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Nagayama M, Monobe H, Sakakibara K, Nakamura KI, Kobayashi Y, Kitahata H. On the reaction-diffusion type modelling of the self-propelled object motion. Sci Rep 2023; 13:12633. [PMID: 37537247 PMCID: PMC10400585 DOI: 10.1038/s41598-023-39395-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 07/25/2023] [Indexed: 08/05/2023] Open
Abstract
In this study, we propose a mathematical model of self-propelled objects based on the Allen-Cahn type phase-field equation. We combine it with the equation for the concentration of surfactant used in previous studies to construct a model that can handle self-propelled object motion with shape change. A distinctive feature of our mathematical model is that it can represent both deformable self-propelled objects, such as droplets, and solid objects, such as camphor disks, by controlling a single parameter. Furthermore, we demonstrate that, by taking the singular limit, this phase-field based model can be reduced to a free boundary model, which is equivalent to the [Formula: see text]-gradient flow model of self-propelled objects derived by the variational principle from the interfacial energy, which gives a physical interpretation to the phase-field model.
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Affiliation(s)
- Masaharu Nagayama
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Hokkaido, 060-0812, Japan.
| | - Harunori Monobe
- Department of Mathematics, Graduate School of Science, Osaka Metropolitan University, Osaka, 599-8531, Japan
| | - Koya Sakakibara
- Institute of Science and Engineering, Kanazawa University, Ishikawa, 920-1192, Japan
- RIKEN iTHEMS, Saitama, 351-0198, Japan
| | - Ken-Ichi Nakamura
- Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Tokyo, 164-8525, Japan
| | - Yasuaki Kobayashi
- Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Hokkaido, 060-0812, Japan
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Okuda S, Hiraiwa T. Modelling contractile ring formation and division to daughter cells for simulating proliferative multicellular dynamics. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:56. [PMID: 37466721 DOI: 10.1140/epje/s10189-023-00315-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Accepted: 06/24/2023] [Indexed: 07/20/2023]
Abstract
Cell proliferation is a fundamental process underlying embryogenesis, homeostasis, wound healing, and cancer. The process involves multiple events during each cell cycle, such as cell growth, contractile ring formation, and division to daughter cells, which affect the surrounding cell population geometrically and mechanically. However, existing methods do not comprehensively describe the dynamics of multicellular structures involving cell proliferation at a subcellular resolution. In this study, we present a novel model for proliferative multicellular dynamics at the subcellular level by building upon the nonconservative fluid membrane (NCF) model that we developed in earlier research. The NCF model utilizes a dynamically-rearranging closed triangular mesh to depict the shape of each cell, enabling us to analyze cell dynamics over extended periods beyond each cell cycle, during which cell surface components undergo dynamic turnover. The proposed model represents the process of cell proliferation by incorporating cell volume growth and contractile ring formation through an energy function and topologically dividing each cell at the cleavage furrow formed by the ring. Numerical simulations demonstrated that the model recapitulated the process of cell proliferation at subcellular resolution, including cell volume growth, cleavage furrow formation, and division to daughter cells. Further analyses suggested that the orientation of actomyosin stress in the contractile ring plays a crucial role in the cleavage furrow formation, i.e., circumferential orientation can form a cleavage furrow but isotropic orientation cannot. Furthermore, the model replicated tissue-scale multicellular dynamics, where the successive proliferation of adhesive cells led to the formation of a cell sheet and stratification on the substrate. Overall, the proposed model provides a basis for analyzing proliferative multicellular dynamics at subcellular resolution.
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Affiliation(s)
- Satoru Okuda
- Nano Life Science Institute, Kakuma-Machi, Kanazawa, Japan.
| | - Tetsuya Hiraiwa
- Mechanobiology Institute, National University of Singapore, Singapore, Singapore
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Okuda S, Hiraiwa T. Long-term adherent cell dynamics emerging from energetic and frictional interactions at the interface. Phys Rev E 2023; 107:034406. [PMID: 37073061 DOI: 10.1103/physreve.107.034406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2022] [Accepted: 02/21/2023] [Indexed: 04/20/2023]
Abstract
Cell adhesion plays an important role in a wide range of biological situations, including embryonic development, cancer invasion, and wound healing. Although several computational models describing adhesion dynamics have been proposed, models applicable to long-term, large-length-scale cell dynamics are lacking. In this study we investigated possible states of long-term adherent cell dynamics in three-dimensional space by constructing a continuum model of interfacial interactions between adhesive surfaces. In this model a pseudointerface is supposed between each pair of triangular elements that discretize cell surfaces. By introducing a distance between each pair of elements, the physical properties of the interface are given by interfacial energy and friction. The proposed model was implemented into the model of a nonconservative fluid cell membrane where the cell membrane dynamically flows with turnover. Using the implemented model, numerical simulations of adherent cell dynamics on a substrate under flow were performed. The simulations not only reproduced the previously reported dynamics of adherent cells, such as detachment, rolling, and fixation on the substrate, but also discovered other dynamic states, including cell slipping and membrane flow patterns, corresponding to behaviors that occur on much longer timescales than the dissociation of adhesion molecules. These results illustrate the variety of long-term adherent cell dynamics, which are more diverse than the short-term ones. The proposed model can be extended to arbitrarily shaped membranes, thus being useful for the mechanical analysis of a wide range of long-term cell dynamics where adhesion is essential.
