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García García OR, Ortiz R, Moreno-Barbosa E, D-Kondo N, Faddegon B, Ramos-Méndez J. TOPAS-Tissue: A Framework for the Simulation of the Biological Response to Ionizing Radiation at the Multi-Cellular Level. Int J Mol Sci 2024; 25:10061. [PMID: 39337547 PMCID: PMC11431975 DOI: 10.3390/ijms251810061] [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: 07/20/2024] [Revised: 08/21/2024] [Accepted: 09/17/2024] [Indexed: 09/30/2024] Open
Abstract
This work aims to develop and validate a framework for the multiscale simulation of the biological response to ionizing radiation in a population of cells forming a tissue. We present TOPAS-Tissue, a framework to allow coupling two Monte Carlo (MC) codes: TOPAS with the TOPAS-nBio extension, capable of handling the track-structure simulation and subsequent chemistry, and CompuCell3D, an agent-based model simulator for biological and environmental behavior of a population of cells. We verified the implementation by simulating the experimental conditions for a clonogenic survival assay of a 2-D PC-3 cell culture model (10 cells in 10,000 µm2) irradiated by MV X-rays at several absorbed dose values from 0-8 Gy. The simulation considered cell growth and division, irradiation, DSB induction, DNA repair, and cellular response. The survival was obtained by counting the number of colonies, defined as a surviving primary (or seeded) cell with progeny, at 2.7 simulated days after irradiation. DNA repair was simulated with an MC implementation of the two-lesion kinetic model and the cell response with a p53 protein-pulse model. The simulated survival curve followed the theoretical linear-quadratic response with dose. The fitted coefficients α = 0.280 ± 0.025/Gy and β = 0.042 ± 0.006/Gy2 agreed with published experimental data within two standard deviations. TOPAS-Tissue extends previous works by simulating in an end-to-end way the effects of radiation in a cell population, from irradiation and DNA damage leading to the cell fate. In conclusion, TOPAS-Tissue offers an extensible all-in-one simulation framework that successfully couples Compucell3D and TOPAS for multiscale simulation of the biological response to radiation.
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Affiliation(s)
- Omar Rodrigo García García
- Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Puebla 72000, Mexico; (O.R.G.G.); (E.M.-B.)
| | - Ramon Ortiz
- Department of Radiation Oncology, University of California San Francisco, San Francisco, CA 94115, USA; (R.O.); (N.D.-K.); (B.F.)
| | - Eduardo Moreno-Barbosa
- Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Puebla 72000, Mexico; (O.R.G.G.); (E.M.-B.)
| | - Naoki D-Kondo
- Department of Radiation Oncology, University of California San Francisco, San Francisco, CA 94115, USA; (R.O.); (N.D.-K.); (B.F.)
| | - Bruce Faddegon
- Department of Radiation Oncology, University of California San Francisco, San Francisco, CA 94115, USA; (R.O.); (N.D.-K.); (B.F.)
| | - Jose Ramos-Méndez
- Department of Radiation Oncology, University of California San Francisco, San Francisco, CA 94115, USA; (R.O.); (N.D.-K.); (B.F.)
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Sivakumar N, Warner HV, Peirce SM, Lazzara MJ. A computational modeling approach for predicting multicell spheroid patterns based on signaling-induced differential adhesion. PLoS Comput Biol 2022; 18:e1010701. [PMID: 36441822 PMCID: PMC9747056 DOI: 10.1371/journal.pcbi.1010701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2021] [Revised: 12/13/2022] [Accepted: 11/01/2022] [Indexed: 11/29/2022] Open
Abstract
Physiological and pathological processes including embryogenesis and tumorigenesis rely on the ability of individual cells to work collectively to form multicell patterns. In these heterogeneous multicell systems, cell-cell signaling induces differential adhesion between cells that leads to tissue-level patterning. However, the sensitivity of pattern formation to changes in the strengths of signaling or cell adhesion processes is not well understood. Prior work has explored these issues using synthetically engineered heterogeneous multicell spheroid systems, in which cell subpopulations engage in bidirectional intercellular signaling to regulate the expression of different cadherins. While engineered cell systems provide excellent experimental tools to observe pattern formation in cell populations, computational models of these systems may be leveraged to explore more systematically how specific combinations of signaling and adhesion parameters can drive the emergence of unique patterns. We developed and validated two- and three-dimensional agent-based models (ABMs) of spheroid patterning for previously described cells engineered with a bidirectional signaling circuit that regulates N- and P-cadherin expression. Systematic exploration of model predictions, some of which were experimentally validated, revealed how cell seeding parameters, the order of signaling events, probabilities of induced cadherin expression, and homotypic adhesion strengths affect pattern formation. Unsupervised clustering was also used to map combinations of signaling and adhesion parameters to these unique spheroid patterns predicted by the ABM. Finally, we demonstrated how the model may be deployed to design new synthetic cell signaling circuits based on a desired final multicell pattern.
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Affiliation(s)
- Nikita Sivakumar
- Department of Biomedical Engineering, University of Virginia, Charlottesville, Virginia, United States of America
| | - Helen V. Warner
- Department of Biomedical Engineering, University of Virginia, Charlottesville, Virginia, United States of America
| | - Shayn M. Peirce
- Department of Biomedical Engineering, University of Virginia, Charlottesville, Virginia, United States of America
| | - Matthew J. Lazzara
- Department of Biomedical Engineering, University of Virginia, Charlottesville, Virginia, United States of America
- Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia, United States of America
- * E-mail:
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MILLAN CLARO LUISFELIPE, MÁRQUEZ FLÓREZ KALENIA, DUQUE-DAZA CARLOSA, GARZÓN-ALVARADO DIEGOA. THREE-DIMENSIONAL COMPUTATIONAL MODEL OF EARLY UPPER LIMB DEVELOPMENT. J MECH MED BIOL 2021. [DOI: 10.1142/s021951942250004x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Limb development begins during embryogenesis when a series of biochemical interactions are triggered between a particular region of the mesoderm and the ectoderm. These processes affect the morphogenesis and growth of bones, joints, and all the other constituent elements of limbs; nevertheless, how the biochemical regulation affects mesenchymal condensation is not entirely clear. In this study, a three-dimensional computational model is designed to predict the appearance and location of the mesenchymal condensation in the stylopod and zeugopod; the biochemical events were described with reaction–diffusion equations that were solved using the finite elements method. The result of the gene expression in our model was consistent with the one reported in literature; the obtained patterns of Fgf8, Fgf10, and Wnt3a can predict the shape of the mesenchymal condensation of early upper limb development; the simple diffusive patterns of molecules were suitable to explain the areas where sox9 is expressed. Furthermore, our results suggest that the expression of Tgf-[Formula: see text] in the upper limb could be due to the inhibition of retinoic acid. These results suggest the importance of building computational scenarios where pathologies may be comprehensively examined.
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Affiliation(s)
| | | | - CARLOS A. DUQUE-DAZA
- Numerical Methods and Modeling Research Group (GNUM), Universidad Nacional de Colombia, Bogotá, Colombia
| | - DIEGO A. GARZÓN-ALVARADO
- Numerical Methods and Modeling Research Group (GNUM), Biotechnology Institute (IBUN), Universidad Nacional de Colombia, Bogotá, Colombia
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Rens EG, Edelstein-Keshet L. Cellular Tango: how extracellular matrix adhesion choreographs Rac-Rho signaling and cell movement. Phys Biol 2021; 18. [PMID: 34544056 DOI: 10.1088/1478-3975/ac2888] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2021] [Accepted: 09/20/2021] [Indexed: 12/14/2022]
Abstract
The small GTPases Rac and Rho are known to regulate eukaryotic cell shape, promoting front protrusion (Rac) or rear retraction (Rho) of the cell edge. Such cell deformation changes the contact and adhesion of cell to the extracellular matrix (ECM), while ECM signaling through integrin receptors also affects GTPase activity. We develop and investigate a model for this three-way feedback loop in 1D and 2D spatial domains, as well as in a fully deforming 2D cell shapes with detailed adhesion-bond biophysics. The model consists of reaction-diffusion equations solved numerically with open-source software, Morpheus, and with custom-built cellular Potts model simulations. We find a variety of patterns and cell behaviors, including persistent polarity, flipped front-back cell polarity oscillations, spiral waves, and random protrusion-retraction. We show that the observed spatial patterns depend on the cell shape, and vice versa.
