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Kang TY, Bocci F, Nie Q, Onuchic JN, Levchenko A. Spatial-temporal order-disorder transition in angiogenic NOTCH signaling controls cell fate specification. eLife 2024; 12:RP89262. [PMID: 38376371 PMCID: PMC10942579 DOI: 10.7554/elife.89262] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/21/2024] Open
Abstract
Angiogenesis is a morphogenic process resulting in the formation of new blood vessels from pre-existing ones, usually in hypoxic micro-environments. The initial steps of angiogenesis depend on robust differentiation of oligopotent endothelial cells into the Tip and Stalk phenotypic cell fates, controlled by NOTCH-dependent cell-cell communication. The dynamics of spatial patterning of this cell fate specification are only partially understood. Here, by combining a controlled experimental angiogenesis model with mathematical and computational analyses, we find that the regular spatial Tip-Stalk cell patterning can undergo an order-disorder transition at a relatively high input level of a pro-angiogenic factor VEGF. The resulting differentiation is robust but temporally unstable for most cells, with only a subset of presumptive Tip cells leading sprout extensions. We further find that sprouts form in a manner maximizing their mutual distance, consistent with a Turing-like model that may depend on local enrichment and depletion of fibronectin. Together, our data suggest that NOTCH signaling mediates a robust way of cell differentiation enabling but not instructing subsequent steps in angiogenic morphogenesis, which may require additional cues and self-organization mechanisms. This analysis can assist in further understanding of cell plasticity underlying angiogenesis and other complex morphogenic processes.
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Affiliation(s)
- Tae-Yun Kang
- Department of Biomedical Engineering, Yale UniversityNew HavenUnited States
- Yale UniversityNew HavenUnited States
| | - Federico Bocci
- NSF-Simons Center for Multiscale Cell Fate Research, University of California IrvineIrvineUnited States
- Department of Mathematics, University of California IrvineIrvineUnited States
| | - Qing Nie
- NSF-Simons Center for Multiscale Cell Fate Research, University of California IrvineIrvineUnited States
- Department of Mathematics, University of California IrvineIrvineUnited States
| | - José N Onuchic
- Center for Theoretical Biological Physics, Rice UniversityHoustonUnited States
| | - Andre Levchenko
- Department of Biomedical Engineering, Yale UniversityNew HavenUnited States
- Yale UniversityNew HavenUnited States
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2
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Knobloch E, Yochelis A. Instability mechanisms of repelling peak solutions in a multi-variable activator-inhibitor system. CHAOS (WOODBURY, N.Y.) 2022; 32:123129. [PMID: 36587350 DOI: 10.1063/5.0125535] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2022] [Accepted: 11/15/2022] [Indexed: 06/17/2023]
Abstract
We study the linear stability properties of spatially localized single- and multi-peak states generated in a subcritical Turing bifurcation in the Meinhardt model of branching. In one spatial dimension, these states are organized in a foliated snaking structure owing to peak-peak repulsion but are shown to be all linearly unstable, with the number of unstable modes increasing with the number of peaks present. Despite this, in two spatial dimensions, direct numerical simulations reveal the presence of stable single- and multi-spot states whose properties depend on the repulsion from nearby spots as well as the shape of the domain and the boundary conditions imposed thereon. Front propagation is shown to trigger the growth of new spots while destabilizing others. The results indicate that multi-variable models may support new types of behavior that are absent from typical two-variable models.
