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Stillman NR, Mayor R. Generative models of morphogenesis in developmental biology. Semin Cell Dev Biol 2023; 147:83-90. [PMID: 36754751 PMCID: PMC10615838 DOI: 10.1016/j.semcdb.2023.02.001] [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] [Received: 12/20/2022] [Revised: 02/02/2023] [Accepted: 02/02/2023] [Indexed: 02/08/2023]
Abstract
Understanding the mechanism by which cells coordinate their differentiation and migration is critical to our understanding of many fundamental processes such as wound healing, disease progression, and developmental biology. Mathematical models have been an essential tool for testing and developing our understanding, such as models of cells as soft spherical particles, reaction-diffusion systems that couple cell movement to environmental factors, and multi-scale multi-physics simulations that combine bottom-up rule-based models with continuum laws. However, mathematical models can often be loosely related to data or have so many parameters that model behaviour is weakly constrained. Recent methods in machine learning introduce new means by which models can be derived and deployed. In this review, we discuss examples of mathematical models of aspects of developmental biology, such as cell migration, and how these models can be combined with these recent machine learning methods.
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Affiliation(s)
- Namid R Stillman
- Department of Cell and Developmental Biology, University College London, Gower Street, London WC1E 6BT, UK.
| | - Roberto Mayor
- Department of Cell and Developmental Biology, University College London, Gower Street, London WC1E 6BT, UK; Center for Integrative Biology, Faculty of Sciences, Universidad Mayor; Santiago, Chile Santiago, Chile..
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2
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Márquez-Flórez K, Garzón-Alvarado DA, Carda C, Sancho-Tello M. Computational model of articular cartilage regeneration induced by scaffold implantation in vivo. J Theor Biol 2023; 561:111393. [PMID: 36572091 DOI: 10.1016/j.jtbi.2022.111393] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2021] [Revised: 11/22/2022] [Accepted: 12/19/2022] [Indexed: 12/24/2022]
Abstract
Computational models allow to explain phenomena that cannot be observed through an animal model, such as the strain and stress states which can highly influence regeneration of the tissue. For this purpose, we have developed a simulation tool to determine the mechanical conditions provided by the polymeric scaffold. The computational model considered the articular cartilage, the subchondral bone, and the scaffold. All materials were modeled as poroelastic, and the cartilage had linear-elastic oriented collagen fibers. This model was able to explain the remodeling process that subchondral bone goes through, and how the scaffold allowed the conditions for cartilage regeneration. These results suggest that the use of scaffolds might lead the cartilaginous tissue growth in vivo by providing a better mechanical environment. Moreover, the developed computational model demonstrated to be useful as a tool prior experimental in vivo studies, by predicting the possible outcome of newly proposed treatments allowing to discard approaches that might not bring good results.
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Affiliation(s)
- K Márquez-Flórez
- Department of Mechanical and Mechatronic Engineering, Universidad Nacional de Colombia, Bogotá, Colombia; Numerical Methods and Modeling Research Group (GNUM), Universidad Nacional de Colombia, Bogotá, Colombia; Department of Pathology, Faculty of Medicine and Odontology, Universitat de València, Valencia, Spain
| | - D A Garzón-Alvarado
- Department of Mechanical and Mechatronic Engineering, Universidad Nacional de Colombia, Bogotá, Colombia; Numerical Methods and Modeling Research Group (GNUM), Universidad Nacional de Colombia, Bogotá, Colombia; Instituto de Biotecnología, Universidad Nacional de Colombia.
| | - C Carda
- Department of Pathology, Faculty of Medicine and Odontology, Universitat de València, Valencia, Spain; INCLIVA Biomedical Research Institute, Valencia, Spain; Biomedical Research Networking Center on Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), Valencia, Spain
| | - M Sancho-Tello
- Department of Pathology, Faculty of Medicine and Odontology, Universitat de València, Valencia, Spain; INCLIVA Biomedical Research Institute, Valencia, Spain
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3
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Wang X, Bai D. Self‐Organization Principles of Cell Cycles and Gene Expressions in the Development of Cell Populations. ADVANCED THEORY AND SIMULATIONS 2021. [DOI: 10.1002/adts.202100005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Xiaoliang Wang
- College of Life Sciences Zhejiang University Hangzhou 310058 China
- School of Physical Sciences University of Science and Technology of China Hefei 230026 China
| | - Dongyun Bai
- School of Physics and Astronomy Shanghai Jiao Tong University Shanghai 200240 China
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4
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Mathematical modeling of chondrogenic pattern formation during limb development: Recent advances in continuous models. Math Biosci 2020; 322:108319. [PMID: 32001201 DOI: 10.1016/j.mbs.2020.108319] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2019] [Revised: 01/17/2020] [Accepted: 01/17/2020] [Indexed: 11/20/2022]
Abstract
The phenomenon of chondrogenic pattern formation in the vertebrate limb is one of the best studied examples of organogenesis. Many different models, mathematical as well as conceptual, have been proposed for it in the last fifty years or so. In this review, we give a brief overview of the fundamental biological background, then describe in detail several models which aim to describe qualitatively and quantitatively the corresponding biological phenomena. We concentrate on several new models that have been proposed in recent years, taking into account recent experimental progress. The major mathematical tools in these approaches are ordinary and partial differential equations. Moreover, we discuss models with non-local flux terms used to account for cell-cell adhesion forces and a structured population model with diffusion. We also include a detailed list of gene products and potential morphogens which have been identified to play a role in the process of limb formation and its growth.
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5
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Song EK, Jeon J, Jang DG, Kim HE, Sim HJ, Kwon KY, Medina-Ruiz S, Jang HJ, Lee AR, Rho JG, Lee HS, Kim SJ, Park CY, Myung K, Kim W, Kwon T, Yang S, Park TJ. ITGBL1 modulates integrin activity to promote cartilage formation and protect against arthritis. Sci Transl Med 2019; 10:10/462/eaam7486. [PMID: 30305454 DOI: 10.1126/scitranslmed.aam7486] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2017] [Accepted: 09/20/2018] [Indexed: 11/02/2022]
Abstract
Developing and mature chondrocytes constantly interact with and remodel the surrounding extracellular matrix (ECM). Recent research indicates that integrin-ECM interaction is differentially regulated during cartilage formation (chondrogenesis). Integrin signaling is also a key source of the catabolic reactions responsible for joint destruction in both rheumatoid arthritis and osteoarthritis. However, we do not understand how chondrocytes dynamically regulate integrin signaling in such an ECM-rich environment. Here, we found that developing chondrocytes express integrin-β-like 1 (Itgbl1) at specific stages, inhibiting integrin signaling and promoting chondrogenesis. Unlike cytosolic integrin inhibitors, ITGBL1 is secreted and physically interacts with integrins to down-regulate activity. We observed that Itgbl1 expression was strongly reduced in the damaged articular cartilage of patients with osteoarthritis (OA). Ectopic expression of Itgbl1 protected joint cartilage against OA development in the destabilization of the medial meniscus-induced OA mouse model. Our results reveal ITGBL1 signaling as an underlying mechanism of protection against destructive cartilage disorders and suggest the potential therapeutic utility of targeting ITGBL1 to modulate integrin signaling in human disease.