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Affiliation(s)
- Elisabeth G Rens
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands.,Department of Mathematics, University of British Columbia, Vancouver, Canada
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Marconi M, Wabnik K. Shaping the Organ: A Biologist Guide to Quantitative Models of Plant Morphogenesis. FRONTIERS IN PLANT SCIENCE 2021; 12:746183. [PMID: 34675952 PMCID: PMC8523991 DOI: 10.3389/fpls.2021.746183] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/23/2021] [Accepted: 09/09/2021] [Indexed: 06/13/2023]
Abstract
Organ morphogenesis is the process of shape acquisition initiated with a small reservoir of undifferentiated cells. In plants, morphogenesis is a complex endeavor that comprises a large number of interacting elements, including mechanical stimuli, biochemical signaling, and genetic prerequisites. Because of the large body of data being produced by modern laboratories, solving this complexity requires the application of computational techniques and analyses. In the last two decades, computational models combined with wet-lab experiments have advanced our understanding of plant organ morphogenesis. Here, we provide a comprehensive review of the most important achievements in the field of computational plant morphodynamics. We present a brief history from the earliest attempts to describe plant forms using algorithmic pattern generation to the evolution of quantitative cell-based models fueled by increasing computational power. We then provide an overview of the most common types of "digital plant" paradigms, and demonstrate how models benefit from diverse techniques used to describe cell growth mechanics. Finally, we highlight the development of computational frameworks designed to resolve organ shape complexity through integration of mechanical, biochemical, and genetic cues into a quantitative standardized and user-friendly environment.
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Affiliation(s)
| | - Krzysztof Wabnik
- Centro de Biotecnología y Genómica de Plantas, Universidad Politécnica de Madrid (UPM) - Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria (INIA), Pozuelo de Alarcón (Madrid), Spain
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Bustamante DJ, Basile EJ, Hildreth BM, Browning NW, Jensen SA, Moldovan L, Petrache HI, Moldovan NI. Biofabrication of spheroids fusion-based tumor models: computational simulation of glucose effects. Biofabrication 2021; 13. [PMID: 33498017 DOI: 10.1088/1758-5090/abe025] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Accepted: 01/26/2021] [Indexed: 01/04/2023]
Abstract
In vitro tumor models consisting of cell spheroids are increasingly used for mechanistic studies and pharmacological testing. However, unless vascularized, the availability of nutrients such as glucose to deeper layers of multicellular aggregates is limited. In addition, recent developments in cells-only biofabrication (e.g. 'scaffold-free bioprinting'), allow the creation of more complex spheroid-based structures, further exposing the cells to nutrient deprivation within these constructs. To explore the impact of glucose availability on such tumor-like structures, we used the CompuCell3D (CC3D) platform for modeling of tumor spheroids. By monitoring the types of cells, fusing pairs geometry and the distance between spheroids centers of mass, we made novel heuristic observations on how binary- and multi-spheroid fusions are impacted by glucose availability. At limiting glucose concentrations mimicking hypoglycemia we noted an abrupt collapse of the tumor spheroids, unexpectedly amplified by the contact with normal cell spheroids. At higher glucose concentrations, we found an increased intermixing of cancerous cells, strong anti-phase oscillations between proliferating and quiescent tumor cells and a structural instability of fusing tumor spheroids, leading to their re-fragmentation. In a model of tumor microenvironment composed of normal cell spheroids fusing around a tumoral one, the competition for glucose lead to either the tumor's disappearance, or to its steady expansion. Moreover, the invasion of this microenvironment by individual tumor cells was also strongly depended on the available glucose. In conclusion, we demonstrate the value of computational simulations for anticipating the properties of biofabricated tumor models, and in generating testable hypotheses regarding the relationship between cancer, nutrition and diabetes.
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Affiliation(s)
- David J Bustamante
- IUPUI BME, 799 W. Michigan Street, Indianapolis, Indiana, 46202-5195, UNITED STATES
| | - Elijah J Basile
- IUPUI, 301 University Boulevard, Indianapolis, Indiana, 46202-5146, UNITED STATES
| | - Brady M Hildreth
- IUPUI, 301 University Boulevard, Indianapolis, Indiana, 46202-5146, UNITED STATES
| | - Nathan W Browning
- IUPUI, 301 University Boulevard, Indianapolis, Indiana, 46202-5146, UNITED STATES
| | - S Alexander Jensen
- IUPUI, 301 University Boulevard Suite, Indianapolis, Indiana, 46202-5146, UNITED STATES
| | - Leni Moldovan
- Surgery, Indiana University School of Medicine, 1481 W. 10th St., Room D-2008, Indianapolis, Indiana, 46202-5114, UNITED STATES
| | - Horia I Petrache
- Department of Physics, Indiana University - Purdue University at Indianapolis, 402 N. Blackford Street, LD 154, Indianapolis, Indiana, 46202, UNITED STATES
| | - Nicanor I Moldovan
- VA Medical Center, Indiana University Purdue University at Indianapolis, 1481 W. 10th St., Room C6128, Indianapolis, Indiana, 46202-5143, UNITED STATES
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7
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Glimm T, Bhat R, Newman SA. Multiscale modeling of vertebrate limb development. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2020; 12:e1485. [PMID: 32212250 DOI: 10.1002/wsbm.1485] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2019] [Revised: 02/14/2020] [Accepted: 02/17/2020] [Indexed: 11/07/2022]
Abstract
We review the current state of mathematical modeling of cartilage pattern formation in vertebrate limbs. We place emphasis on several reaction-diffusion type models that have been proposed in the last few years. These models are grounded in more detailed knowledge of the relevant regulatory processes than previous ones but generally refer to different molecular aspects of these processes. Considering these models in light of comparative phylogenomics permits framing of hypotheses on the evolutionary order of appearance of the respective mechanisms and their roles in the fin-to-limb transition. This article is categorized under: Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Mechanistic Models Developmental Biology > Developmental Processes in Health and Disease Analytical and Computational Methods > Analytical Methods.
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Affiliation(s)
- Tilmann Glimm
- Department of Mathematics, Western Washington University, Bellingham, Washington
| | - Ramray Bhat
- Department of Molecular Reproduction, Development and Genetics, Indian Institute of Science, Bangalore, India
| | - Stuart A Newman
- Department of Cell Biology and Anatomy, New York Medical College, Valhalla, New York
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Dalle Nogare D, Chitnis AB. NetLogo agent-based models as tools for understanding the self-organization of cell fate, morphogenesis and collective migration of the zebrafish posterior Lateral Line primordium. Semin Cell Dev Biol 2019; 100:186-198. [PMID: 31901312 DOI: 10.1016/j.semcdb.2019.12.015] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2019] [Revised: 12/20/2019] [Accepted: 12/21/2019] [Indexed: 01/25/2023]
Abstract
Interactions between primordium cells and their environment determines the self-organization of the zebrafish posterior Lateral Line primordium as it migrates under the skin from the ear to the tip of the tail forming and depositing neuromasts to spearhead formation of the posterior Lateral Line sensory system. In this review we describe how the NetLogo agent-based programming environment has been used in our lab to visualize and explore how self-generated chemokine gradients determine collective migration, how the dynamics of Wnt signaling can be used to predict patterns of neuromast deposition, and how previously defined interactions between Wnt and Fgf signaling systems have the potential to determine the periodic formation of center-biased Fgf signaling centers in the wake of a shrinking Wnt system. We also describe how NetLogo was used as a database for storing and visualizing the results of in toto lineage analysis of all cells in the migrating primordium. Together, the models illustrate how this programming environment can be used in diverse ways to integrate what has been learnt from biological experiments about the nature of interactions between cells and their environment, and explore how these interactions could potentially determine emergent patterns of cell fate specification, morphogenesis and collective migration of the zebrafish posterior Lateral Line primordium.
