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Martinson WD, Volkening A, Schmidtchen M, Venkataraman C, Carrillo JA. Linking discrete and continuous models of cell birth and migration. ROYAL SOCIETY OPEN SCIENCE 2024; 11:232002. [PMID: 39021774 PMCID: PMC11252671 DOI: 10.1098/rsos.232002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/22/2023] [Accepted: 05/10/2024] [Indexed: 07/20/2024]
Abstract
Self-organization of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of biological intuition. Discrete models provide straightforward interpretations by tracking each individual yet can be computationally expensive. Alternatively, continuous models supply a large-scale perspective by representing the 'effective' dynamics of infinite agents, but their results are often difficult to translate into experimentally relevant insights. We address this challenge by quantitatively linking spatio-temporal dynamics of continuous models and individual-based data in settings with biologically realistic, time-varying cell numbers. Specifically, we introduce and fit scaling parameters in continuous models to account for discrepancies that can arise from low cell numbers and localized interactions. We illustrate our approach on an example motivated by zebrafish-skin pattern formation, in which we create a continuous framework describing the movement and proliferation of a single cell population by upscaling rules from a discrete model. Our resulting continuous models accurately depict ensemble average agent-based solutions when migration or proliferation act alone. Interestingly, the same parameters are not optimal when both processes act simultaneously, highlighting a rich difference in how combining migration and proliferation affects discrete and continuous dynamics.
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Affiliation(s)
| | | | - Markus Schmidtchen
- Institute of Scientific Computing, Technische Universität Dresden, Dresden, Germany
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2
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Munaò G, Costa D, Malescio G, Bomont JM, Prestipino S. Like aggregation from unlike attraction: stripes in symmetric mixtures of cross-attracting hard spheres. Phys Chem Chem Phys 2023. [PMID: 37194397 DOI: 10.1039/d3cp01026k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
Self-assembly of colloidal particles into striped phases is at once a process of relevant technological interest-just think about the possibility to realise photonic crystals with a dielectric structure modulated along a specific direction-and a challenging task, since striped patterns emerge in a variety of conditions, suggesting that the connection between the onset of stripes and the shape of the intermolecular potential is yet to be fully unravelled. Hereby, we devise an elementary mechanism for the formation of stripes in a basic model consisting of a symmetric binary mixture of hard spheres that interact via a square-well cross attraction. Such a model would mimic a colloid in which the interspecies affinity is of longer range and significantly stronger than the intraspecies interaction. For attraction ranges shorter enough than the particle size the mixture behaves like a compositionally-disordered simple fluid. Instead, for wider square-wells, we document by numerical simulations the existence of striped patterns in the solid phase, where layers of particles of one species are interspersed with layers of the other species; increasing the attraction range stabilises the stripes further, in that they also appear in the bulk liquid and become thicker in the crystal. Our results lead to the counterintuitive conclusion that a flat and sufficiently long-ranged unlike attraction promotes the aggregation of like particles into stripes. This finding opens a novel way for the synthesis of colloidal particles with interactions tailored at the development of stripe-modulated structures.
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Affiliation(s)
- Gianmarco Munaò
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy.
| | - Dino Costa
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy.
| | - Gianpietro Malescio
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy.
| | | | - Santi Prestipino
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy.
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Abstract
The Turing model (or reaction-diffusion model), first published in 1952, is a mathematical model that can account for autonomy in the morphogenesis of organisms. Although initially controversial, the model has gradually gained wider acceptance among experimental embryologists due to the accumulation of experimental data to support it. More recently, this model and others based on it have been used not only to explain biological phenomena conceptually but also as working hypotheses for molecular-level experiments and as internal components of more-complex 3D models. In this Spotlight, I will provide a personal perspective from an experimental biologist on some of the recent developments of the Turing model.