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Affiliation(s)
- Eun Kyung Song
- School of Life Sciences, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea.,Center for Genomic Integrity, Institute for Basic Science, Ulsan 44919, Republic of Korea
| | - Jimin Jeon
- Department of Pharmacology, Ajou University School of Medicine, Suwon 16499, Republic of Korea.,Department of Biomedical Sciences, Graduate School, Ajou University, Suwon 16499, Republic of Korea.,CIRNO, Sungkyunkwan University, Suwon 16419, Republic of Korea
| | - Dong Gil Jang
- School of Life Sciences, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
| | - Ha Eun Kim
- School of Life Sciences, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
| | - Hyo Jung Sim
- School of Life Sciences, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
| | - Keun Yeong Kwon
- School of Life Sciences, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
| | - Sofia Medina-Ruiz
- Department of Molecular and Cell Biology, University of California, Berkeley, CA 94720, USA
| | - Hyun-Jun Jang
- School of Life Sciences, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
| | - Ah Reum Lee
- School of Life Sciences, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
| | - Jun Gi Rho
- Department of Molecular Science and Technology, Ajou University, Suwon 16499, Republic of Korea
| | - Hyun-Shik Lee
- KNU-Center for Nonlinear Dynamics, CMRI, School of Life Sciences, BK21 Plus KNU Creative BioResearch Group, College of Natural Sciences, Kyungpook National University, Daegu 41566, Republic of Korea
| | - Seok Jung Kim
- Department of Orthopaedic Surgery, College of Medicine, The Catholic University of Korea, Seoul 06591, Republic of Korea
| | - Chan Young Park
- School of Life Sciences, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
| | - Kyungjae Myung
- Center for Genomic Integrity, Institute for Basic Science, Ulsan 44919, Republic of Korea
| | - Wook Kim
- Department of Molecular Science and Technology, Ajou University, Suwon 16499, Republic of Korea
| | - Taejoon Kwon
- School of Life Sciences, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
| | - Siyoung Yang
- Department of Pharmacology, Ajou University School of Medicine, Suwon 16499, Republic of Korea. .,Department of Biomedical Sciences, Graduate School, Ajou University, Suwon 16499, Republic of Korea.,CIRNO, Sungkyunkwan University, Suwon 16419, Republic of Korea
| | - Tae Joo Park
- School of Life Sciences, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea. .,Center for Genomic Integrity, Institute for Basic Science, Ulsan 44919, Republic of Korea
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Newman SA, Glimm T, Bhat R. The vertebrate limb: An evolving complex of self-organizing systems. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2018; 137:12-24. [PMID: 29325895 DOI: 10.1016/j.pbiomolbio.2018.01.002] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2017] [Revised: 01/03/2018] [Accepted: 01/04/2018] [Indexed: 11/28/2022]
Abstract
The paired appendages (fins or limbs) of jawed vertebrates contain an endoskeleton consisting of nodules, bars and, in some groups, plates of cartilage, or bone arising from replacement of cartilaginous templates. The generation of the endoskeletal elements occurs by processes involving production and diffusion of morphogens, with, variously, positive and negative feedback circuits, adhesion, and receptor dynamics with similarities to the mechanism for chemical pattern formation proposed by Alan Turing. This review presents a unified interpretation of the evolution and functioning of these mechanisms. Studies are described indicating that protocondensations, compacted mesenchymal cell aggregates that prefigure the appendicular skeleton, arise through the adhesive activity of galectin-1, a matricellular protein with skeletogenic homologs in all jawed vertebrates. In the cartilaginous and lobe-finned fishes (and to a variable extent in ray-finned fishes) it additionally cooperates with an isoform of galectin-8 to constitute a self-organizing network capable of generating arrays of preskeletal nodules, bars and plates. Further, in the tetrapods, a putative galectin-8 control module was acquired that may have enabled proximodistal increase in the number of protocondensations. In parallel to this, other self-organizing networks emerged that acted, via Bmp, Wnt, Sox9 and Runx2, as well as transforming factor-β and fibronectin, to convert protocondensations into skeletal tissues. The progressive appearance and integration of these skeletogenic networks over evolution occurred in the context of an independently evolved system of Hox protein and Shh gradients that interfaced with them to tune the spatial wavelengths and refine the identities of the resulting arrays of elements.
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Affiliation(s)
- Stuart A Newman
- Department of Cell Biology and Anatomy, New York Medical College, Valhalla, NY, 10595, USA.
| | - Tilmann Glimm
- Department of Mathematics, Western Washington University, Bellingham, WA, 98229, USA
| | - Ramray Bhat
- Department of Molecular Reproduction, Development and Genetics, Biological Sciences Division, Indian Institute of Science, Bangalore, 560012, India
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7
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Bhattacharya P, Viceconti M. Multiscale modeling methods in biomechanics. WILEY INTERDISCIPLINARY REVIEWS. SYSTEMS BIOLOGY AND MEDICINE 2017; 9:e1375. [PMID: 28102563 PMCID: PMC5412936 DOI: 10.1002/wsbm.1375] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/04/2016] [Revised: 11/09/2016] [Accepted: 11/17/2016] [Indexed: 01/08/2023]
Abstract
More and more frequently, computational biomechanics deals with problems where the portion of physical reality to be modeled spans over such a large range of spatial and temporal dimensions, that it is impossible to represent it as a single space-time continuum. We are forced to consider multiple space-time continua, each representing the phenomenon of interest at a characteristic space-time scale. Multiscale models describe a complex process across multiple scales, and account for how quantities transform as we move from one scale to another. This review offers a set of definitions for this emerging field, and provides a brief summary of the most recent developments on multiscale modeling in biomechanics. Of all possible perspectives, we chose that of the modeling intent, which vastly affect the nature and the structure of each research activity. To the purpose we organized all papers reviewed in three categories: 'causal confirmation,' where multiscale models are used as materializations of the causation theories; 'predictive accuracy,' where multiscale modeling is aimed to improve the predictive accuracy; and 'determination of effect,' where multiscale modeling is used to model how a change at one scale manifests in an effect at another radically different space-time scale. Consistent with how the volume of computational biomechanics research is distributed across application targets, we extensively reviewed papers targeting the musculoskeletal and the cardiovascular systems, and covered only a few exemplary papers targeting other organ systems. The review shows a research subdomain still in its infancy, where causal confirmation papers remain the most common. WIREs Syst Biol Med 2017, 9:e1375. doi: 10.1002/wsbm.1375 For further resources related to this article, please visit the WIREs website.
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Affiliation(s)
- Pinaki Bhattacharya
- Department of Mechanical Engineering and INSIGNEO Institute for in silico MedicineUniversity of SheffieldSheffieldUK
| | - Marco Viceconti
- Department of Mechanical Engineering and INSIGNEO Institute for in silico MedicineUniversity of SheffieldSheffieldUK
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8
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Ollé-Vila A, Duran-Nebreda S, Conde-Pueyo N, Montañez R, Solé R. A morphospace for synthetic organs and organoids: the possible and the actual. Integr Biol (Camb) 2016; 8:485-503. [PMID: 27032985 DOI: 10.1039/c5ib00324e] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Efforts in evolutionary developmental biology have shed light on how organs are developed and why evolution has selected some structures instead of others. These advances in the understanding of organogenesis along with the most recent techniques of organotypic cultures, tissue bioprinting and synthetic biology provide the tools to hack the physical and genetic constraints in organ development, thus opening new avenues for research in the form of completely designed or merely altered settings. Here we propose a unifying framework that connects the concept of morphospace (i.e. the space of possible structures) with synthetic biology and tissue engineering. We aim for a synthesis that incorporates our understanding of both evolutionary and architectural constraints and can be used as a guide for exploring alternative design principles to build artificial organs and organoids. We present a three-dimensional morphospace incorporating three key features associated to organ and organoid complexity. The axes of this space include the degree of complexity introduced by developmental mechanisms required to build the structure, its potential to store and react to information and the underlying physical state. We suggest that a large fraction of this space is empty, and that the void might offer clues for alternative ways of designing and even inventing new organs.