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Affiliation(s)
- Edgar Knobloch
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Arik Yochelis
- Department of Solar Energy and Environmental Physics, Swiss Institute for Dryland Environmental and Energy Research, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 8499000, Israel
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3
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Jia Y, Zhao Q, Yin H, Guo S, Sun M, Yang Z, Zhao X. Reaction-Diffusion Model-Based Research on Formation Mechanism of Neuron Dendritic Spine Patterns. Front Neurorobot 2021; 15:563682. [PMID: 34194309 PMCID: PMC8236519 DOI: 10.3389/fnbot.2021.563682] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2020] [Accepted: 05/17/2021] [Indexed: 11/13/2022] Open
Abstract
The pattern abnormalities of dendritic spine, tiny protrusions on neuron dendrites, have been found related to multiple nervous system diseases, such as Parkinson's disease and schizophrenia. The determination of the factors affecting spine patterns is of vital importance to explore the pathogenesis of these diseases, and further, search the treatment method for them. Although the study of dendritic spines is a hot topic in neuroscience in recent years, there is still a lack of systematic study on the formation mechanism of its pattern. This paper provided a reinterpretation of reaction-diffusion model to simulate the formation process of dendritic spine, and further, study the factors affecting spine patterns. First, all four classic shapes of spines, mushroom-type, stubby-type, thin-type, and branched-type were reproduced using the model. We found that the consumption rate of substrates by the cytoskeleton is a key factor to regulate spine shape. Moreover, we found that the density of spines can be regulated by the amount of an exogenous activator and inhibitor, which is in accordance with the anatomical results found in hippocampal CA1 in SD rats with glioma. Further, we analyzed the inner mechanism of the above model parameters regulating the dendritic spine pattern through Turing instability analysis and drew a conclusion that an exogenous inhibitor and activator changes Turing wavelength through which to regulate spine densities. Finally, we discussed the deep regulation mechanisms of several reported regulators of dendritic spine shape and densities based on our simulation results. Our work might evoke attention to the mathematic model-based pathogenesis research for neuron diseases which are related to the dendritic spine pattern abnormalities and spark inspiration in the treatment research for these diseases.
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Affiliation(s)
- Yiqing Jia
- Institute of Robotics and Automatic Information Systems, College of Artificial Intelligence, Nankai University, Tianjin, China
| | - Qili Zhao
- Institute of Robotics and Automatic Information Systems, College of Artificial Intelligence, Nankai University, Tianjin, China
| | - Hongqiang Yin
- State Key Laboratory of Medicinal Chemical Biology, School of Medicine, Nankai University, Tianjin, China
| | - Shan Guo
- Institute of Robotics and Automatic Information Systems, College of Artificial Intelligence, Nankai University, Tianjin, China
| | - Mingzhu Sun
- Institute of Robotics and Automatic Information Systems, College of Artificial Intelligence, Nankai University, Tianjin, China
| | - Zhuo Yang
- State Key Laboratory of Medicinal Chemical Biology, School of Medicine, Nankai University, Tianjin, China
| | - Xin Zhao
- Institute of Robotics and Automatic Information Systems, College of Artificial Intelligence, Nankai University, Tianjin, China
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4
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Yochelis A. The nonlinear initiation of side-branching by activator-inhibitor-substrate (Turing) morphogenesis. CHAOS (WOODBURY, N.Y.) 2021; 31:051102. [PMID: 34240921 DOI: 10.1063/5.0050630] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2021] [Accepted: 04/21/2021] [Indexed: 06/13/2023]
Abstract
An understanding of the underlying mechanism of side-branching is paramount in controlling and/or therapeutically treating mammalian organs, such as lungs, kidneys, and glands. Motivated by an activator-inhibitor-substrate approach that is conjectured to dominate the initiation of side-branching in a pulmonary vascular pattern, I demonstrate a distinct transverse front instability in which new fingers grow out of an oscillatory breakup dynamics at the front line without any typical length scale. These two features are attributed to unstable peak solutions in 1D that subcritically emanate from Turing bifurcation and that exhibit repulsive interactions. The results are based on a bifurcation analysis and numerical simulations and provide a potential strategy toward also developing a framework of side-branching for other biological systems, such as plant roots and cellular protrusions.
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Affiliation(s)
- Arik Yochelis
- Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research (BIDR), Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 8499000, Israel and Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 8410501, Israel
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5
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Guo S, Sun MZ, Zhao X. Wavelength of a Turing-type mechanism regulates the morphogenesis of meshwork patterns. Sci Rep 2021; 11:4813. [PMID: 33649396 PMCID: PMC7921672 DOI: 10.1038/s41598-021-84313-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2020] [Accepted: 02/15/2021] [Indexed: 11/08/2022] Open
Abstract
The meshwork pattern is a significant pattern in the development of biological tissues and organs. It is necessary to explore the mathematical mechanism of meshwork pattern formation. In this paper, we found that the meshwork pattern is formed by four kinds of stalk behaviours: stalk extension, tip bifurcation, side branching and tip fusion. The Turing-type pattern underlying the meshwork pattern is a Turing spot pattern, which indicates that the Turing instability of the spot pattern promotes activator peak formation and then guides the formation of meshwork patterns. Then, we found that the Turing wavelength decreased in turn from tip bifurcation to side branching to tip fusion via statistical evaluation. Through the functional relationship between the Turing wavelength and model parameters ([Formula: see text] and [Formula: see text]), we found that parameters [Formula: see text] and [Formula: see text] had monotonic effects on the Turing wavelength and that parameter [Formula: see text] had nonmonotonic effects. Furthermore, we performed simulations of local meshwork pattern formation under variable model parameter values. The simulation results verified the corresponding relationship between the Turing wavelength and stalk behaviours and the functional relationship between the Turing wavelength and model parameters. The simulation results showed that the Turing wavelength regulated the meshwork pattern and that the small Turing wavelength facilitated dense meshwork pattern formation. Our work provides novel insight into and understanding of the formation of meshwork patterns. We believe that studies associated with network morphogenesis can benefit from our work.