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Affiliation(s)
- Damian Dalle Nogare
- Section on Neural Developmental Dynamics, Division of Developmental Biology, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Bethesda, MD USA
| | - Ajay B Chitnis
- Section on Neural Developmental Dynamics, Division of Developmental Biology, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Bethesda, MD USA.
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Erkurt M. Emergence of form in embryogenesis. J R Soc Interface 2018; 15:20180454. [PMID: 30429261 PMCID: PMC6283983 DOI: 10.1098/rsif.2018.0454] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2018] [Accepted: 10/12/2018] [Indexed: 11/23/2022] Open
Abstract
The development of form in an embryo is the result of a series of topological and informational symmetry breakings. We introduce the vector-reaction-diffusion-drift (VRDD) system where the limit cycle of spatial dynamics is morphogen concentrations with Dirac delta-type distributions. This is fundamentally different from the Turing reaction-diffusion system, as VRDD generates system-wide broken symmetry. We developed 'fundamental forms' from spherical blastula with a single organizing axis (rotational symmetry), double axis (mirror symmetry) and triple axis (no symmetry operator in three dimensions). We then introduced dynamics for cell differentiation, where genetic regulatory states are modelled as a finite-state machine (FSM). The state switching of an FSM is based on local morphogen concentrations as epigenetic information that changes dynamically. We grow complicated forms hierarchically in spatial subdomains using the FSM model coupled with the VRDD system. Using our integrated simulation model with four layers (topological, physical, chemical and regulatory), we generated life-like forms such as hydra. Genotype-phenotype mapping was investigated with continuous and jump mutations. Our study can have applications in morphogenetic engineering, soft robotics and biomimetic design.
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Affiliation(s)
- Murat Erkurt
- Department of Mathematics, Centre for Complexity Science, Imperial College London, London SW7 2AZ, UK
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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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Hirashima T, Rens EG, Merks RMH. Cellular Potts modeling of complex multicellular behaviors in tissue morphogenesis. Dev Growth Differ 2017; 59:329-339. [DOI: 10.1111/dgd.12358] [Citation(s) in RCA: 54] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2017] [Accepted: 03/24/2017] [Indexed: 12/14/2022]
Affiliation(s)
- Tsuyoshi Hirashima
- Institute for Frontier Life and Medical Sciences Kyoto University 53 Kawahara, Shogoin, Sakyo‐ku Kyoto 606‐8507 Japan
| | - Elisabeth G. Rens
- Centrum Wiskunde & Informatica Life Sciences Group Science Park 123 1098 XG Amsterdam the Netherlands
- Mathematical Institute Leiden University Niels Bohrweg 1 2333 CA Leiden the Netherlands
| | - Roeland M. H. Merks
- Centrum Wiskunde & Informatica Life Sciences Group Science Park 123 1098 XG Amsterdam the Netherlands
- Mathematical Institute Leiden University Niels Bohrweg 1 2333 CA Leiden the Netherlands
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12
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Lange A, Müller GB. Polydactyly in Development, Inheritance, and Evolution. QUARTERLY REVIEW OF BIOLOGY 2017; 92:1-38. [DOI: 10.1086/690841] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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Abstract
This chapter aims at discussing the content of multi-agent based simulation (MABS) applied to computational biology i.e., to modelling and simulating biological systems by means of computational models, methodologies, and frameworks. In particular, the adoption of agent-based modelling (ABM) in the field of multicellular systems biology is explored, focussing on the challenging scenarios of developmental biology. After motivating why agent-based abstractions are critical in representing multicellular systems behaviour, MABS is discussed as the source of the most natural and appropriate mechanism for analysing the self-organising behaviour of systems of cells. As a case study, an application of MABS to the development of Drosophila Melanogaster is finally presented, which exploits the ALCHEMIST platform for agent-based simulation.
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Muzzio NE, Pasquale MA, Huergo MAC, Bolzán AE, González PH, Arvia AJ. Spatio-temporal morphology changes in and quenching effects on the 2D spreading dynamics of cell colonies in both plain and methylcellulose-containing culture media. J Biol Phys 2016; 42:477-502. [PMID: 27270331 DOI: 10.1007/s10867-016-9418-3] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2015] [Accepted: 04/04/2016] [Indexed: 10/21/2022] Open
Abstract
To deal with complex systems, microscopic and global approaches become of particular interest. Our previous results from the dynamics of large cell colonies indicated that their 2D front roughness dynamics is compatible with the standard Kardar-Parisi-Zhang (KPZ) or the quenched KPZ equations either in plain or methylcellulose (MC)-containing gel culture media, respectively. In both cases, the influence of a non-uniform distribution of the colony constituents was significant. These results encouraged us to investigate the overall dynamics of those systems considering the morphology and size, the duplication rate, and the motility of single cells. For this purpose, colonies with different cell populations (N) exhibiting quasi-circular and quasi-linear growth fronts in plain and MC-containing culture media are investigated. For small N, the average radial front velocity and its change with time depend on MC concentration. MC in the medium interferes with cell mitosis, contributes to the local enlargement of cells, and increases the distribution of spatio-temporal cell density heterogeneities. Colony spreading in MC-containing media proceeds under two main quenching effects, I and II; the former mainly depending on the culture medium composition and structure and the latter caused by the distribution of enlarged local cell domains. For large N, colony spreading occurs at constant velocity. The characteristics of cell motility, assessed by measuring their trajectories and the corresponding velocity field, reflect the effect of enlarged, slow-moving cells and the structure of the medium. Local average cell size distribution and individual cell motility data from plain and MC-containing media are qualitatively consistent with the predictions of both the extended cellular Potts models and the observed transition of the front roughness dynamics from a standard KPZ to a quenched KPZ. In this case, quenching effects I and II cooperate and give rise to the quenched-KPZ equation. Seemingly, these results show a possible way of linking the cellular Potts models and the 2D colony front roughness dynamics.
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Affiliation(s)
- N E Muzzio
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA), Universidad Nacional de La Plata (UNLP), CONICET, Sucursal 4, Casilla de Correo 16, 1900, La Plata, Argentina
| | - M A Pasquale
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA), Universidad Nacional de La Plata (UNLP), CONICET, Sucursal 4, Casilla de Correo 16, 1900, La Plata, Argentina.
| | - M A C Huergo
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA), Universidad Nacional de La Plata (UNLP), CONICET, Sucursal 4, Casilla de Correo 16, 1900, La Plata, Argentina
| | - A E Bolzán
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA), Universidad Nacional de La Plata (UNLP), CONICET, Sucursal 4, Casilla de Correo 16, 1900, La Plata, Argentina
| | - P H González
- Cátedra de Patología, Facultad de Ciencias Médicas, UNLP, CIC, Calle 60 y 120, 1900, La Plata, Bs. As., Argentina
| | - A J Arvia
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA), Universidad Nacional de La Plata (UNLP), CONICET, Sucursal 4, Casilla de Correo 16, 1900, La Plata, Argentina
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Tourdot RW, Bradley RP, Ramakrishnan N, Radhakrishnan R. Multiscale computational models in physical systems biology of intracellular trafficking. IET Syst Biol 2014; 8:198-213. [PMID: 25257021 PMCID: PMC4336166 DOI: 10.1049/iet-syb.2013.0057] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2013] [Revised: 07/03/2014] [Accepted: 08/08/2014] [Indexed: 01/19/2023] Open
Abstract
In intracellular trafficking, a definitive understanding of the interplay between protein binding and membrane morphology remains incomplete. The authors describe a computational approach by integrating coarse-grained molecular dynamics (CGMD) simulations with continuum Monte Carlo (CM) simulations of the membrane to study protein-membrane interactions and the ensuing membrane curvature. They relate the curvature field strength discerned from the molecular level to its effect at the cellular length-scale. They perform thermodynamic integration on the CM model to describe the free energy landscape of vesiculation in clathrin-mediated endocytosis. The method presented here delineates membrane morphologies and maps out the free energy changes associated with membrane remodeling due to varying coat sizes, coat curvature strengths, membrane bending rigidities, and tensions; furthermore several constraints on mechanisms underlying clathrin-mediated endocytosis have also been identified, Their CGMD simulations have revealed the importance of PIP2 for stable binding of proteins essential for curvature induction in the bilayer and have provided a molecular basis for the positive curvature induction by the epsin N-terminal homology (EIMTH) domain. Calculation of the free energy landscape for vesicle budding has identified the critical size and curvature strength of a clathrin coat required for nucleation and stabilisation of a mature vesicle.