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Affiliation(s)
- Aina Ollé-Vila
- ICREA-Complex Systems Lab, Department of Experimental and Health Sciences, Universitat Pompeu Fabra, 08003 Barcelona, Spain.
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9
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Kassab GS, An G, Sander EA, Miga MI, Guccione JM, Ji S, Vodovotz Y. Augmenting Surgery via Multi-scale Modeling and Translational Systems Biology in the Era of Precision Medicine: A Multidisciplinary Perspective. Ann Biomed Eng 2016; 44:2611-25. [PMID: 27015816 DOI: 10.1007/s10439-016-1596-4] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2015] [Accepted: 03/18/2016] [Indexed: 12/18/2022]
Abstract
In this era of tremendous technological capabilities and increased focus on improving clinical outcomes, decreasing costs, and increasing precision, there is a need for a more quantitative approach to the field of surgery. Multiscale computational modeling has the potential to bridge the gap to the emerging paradigms of Precision Medicine and Translational Systems Biology, in which quantitative metrics and data guide patient care through improved stratification, diagnosis, and therapy. Achievements by multiple groups have demonstrated the potential for (1) multiscale computational modeling, at a biological level, of diseases treated with surgery and the surgical procedure process at the level of the individual and the population; along with (2) patient-specific, computationally-enabled surgical planning, delivery, and guidance and robotically-augmented manipulation. In this perspective article, we discuss these concepts, and cite emerging examples from the fields of trauma, wound healing, and cardiac surgery.
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Affiliation(s)
- Ghassan S Kassab
- California Medical Innovations Institute, San Diego, CA, 92121, USA
| | - Gary An
- Department of Surgery, University of Chicago, Chicago, IL, 60637, USA
| | - Edward A Sander
- Department of Biomedical Engineering, University of Iowa, Iowa City, IA, 52242, USA
| | - Michael I Miga
- Department of Biomedical Engineering, Vanderbilt University, Nashville, TN, 37235, USA
| | - Julius M Guccione
- Department of Surgery, University of California, San Francisco, CA, 94143, USA
| | - Songbai Ji
- Thayer School of Engineering, Dartmouth College, Hanover, NH, 03755, USA.,Department of Surgery and of Orthopaedic Surgery, Geisel School of Medicine, Dartmouth College, Hanover, NH, 03755, USA
| | - Yoram Vodovotz
- Department of Surgery, University of Pittsburgh, W944 Starzl Biomedical Sciences Tower, 200 Lothrop St., Pittsburgh, PA, 15213, USA. .,Center for Inflammation and Regenerative Modeling, McGowan Institute for Regenerative Medicine, University of Pittsburgh, Pittsburgh, PA, 15219, USA.
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10
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Hiscock TW, Megason SG. Mathematically guided approaches to distinguish models of periodic patterning. Development 2015; 142:409-19. [PMID: 25605777 PMCID: PMC4302999 DOI: 10.1242/dev.107441] [Citation(s) in RCA: 50] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
How periodic patterns are generated is an open question. A number of mechanisms have been proposed--most famously, Turing's reaction-diffusion model. However, many theoretical and experimental studies focus on the Turing mechanism while ignoring other possible mechanisms. Here, we use a general model of periodic patterning to show that different types of mechanism (molecular, cellular, mechanical) can generate qualitatively similar final patterns. Observation of final patterns is therefore not sufficient to favour one mechanism over others. However, we propose that a mathematical approach can help to guide the design of experiments that can distinguish between different mechanisms, and illustrate the potential value of this approach with specific biological examples.
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Affiliation(s)
- Tom W Hiscock
- Department of Systems Biology, Harvard Medical School, Boston, MA 02115, USA
| | - Sean G Megason
- Department of Systems Biology, Harvard Medical School, Boston, MA 02115, USA
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Evolutionary Developmental Biology and the Limits of Philosophical Accounts of Mechanistic Explanation. HISTORY, PHILOSOPHY AND THEORY OF THE LIFE SCIENCES 2015. [DOI: 10.1007/978-94-017-9822-8_7] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
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12
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Abstract
In many animals, regenerative processes can replace lost body parts. Organ and tissue regeneration consequently also hold great medical promise. The regulation of regenerative processes is achieved through concerted actions of multiple organizational levels of the organism, from diffusing molecules and cellular gene expression patterns up to tissue mechanics. Our intuition is usually not adapted well to this degree of complexity and the quantitative aspects of the regulation of regenerative processes remain poorly understood. One way out of this dilemma lies in the combination of experimentation and mathematical modeling within an iterative process of model development/refinement, model predictions for novel experimental conditions, quantitative experiments testing these predictions, and subsequent model refinement. This interdisciplinary approach has already provided key insights into smaller scale processes during embryonic development and a so-far limited number of more complex regeneration processes. This review discusses selected theoretical and interdisciplinary studies and is structured along the three phases of regeneration: (1) initiation of a regeneration response, (2) tissue patterning during regenerate growth, (3) arresting the regeneration response. Moreover, we highlight the opportunities provided by extensions of mathematical models from developmental processes toward the study of related regenerative processes.
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Affiliation(s)
- Osvaldo Chara
- Center for Information Services and High Performance Computing (ZIH), Technische Universität Dresden, Dresden, Germany
| | - Elly M Tanaka
- Center for Regenerative Therapies Dresden (CRTD), Dresden, Germany
| | - Lutz Brusch
- Center for Information Services and High Performance Computing (ZIH), Technische Universität Dresden, Dresden, Germany.
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13
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Biased Polyphenism in Polydactylous Cats Carrying a Single Point Mutation: The Hemingway Model for Digit Novelty. Evol Biol 2013. [DOI: 10.1007/s11692-013-9267-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
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14
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Glimm T, Bhat R, Newman SA. Modeling the morphodynamic galectin patterning network of the developing avian limb skeleton. J Theor Biol 2013; 346:86-108. [PMID: 24355216 DOI: 10.1016/j.jtbi.2013.12.004] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2013] [Revised: 11/27/2013] [Accepted: 12/02/2013] [Indexed: 11/28/2022]
Abstract
We present a mathematical model for the morphogenesis and patterning of the mesenchymal condensations that serve as primordia of the avian limb skeleton. The model is based on the experimentally established dynamics of a multiscale regulatory network consisting of two glycan-binding proteins expressed early in limb development: CG (chicken galectin)-1A, CG-8 and their counterreceptors that determine the formation, size, number and spacing of the "protocondensations" that give rise to the condensations and subsequently the cartilaginous elements that serve as the templates of the bones. The model, a system of partial differential and integro-differential equations containing a flux term to represent local adhesion gradients, is simulated in a "full" and a "reduced" form to confirm that the system has pattern-forming capabilities and to explore the nature of the patterning instability. The full model recapitulates qualitatively and quantitatively the experimental results of network perturbation and leads to new predictions, which are verified by further experimentation. The reduced model is used to demonstrate that the patterning process is inherently morphodynamic, with cell motility being intrinsic to it. Furthermore, subtle relationships between cell movement and the positive and negative interactions between the morphogens produce regular patterns without the requirement for activators and inhibitors with widely separated diffusion coefficients. The described mechanism thus represents an extension of the category of activator-inhibitor processes capable of generating biological patterns with repetitive elements beyond the morphostatic mechanisms of the Turing/Gierer-Meinhardt type.
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Affiliation(s)
- T Glimm
- Department of Mathematics, Western Washington University, Bellingham, WA 98229, USA.
| | - R Bhat
- Life Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
| | - S A Newman
- Department of Cell Biology & Anatomy, Basic Sciences Building, Valhalla, NY 10595, USA.