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Affiliation(s)
- Shigeru Kondo
- Osaka University, Faculty of Frontia Bioscience, Osaka 565-0871, Japan
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4
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Kondo S, Watanabe M, Miyazawa S. Studies of Turing pattern formation in zebrafish skin. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2021; 379:20200274. [PMID: 34743596 PMCID: PMC8580470 DOI: 10.1098/rsta.2020.0274] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 06/16/2021] [Indexed: 05/08/2023]
Abstract
Skin patterns are the first example of the existence of Turing patterns in living organisms. Extensive research on zebrafish, a model organism with stripes on its skin, has revealed the principles of pattern formation at the molecular and cellular levels. Surprisingly, although the networks of cell-cell interactions have been observed to satisfy the 'short-range activation and long-range inhibition' prerequisites for Turing pattern formation, numerous individual reactions were not envisioned based on the classical reaction-diffusion model. For example, in real skin, it is not an alteration in concentrations of chemicals, but autonomous migration and proliferation of pigment cells that establish patterns, and cell-cell interactions are mediated via direct contact through cell protrusions. Therefore, the classical reaction-diffusion mechanism cannot be used as it is for modelling skin pattern formation. Various studies are underway to adapt mathematical models to the experimental findings on research into skin patterns, and the purpose of this review is to organize and present them. These novel theoretical methods could be applied to autonomous pattern formation phenomena other than skin patterns. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.
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Affiliation(s)
- Shigeru Kondo
- Graduate School of Frontier Biosciences, Osaka University, 1-3 Yamadaoka, Suita, Osaka 565-0871, Japan
| | - Masakatsu Watanabe
- Graduate School of Frontier Biosciences, Osaka University, 1-3 Yamadaoka, Suita, Osaka 565-0871, Japan
| | - Seita Miyazawa
- Graduate School of Frontier Biosciences, Osaka University, 1-3 Yamadaoka, Suita, Osaka 565-0871, Japan
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5
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Leyshon T, Tonello E, Schnoerr D, Siebert H, Stumpf MPH. The design principles of discrete turing patterning systems. J Theor Biol 2021; 531:110901. [PMID: 34530030 DOI: 10.1016/j.jtbi.2021.110901] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2021] [Revised: 08/15/2021] [Accepted: 09/06/2021] [Indexed: 10/20/2022]
Abstract
The formation of spatial structures lies at the heart of developmental processes. However, many of the underlying gene regulatory and biochemical processes remain poorly understood. Turing patterns constitute a main candidate to explain such processes, but they appear sensitive to fluctuations and variations in kinetic parameters, raising the question of how they may be adopted and realised in naturally evolved systems. The vast majority of mathematical studies of Turing patterns have used continuous models specified in terms of partial differential equations. Here, we complement this work by studying Turing patterns using discrete cellular automata models. We perform a large-scale study on all possible two-species networks and find the same Turing pattern producing networks as in the continuous framework. In contrast to continuous models, however, we find these Turing pattern topologies to be substantially more robust to changes in the parameters of the model. We also find that diffusion-driven instabilities are substantially weaker predictors for Turing patterns in our discrete modelling framework in comparison to the continuous case, in the sense that the presence of an instability does not guarantee a pattern emerging in simulations. We show that a more refined criterion constitutes a stronger predictor. The similarity of the results for the two modelling frameworks suggests a deeper underlying principle of Turing mechanisms in nature. Together with the larger robustness in the discrete case this suggests that Turing patterns may be more robust than previously thought.
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Affiliation(s)
- Thomas Leyshon
- Department of Life Sciences, Imperial College London, UK
| | - Elisa Tonello
- FB Mathematik und Informatik, Freine Universität Berlin, Germany
| | - David Schnoerr
- Department of Life Sciences, Imperial College London, UK
| | - Heike Siebert
- FB Mathematik und Informatik, Freine Universität Berlin, Germany
| | - Michael P H Stumpf
- Department of Life Sciences, Imperial College London, UK; Melbourne Integrated Genomics, University of Melbourne, Australia; School of BioScience, University of Melbourne, Australia; School of Mathematics and Statistics, University of Melbourne, Australia.