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Affiliation(s)
- Richard W Tourdot
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Ryan P Bradley
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Natesan Ramakrishnan
- Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Ravi Radhakrishnan
- Department of Biochemistry and Biophysics, University of Pennsylvania, Philadelphia, PA 19104, USA.
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16
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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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17
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Abstract
As the complexity of synthetic genetic circuits increases, modeling is becoming a necessary first step to inform subsequent experimental efforts. In recent years, the design automation community has developed a wealth of computational tools for assisting experimentalists in designing and analyzing new genetic circuits at several scales. However, existing software primarily caters to either the DNA- or single-cell level, with little support for the multicellular level. To address this need, the iBioSim software package has been enhanced to provide support for modeling, simulating, and visualizing dynamic cellular populations in a two-dimensional space. This capacity is fully integrated into the software, capitalizing on iBioSim's strengths in modeling, simulating, and analyzing single-celled systems.
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Affiliation(s)
- Jason T. Stevens
- Department
of Electrical and Computer Engineering, University of Utah, Salt Lake City, Utah 84112, United
States
| | - Chris J. Myers
- Department
of Electrical and Computer Engineering, University of Utah, Salt Lake City, Utah 84112, United
States
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18
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Mortazavi V, D'Souza RM, Nosonovsky M. Study of contact angle hysteresis using the Cellular Potts Model. Phys Chem Chem Phys 2013; 15:2749-56. [DOI: 10.1039/c2cp44039c] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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19
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Abate A, Vincent S, Dobbe R, Silletti A, Master N, Axelrod JD, Tomlin CJ. A mathematical model to study the dynamics of epithelial cellular networks. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2012; 9:1607-1620. [PMID: 23221083 PMCID: PMC3558995 DOI: 10.1109/tcbb.2012.126] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Epithelia are sheets of connected cells that are essential across the animal kingdom. Experimental observations suggest that the dynamical behavior of many single-layered epithelial tissues has strong analogies with that of specific mechanical systems, namely large networks consisting of point masses connected through spring-damper elements and undergoing the influence of active and dissipating forces. Based on this analogy, this work develops a modeling framework to enable the study of the mechanical properties and of the dynamic behavior of large epithelial cellular networks. The model is built first by creating a network topology that is extracted from the actual cellular geometry as obtained from experiments, then by associating a mechanical structure and dynamics to the network via spring-damper elements. This scalable approach enables running simulations of large network dynamics: the derived modeling framework in particular is predisposed to be tailored to study general dynamics (for example, morphogenesis) of various classes of single-layered epithelial cellular networks. In this contribution, we test the model on a case study of the dorsal epithelium of the Drosophila melanogaster embryo during early dorsal closure (and, less conspicuously, germband retraction).
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Affiliation(s)
- Alessandro Abate
- Delft Center for Systems and Control, TU Delft, Delft, The Netherlands
| | | | - Roel Dobbe
- Delft Center for Systems and Control, TU Delft, Delft, The Netherlands
| | - Alberto Silletti
- Department of Information Engineering, University of Padova, Padova, Italy
| | - Neal Master
- Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA, USA
| | - Jeffrey D. Axelrod
- Department of Pathology, Stanford University School of Medicine, Stanford, CA, USA
| | - Claire J. Tomlin
- Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA, USA
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20
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Glimm T, Headon D, Kiskowski MA. Computational and mathematical models of chondrogenesis in vertebrate limbs. ACTA ACUST UNITED AC 2012; 96:176-92. [PMID: 22692890 DOI: 10.1002/bdrc.21014] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
The production of cartilage (chondrogenic patterning) in the limb is one of the best-studied examples of the emergence of form in developmental biology. At the core of the theoretical study is an effort to understand the mechanism that establishes the characteristic distribution of cartilage in the embryonic limb, which defines the future sites and shapes of bones that will be present in the mature limb. This review article gives an overview of the history and current state of a rich literature of mathematical and computational models that seek to contribute to this problem. We describe models for the mechanisms of limb growth and shaping via interaction with various chemical fields, as well as models addressing the intrinsic self-organization capabilities of the embryonic mesenchymal tissue, such as reaction-diffusion and mechanochemical models. We discuss the contributions of these models to the current understanding of chondrogenesis in vertebrate limbs, as well as their relation to the varied conceptual models that have been proposed by experimentalists.
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Affiliation(s)
- T Glimm
- Department of Mathematics, Western Washington University, Bellingham, WA 98225, USA.
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21
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Computer simulations of in vitro morphogenesis. Biosystems 2012; 109:430-43. [DOI: 10.1016/j.biosystems.2012.06.002] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2012] [Revised: 06/15/2012] [Accepted: 06/15/2012] [Indexed: 01/08/2023]
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22
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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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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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Engelberg JA, Datta A, Mostov KE, Hunt CA. MDCK cystogenesis driven by cell stabilization within computational analogues. PLoS Comput Biol 2011; 7:e1002030. [PMID: 21490722 PMCID: PMC3072361 DOI: 10.1371/journal.pcbi.1002030] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2010] [Accepted: 02/24/2011] [Indexed: 12/17/2022] Open
Abstract
The study of epithelial morphogenesis is fundamental to increasing our
understanding of organ function and disease. Great progress has been made
through study of culture systems such as Madin-Darby canine kidney (MDCK) cells,
but many aspects of even simple morphogenesis remain unclear. For example, are
specific cell actions tightly coupled to the characteristics of the cell's
environment or are they more often cell state dependent? How does the single
lumen, single cell layer cyst consistently emerge from a variety of cell
actions? To improve insight, we instantiated in silico analogues that used
hypothesized cell behavior mechanisms to mimic MDCK cystogenesis. We tested them
through in vitro experimentation and quantitative validation. We observed novel
growth patterns, including a cell behavior shift that began around day five of
growth. We created agent-oriented analogues that used the cellular Potts model
along with an Iterative Refinement protocol. Following several refinements, we
achieved a degree of validation for two separate mechanisms. Both survived
falsification and achieved prespecified measures of similarity to cell culture
properties. In silico components and mechanisms mapped to in vitro counterparts.
In silico, the axis of cell division significantly affects lumen number without
changing cell number or cyst size. Reducing the amount of in silico luminal cell
death had limited effect on cystogenesis. Simulations provide an observable
theory for cystogenesis based on hypothesized, cell-level operating
principles. Epithelial cells perform essential functions throughout the body, acting as both
barrier and transporter and allowing an organism to survive and thrive in varied
environments. Although the details of many processes that occur within
individual cells are well understood, we still lack a thorough understanding of
how cells coordinate their behaviors to create complex tissues. In order to
achieve deeper insight, we created a list of targeted attributes and plausible
rules for the growth of multicellular cysts formed by Madin-Darby canine kidney
(MDCK) cells grown in vitro. We then designed in silico analogues of MDCK
cystogenesis using object-oriented programming. In silico components (such as
the cells and lumens) and their behaviors directly mapped to in vitro components
and mechanisms. We conducted in vitro experiments to generate data that would
validate or falsify the in silico analogues and then iteratively refined the
analogues to mimic that data. Cells in vitro begin to stabilize at around the
fifth day even as cysts continue to expand. The in silico system mirrored that
behavior and others, achieving new insights. For example, luminal cell death is
not strictly required for cystogenesis, and cell division orientation is very
important for normal cyst growth.