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15
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Woolley TE, Baker RE, Tickle C, Maini PK, Towers M. Mathematical modelling of digit specification by a sonic hedgehog gradient. Dev Dyn 2013; 243:290-8. [PMID: 24115161 DOI: 10.1002/dvdy.24068] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2013] [Revised: 09/17/2013] [Accepted: 09/18/2013] [Indexed: 11/11/2022] Open
Abstract
BACKGROUND The three chick wing digits represent a classical example of a pattern specified by a morphogen gradient. Here we have investigated whether a mathematical model of a Shh gradient can describe the specification of the identities of the three chick wing digits and if it can be applied to limbs with more digits. RESULTS We have produced a mathematical model for specification of chick wing digit identities by a Shh gradient that can be extended to the four digits of the chick leg with Shh-producing cells forming a digit. This model cannot be extended to specify the five digits of the mouse limb. CONCLUSIONS Our data suggest that the parameters of a classical-type morphogen gradient are sufficient to specify the identities of three different digits. However, to specify more digit identities, this core mechanism has to be coupled to alternative processes, one being that in the chick leg and mouse limb, Shh-producing cells give rise to digits; another that in the mouse limb, the cellular response to the Shh gradient adapts over time so that digit specification does not depend simply on Shh concentration.
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Affiliation(s)
- Thomas E Woolley
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Oxford, United Kingdom; Oxford Centre for Collaborative Applied Mathematics, Mathematical Institute, University of Oxford, Oxford, United Kingdom
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16
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Walpole J, Papin JA, Peirce SM. Multiscale computational models of complex biological systems. Annu Rev Biomed Eng 2013; 15:137-54. [PMID: 23642247 DOI: 10.1146/annurev-bioeng-071811-150104] [Citation(s) in RCA: 121] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Integration of data across spatial, temporal, and functional scales is a primary focus of biomedical engineering efforts. The advent of powerful computing platforms, coupled with quantitative data from high-throughput experimental methodologies, has allowed multiscale modeling to expand as a means to more comprehensively investigate biological phenomena in experimentally relevant ways. This review aims to highlight recently published multiscale models of biological systems, using their successes to propose the best practices for future model development. We demonstrate that coupling continuous and discrete systems best captures biological information across spatial scales by selecting modeling techniques that are suited to the task. Further, we suggest how to leverage these multiscale models to gain insight into biological systems using quantitative biomedical engineering methods to analyze data in nonintuitive ways. These topics are discussed with a focus on the future of the field, current challenges encountered, and opportunities yet to be realized.
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Affiliation(s)
- Joseph Walpole
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA 22908, USA
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17
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Badugu A, Kraemer C, Germann P, Menshykau D, Iber D. Digit patterning during limb development as a result of the BMP-receptor interaction. Sci Rep 2012; 2:991. [PMID: 23251777 PMCID: PMC3524521 DOI: 10.1038/srep00991] [Citation(s) in RCA: 55] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2012] [Accepted: 11/30/2012] [Indexed: 01/07/2023] Open
Abstract
Turing models have been proposed to explain the emergence of digits during limb development. However, so far the molecular components that would give rise to Turing patterns are elusive. We have recently shown that a particular type of receptor-ligand interaction can give rise to Schnakenberg-type Turing patterns, which reproduce patterning during lung and kidney branching morphogenesis. Recent knockout experiments have identified Smad4 as a key protein in digit patterning. We show here that the BMP-receptor interaction meets the conditions for a Schnakenberg-type Turing pattern, and that the resulting model reproduces available wildtype and mutant data on the expression patterns of BMP, its receptor, and Fgfs in the apical ectodermal ridge (AER) when solved on a realistic 2D domain that we extracted from limb bud images of E11.5 mouse embryos. We propose that receptor-ligand-based mechanisms serve as a molecular basis for the emergence of Turing patterns in many developing tissues.
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Affiliation(s)
- Amarendra Badugu
- Department for Biosystems Science and Engineering (D-BSSE) , ETH Zurich, Basel, Switzerland
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Zhang YT, Alber MS, Newman SA. Mathematical modeling of vertebrate limb development. Math Biosci 2012; 243:1-17. [PMID: 23219575 DOI: 10.1016/j.mbs.2012.11.003] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2012] [Revised: 11/09/2012] [Accepted: 11/15/2012] [Indexed: 01/15/2023]
Abstract
In this paper, we review the major mathematical and computational models of vertebrate limb development and their roles in accounting for different aspects of this process. The main aspects of limb development that have been modeled include outgrowth and shaping of the limb bud, establishment of molecular gradients within the bud, and formation of the skeleton. These processes occur interdependently during development, although (as described in this review), there are various interpretations of the biological relationships among them. A wide range of mathematical and computational methods have been used to study these processes, including ordinary and partial differential equation systems, cellular automata and discrete, stochastic models, finite difference methods, finite element methods, the immersed boundary method, and various combinations of the above. Multiscale mathematical modeling and associated computational simulation have become integrated into the study of limb morphogenesis and pattern formation to an extent with few parallels in the field of developmental biology. These methods have contributed to the design and analysis of experiments employing microsurgical and genetic manipulations, evaluation of hypotheses for limb bud outgrowth, interpretation of the effects of natural mutations, and the formulation of scenarios for the origination and evolution of the limb skeleton.
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Affiliation(s)
- Yong-Tao Zhang
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA.
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Narang V, Decraene J, Wong SY, Aiswarya BS, Wasem AR, Leong SR, Gouaillard A. Systems immunology: a survey of modeling formalisms, applications and simulation tools. Immunol Res 2012; 53:251-65. [PMID: 22528121 DOI: 10.1007/s12026-012-8305-7] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
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Urdy S. On the evolution of morphogenetic models: mechano-chemical interactions and an integrated view of cell differentiation, growth, pattern formation and morphogenesis. Biol Rev Camb Philos Soc 2012; 87:786-803. [PMID: 22429266 DOI: 10.1111/j.1469-185x.2012.00221.x] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
In the 1950s, embryology was conceptualized as four relatively independent problems: cell differentiation, growth, pattern formation and morphogenesis. The mechanisms underlying the first three traditionally have been viewed as being chemical in nature, whereas those underlying morphogenesis have usually been discussed in terms of mechanics. Often, morphogenesis and its mechanical processes have been regarded as subordinate to chemical ones. However, a growing body of evidence indicates that the biomechanics of cells and tissues affect in striking ways those phenomena often thought of as mainly under the control of cell-cell signalling. This accumulation of data has led to a revival of the mechano-transduction concept in particular, and of complexity in general, causing us now to consider whether we should retain the traditional conceptualization of development. The researchers' semantic preferences for the terms 'patterning', 'pattern formation' or 'morphogenesis' can be used to describe three main 'schools of thought' which emerged in the late 1970s. In the 'molecular school', the term patterning is deeply tied to the positional information concept. In the 'chemical school', the term 'pattern formation' regularly implies reaction-diffusion models. In the 'mechanical school', the term 'morphogenesis' is more frequently used in relation to mechanical instabilities. Major differences among these three schools pertain to the concept of self-organization, and models can be classified as morphostatic or morphodynamic. Various examples illustrate the distorted picture that arises from the distinction among differentiation, growth, pattern formation and morphogenesis, based on the idea that the underlying mechanisms are respectively chemical or mechanical. Emerging quantitative approaches integrate the concepts and methods of complex sciences and emphasize the interplay between hierarchical levels of organization via mechano-chemical interactions. They draw upon recent improvements in mathematical and numerical morphogenetic models and upon considerable progress in collecting new quantitative data. This review highlights a variety of such models, which exhibit important advances, such as hybrid, stochastic and multiscale simulations.