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6
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Volkening A, Abbott MR, Chandra N, Dubois B, Lim F, Sexton D, Sandstede B. Modeling Stripe Formation on Growing Zebrafish Tailfins. Bull Math Biol 2020; 82:56. [PMID: 32356149 DOI: 10.1007/s11538-020-00731-0] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2019] [Accepted: 04/03/2020] [Indexed: 12/26/2022]
Abstract
As zebrafish develop, black and gold stripes form across their skin due to the interactions of brightly colored pigment cells. These characteristic patterns emerge on the growing fish body, as well as on the anal and caudal fins. While wild-type stripes form parallel to a horizontal marker on the body, patterns on the tailfin gradually extend distally outward. Interestingly, several mutations lead to altered body patterns without affecting fin stripes. Through an exploratory modeling approach, our goal is to help better understand these differences between body and fin patterns. By adapting a prior agent-based model of cell interactions on the fish body, we present an in silico study of stripe development on tailfins. Our main result is a demonstration that two cell types can produce stripes on the caudal fin. We highlight several ways that bone rays, growth, and the body-fin interface may be involved in patterning, and we raise questions for future work related to pattern robustness.
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Affiliation(s)
- A Volkening
- NSF-Simons Center for Quantitative Biology, Northwestern University, Evanston, IL, USA.
| | - M R Abbott
- Mathematics, Statistics, and Computer Science, Macalester College, St. Paul, MN, USA
| | - N Chandra
- Division of Applied Mathematics, Brown University, Providence, RI, USA
| | - B Dubois
- Division of Applied Mathematics, Brown University, Providence, RI, USA
| | - F Lim
- Division of Applied Mathematics, Brown University, Providence, RI, USA
| | - D Sexton
- Department of Mathematics, University of Idaho, Moscow, ID, USA
| | - B Sandstede
- Division of Applied Mathematics, Brown University, Providence, RI, USA
- Data Science Initiative, Brown University, Providence, RI, USA
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7
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Abstract
Self-organized pattern behavior is ubiquitous throughout nature, from fish schooling to collective cell dynamics during organism development. Qualitatively these patterns display impressive consistency, yet variability inevitably exists within pattern-forming systems on both microscopic and macroscopic scales. Quantifying variability and measuring pattern features can inform the underlying agent interactions and allow for predictive analyses. Nevertheless, current methods for analyzing patterns that arise from collective behavior capture only macroscopic features or rely on either manual inspection or smoothing algorithms that lose the underlying agent-based nature of the data. Here we introduce methods based on topological data analysis and interpretable machine learning for quantifying both agent-level features and global pattern attributes on a large scale. Because the zebrafish is a model organism for skin pattern formation, we focus specifically on analyzing its skin patterns as a means of illustrating our approach. Using a recent agent-based model, we simulate thousands of wild-type and mutant zebrafish patterns and apply our methodology to better understand pattern variability in zebrafish. Our methodology is able to quantify the differential impact of stochasticity in cell interactions on wild-type and mutant patterns, and we use our methods to predict stripe and spot statistics as a function of varying cellular communication. Our work provides an approach to automatically quantifying biological patterns and analyzing agent-based dynamics so that we can now answer critical questions in pattern formation at a much larger scale.
