acinetobacter/genética , Acinetobacter/metabolismo , Técnicas Biossensoriais/instrumentação , Escherichia coli/genética , Regulação Bacteriana da Expressão Gênica , Redes Reguladoras de Genes , Regiões Promotoras Genéticas , Salicilatos/metabolismo
13.
Nucleic Acids Res ; 46(18): 9875-9889, 2018 10 12.
Artigo em Inglês | MEDLINE | ID: mdl-30212900

RESUMO

Negative feedback is known to enable biological and man-made systems to perform reliably in the face of uncertainties and disturbances. To date, synthetic biological feedback circuits have primarily relied upon protein-based, transcriptional regulation to control circuit output. Small RNAs (sRNAs) are non-coding RNA molecules that can inhibit translation of target messenger RNAs (mRNAs). In this work, we modelled, built and validated two synthetic negative feedback circuits that use rationally-designed sRNAs for the first time. The first circuit builds upon the well characterised tet-based autorepressor, incorporating an externally-inducible sRNA to tune the effective feedback strength. This allows more precise fine-tuning of the circuit output in contrast to the sigmoidal, steep input-output response of the autorepressor alone. In the second circuit, the output is a transcription factor that induces expression of an sRNA, which inhibits translation of the mRNA encoding the output, creating direct, closed-loop, negative feedback. Analysis of the noise profiles of both circuits showed that the use of sRNAs did not result in large increases in noise. Stochastic and deterministic modelling of both circuits agreed well with experimental data. Finally, simulations using fitted parameters allowed dynamic attributes of each circuit such as response time and disturbance rejection to be investigated.


Assuntos
Escherichia coli/genética , Retroalimentação Fisiológica , RNA Bacteriano/genética , RNA Mensageiro/genética , Pequeno RNA não Traduzido/genética , Proteínas Repressoras/genética , Escherichia coli/metabolismo , Regulação da Expressão Gênica , Modelos Genéticos , Plasmídeos/genética , RNA Bacteriano/metabolismo , RNA Mensageiro/metabolismo , Pequeno RNA não Traduzido/metabolismo , Proteínas Repressoras/metabolismo
14.
ACS Synth Biol ; 7(6): 1528-1537, 2018 06 15.
Artigo em Inglês | MEDLINE | ID: mdl-29799736

RESUMO

The measurement of noise is critical when assessing the design and function of synthetic biological systems. Cell-to-cell variability can be quantified experimentally using single-cell measurement techniques such as flow cytometry and fluorescent microscopy. However, these approaches are costly and impractical for high-throughput parallelized experiments, which are frequently conducted using plate-reader devices. In this paper we describe reporter systems that allow estimation of the cell-to-cell variability in a biological system's output using only measurements of a cell culture's bulk properties. We analyze one potential implementation of such a system that is based upon a fluorescent protein FRET reporter pair, finding that with typical parameters from the literature it is able to reliably estimate variability. We also briefly describe an alternate implementation based upon an activating sRNA circuit. The feasible region of parameter values for which the reporter system can function is assessed, and the dependence of its performance on both extrinsic and intrinsic noise is investigated. Experimental realization of these constructs can yield novel reporter systems that allow measurement of a synthetic gene circuit's output, as well as the intrapopulation variability of this output, at little added cost.


Assuntos
Transferência Ressonante de Energia de Fluorescência/métodos , Redes Reguladoras de Genes , Biologia Sintética/métodos , Técnicas de Cultura de Células , Transferência Ressonante de Energia de Fluorescência/estatística & dados numéricos , Regulação da Expressão Gênica , Proteínas Luminescentes/genética , Proteínas Luminescentes/metabolismo , RNA de Transferência/genética , Sensibilidade e Especificidade
15.
Sci Rep ; 7(1): 4599, 2017 07 04.
Artigo em Inglês | MEDLINE | ID: mdl-28676696