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Affiliation(s)
- Séverine Urdy
- Paläontologisches Institut und Museum der Universität Zürich, Switzerland.
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21
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Lefebvre C, Rieckhof G, Califano A. Reverse-engineering human regulatory networks. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2012; 4:311-25. [PMID: 22246697 DOI: 10.1002/wsbm.1159] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
The explosion of genomic, transcriptomic, proteomic, metabolomic, and other omics data is challenging the research community to develop rational models for their organization and interpretation to generate novel biological knowledge. The development and use of gene regulatory networks to mechanistically interpret this data is an important development in molecular biology, usually captured under the banner of systems biology. As a result, the repertoire of methods for the reconstruction of comprehensive and cell-context-specific maps of regulatory interactions, or interactomes, has also exploded in the past few years. In this review, we focus on Network Biology and more specifically on methods for reverse engineering transcriptional, post-transcriptional, and post-translational human interaction networks and show how their interrogation is starting to impact our understanding of cellular pathophysiology and one's ability to predict cellular phenotypes from genome-wide molecular observations.
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Affiliation(s)
- Celine Lefebvre
- Center for Computational Biology and Bioinformatics, Columbia University, New York, NY, USA
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22
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23
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Glimm T, Zhang J, Shen YQ, Newman SA. Reaction–Diffusion Systems and External Morphogen Gradients: The Two-Dimensional Case, with an Application to Skeletal Pattern Formation. Bull Math Biol 2011; 74:666-87. [DOI: 10.1007/s11538-011-9689-6] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2010] [Accepted: 08/05/2011] [Indexed: 11/30/2022]
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Woolley TE, Baker RE, Gaffney EA, Maini PK. Influence of stochastic domain growth on pattern nucleation for diffusive systems with internal noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:041905. [PMID: 22181173 DOI: 10.1103/physreve.84.041905] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2011] [Revised: 05/27/2011] [Indexed: 05/21/2023]
Abstract
Numerous mathematical models exploring the emergence of complexity within developmental biology incorporate diffusion as the dominant mechanism of transport. However, self-organizing paradigms can exhibit the biologically undesirable property of extensive sensitivity, as illustrated by the behavior of the French-flag model in response to intrinsic noise and Turing's model when subjected to fluctuations in initial conditions. Domain growth is known to be a stabilizing factor for the latter, though the interaction of intrinsic noise and domain growth is underexplored, even in the simplest of biophysical settings. Previously, we developed analytical Fourier methods and a description of domain growth that allowed us to characterize the effects of deterministic domain growth on stochastically diffusing systems. In this paper we extend our analysis to encompass stochastically growing domains. This form of growth can be used only to link the meso- and macroscopic domains as the "box-splitting" form of growth on the microscopic scale has an ill-defined thermodynamic limit. The extension is achieved by allowing the simulated particles to undergo random walks on a discretized domain, while stochastically controlling the length of each discretized compartment. Due to the dependence of diffusion on the domain discretization, we find that the description of diffusion cannot be uniquely derived. We apply these analytical methods to two justified descriptions, where it is shown that, under certain conditions, diffusion is able to support a consistent inhomogeneous state that is far removed from the deterministic equilibrium, without additional kinetics. Finally, a logistically growing domain is considered. Not only does this show that we can deal with nonmonotonic descriptions of stochastic growth, but it is also seen that diffusion on a stationary domain produces different effects to diffusion on a domain that is stationary "on average."
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Affiliation(s)
- Thomas E Woolley
- Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB, United Kingdom.
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25
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Mammoto T, Mammoto A, Torisawa YS, Tat T, Gibbs A, Derda R, Mannix R, de Bruijn M, Yung CW, Huh D, Ingber DE. Mechanochemical control of mesenchymal condensation and embryonic tooth organ formation. Dev Cell 2011; 21:758-69. [PMID: 21924961 DOI: 10.1016/j.devcel.2011.07.006] [Citation(s) in RCA: 128] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2011] [Revised: 05/28/2011] [Accepted: 07/11/2011] [Indexed: 12/24/2022]
Abstract
Mesenchymal condensation is critical for organogenesis, yet little is known about how this process is controlled. Here we show that Fgf8 and Sema3f, produced by early dental epithelium, respectively, attract and repulse mesenchymal cells, which cause them to pack tightly together during mouse tooth development. Resulting mechanical compaction-induced changes in cell shape induce odontogenic transcription factors (Pax9, Msx1) and a chemical cue (BMP4), and mechanical compression of mesenchyme is sufficient to induce tooth-specific cell fate switching. The inductive effects of cell compaction are mediated by suppression of the mechanical signaling molecule RhoA, and its overexpression prevents odontogenic induction. Thus, the mesenchymal condensation that drives tooth formation is induced by antagonistic epithelial morphogens that manifest their pattern-generating actions mechanically via changes in mesenchymal cell shape and altered mechanotransduction.
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Affiliation(s)
- Tadanori Mammoto
- Vascular Biology Program, Children's Hospital and Harvard Medical School, Boston, MA 02115, USA
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Bhat R, Lerea KM, Peng H, Kaltner H, Gabius HJ, Newman SA. A regulatory network of two galectins mediates the earliest steps of avian limb skeletal morphogenesis. BMC DEVELOPMENTAL BIOLOGY 2011; 11:6. [PMID: 21284876 PMCID: PMC3042966 DOI: 10.1186/1471-213x-11-6] [Citation(s) in RCA: 55] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/07/2011] [Accepted: 02/01/2011] [Indexed: 01/31/2023]
Abstract
BACKGROUND The skeletal elements of vertebrate embryonic limbs are prefigured by rod- and spot-like condensations of precartilage mesenchymal cells. The formation of these condensations depends on cell-matrix and cell-cell interactions, but how they are initiated and patterned is as yet unresolved. RESULTS Here we provide evidence that galectins, β-galactoside-binding lectins with β-sandwich folding, play fundamental roles in these processes. We show that among the five chicken galectin (CG) genes, two, CG-1A, and CG-8, are markedly elevated in expression at prospective sites of condensation in vitro and in vivo, with their protein products appearing earlier in development than any previously described marker. The two molecules enhance one another's gene expression but have opposite effects on condensation formation and cartilage development in vivo and in vitro: CG-1A, a non-covalent homodimer, promotes this process, while the tandem-repeat-type CG-8 antagonizes it. Correspondingly, knockdown of CG-1A inhibits the formation of skeletal elements while knockdown of CG-8 enhances it. The apparent paradox of mutual activation at the gene expression level coupled with antagonistic roles in skeletogenesis is resolved by analysis of the direct effect of the proteins on precartilage cells. Specifically, CG-1A causes their aggregation, whereas CG-8, which has no adhesive function of its own, blocks this effect. The developmental appearance and regulation of the unknown cell surface moieties ("ligands") to which CG-1A and CG-8 bind were indicative of specific cognate- and cross-regulatory interactions. CONCLUSION Our findings indicate that CG-1A and CG-8 constitute a multiscale network that is a major mediator, earlier-acting than any previously described, of the formation and patterning of precartilage mesenchymal condensations in the developing limb. This network functions autonomously of limb bud signaling centers or other limb bud positional cues.