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Affiliation(s)
- Shan Guo
- Institute of Robotics and Automatic Information Systems, Nankai University, College of Artificial Intelligence, 201-02, Tianjin, 300350, People's Republic of China
- Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin, 300350, People's Republic of China
| | - Ming-Zhu Sun
- Institute of Robotics and Automatic Information Systems, Nankai University, College of Artificial Intelligence, 201-02, Tianjin, 300350, People's Republic of China
- Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin, 300350, People's Republic of China
| | - Xin Zhao
- Institute of Robotics and Automatic Information Systems, Nankai University, College of Artificial Intelligence, 201-02, Tianjin, 300350, People's Republic of China.
- Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin, 300350, People's Republic of China.
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Shapira AZ, Uecker H, Yochelis A. Stripes on finite domains: Why the zigzag instability is only a partial story. CHAOS (WOODBURY, N.Y.) 2020; 30:073104. [PMID: 32752648 DOI: 10.1063/5.0006126] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2020] [Accepted: 06/15/2020] [Indexed: 06/11/2023]
Abstract
Stationary periodic patterns are widespread in natural sciences, ranging from nano-scale electrochemical and amphiphilic systems to mesoscale fluid, chemical, and biological media and to macro-scale vegetation and cloud patterns. Their formation is usually due to a primary symmetry breaking of a uniform state to stripes, often followed by secondary instabilities to form zigzag and labyrinthine patterns. These secondary instabilities are well studied under idealized conditions of an infinite domain; however, on finite domains, the situation is more subtle since the unstable modes depend also on boundary conditions. Using two prototypical models, the Swift-Hohenberg equation and the forced complex Ginzburg-Landau equation, we consider finite size domains with no flux boundary conditions transversal to the stripes and reveal a distinct mixed-mode instability that lies in between the classical zigzag and the Eckhaus lines. This explains the stability of stripes in the mildly zigzag unstable regime and, after crossing the mixed-mode line, the evolution of zigzag stripes in the bulk of the domain and the formation of defects near the boundaries. The results are of particular importance for problems with large timescale separation, such as bulk-heterojunction deformations in organic photovoltaic and vegetation in semi-arid regions, where early temporal transients may play an important role.
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Affiliation(s)
- Alon Z Shapira
- Department of Solar Energy and Environmental Physics, Swiss Institute for Dryland Environmental and Energy Research, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 8499000, Israel
| | - Hannes Uecker
- Institute for Mathematics, Carl von Ossietzky University of Oldenburg, PF 2503, 26111 Oldenburg, Germany
| | - Arik Yochelis
- Department of Solar Energy and Environmental Physics, Swiss Institute for Dryland Environmental and Energy Research, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 8499000, Israel
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7
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Nakamasu A, Higaki T. Theoretical models for branch formation in plants. JOURNAL OF PLANT RESEARCH 2019; 132:325-333. [PMID: 31004242 PMCID: PMC7082385 DOI: 10.1007/s10265-019-01107-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/08/2019] [Accepted: 04/09/2019] [Indexed: 06/09/2023]
Abstract
Various branch architectures are observed in living organisms including plants. Branch formation has traditionally been an area of interest in the field of developmental biology, and theoretical approaches are now commonly used to understand the complex mechanisms involved. In this review article, we provide an overview of theoretical approaches including mathematical models and computer simulations for studying plant branch formation. These approaches cover a wide range of topics. In particular, we focus on the importance of positional information in branch formation, which has been especially revealed by theoretical research in plants including computations of developmental processes.
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Affiliation(s)
- Akiko Nakamasu
- International Research Organization for Advanced Science and Technology, Kumamoto University, 2-39-1 Kurokami, Chuou-ku, Kumamoto, 860-8555, Japan.
| | - Takumi Higaki
- International Research Organization for Advanced Science and Technology, Kumamoto University, 2-39-1 Kurokami, Chuou-ku, Kumamoto, 860-8555, Japan.