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Affiliation(s)
- Jesse A. Engelberg
- UCSF/UC Berkeley Joint Graduate Group in Bioengineering, University of
California, San Francisco, California, United States of America
| | - Anirban Datta
- Department of Anatomy, University of California, San Francisco,
California, United States of America
| | - Keith E. Mostov
- Department of Anatomy, University of California, San Francisco,
California, United States of America
| | - C. Anthony Hunt
- UCSF/UC Berkeley Joint Graduate Group in Bioengineering, University of
California, San Francisco, California, United States of America
- Department of Bioengineering and Therapeutic Sciences, University of
California, San Francisco, California, United States of America
- * E-mail:
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25
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Christley S, Lee B, Dai X, Nie Q. Integrative multicellular biological modeling: a case study of 3D epidermal development using GPU algorithms. BMC SYSTEMS BIOLOGY 2010; 4:107. [PMID: 20696053 PMCID: PMC2936904 DOI: 10.1186/1752-0509-4-107] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/28/2010] [Accepted: 08/09/2010] [Indexed: 12/18/2022]
Abstract
BACKGROUND Simulation of sophisticated biological models requires considerable computational power. These models typically integrate together numerous biological phenomena such as spatially-explicit heterogeneous cells, cell-cell interactions, cell-environment interactions and intracellular gene networks. The recent advent of programming for graphical processing units (GPU) opens up the possibility of developing more integrative, detailed and predictive biological models while at the same time decreasing the computational cost to simulate those models. RESULTS We construct a 3D model of epidermal development and provide a set of GPU algorithms that executes significantly faster than sequential central processing unit (CPU) code. We provide a parallel implementation of the subcellular element method for individual cells residing in a lattice-free spatial environment. Each cell in our epidermal model includes an internal gene network, which integrates cellular interaction of Notch signaling together with environmental interaction of basement membrane adhesion, to specify cellular state and behaviors such as growth and division. We take a pedagogical approach to describing how modeling methods are efficiently implemented on the GPU including memory layout of data structures and functional decomposition. We discuss various programmatic issues and provide a set of design guidelines for GPU programming that are instructive to avoid common pitfalls as well as to extract performance from the GPU architecture. CONCLUSIONS We demonstrate that GPU algorithms represent a significant technological advance for the simulation of complex biological models. We further demonstrate with our epidermal model that the integration of multiple complex modeling methods for heterogeneous multicellular biological processes is both feasible and computationally tractable using this new technology. We hope that the provided algorithms and source code will be a starting point for modelers to develop their own GPU implementations, and encourage others to implement their modeling methods on the GPU and to make that code available to the wider community.
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Affiliation(s)
- Scott Christley
- Department of Mathematics, University of California, Irvine, CA 92697, USA.
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26
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Boyle CJ, Lennon AB, Early M, Kelly DJ, Lally C, Prendergast PJ. Computational simulation methodologies for mechanobiological modelling: a cell-centred approach to neointima development in stents. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2010; 368:2919-35. [PMID: 20478914 PMCID: PMC2944394 DOI: 10.1098/rsta.2010.0071] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
The design of medical devices could be very much improved if robust tools were available for computational simulation of tissue response to the presence of the implant. Such tools require algorithms to simulate the response of tissues to mechanical and chemical stimuli. Available methodologies include those based on the principle of mechanical homeostasis, those which use continuum models to simulate biological constituents, and the cell-centred approach, which models cells as autonomous agents. In the latter approach, cell behaviour is governed by rules based on the state of the local environment around the cell; and informed by experiment. Tissue growth and differentiation requires simulating many of these cells together. In this paper, the methodology and applications of cell-centred techniques--with particular application to mechanobiology--are reviewed, and a cell-centred model of tissue formation in the lumen of an artery in response to the deployment of a stent is presented. The method is capable of capturing some of the most important aspects of restenosis, including nonlinear lesion growth with time. The approach taken in this paper provides a framework for simulating restenosis; the next step will be to couple it with more patient-specific geometries and quantitative parameter data.
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Affiliation(s)
- C. J. Boyle
- Trinity Centre for Bioengineering, School of Engineering, Trinity College Dublin, Dublin, Republic of Ireland
| | - A. B. Lennon
- Trinity Centre for Bioengineering, School of Engineering, Trinity College Dublin, Dublin, Republic of Ireland
| | - M. Early
- Trinity Centre for Bioengineering, School of Engineering, Trinity College Dublin, Dublin, Republic of Ireland
| | - D. J. Kelly
- Trinity Centre for Bioengineering, School of Engineering, Trinity College Dublin, Dublin, Republic of Ireland
| | - C. Lally
- Trinity Centre for Bioengineering, School of Engineering, Trinity College Dublin, Dublin, Republic of Ireland
- Department of Mechanical and Manufacturing Engineering, Dublin City University, Dublin, Republic of Ireland
| | - P. J. Prendergast
- Trinity Centre for Bioengineering, School of Engineering, Trinity College Dublin, Dublin, Republic of Ireland
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27
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Poplawski NJ, Shirinifard A, Agero U, Gens JS, Swat M, Glazier JA. Front instabilities and invasiveness of simulated 3D avascular tumors. PLoS One 2010; 5:e10641. [PMID: 20520818 PMCID: PMC2877086 DOI: 10.1371/journal.pone.0010641] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2009] [Accepted: 04/13/2010] [Indexed: 12/21/2022] Open
Abstract
We use the Glazier-Graner-Hogeweg model to simulate three-dimensional (3D), single-phenotype, avascular tumors growing in an homogeneous tissue matrix (TM) supplying a single limiting nutrient. We study the effects of two parameters on tumor morphology: a diffusion-limitation parameter defined as the ratio of the tumor-substrate consumption rate to the substrate-transport rate, and the tumor-TM surface tension. This initial model omits necrosis and oxidative/hypoxic metabolism effects, which can further influence tumor morphology, but our simplified model still shows significant parameter dependencies. The diffusion-limitation parameter determines whether the growing solid tumor develops a smooth (noninvasive) or fingered (invasive) interface, as in our earlier two-dimensional (2D) simulations. The sensitivity of 3D tumor morphology to tumor-TM surface tension increases with the size of the diffusion-limitation parameter, as in 2D. The 3D results are unexpectedly close to those in 2D. Our results therefore may justify using simpler 2D simulations of tumor growth, instead of more realistic but more computationally expensive 3D simulations. While geometrical artifacts mean that 2D sections of connected 3D tumors may be disconnected, the morphologies of 3D simulated tumors nevertheless correlate with the morphologies of their 2D sections, especially for low-surface-tension tumors, allowing the use of 2D sections to partially reconstruct medically-important 3D-tumor structures.
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Affiliation(s)
- Nikodem J Poplawski
- Biocomplexity Institute and Department of Physics, Indiana University, Bloomington, Indiana, USA.