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Affiliation(s)
- Ramray Bhat
- Department of Cell Biology and Anatomy, New York Medical College, Valhalla, NY 10595, USA
| | - Kenneth M Lerea
- Department of Cell Biology and Anatomy, New York Medical College, Valhalla, NY 10595, USA
| | - Hong Peng
- Department of Cell Biology and Anatomy, New York Medical College, Valhalla, NY 10595, USA
| | - Herbert Kaltner
- Chair of Physiological Chemistry, Fakulty of Veterinary Medicine, Ludwig-Maximilians-University Munich, Veterinärstrasse13, D-80539 Munich, Germany
| | - Hans-Joachim Gabius
- Chair of Physiological Chemistry, Fakulty of Veterinary Medicine, Ludwig-Maximilians-University Munich, Veterinärstrasse13, D-80539 Munich, Germany
| | - Stuart A Newman
- Department of Cell Biology and Anatomy, New York Medical College, Valhalla, NY 10595, USA
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Larsen M, Yamada KM, Musselmann K. Systems analysis of salivary gland development and disease. WILEY INTERDISCIPLINARY REVIEWS. SYSTEMS BIOLOGY AND MEDICINE 2010; 2:670-82. [PMID: 20890964 PMCID: PMC3398465 DOI: 10.1002/wsbm.94] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
Branching morphogenesis is a crucial developmental process in which vertebrate organs generate extensive epithelial surface area while retaining a compact size. In the vertebrate submandibular salivary gland, branching morphogenesis is crucial for the generation of the large surface area necessary to produce sufficient saliva. However, in many salivary gland diseases, saliva-producing acinar cells are destroyed, resulting in dry mouth and secondary health conditions. Systems-based approaches can provide insights into understanding salivary gland development, function, and disease. The traditional approach to understanding these processes is the identification of molecular signals using reductionist approaches; we review current progress with such methods in understanding salivary gland development. Taking a more global approach, multiple groups are currently profiling the transcriptome, the proteome, and other 'omes' in both developing mouse tissues and in human patient samples. Computational methods have been successful in deciphering large data sets, and mathematical models are starting to make predictions regarding the contribution of molecules to the physical processes of morphogenesis and cellular function. A challenge for the future will be to establish comprehensive, publicly accessible salivary gland databases spanning the full range of genes and proteins; plans are underway to provide these resources to researchers in centralized repositories. The greatest challenge for the future will be to develop realistic models that integrate multiple types of data to both describe and predict embryonic development and disease pathogenesis.
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Affiliation(s)
- Melinda Larsen
- Department of Biological Sciences, University at Albany, State University of New York
| | - Kenneth M. Yamada
- Laboratory of Cell and Developmental Biology, National Institute of Dental and Craniofacial Research, National Institutes of Health
| | - Kurt Musselmann
- Laboratory of Cell and Developmental Biology, National Institute of Dental and Craniofacial Research, National Institutes of Health
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Zhu J, Zhang YT, Alber MS, Newman SA. Bare bones pattern formation: a core regulatory network in varying geometries reproduces major features of vertebrate limb development and evolution. PLoS One 2010; 5:e10892. [PMID: 20531940 PMCID: PMC2878345 DOI: 10.1371/journal.pone.0010892] [Citation(s) in RCA: 65] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2010] [Accepted: 05/07/2010] [Indexed: 11/22/2022] Open
Abstract
BACKGROUND Major unresolved questions regarding vertebrate limb development concern how the numbers of skeletal elements along the proximodistal (P-D) and anteroposterior (A-P) axes are determined and how the shape of a growing limb affects skeletal element formation. There is currently no generally accepted model for these patterning processes, but recent work on cartilage development (chondrogenesis) indicates that precartilage tissue self-organizes into nodular patterns by cell-molecular circuitry with local auto-activating and lateral inhibitory (LALI) properties. This process is played out in the developing limb in the context of a gradient of fibroblast growth factor (FGF) emanating from the apical ectodermal ridge (AER). RESULTS We have simulated the behavior of the core chondrogenic mechanism of the developing limb in the presence of an FGF gradient using a novel computational environment that permits simulation of LALI systems in domains of varying shape and size. The model predicts the normal proximodistal pattern of skeletogenesis as well as distal truncations resulting from AER removal. Modifications of the model's parameters corresponding to plausible effects of Hox proteins and formins, and of the reshaping of the model limb, bud yielded simulated phenotypes resembling mutational and experimental variants of the limb. Hypothetical developmental scenarios reproduce skeletal morphologies with features of fossil limbs. CONCLUSIONS The limb chondrogenic regulatory system operating in the presence of a gradient has an inherent, robust propensity to form limb-like skeletal structures. The bare bones framework can accommodate ancillary gene regulatory networks controlling limb bud shaping and establishment of Hox expression domains. This mechanism accounts for major features of the normal limb pattern and, under variant geometries and different parameter values, those of experimentally manipulated, genetically aberrant and evolutionary early forms, with no requirement for an independent system of positional information.
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Affiliation(s)
- Jianfeng Zhu
- Department of Mathematics, University of Notre Dame, Notre Dame, Indiana, United States of America
| | - Yong-Tao Zhang
- Department of Mathematics, University of Notre Dame, Notre Dame, Indiana, United States of America
| | - Mark S. Alber
- Department of Mathematics, University of Notre Dame, Notre Dame, Indiana, United States of America
- Center for the Study of Biocomplexity, University of Notre Dame, Notre Dame, Indiana, United States of America
| | - Stuart A. Newman
- Department of Cell Biology and Anatomy, New York Medical College, Valhalla, New York, United States of America
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Lin CM, Jiang TX, Baker RE, Maini PK, Widelitz RB, Chuong CM. Spots and stripes: pleomorphic patterning of stem cells via p-ERK-dependent cell chemotaxis shown by feather morphogenesis and mathematical simulation. Dev Biol 2009; 334:369-82. [PMID: 19647731 PMCID: PMC2811698 DOI: 10.1016/j.ydbio.2009.07.036] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2008] [Revised: 07/22/2009] [Accepted: 07/27/2009] [Indexed: 02/01/2023]
Abstract
A key issue in stem cell biology is the differentiation of homogeneous stem cells towards different fates which are also organized into desired configurations. Little is known about the mechanisms underlying the process of periodic patterning. Feather explants offer a fundamental and testable model in which multi-potential cells are organized into hexagonally arranged primordia and the spacing between primordia. Previous work explored roles of a Turing reaction-diffusion mechanism in establishing chemical patterns. Here we show that a continuum of feather patterns, ranging from stripes to spots, can be obtained when the level of p-ERK activity is adjusted with chemical inhibitors. The patterns are dose-dependent, tissue stage-dependent, and irreversible. Analyses show that ERK activity-dependent mesenchymal cell chemotaxis is essential for converting micro-signaling centers into stable feather primordia. A mathematical model based on short-range activation, long-range inhibition, and cell chemotaxis is developed and shown to simulate observed experimental results. This generic cell behavior model can be applied to model stem cell patterning behavior at large.