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Affiliation(s)
- Melissa R McGuirl
- Division of Applied Mathematics, Brown University, Providence, RI 02912;
| | - Alexandria Volkening
- NSF-Simons Center for Quantitative Biology, Northwestern University, Evanston, IL 60208
| | - Björn Sandstede
- Division of Applied Mathematics, Brown University, Providence, RI 02912
- Data Science Initiative, Brown University, Providence, RI 02912
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8
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Method for disarranging the pigment pattern of zebrafish by optogenetics. Dev Biol 2018; 460:12-19. [PMID: 30578760 DOI: 10.1016/j.ydbio.2018.12.019] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2018] [Revised: 12/17/2018] [Accepted: 12/17/2018] [Indexed: 11/23/2022]
Abstract
To investigate the spatiotemporal dynamics of skin pattern formation, we developed a simple method for artificially disarranging the placement of all three pigment cell types in the body trunk of zebrafish (Danio rerio). We generated transgenic fish with melanophores that ectopically expressed a variant of channelrhodopsin-2 (ChR2). Blue light (BL) irradiation induced melanophore depolarization and random migration; the latter resulted in the disarrangement of the two other pigment cell types (xanthophores and iridophores). This BL disarrangement (BLD) method was effective in both young and adult fish, but it did not affect the initial placement of pigment cells in juvenile fish (approximately 5 weeks post-fertilization). Irradiation with BL was not harmful to cells, and the patterning process immediately resumed when BL was switched off. Using the BLD method, we demonstrated that interactions between pigment cells determined stripe width in the absence of any pre-set positional cues, while the initial horizontal alignment of iridophores determined their directionality. The BLD method can be adapted to any zebrafish skin-pattern mutant, providing a novel tool for analyzing pattern formation mechanisms under a variety of conditions and facilitating further study in this field.
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Volkening A, Sandstede B. Iridophores as a source of robustness in zebrafish stripes and variability in Danio patterns. Nat Commun 2018; 9:3231. [PMID: 30104716 PMCID: PMC6089994 DOI: 10.1038/s41467-018-05629-z] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2017] [Accepted: 07/13/2018] [Indexed: 11/11/2022] Open
Abstract
Zebrafish (Danio rerio) feature black and yellow stripes, while related Danios display different patterns. All these patterns form due to the interactions of pigment cells, which self-organize on the fish skin. Until recently, research focused on two cell types (melanophores and xanthophores), but newer work has uncovered the leading role of a third type, iridophores: by carefully orchestrated transitions in form, iridophores instruct the other cells, but little is known about what drives their form changes. Here we address this question from a mathematical perspective: we develop a model (based on known interactions between the original two cell types) that allows us to assess potential iridophore behavior. We identify a set of mechanisms governing iridophore form that is consistent across a range of empirical data. Our model also suggests that the complex cues iridophores receive may act as a key source of redundancy, enabling both robust patterning and variability within Danio.
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Affiliation(s)
- Alexandria Volkening
- Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI, 02912, USA.
- Mathematical Biosciences Institute, Ohio State University, 1735 Neil Avenue, Columbus, OH, 43210, USA.
| | - Björn Sandstede
- Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI, 02912, USA
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10
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Volkening A, Sandstede B. Modelling stripe formation in zebrafish: an agent-based approach. J R Soc Interface 2015; 12:20150812. [PMID: 26538560 PMCID: PMC4685853 DOI: 10.1098/rsif.2015.0812] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2015] [Accepted: 10/13/2015] [Indexed: 11/12/2022] Open
Abstract
Zebrafish have distinctive black stripes and yellow interstripes that form owing to the interaction of different pigment cells. We present a two-population agent-based model for the development and regeneration of these stripes and interstripes informed by recent experimental results. Our model describes stripe pattern formation, laser ablation and mutations. We find that fish growth shortens the necessary scale for long-range interactions and that iridophores, a third type of pigment cell, help align stripes and interstripes.