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28
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Neagu A, Mironov V, Kosztin I, Barz B, Neagu M, Moreno-Rodriguez RA, Markwald RR, Forgacs G. Computational modeling of epithelial-mesenchymal transformations. Biosystems 2009; 100:23-30. [PMID: 20005917 DOI: 10.1016/j.biosystems.2009.12.004] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2009] [Revised: 11/17/2009] [Accepted: 12/03/2009] [Indexed: 12/22/2022]
Abstract
An epithelial-mesenchymal transformation (EMT) involves alterations in cell-cell and cell-matrix adhesion, the detachment of epithelial cells from their neighbors, the degradation of the basal lamina and acquisition of mesenchymal phenotype. Here we present Monte Carlo simulations for a specific EMT in early heart development: the formation of cardiac cushions. Cell rearrangements are described in accordance with Steinberg's differential adhesion hypothesis, which states that cells possess a type-dependent adhesion apparatus and are sufficiently motile to give rise to the tissue conformation with the largest number of strong bonds. We also implement epithelial and mesenchymal cell proliferation, cell type change and extracellular matrix production by mesenchymal cells. Our results show that an EMT is promoted more efficiently by an increase in cell-substrate adhesion than by a decrease in cell-cell adhesion. In addition to cushion tissue formation, the model also accounts for the phenomena of matrix invasion and mesenchymal condensation. We conclude that in order to maintain epithelial integrity during EMT the number of epithelial cells must increase at a controlled rate. Our model predictions are in qualitative agreement with available experimental data.
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Affiliation(s)
- Adrian Neagu
- Department of Physics, University of Missouri, Columbia, MO 65211, USA
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29
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Ouaknin GY, Bar-Yoseph PZ. Stochastic collective movement of cells and fingering morphology: no maverick cells. Biophys J 2009; 97:1811-21. [PMID: 19804711 PMCID: PMC2756401 DOI: 10.1016/j.bpj.2009.05.064] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2008] [Revised: 05/07/2009] [Accepted: 05/26/2009] [Indexed: 12/14/2022] Open
Abstract
The classical approach to model collective biological cell movement is through coupled nonlinear reaction-diffusion equations for biological cells and diffusive chemicals that interact with the biological cells. This approach takes into account the diffusion of cells, proliferation, death of cells, and chemotaxis. Whereas the classical approach has many advantages, it fails to consider many factors that affect multicell movement. In this work, a multiscale approach, the Glazier-Graner-Hogeweg model, is used. This model is implemented for biological cells coupled with the finite element method for a diffusive chemical. The Glazier-Graner-Hogeweg model takes the biological cell state as discrete and allows it to include cohesive forces between biological cells, deformation of cells, following the path of a single cell, and stochastic behavior of the cells. Where the continuity of the tissue at the epidermis is violated, biological cells regenerate skin to heal the wound. We assume that the cells secrete a diffusive chemical when they feel a wounded region and that the cells are attracted by the chemical they release (chemotaxis). Under certain parameters, the front encounters a fingering morphology, and two fronts progressing against each other are attracted and correlated. Cell flow exhibits interesting patterns, and a drift effect on the chemical may influence the cells' motion. The effects of a polarized substrate are also discussed.
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Affiliation(s)
- Gaddiel Yonathan Ouaknin
- Computational Biomechanics Laboratory, Faculty of Mechanical Engineering, Technion, Israel Institute of Technology, Haifa, Israel.
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30
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Geard N, Willadsen K. Dynamical approaches to modeling developmental gene regulatory networks. ACTA ACUST UNITED AC 2009; 87:131-42. [PMID: 19530129 DOI: 10.1002/bdrc.20150] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
The network of interacting regulatory signals within a cell comprises one of the most complex and powerful computational systems in biology. Gene regulatory networks (GRNs) play a key role in transforming the information encoded in a genome into morphological form. To achieve this feat, GRNs must respond to and integrate environmental signals with their internal dynamics in a robust and coordinated fashion. The highly dynamic nature of this process lends itself to interpretation and analysis in the language of dynamical models. Modeling provides a means of systematically untangling the complicated structure of GRNs, a framework within which to simulate the behavior of reconstructed systems and, in some cases, suites of analytic tools for exploring that behavior and its implications. This review provides a general background to the idea of treating a regulatory network as a dynamical system, and describes a variety of different approaches that have been taken to the dynamical modeling of GRNs.
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Affiliation(s)
- Nicholas Geard
- School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, United Kingdom.
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31
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Qutub AA, Mac Gabhann F, Karagiannis ED, Vempati P, Popel AS. Multiscale models of angiogenesis. ACTA ACUST UNITED AC 2009; 28:14-31. [PMID: 19349248 DOI: 10.1109/memb.2009.931791] [Citation(s) in RCA: 102] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Vascular disease, cancer, stroke, neurodegeneration, diabetes, inflammation, asthma, obesity, arthritis--the list of conditions that involve angiogenesis reads like main chapters in a book on pathology. Angiogenesis, the growth of capillaries from preexisting vessels, also occurs in normal physiology, in response to exercise or in the process of wound healing.Why and when is angiogenesis prevalent? What controls the process? How can we intelligently control it? These are the key questions driving researchers in fields as diverse as cell biology, oncology, cardiology, neurology, biomathematics, systems biology, and biomedical engineering. As bioengineers, we approach angiogenesis as a complex, interconnected system of events occurring in sequence and in parallel, on multiple levels, triggered by a main stimulus, e.g., hypoxia.
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Affiliation(s)
- Amina A Qutub
- Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD 21205, USA.
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32
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Popławski NJ, Agero U, Gens JS, Swat M, Glazier JA, Anderson ARA. Front instabilities and invasiveness of simulated avascular tumors. Bull Math Biol 2009; 71:1189-227. [PMID: 19234746 PMCID: PMC2739624 DOI: 10.1007/s11538-009-9399-5] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2008] [Accepted: 01/15/2009] [Indexed: 10/21/2022]
Abstract
We study the interface morphology of a 2D simulation of an avascular tumor composed of identical cells growing in an homogeneous healthy tissue matrix (TM), in order to understand the origin of the morphological changes often observed during real tumor growth. We use the Glazier-Graner-Hogeweg model, which treats tumor cells as extended, deformable objects, to study the effects of two parameters: a dimensionless diffusion-limitation parameter defined as the ratio of the tumor consumption rate to the substrate transport rate, and the tumor-TM surface tension. We model TM as a nondiffusing field, neglecting the TM pressure and haptotactic repulsion acting on a real growing tumor; thus, our model is appropriate for studying tumors with highly motile cells, e.g., gliomas. We show that the diffusion-limitation parameter determines whether the growing tumor develops a smooth (noninvasive) or fingered (invasive) interface, and that the sensitivity of tumor morphology to tumor-TM surface tension increases with the size of the dimensionless diffusion-limitation parameter. For large diffusion-limitation parameters, we find a transition (missed in previous work) between dendritic structures, produced when tumor-TM surface tension is high, and seaweed-like structures, produced when tumor-TM surface tension is low. This observation leads to a direct analogy between the mathematics and dynamics of tumors and those observed in nonbiological directional solidification. Our results are also consistent with the biological observation that hypoxia promotes invasive growth of tumor cells by inducing higher levels of receptors for scatter factors that weaken cell-cell adhesion and increase cell motility. These findings suggest that tumor morphology may have value in predicting the efficiency of antiangiogenic therapy in individual patients.