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Miyoshi S, Kimura S, Ootsuki R, Higaki T, Nakamasu A. Developmental analyses of divarications in leaves of an aquatic fern Microsorum pteropus and its varieties. PLoS One 2019; 14:e0210141. [PMID: 30682033 PMCID: PMC6347172 DOI: 10.1371/journal.pone.0210141] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2017] [Accepted: 12/18/2018] [Indexed: 11/18/2022] Open
Abstract
Plant leaves occur in diverse shapes. Divarication patterns that develop during early growths are one of key factors that determine leaf shapes. We utilized leaves of Microsorum pteropus, a semi-aquatic fern, and closely related varieties to analyze a variation in the divarication patterns. The leaves exhibited three major types of divarication: no lobes, bifurcation, and trifurcation (i.e., monopodial branching). Our investigation of their developmental processes, using time-lapse imaging, revealed localized growths and dissections of blades near each leaf apex. Restricted cell divisions responsible for the apical growths were confirmed using a pulse-chase strategy for EdU labeling assays.
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Affiliation(s)
- Saori Miyoshi
- Department of Bioresource and Environmental Sciences, Faculty of Life Sciences, Kyoto Sangyo University, Kyoto, Japan
| | - Seisuke Kimura
- Department of Bioresource and Environmental Sciences, Faculty of Life Sciences, Kyoto Sangyo University, Kyoto, Japan
- Center for Ecological Evolutionary Developmental Biology, Kyoto Sangyo University, Kyoto, Japan
| | - Ryo Ootsuki
- Department of Natural Sciences, Faculty of Arts and Sciences, Komazawa University, Tokyo, Japan
- Faculty of Chemical and Biological Sciences, Japan Women's University, Tokyo, Japan
| | - Takumi Higaki
- International Research Organization for Advanced Science and Technology, Kumamoto University, Kumamoto, Japan
| | - Akiko Nakamasu
- Department of Bioresource and Environmental Sciences, Faculty of Life Sciences, Kyoto Sangyo University, Kyoto, Japan
- International Research Organization for Advanced Science and Technology, Kumamoto University, Kumamoto, Japan
- Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Tokyo, Japan
- * E-mail:
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9
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Lang C, Conrad L, Michos O. Mathematical Approaches of Branching Morphogenesis. Front Genet 2018; 9:673. [PMID: 30631344 PMCID: PMC6315180 DOI: 10.3389/fgene.2018.00673] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2018] [Accepted: 12/04/2018] [Indexed: 12/16/2022] Open
Abstract
Many organs require a high surface to volume ratio to properly function. Lungs and kidneys, for example, achieve this by creating highly branched tubular structures during a developmental process called branching morphogenesis. The genes that control lung and kidney branching share a similar network structure that is based on ligand-receptor reciprocal signalling interactions between the epithelium and the surrounding mesenchyme. Nevertheless, the temporal and spatial development of the branched epithelial trees differs, resulting in organs of distinct shape and size. In the embryonic lung, branching morphogenesis highly depends on FGF10 signalling, whereas GDNF is the driving morphogen in the kidney. Knockout of Fgf10 and Gdnf leads to lung and kidney agenesis, respectively. However, FGF10 plays a significant role during kidney branching and both the FGF10 and GDNF pathway converge on the transcription factors ETV4/5. Although the involved signalling proteins have been defined, the underlying mechanism that controls lung and kidney branching morphogenesis is still elusive. A wide range of modelling approaches exists that differ not only in the mathematical framework (e.g., stochastic or deterministic) but also in the spatial scale (e.g., cell or tissue level). Due to advancing imaging techniques, image-based modelling approaches have proven to be a valuable method for investigating the control of branching events with respect to organ-specific properties. Here, we review several mathematical models on lung and kidney branching morphogenesis and suggest that a ligand-receptor-based Turing model represents a potential candidate for a general but also adaptive mechanism to control branching morphogenesis during development.