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Affiliation(s)
| | - Björn Sandstede
- Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
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11
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Painter KJ, Bloomfield JM, Sherratt JA, Gerisch A. A Nonlocal Model for Contact Attraction and Repulsion in Heterogeneous Cell Populations. Bull Math Biol 2015; 77:1132-65. [DOI: 10.1007/s11538-015-0080-x] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2014] [Accepted: 04/01/2015] [Indexed: 01/31/2023]
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12
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Setty Y. In-silico models of stem cell and developmental systems. Theor Biol Med Model 2014; 11:1. [PMID: 24401000 PMCID: PMC3896968 DOI: 10.1186/1742-4682-11-1] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2013] [Accepted: 12/23/2013] [Indexed: 11/10/2022] Open
Abstract
Understanding how developmental systems evolve over time is a key question in stem cell and developmental biology research. However, due to hurdles of existing experimental techniques, our understanding of these systems as a whole remains partial and coarse. In recent years, we have been constructing in-silico models that synthesize experimental knowledge using software engineering tools. Our approach integrates known isolated mechanisms with simplified assumptions where the knowledge is limited. This has proven to be a powerful, yet underutilized, tool to analyze the developmental process. The models provide a means to study development in-silico by altering the model’s specifications, and thereby predict unforeseen phenomena to guide future experimental trials. To date, three organs from diverse evolutionary organisms have been modeled: the mouse pancreas, the C. elegans gonad, and partial rodent brain development. Analysis and execution of the models recapitulated the development of the organs, anticipated known experimental results and gave rise to novel testable predictions. Some of these results had already been validated experimentally. In this paper, I review our efforts in realistic in-silico modeling of stem cell research and developmental biology and discuss achievements and challenges. I envision that in the future, in-silico models as presented in this paper would become a common and useful technique for research in developmental biology and related research fields, particularly regenerative medicine, tissue engineering and cancer therapeutics.
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Affiliation(s)
- Yaki Setty
- Computational Systems Biology, Max-Planck-Institut für Informatik, Saarbrücken 66123, Germany.
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13
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Bloomfield JM, Painter KJ, Sherratt JA. How does cellular contact affect differentiation mediated pattern formation? Bull Math Biol 2010; 73:1529-58. [PMID: 20798994 DOI: 10.1007/s11538-010-9578-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2010] [Accepted: 08/03/2010] [Indexed: 12/24/2022]
Abstract
In this paper, we present a two-population continuous integro-differential model of cell differentiation, using a non-local term to describe the influence of the local environment on differentiation. We investigate three different versions of the model, with differentiation being cell autonomous, regulated via a community effect, or weakly dependent on the local cellular environment. We consider the spatial patterns that such different modes of differentiation produce, and investigate the formation of both stripes and spots by the model. We show that pattern formation only occurs when differentiation is regulated by a strong community effect. In this case, permanent spatial patterns only occur under a precise relationship between the parameters characterising cell dynamics, although transient patterns can persist for biologically relevant timescales when this condition is relaxed. In all cases, the long-lived patterns consist only of stripes, not spots.
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Affiliation(s)
- J M Bloomfield
- Department of Mathematics and the Maxwell Institute for Mathematical Sciences, School of Mathematical and Computer Sciences, Heriot Watt University, Edinburgh, UK.
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Norton KA, Wininger M, Bhanot G, Ganesan S, Barnard N, Shinbrot T. A 2D mechanistic model of breast ductal carcinoma in situ (DCIS) morphology and progression. J Theor Biol 2010; 263:393-406. [PMID: 20006623 PMCID: PMC2839055 DOI: 10.1016/j.jtbi.2009.11.024] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2008] [Revised: 11/24/2009] [Accepted: 11/28/2009] [Indexed: 02/07/2023]
Abstract
Ductal carcinoma in situ (DCIS) of the breast is a non-invasive tumor in which cells proliferate abnormally, but remain confined within a duct. Although four distinguishable DCIS morphologies are recognized, the mechanisms that generate these different morphological classes remain unclear, and consequently the prognostic strength of DCIS classification is not strong. To improve the understanding of the relation between morphology and time course, we have developed a 2D in silico particle model of the growth of DCIS within a single breast duct. This model considers mechanical effects such as cellular adhesion and intra-ductal pressure, and biological features including proliferation, apoptosis, necrosis, and cell polarity. Using this model, we find that different regions of parameter space generate distinct morphological subtypes of DCIS, so elucidating the relation between morphology and time course. Furthermore, we find that tumors with similar architectures may in fact be produced through different mechanisms, and we propose future work to further disentangle the mechanisms involved in DCIS progression.
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Affiliation(s)
- Kerri-Ann Norton
- BioMaPS Institute, Rutgers University, Piscataway, NJ 08854, USA.