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Affiliation(s)
- Nikodem J. Popławski
- Biocomplexity Institute and Department of Physics, Indiana University, Simon Hall 047, 212 South Hawthorne Drive, Bloomington, Indiana 47405-7105, USA
| | - Ubirajara Agero
- Departamento de Física, Universidade Federal de Minas Gerais, Caixa Postal 702, Belo Horizonte, CEP 31.270-901, Brazil
| | - J. Scott Gens
- Biocomplexity Institute and Department of Physics, Indiana University, Simon Hall 047, 212 South Hawthorne Drive, Bloomington, Indiana 47405-7105, USA
| | - Maciej Swat
- Biocomplexity Institute and Department of Physics, Indiana University, Simon Hall 047, 212 South Hawthorne Drive, Bloomington, Indiana 47405-7105, USA
| | - James A. Glazier
- Biocomplexity Institute and Department of Physics, Indiana University, Simon Hall 047, 212 South Hawthorne Drive, Bloomington, Indiana 47405-7105, USA
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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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34
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Individual-based and continuum models of growing cell populations: a comparison. J Math Biol 2008; 58:657-87. [PMID: 18841363 DOI: 10.1007/s00285-008-0212-0] [Citation(s) in RCA: 127] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2007] [Revised: 05/12/2008] [Indexed: 10/21/2022]
Abstract
In this paper we compare two alternative theoretical approaches for simulating the growth of cell aggregates in vitro: individual cell (agent)-based models and continuum models. We show by a quantitative analysis of both a biophysical agent-based and a continuum mechanical model that for densely packed aggregates the expansion of the cell population is dominated by cell proliferation controlled by mechanical stress. The biophysical agent-based model introduced earlier (Drasdo and Hoehme in Phys Biol 2:133-147, 2005) approximates each cell as an isotropic, homogeneous, elastic, spherical object parameterised by measurable biophysical and cell-biological quantities and has been shown by comparison to experimental findings to explain the growth patterns of dense monolayers and multicellular spheroids. Both models exhibit the same growth kinetics, with initial exponential growth of the population size and aggregate diameter followed by linear growth of the diameter and power-law growth of the cell population size. Very sparse monolayers can be explained by a very small or absent cell-cell adhesion and large random cell migration. In this case the expansion speed is not controlled by mechanical stress but by random cell migration and can be modelled by the Fisher-Kolmogorov-Petrovskii-Piskounov (FKPP) reaction-diffusion equation. The growth kinetics differs from that of densely packed aggregates in that the initial spread, as quantified by the radius of gyration, is diffusive. Since simulations of the lattice-free agent-based model in the case of very large random migration are too long to be practical, lattice-based cellular automaton (CA) models have to be used for a quantitative analysis of sparse monolayers. Analysis of these dense monolayers leads to the identification of a critical parameter of the CA model so that eventually a hierarchy of three model types (a detailed biophysical lattice-free model, a rule-based cellular automaton and a continuum approach) emerge which yield the same growth pattern for dense and sparse cell aggregates.
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Morishita Y, Iwasa Y. Growth based morphogenesis of vertebrate limb bud. Bull Math Biol 2008; 70:1957-78. [PMID: 18668295 PMCID: PMC2792361 DOI: 10.1007/s11538-008-9334-1] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2007] [Accepted: 04/29/2008] [Indexed: 11/03/2022]
Abstract
Many genes and their regulatory relationships are involved in developmental phenomena. However, by chemical information alone, we cannot fully understand changing organ morphologies through tissue growth because deformation and growth of the organ are essentially mechanical processes. Here, we develop a mathematical model to describe the change of organ morphologies through cell proliferation. Our basic idea is that the proper specification of localized volume source (e.g., cell proliferation) is able to guide organ morphogenesis, and that the specification is given by chemical gradients. We call this idea "growth-based morphogenesis." We find that this morphogenetic mechanism works if the tissue is elastic for small deformation and plastic for large deformation. To illustrate our concept, we study the development of vertebrate limb buds, in which a limb bud protrudes from a flat lateral plate and extends distally in a self-organized manner. We show how the proportion of limb bud shape depends on different parameters and also show the conditions needed for normal morphogenesis, which can explain abnormal morphology of some mutants. We believe that the ideas shown in the present paper are useful for the morphogenesis of other organs.
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Affiliation(s)
- Yoshihiro Morishita
- PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho Kawaguchi, Saitama, Japan.
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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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37
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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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Mitha F, Lucas TA, Feng F, Kepler TB, Chan C. The Multiscale Systems Immunology project: software for cell-based immunological simulation. SOURCE CODE FOR BIOLOGY AND MEDICINE 2008; 3:6. [PMID: 18442405 PMCID: PMC2426691 DOI: 10.1186/1751-0473-3-6] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/04/2007] [Accepted: 04/28/2008] [Indexed: 11/21/2022]
Abstract
Background Computer simulations are of increasing importance in modeling biological phenomena. Their purpose is to predict behavior and guide future experiments. The aim of this project is to model the early immune response to vaccination by an agent based immune response simulation that incorporates realistic biophysics and intracellular dynamics, and which is sufficiently flexible to accurately model the multi-scale nature and complexity of the immune system, while maintaining the high performance critical to scientific computing. Results The Multiscale Systems Immunology (MSI) simulation framework is an object-oriented, modular simulation framework written in C++ and Python. The software implements a modular design that allows for flexible configuration of components and initialization of parameters, thus allowing simulations to be run that model processes occurring over different temporal and spatial scales. Conclusion MSI addresses the need for a flexible and high-performing agent based model of the immune system.
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Affiliation(s)
- Faheem Mitha
- Center for Computational Immunology, Department of Biostatistics & Bioinformatics, Duke University Medical Center, 2424 Erwin Road, Hock Plaza Suite G06, Durham NC 27705, USA.
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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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Newman SA, Christley S, Glimm T, Hentschel HGE, Kazmierczak B, Zhang YT, Zhu J, Alber M. Multiscale models for vertebrate limb development. Curr Top Dev Biol 2008; 81:311-40. [PMID: 18023733 DOI: 10.1016/s0070-2153(07)81011-8] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Dynamical systems in which geometrically extended model cells produce and interact with diffusible (morphogen) and nondiffusible (extracellular matrix) chemical fields have proved very useful as models for developmental processes. The embryonic vertebrate limb is an apt system for such mathematical and computational modeling since it has been the subject of hundreds of experimental studies, and its normal and variant morphologies and spatiotemporal organization of expressed genes are well known. Because of its stereotypical proximodistally generated increase in the number of parallel skeletal elements, the limb lends itself to being modeled by Turing-type systems which are capable of producing periodic, or quasiperiodic, arrangements of spot- and stripe-like elements. This chapter describes several such models, including, (i) a system of partial differential equations in which changing cell density enters into the dynamics explicitly, (ii) a model for morphogen dynamics alone, derived from the latter system in the "morphostatic limit" where cell movement relaxes on a much slower time-scale than cell differentiation, (iii) a discrete stochastic model for the simplified pattern formation that occurs when limb cells are placed in planar culture, and (iv) several hybrid models in which continuum morphogen systems interact with cells represented as energy-minimizing mesoscopic entities. Progress in devising computational methods for handling 3D, multiscale, multimodel simulations of organogenesis is discussed, as well as for simulating reaction-diffusion dynamics in domains of irregular shape.
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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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41
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Chuai M, Weijer CJ. The mechanisms underlying primitive streak formation in the chick embryo. Curr Top Dev Biol 2008; 81:135-56. [PMID: 18023726 DOI: 10.1016/s0070-2153(07)81004-0] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
Formation of the primitive streak is one of the key events in the early development of amniote embryos. The streak is the site where during gastrulation the mesendoderm cells ingress to take up their correct topographical positions in the embryo. The process of streak formation can be conveniently observed in the chick embryo, where the streak forms as an accumulation of cells in the epiblast in the posterior pole of the embryo and extends subsequently in anterior direction until it covers 80% of the epiblast. A prerequisite for streak formation is the differentiation of mesoderm, which is induced in the epiblast at the interface between the posterior Area Opaca and Area Pellucida in a sickle shaped domain overlying Koller's sickle. Current views on the molecular mechanisms of mesoderm induction by inducing signals from the Area Opaca and inhibitory signals from the hypoblast are briefly discussed. During streak formation the sickle of mesoderm cells transforms into an elongated structure in the central midline of the embryo. We discuss possible cellular mechanisms underlying this process, such as oriented cell division, cell-cell intercalation, chemotactic cell movement in response to attractive and repulsive signals and a combination of chemotaxis and contact following. We review current experimental evidence in favor and against these different hypotheses and outline some the outstanding questions. Since many of the interactions between cells signaling and moving are dynamic and nonlinear in nature they will require detailed modeling and computer simulations to be understood in detail.