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Affiliation(s)
| | | | - Odyssé Michos
- Department of Biosystems Science and Engineering, ETH Zürich, Basel, Switzerland
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10
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Fontana JM, Khodus GR, Unnersjö-Jess D, Blom H, Aperia A, Brismar H. Spontaneous calcium activity in metanephric mesenchymal cells regulates branching morphogenesis in the embryonic kidney. FASEB J 2018; 33:4089-4096. [PMID: 30496703 PMCID: PMC6404591 DOI: 10.1096/fj.201802054r] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
The central role of calcium signaling during development of early vertebrates is well documented, but little is known about its role in mammalian embryogenesis. We have used immunofluorescence and time-lapse calcium imaging of cultured explanted embryonic rat kidneys to study the role of calcium signaling for branching morphogenesis. In mesenchymal cells, we recorded spontaneous calcium activity that was characterized by irregular calcium transients. The calcium signals were dependent on release of calcium from intracellular stores in the endoplasmic reticulum. Down-regulation of the calcium activity, both by blocking the sarco-endoplasmic reticulum Ca2+-ATPase and by chelating cytosolic calcium, resulted in retardation of branching morphogenesis and a reduced formation of primitive nephrons but had no effect on cell proliferation. We propose that spontaneous calcium activity contributes with a stochastic factor to the self-organizing process that controls branching morphogenesis, a major determinant of the ultimate number of nephrons in the kidney.-Fontana, J. M., Khodus, G. R., Unnersjö-Jess, D., Blom, H., Aperia, A., Brismar, H. Spontaneous calcium activity in metanephric mesenchymal cells regulates branching morphogenesis in the embryonic kidney.
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Affiliation(s)
- Jacopo M Fontana
- Department of Applied Physics, Science for Life Laboratory, Kungliga Tekniska Högskolan (KTH) Royal Institute of Technology, Solna, Sweden
| | - Georgiy R Khodus
- Department of Applied Physics, Science for Life Laboratory, Kungliga Tekniska Högskolan (KTH) Royal Institute of Technology, Solna, Sweden
| | - David Unnersjö-Jess
- Department of Applied Physics, Science for Life Laboratory, Kungliga Tekniska Högskolan (KTH) Royal Institute of Technology, Solna, Sweden
| | - Hans Blom
- Department of Applied Physics, Science for Life Laboratory, Kungliga Tekniska Högskolan (KTH) Royal Institute of Technology, Solna, Sweden
| | - Anita Aperia
- Department of Women's and Children's Health, Science for Life Laboratory, Karolinska Institutet, Solna, Sweden
| | - Hjalmar Brismar
- Department of Applied Physics, Science for Life Laboratory, Kungliga Tekniska Högskolan (KTH) Royal Institute of Technology, Solna, Sweden.,Department of Women's and Children's Health, Science for Life Laboratory, Karolinska Institutet, Solna, Sweden
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Zhu X, Yang H. Turing Instability-Driven Biofabrication of Branching Tissue Structures: A Dynamic Simulation and Analysis Based on the Reaction⁻Diffusion Mechanism †. MICROMACHINES 2018; 9:E109. [PMID: 30424043 PMCID: PMC6187743 DOI: 10.3390/mi9030109] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/01/2018] [Revised: 02/20/2018] [Accepted: 03/01/2018] [Indexed: 12/17/2022]
Abstract
Four-dimensional (4D) biofabrication techniques aim to dynamically produce and control three-dimensional (3D) biological structures that would transform their shapes or functionalities with time, when a stimulus is imposed or cell post-printing self-assembly occurs. The evolution of 3D branching patterns via self-assembly of cells is critical for the 4D biofabrication of artificial organs or tissues with branched geometry. However, it is still unclear how the formation and evolution of these branching patterns are biologically encoded. Here, we study the biofabrication of lung branching structures utilizing a simulation model based on Turing instability that raises a dynamic reaction⁻diffusion (RD) process of the biomolecules and cells. The simulation model incorporates partial differential equations of four variables, describing the tempo-spatial distribution of the variables in 3D over time. The simulation results present the formation and evolution process of 3D branching patterns over time and also interpret both the behaviors of side-branching and tip-splitting as the stalk grows and the fabrication style under an external concentration gradient of morphogen, through 3D visualization. This provides a theoretical framework for rationally guiding the 4D biofabrication of lung airway grafts via cellular self-organization, which would potentially reduce the complexity of future experimental research and number of trials.
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Affiliation(s)
- Xiaolu Zhu
- College of Mechanical & Electrical Engineering, Hohai University, Changzhou 213022, Jiangsu, China.
- Changzhou Key Laboratory of Digital Manufacture Technology, Hohai University, Changzhou 213022, Jiangsu, China.
| | - Hao Yang
- College of Mechanical & Electrical Engineering, Hohai University, Changzhou 213022, Jiangsu, China.
- Jiangsu Key Laboratory of Special Robot Technology, Hohai University, Changzhou 213022, Jiangsu, China.
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