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Affiliation(s)
- Chih-Min Lin
- Department of Pathology, University of Southern California, Los Angeles, California 90033, USA
| | - Ting Xin Jiang
- Department of Pathology, University of Southern California, Los Angeles, California 90033, USA
| | - Ruth E. Baker
- Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB, UK
| | - Philip K. Maini
- Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB, UK
- Oxford Centre for Integrative Systems Biology, Department for Biochemistry, University of Oxford, South Parks Road, Oxford, OX1 3QU, UK
| | - Randall B. Widelitz
- Department of Pathology, University of Southern California, Los Angeles, California 90033, USA
| | - Cheng-Ming Chuong
- Department of Pathology, University of Southern California, Los Angeles, California 90033, USA
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Hunt CA, Ropella GEP, Lam TN, Tang J, Kim SHJ, Engelberg JA, Sheikh-Bahaei S. At the biological modeling and simulation frontier. Pharm Res 2009; 26:2369-400. [PMID: 19756975 PMCID: PMC2763179 DOI: 10.1007/s11095-009-9958-3] [Citation(s) in RCA: 66] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2009] [Accepted: 08/13/2009] [Indexed: 01/03/2023]
Abstract
We provide a rationale for and describe examples of synthetic modeling and simulation (M&S) of biological systems. We explain how synthetic methods are distinct from familiar inductive methods. Synthetic M&S is a means to better understand the mechanisms that generate normal and disease-related phenomena observed in research, and how compounds of interest interact with them to alter phenomena. An objective is to build better, working hypotheses of plausible mechanisms. A synthetic model is an extant hypothesis: execution produces an observable mechanism and phenomena. Mobile objects representing compounds carry information enabling components to distinguish between them and react accordingly when different compounds are studied simultaneously. We argue that the familiar inductive approaches contribute to the general inefficiencies being experienced by pharmaceutical R&D, and that use of synthetic approaches accelerates and improves R&D decision-making and thus the drug development process. A reason is that synthetic models encourage and facilitate abductive scientific reasoning, a primary means of knowledge creation and creative cognition. When synthetic models are executed, we observe different aspects of knowledge in action from different perspectives. These models can be tuned to reflect differences in experimental conditions and individuals, making translational research more concrete while moving us closer to personalized medicine.
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Affiliation(s)
- C Anthony Hunt
- Department of Bioengineering and Therapeutic Sciences, University of California, San Francisco, California, USA.
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31
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Kim SHJ, Yu W, Mostov K, Matthay MA, Hunt CA. A computational approach to understand in vitro alveolar morphogenesis. PLoS One 2009; 4:e4819. [PMID: 19283073 PMCID: PMC2653231 DOI: 10.1371/journal.pone.0004819] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2009] [Accepted: 02/11/2009] [Indexed: 12/16/2022] Open
Abstract
Primary human alveolar type II (AT II) epithelial cells maintained in Matrigel cultures form alveolar-like cysts (ALCs) using a cytogenesis mechanism that is different from that of other studied epithelial cell types: neither proliferation nor death is involved. During ALC formation, AT II cells engage simultaneously in fundamentally different, but not fully characterized activities. Mechanisms enabling these activities and the roles they play during different process stages are virtually unknown. Identifying, characterizing, and understanding the activities and mechanisms are essential to achieving deeper insight into this fundamental feature of morphogenesis. That deeper insight is needed to answer important questions. When and how does an AT cell choose to switch from one activity to another? Why does it choose one action rather than another? We report obtaining plausible answers using a rigorous, multi-attribute modeling and simulation approach that leveraged earlier efforts by using new, agent and object-oriented capabilities. We discovered a set of cell-level operating principles that enabled in silico cells to self-organize and generate systemic cystogenesis phenomena that are quantitatively indistinguishable from those observed in vitro. Success required that the cell components be quasi-autonomous. As simulation time advances, each in silico cell autonomously updates its environment information to reclassify its condition. It then uses the axiomatic operating principles to execute just one action for each possible condition. The quasi-autonomous actions of individual in silico cells were sufficient for developing stable cyst-like structures. The results strengthen in silico to in vitro mappings at three levels: mechanisms, behaviors, and operating principles, thereby achieving a degree of validation and enabling answering the questions posed. We suggest that the in silico operating principles presented may have a biological counterpart and that a semiquantitative mapping exists between in silico causal events and in vitro causal events.
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Affiliation(s)
- Sean H. J. Kim
- UCSF/UC Berkeley Joint Graduate Group in Bioengineering, University of California, Berkeley, California, United States of America
| | - Wei Yu
- Department of Anatomy, University of California San Francisco, San Francisco, California, United States of America
| | - Keith Mostov
- Department of Anatomy, University of California San Francisco, San Francisco, California, United States of America
| | - Michael A. Matthay
- Cardiovascular Research Institute, University of California San Francisco, San Francisco, California, United States of America
| | - C. Anthony Hunt
- UCSF/UC Berkeley Joint Graduate Group in Bioengineering, University of California, Berkeley, California, United States of America
- Department of Bioengineering and Therapeutic Sciences, University of California San Francisco, San Francisco, California, United States of America
- * E-mail:
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Huang AC, Hu L, Kauffman SA, Zhang W, Shmulevich I. Using cell fate attractors to uncover transcriptional regulation of HL60 neutrophil differentiation. BMC SYSTEMS BIOLOGY 2009; 3:20. [PMID: 19222862 PMCID: PMC2652435 DOI: 10.1186/1752-0509-3-20] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/21/2008] [Accepted: 02/18/2009] [Indexed: 12/16/2022]
Abstract
BACKGROUND The process of cellular differentiation is governed by complex dynamical biomolecular networks consisting of a multitude of genes and their products acting in concert to determine a particular cell fate. Thus, a systems level view is necessary for understanding how a cell coordinates this process and for developing effective therapeutic strategies to treat diseases, such as cancer, in which differentiation plays a significant role. Theoretical considerations and recent experimental evidence support the view that cell fates are high dimensional attractor states of the underlying molecular networks. The temporal behavior of the network states progressing toward different cell fate attractors has the potential to elucidate the underlying molecular mechanisms governing differentiation. RESULTS Using the HL60 multipotent promyelocytic leukemia cell line, we performed experiments that ultimately led to two different cell fate attractors by two treatments of varying dosage and duration of the differentiation agent all-trans-retinoic acid (ATRA). The dosage and duration combinations of the two treatments were chosen by means of flow cytometric measurements of CD11b, a well-known early differentiation marker, such that they generated two intermediate populations that were poised at the apparently same stage of differentiation. However, the population of one treatment proceeded toward the terminally differentiated neutrophil attractor while that of the other treatment reverted back toward the undifferentiated promyelocytic attractor. We monitored the gene expression changes in the two populations after their respective treatments over a period of five days and identified a set of genes that diverged in their expression, a subset of which promotes neutrophil differentiation while the other represses cell cycle progression. By employing promoter based transcription factor binding site analysis, we found enrichment in the set of divergent genes, of transcription factors functionally linked to tumor progression, cell cycle, and development. CONCLUSION Since many of the transcription factors identified by this approach are also known to be implicated in hematopoietic differentiation and leukemia, this study points to the utility of incorporating a dynamical systems level view into a computational analysis framework for elucidating transcriptional mechanisms regulating differentiation.
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Lushnikov PM, Chen N, Alber M. Macroscopic dynamics of biological cells interacting via chemotaxis and direct contact. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:061904. [PMID: 19256865 DOI: 10.1103/physreve.78.061904] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2008] [Revised: 10/12/2008] [Indexed: 05/13/2023]
Abstract
A connection is established between discrete stochastic model describing microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards chemical gradient (process called chemotaxis) with their shapes randomly fluctuating. Nonlinear diffusion equation is derived from microscopic dynamics in dimensions one and two using excluded volume approach. Nonlinear diffusion coefficient depends on cellular volume fraction and it is demonstrated to prevent collapse of cellular density. A very good agreement is shown between Monte Carlo simulations of the microscopic cellular Potts model and numerical solutions of the macroscopic equations for relatively large cellular volume fractions. Combination of microscopic and macroscopic models were used to simulate growth of structures similar to early vascular networks.
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Affiliation(s)
- Pavel M Lushnikov
- Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, USA.