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Affiliation(s)
- Manli Chuai
- Division of Cell and Developmental Biology, Wellcome Trust Biocentre, College of Life Sciences, University of Dundee, Dundee DD1 5EH, United Kingdom
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42
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Alber M, Glimm T, Hentschel HGE, Kazmierczak B, Zhang YT, Zhu J, Newman SA. The Morphostatic Limit for a Model of Skeletal Pattern Formation in the Vertebrate Limb. Bull Math Biol 2007; 70:460-83. [DOI: 10.1007/s11538-007-9264-3] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2006] [Accepted: 08/08/2007] [Indexed: 10/22/2022]
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43
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Steinberg MS. Differential adhesion in morphogenesis: a modern view. Curr Opin Genet Dev 2007; 17:281-6. [PMID: 17624758 DOI: 10.1016/j.gde.2007.05.002] [Citation(s) in RCA: 232] [Impact Index Per Article: 13.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2007] [Revised: 05/01/2007] [Accepted: 05/02/2007] [Indexed: 12/27/2022]
Abstract
The spreading of one embryonic tissue over another, the sorting out of their cells when intermixed and the formation of intertissue boundaries respected by the motile border cells all have counterparts in the behavior of immiscible liquids. The 'differential adhesion hypothesis' (DAH) explains these liquid-like tissue behaviors as consequences of the generation of tissue surface and interfacial tensions arising from the adhesion energies between motile cells. The experimental verification of the DAH, the recent computational models simulating adhesion-mediated morphogenesis, and the evidence concerning the role of differential adhesion in a number of morphodynamic events, including teleost epiboly, the specification of boundaries between rhombomeres in the developing vertebrate hindbrain, epithelial-mesenchymal transitions in embryos, and malignant invasion are reviewed here.
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Affiliation(s)
- Malcolm S Steinberg
- Department of Molecular Biology, Princeton University, Princeton, NJ 08544, United States.
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44
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Cickovski T, Aras K, Alber MS, Izaguirre JA, Swat M, Glazier JA, Merks RMH, Glimm T, Hentschel HGE, Newman SA. From Genes to Organisms Via the Cell A Problem-Solving Environment for Multicellular Development. Comput Sci Eng 2007; 9:50-60. [PMID: 19526065 PMCID: PMC2695324 DOI: 10.1109/mcse.2007.74] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
To gain performance, developers often build scientific applications in procedural languages, such as C or Fortran, which unfortunately reduces flexibility. To address this imbalance, the authors present CompuCell3D, a multitiered, flexible, and scalable problem-solving environment for morphogenesis simulations that's written in C++ using object-oriented design patterns.
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45
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46
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Schaller G, Meyer-Hermann M. A modelling approach towards epidermal homoeostasis control. J Theor Biol 2007; 247:554-73. [PMID: 17466340 DOI: 10.1016/j.jtbi.2007.03.023] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2006] [Revised: 03/16/2007] [Accepted: 03/17/2007] [Indexed: 11/28/2022]
Abstract
In order to grasp the features arising from cellular discreteness and individuality, in large parts of cell tissue modelling agent-based models are favoured. The subclass of off-lattice models allows for a physical motivation of the intercellular interaction rules. We apply an improved version of a previously introduced off-lattice agent-based model to the steady-state flow equilibrium of skin. The dynamics of cells is determined by conservative and drag forces, supplemented with delta-correlated random forces. Cellular adjacency is detected by a weighted Delaunay triangulation. The cell cycle time of keratinocytes is controlled by a diffusible substance provided by the dermis. Its concentration is calculated from a diffusion equation with time-dependent boundary conditions and varying diffusion coefficients. The dynamics of a nutrient is also taken into account by a reaction-diffusion equation. It turns out that the analysed control mechanism suffices to explain several characteristics of epidermal homoeostasis formation. In addition, we examine the question of how in silico melanoma with decreased basal adhesion manage to persist within the steady-state flow equilibrium of the skin. Interestingly, even for melanocyte cell cycle times being substantially shorter than for keratinocytes, tiny stochastic effects can lead to completely different outcomes. The results demonstrate that the understanding of initial states of tumour growth can profit significantly from the application of off-lattice agent-based models in computer simulations.
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Affiliation(s)
- Gernot Schaller
- Frankfurt Institute for Advanced Studies (FIAS), Johann Wolfgang Goethe-Universität, Max von Laue-Strasse 1, D-60438 Frankfurt am Main, Germany.
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47
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Popławski NJ, Swat M, Gens JS, Glazier JA. Adhesion between cells, diffusion of growth factors, and elasticity of the AER produce the paddle shape of the chick limb. PHYSICA A 2007; 373:521-532. [PMID: 18167520 PMCID: PMC2168394 DOI: 10.1016/j.physa.2006.05.028] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
A central question in developmental biology is how cells interact to organize into tissues? In this paper, we study the role of mesenchyme-ectoderm interaction in the growing chick limb bud using Glazier and Graner's cellular Potts model, a grid-based stochastic framework designed to simulate cell interactions and movement. We simulate cellular mechanisms including cell adhesion, growth, and division and diffusion of morphogens, to show that differential adhesion between the cells, diffusion of growth factors through the extracellular matrix, and the elastic properties of the apical ectodermal ridge together can produce the proper shape of the limb bud.
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Affiliation(s)
- Nikodem J Popławski
- Biocomplexity Institute and Department of Physics, Indiana University, 727 East Third Street, Swain Hall West 117, Bloomington, IN 47405-7105, USA
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48
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Chaturvedi R, Huang C, Kazmierczak B, Schneider T, Izaguirre J, Glimm T, Hentschel H, Glazier J, Newman S, Alber M. On multiscale approaches to three-dimensional modelling of morphogenesis. J R Soc Interface 2006; 2:237-53. [PMID: 16849182 PMCID: PMC1629079 DOI: 10.1098/rsif.2005.0033] [Citation(s) in RCA: 101] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
In this paper we present the foundation of a unified, object-oriented, three-dimensional biomodelling environment, which allows us to integrate multiple submodels at scales from subcellular to those of tissues and organs. Our current implementation combines a modified discrete model from statistical mechanics, the Cellular Potts Model, with a continuum reaction-diffusion model and a state automaton with well-defined conditions for cell differentiation transitions to model genetic regulation. This environment allows us to rapidly and compactly create computational models of a class of complex-developmental phenomena. To illustrate model development, we simulate a simplified version of the formation of the skeletal pattern in a growing embryonic vertebrate limb.
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Affiliation(s)
- R Chaturvedi
- Department of Mathematics, Department of Physics and Center for the Study of Biocomplexity, University of Notre DameNotre Dame, IN 46556-5670, USA
| | - C Huang
- Department of Computer Science and Engineering, University of Notre DameNotre Dame, IN 46556-5670, USA
| | - B Kazmierczak
- Department of Mathematics, Department of Physics and Center for the Study of Biocomplexity, University of Notre DameNotre Dame, IN 46556-5670, USA
| | - T Schneider
- Department of Computer Science and Engineering, University of Notre DameNotre Dame, IN 46556-5670, USA
| | - J.A Izaguirre
- Department of Computer Science and Engineering, University of Notre DameNotre Dame, IN 46556-5670, USA
| | - T Glimm
- Department of Physics, Emory UniversityAtlanta, GA 30322, USA
| | - H.G.E Hentschel
- Department of Physics, Emory UniversityAtlanta, GA 30322, USA
| | - J.A Glazier
- Biocomplexity Institute and Department of Physics, Indiana University727 East 3rd Street, Swain Hall West 159, Bloomington, IN 47405-7105, USA
| | - S.A Newman
- Department of Cell Biology & Anatomy, New York Medical CollegeBasic Science Building, Valhalla, NY 10595, USA
- Authors for correspondence. () ()
| | - M.S Alber
- Department of Mathematics, Department of Physics and Center for the Study of Biocomplexity, University of Notre DameNotre Dame, IN 46556-5670, USA
- Authors for correspondence. () ()
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49
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Merks R, Hoekstra A, Kaandorp J, Sloot P, Hogeweg P. Problem-solving environments for biological morphogenesis. Comput Sci Eng 2006. [DOI: 10.1109/mcse.2006.11] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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