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15
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Shinbrot T, Chun Y, Caicedo-Carvajal C, Foty R. Cellular morphogenesis in silico. Biophys J 2009; 97:958-67. [PMID: 19686642 PMCID: PMC2726306 DOI: 10.1016/j.bpj.2009.05.020] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2008] [Revised: 05/09/2009] [Accepted: 05/13/2009] [Indexed: 10/20/2022] Open
Abstract
We describe a model that simulates spherical cells of different types that can migrate and interact either attractively or repulsively. We find that both expected morphologies and previously unreported patterns spontaneously self-assemble. Among the newly discovered patterns are a segmented state of alternating discs, and a "shish-kebab" state, in which one cell type forms a ring around a second type. We show that these unique states result from cellular attraction that increases with distance (e.g., as membranes stretch viscoelastically), and would not be seen in traditional, e.g., molecular, potentials that diminish with distance. Most of the states found computationally have been observed in vitro, and it remains to be established what role these self-assembled states may play in in vivo morphogenesis.
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Affiliation(s)
- Troy Shinbrot
- Department of Biomedical Engineering, Rutgers University, Piscataway, New Jersey 08854, USA.
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16
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Theoretical analysis of mechanisms that generate the pigmentation pattern of animals. Semin Cell Dev Biol 2009; 20:82-9. [DOI: 10.1016/j.semcdb.2008.10.008] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2007] [Accepted: 10/07/2008] [Indexed: 01/05/2023]
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17
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Othmer HG, Painter K, Umulis D, Xue C. The Intersection of Theory and Application in Elucidating Pattern Formation in Developmental Biology. MATHEMATICAL MODELLING OF NATURAL PHENOMENA 2009; 4:3-82. [PMID: 19844610 PMCID: PMC2763616 DOI: 10.1051/mmnp/20094401] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
We discuss theoretical and experimental approaches to three distinct developmental systems that illustrate how theory can influence experimental work and vice-versa. The chosen systems - Drosophila melanogaster, bacterial pattern formation, and pigmentation patterns - illustrate the fundamental physical processes of signaling, growth and cell division, and cell movement involved in pattern formation and development. These systems exemplify the current state of theoretical and experimental understanding of how these processes produce the observed patterns, and illustrate how theoretical and experimental approaches can interact to lead to a better understanding of development. As John Bonner said long ago'We have arrived at the stage where models are useful to suggest experiments, and the facts of the experiments in turn lead to new and improved models that suggest new experiments. By this rocking back and forth between the reality of experimental facts and the dream world of hypotheses, we can move slowly toward a satisfactory solution of the major problems of developmental biology.'
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Affiliation(s)
- Hans G. Othmer
- School of Mathematics and Digital Technology Center, University of Minnesota, Minneapolis, MN 55455 USA
| | - Kevin Painter
- Department of Mathematics, Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK
| | - David Umulis
- Agricultural & Biological Engineering, Purdue University, West Lafayette, IN USA 47907 USA
| | - Chuan Xue
- Mathematical Biosciences Institute, Ohio State University, Columbus, OH 43210 USA
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18
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Mills MG, Patterson LB. Not just black and white: pigment pattern development and evolution in vertebrates. Semin Cell Dev Biol 2008; 20:72-81. [PMID: 19073271 DOI: 10.1016/j.semcdb.2008.11.012] [Citation(s) in RCA: 86] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2008] [Accepted: 11/19/2008] [Indexed: 02/08/2023]
Abstract
Animals display diverse colors and patterns that vary within and between species. Similar phenotypes appear in both closely related and widely divergent taxa. Pigment patterns thus provide an opportunity to explore how development is altered to produce differences in form and whether similar phenotypes share a common genetic basis. Understanding the development and evolution of pigment patterns requires knowledge of the cellular interactions and signaling pathways that produce those patterns. These complex traits provide unparalleled opportunities for integrating studies from ecology and behavior to molecular biology and biophysics.
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Affiliation(s)
- Margaret G Mills
- Department of Biology, Box 351800, University of Washington, Seattle, WA 98195, USA.
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