RESUMO

Riboswitches are structural genetic regulatory elements that directly couple the sensing of small molecules to gene expression. They have considerable potential for applications throughout synthetic biology and bio-manufacturing as they are able to sense a wide range of small molecules and regulate gene expression in response. Despite over a decade of research they have yet to reach this considerable potential as they cannot yet be treated as modular components. This is due to several limitations including sensitivity to changes in genetic context, low tunability, and variability in performance. To overcome the associated difficulties with riboswitches, we have designed and introduced a novel genetic element called a ribo-attenuator in Bacteria. This genetic element allows for predictable tuning, insulation from contextual changes, and a reduction in expression variation. Ribo-attenuators allow riboswitches to be treated as truly modular and tunable components, thus increasing their reliability for a wide range of applications.


Assuntos
Escherichia coli/crescimento & desenvolvimento , Engenharia Genética/métodos , Riboswitch , Proteínas de Bactérias/genética , Clonagem Molecular , Escherichia coli/genética , Biologia Sintética , Vibrio vulnificus/genética , Vibrio vulnificus/metabolismo
16.
ACS Synth Biol ; 6(9): 1663-1671, 2017 09 15.
Artigo em Inglês | MEDLINE | ID: mdl-28602075

RESUMO

Accurate control of a biological process is essential for many critical functions in biology, from the cell cycle to proteome regulation. To achieve this, negative feedback is frequently employed to provide a highly robust and reliable output. Feedback is found throughout biology and technology, but due to challenges posed by its implementation, it is yet to be widely adopted in synthetic biology. In this paper we design a synthetic feedback network using a class of recombinase proteins called integrases, which can be re-engineered to flip the orientation of DNA segments in a digital manner. This system is highly orthogonal, and demonstrates a strong capability for regulating and reducing the expression variability of genes being transcribed under its control. An excisionase protein provides the negative feedback signal to close the loop in this system, by flipping DNA segments in the reverse direction. Our integrase/excisionase negative feedback system thus provides a modular architecture that can be tuned to suit applications throughout synthetic biology and biomanufacturing that require a highly robust and orthogonally controlled output.


Assuntos
DNA/genética , Retroalimentação Fisiológica/fisiologia , Regulação da Expressão Gênica/genética , Genes de Troca/genética , Genes Sintéticos/genética , Modelos Genéticos , Recombinases/genética , Simulação por Computador , Escherichia coli/genética , Melhoramento Genético/métodos , Engenharia de Proteínas/métodos , Proteínas Recombinantes/biossíntese , Proteínas Recombinantes/genética , Biologia Sintética/métodos
17.
Artigo em Inglês | MEDLINE | ID: mdl-24229239

RESUMO

Formation of localized propagating patterns is a fascinating self-organizing phenomenon that happens in a wide range of spatially extended, excitable systems in which individual elements have resting, activated, and refractory states. Here we study a type of stochastic three-state excitable network model that has been recently developed; this model is able to generate a rich range of pattern dynamics, including localized wandering patterns and localized propagating patterns with crescent shapes and long-range propagation. The collective dynamics of these localized patterns have anomalous subdiffusive dynamics before symmetry breaking and anomalous superdiffusive dynamics after that, showing long-range spatiotemporal coherence in the system. In this study, the stability of the localized wandering patterns is analyzed by treating an individual localized pattern as a subpopulation to develop its average response function. This stability analysis indicates that when the average refractory period is greater than a certain value, there are too many elements in the refractory state after being activated to allow the subpopulation to support a self-sustained pattern; this is consistent with symmetry breaking identified by using an order parameter. Furthermore, in a broad parameter space, the simple network model is able to generate a range of interactions between different localized propagating patterns including repulsive collisions and partial and full annihilations, and interactions between localized propagating patterns and the refractory wake behind others; in this study, these interaction dynamics are systematically quantified based on their relative propagation directions and the resultant angles between them before and after their collisions. These results suggest that the model potentially provides a modeling framework to understand the formation of localized propagating patterns in a broad class of systems with excitable properties.

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