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Xu Z, Chen N, Kamocka MM, Rosen ED, Alber M. A multiscale model of thrombus development. J R Soc Interface 2008; 5:705-22. [PMID: 17925274 PMCID: PMC2607450 DOI: 10.1098/rsif.2007.1202] [Citation(s) in RCA: 112] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2007] [Revised: 09/18/2007] [Accepted: 09/18/2007] [Indexed: 11/12/2022] Open
Abstract
A two-dimensional multiscale model is introduced for studying formation of a thrombus (clot) in a blood vessel. It involves components for modelling viscous, incompressible blood plasma; non-activated and activated platelets; blood cells; activating chemicals; fibrinogen; and vessel walls and their interactions. The macroscale dynamics of the blood flow is described by the continuum Navier-Stokes equations. The microscale interactions between the activated platelets, the platelets and fibrinogen and the platelets and vessel wall are described through an extended stochastic discrete cellular Potts model. The model is tested for robustness with respect to fluctuations of basic parameters. Simulation results demonstrate the development of an inhomogeneous internal structure of the thrombus, which is confirmed by the preliminary experimental data. We also make predictions about different stages in thrombus development, which can be tested experimentally and suggest specific experiments. Lastly, we demonstrate that the dependence of the thrombus size on the blood flow rate in simulations is close to the one observed experimentally.
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Affiliation(s)
- Zhiliang Xu
- Department of Mathematics, University of Notre DameNotre Dame, IN 46556, USA
| | - Nan Chen
- Department of Mathematics, University of Notre DameNotre Dame, IN 46556, USA
| | - Malgorzata M Kamocka
- Department of Medical and Molecular Genetics, Indiana University School of MedicineIndianapolis, IN 46202, USA
| | - Elliot D Rosen
- Department of Medical and Molecular Genetics, Indiana University School of MedicineIndianapolis, IN 46202, USA
| | - Mark Alber
- Department of Mathematics, University of Notre DameNotre Dame, IN 46556, USA
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Limb bud and flank mesoderm have distinct "physical phenotypes" that may contribute to limb budding. Dev Biol 2008; 321:319-30. [PMID: 18601915 DOI: 10.1016/j.ydbio.2008.06.018] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2007] [Revised: 05/09/2008] [Accepted: 06/04/2008] [Indexed: 02/03/2023]
Abstract
Limb bud outgrowth in chicken embryos is initiated during the third day of development by Fibroblast Growth Factor 8 (FGF8) produced by the newly formed apical ectodermal ridge (AER). One of the earliest effects of this induction is a change in the properties of the limb field mesoderm leading to bulging of the limb buds from the body wall. Heintzelman et al. [Heintzelman, K.F., Phillips, H.M., Davis, G.S., 1978. Liquid-tissue behavior and differential cohesiveness during chick limb budding. J. Embryol. Exp. Morphol. 47, 1-15.] suggested that budding of the limbs is caused by a higher liquid-like cohesivity of limb bud tissue compared with flank. We sought additional evidence relevant to this hypothesis by performing direct measurements of the effective surface tension, a measure of relative tissue cohesivity, of 4-day embryonic chicken wing and leg bud mesenchymal tissue, and adjacent flank mesoderm. As predicted, the two types of limb tissues were 1.5- to 2-fold more cohesive than the flank tissue. These differences paralleled cell number and volume density differences: 4-day limb buds had 2- to 2.5-fold as many cells per unit area of tissue as surrounding flank, a difference also seen at 3 days, when limb budding begins. Exposure of flank tissue to exogenous FGF8 for 24 h increased its cell number and raised its cohesivity to limb-like values. Four-day flank tissue exhibited a novel and unique active rebound response to compression, which was suppressed by the drug latrunculin and therefore dependent on an intact actin cytoskeleton. Correspondingly, flank at this stage expressed high levels of alpha-smooth muscle actin (SMA) mRNA and protein and a dense network of microfilaments. Treatment of flank with FGF8 eliminated the rebound response. We term material properties of tissues, such as cohesivity and mechanical excitability, the "physical phenotype", and propose that changes thereof are driving forces of morphogenesis. Our results indicate that two independent aspects of the physical phenotype of flank mesoderm can be converted to a limb-like state in response to treatment with FGF8. The higher tissue cohesivity induced by this effect will cause the incipient limb bud to phase separate from the surrounding flank, while the active mechanical response of the flank could help ensure that the limb bud bulges out from, rather than becoming engulfed by, this less cohesive tissue.
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36
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A computational model of chemotaxis-based cell aggregation. Biosystems 2008; 93:226-39. [PMID: 18602744 DOI: 10.1016/j.biosystems.2008.05.005] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2007] [Revised: 04/17/2008] [Accepted: 05/14/2008] [Indexed: 11/21/2022]
Abstract
We present a computational model that successfully captures the cell behaviors that play important roles in 2-D cell aggregation. A virtual cell in our model is designed as an independent, discrete unit with a set of parameters and actions. Each cell is defined by its location, size, rates of chemoattractant emission and response, age, life cycle stage, proliferation rate and number of attached cells. All cells are capable of emitting and sensing a chemoattractant chemical, moving, attaching to other cells, dividing, aging and dying. We validated and fine-tuned our in silico model by comparing simulated 24-h aggregation experiments with data derived from in vitro experiments using PC12 pheochromocytoma cells. Quantitative comparisons of the aggregate size distributions from the two experiments are produced using the Earth Mover's Distance (EMD) metric. We compared the two size distributions produced after 24 h of in vitro cell aggregation and the corresponding computer simulated process. Iteratively modifying the model's parameter values and measuring the difference between the in silico and in vitro results allow us to determine the optimal values that produce simulated aggregation outcomes closely matched to the PC12 experiments. Simulation results demonstrate the ability of the model to recreate large-scale aggregation behaviors seen in live cell experiments.
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37
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Newman SA, Bhat R. Activator-inhibitor dynamics of vertebrate limb pattern formation. ACTA ACUST UNITED AC 2008; 81:305-19. [PMID: 18228262 DOI: 10.1002/bdrc.20112] [Citation(s) in RCA: 61] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
The development of the vertebrate limb depends on an interplay of cellular differentiation, pattern formation, and tissue morphogenesis on multiple spatial and temporal scales. While numerous gene products have been described that participate in, and influence, the generation of the limb skeletal pattern, an understanding of the most salient feature of the developing limb--its quasiperiodic arrangement of bones, requires additional organizational principles. We review several such principles, drawing on concepts of physics and chemical dynamics along with molecular genetics and cell biology. First, a "core mechanism" for precartilage mesenchymal condensation is described, based on positive autoregulation of the morphogen transforming growth factor (TGF)-beta, induction of the extracellular matrix (ECM) protein fibronectin, and focal accumulation of cells via haptotaxis. This core mechanism is shown to be part of a local autoactivation-lateral inhibition (LALI) system that ensures that the condensations will be regularly spaced. Next, a "bare-bones" model for limb development is described in which the LALI-core mechanism is placed in a growing geometric framework with predifferentiated "apical," differentiating "active," and irreversibly differentiated "frozen" zones defined by distance from an apical source of a fibroblast growth factor (FGF)-type morphogen. This model is shown to account for classic features of the developing limb, including the proximodistal (PD) emergence over time of increasing numbers of bones. We review earlier and recent work suggesting that the inhibitory component of the LALI system for condensation may not be a diffusible morphogen, and propose an alternative mechanism for lateral inhibition, based on synchronization of oscillations of a Hes mediator of the Notch signaling pathway. Finally, we discuss how viewing development as an interplay between molecular-genetic and dynamic physical processes can provide new insight into the origin of congenital anomalies.
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Affiliation(s)
- Stuart A Newman
- Department of Cell Biology and Anatomy, New York Medical College, Valhalla, New York 10595, USA.
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