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Affiliation(s)
- Satoru Okuda
- Nano Life Science Institute, Kakuma-machi, Kanazawa 920-1192, Japan
| | - Tetsuya Hiraiwa
- Mechanobiology Institute, National University of Singapore, 5A Engineering Drive 117411, Singapore
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Kuang X, Guan G, Tang C, Zhang L. MorphoSim: an efficient and scalable phase-field framework for accurately simulating multicellular morphologies. NPJ Syst Biol Appl 2023; 9:6. [PMID: 36806172 PMCID: PMC9938209 DOI: 10.1038/s41540-023-00265-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2022] [Accepted: 01/04/2023] [Indexed: 02/19/2023] Open
Abstract
The phase field model can accurately simulate the evolution of microstructures with complex morphologies, and it has been widely used for cell modeling in the last two decades. However, compared to other cellular models such as the coarse-grained model and the vertex model, its high computational cost caused by three-dimensional spatial discretization hampered its application and scalability, especially for multicellular organisms. Recently, we built a phase field model coupled with in vivo imaging data to accurately reconstruct the embryonic morphogenesis of Caenorhabditis elegans from 1- to 8-cell stages. In this work, we propose an improved phase field model by using the stabilized numerical scheme and modified volume constriction. Then we present a scalable phase-field framework, MorphoSim, which is 100 times more efficient than the previous one and can simulate over 100 mechanically interacting cells. Finally, we demonstrate how MorphoSim can be successfully applied to reproduce the assembly, self-repairing, and dissociation of a synthetic artificial multicellular system - the synNotch system.
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Affiliation(s)
- Xiangyu Kuang
- grid.11135.370000 0001 2256 9319Center for Quantitative Biology, Peking University, Beijing, 100871 China
| | - Guoye Guan
- grid.11135.370000 0001 2256 9319Center for Quantitative Biology, Peking University, Beijing, 100871 China
| | - Chao Tang
- Center for Quantitative Biology, Peking University, Beijing, 100871, China. .,Peking-Tsinghua Center for Life Sciences, Peking University, Beijing, 100871, China. .,School of Physics, Peking University, Beijing, 100871, China.
| | - Lei Zhang
- Center for Quantitative Biology, Peking University, Beijing, 100871, China. .,Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China. .,Center for Machine Learning Research, Peking University, Beijing, 100871, China.
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5
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A mathematical model of fibrinogen-mediated erythrocyte-erythrocyte adhesion. Commun Biol 2023; 6:192. [PMID: 36801914 PMCID: PMC9938206 DOI: 10.1038/s42003-023-04560-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2022] [Accepted: 02/06/2023] [Indexed: 02/19/2023] Open
Abstract
Erythrocytes are deformable cells that undergo progressive biophysical and biochemical changes affecting the normal blood flow. Fibrinogen, one of the most abundant plasma proteins, is a primary determinant for changes in haemorheological properties, and a major independent risk factor for cardiovascular diseases. In this study, the adhesion between human erythrocytes is measured by atomic force microscopy (AFM) and its effect observed by micropipette aspiration technique, in the absence and presence of fibrinogen. These experimental data are then used in the development of a mathematical model to examine the biomedical relevant interaction between two erythrocytes. Our designed mathematical model is able to explore the erythrocyte-erythrocyte adhesion forces and changes in erythrocyte morphology. AFM erythrocyte-erythrocyte adhesion data show that the work and detachment force necessary to overcome the adhesion between two erythrocytes increase in the presence of fibrinogen. The changes in erythrocyte morphology, the strong cell-cell adhesion and the slow separation of the two cells are successfully followed in the mathematical simulation. Erythrocyte-erythrocyte adhesion forces and energies are quantified and matched with experimental data. The changes observed on erythrocyte-erythrocyte interactions may give important insights about the pathophysiological relevance of fibrinogen and erythrocyte aggregation in hindering microcirculatory blood flow.
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Fuji K, Tanida S, Sano M, Nonomura M, Riveline D, Honda H, Hiraiwa T. Computational approaches for simulating luminogenesis. Semin Cell Dev Biol 2022; 131:173-185. [PMID: 35773151 DOI: 10.1016/j.semcdb.2022.05.021] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2022] [Revised: 05/24/2022] [Accepted: 05/24/2022] [Indexed: 12/14/2022]
Abstract
Lumens, liquid-filled cavities surrounded by polarized tissue cells, are elementary units involved in the morphogenesis of organs. Theoretical modeling and computations, which can integrate various factors involved in biophysics of morphogenesis of cell assembly and lumens, may play significant roles to elucidate the mechanisms in formation of such complex tissue with lumens. However, up to present, it has not been documented well what computational approaches or frameworks can be applied for this purpose and how we can choose the appropriate approach for each problem. In this review, we report some typical lumen morphologies and basic mechanisms for the development of lumens, focusing on three keywords - mechanics, hydraulics and geometry - while outlining pros and cons of the current main computational strategies. We also describe brief guidance of readouts, i.e., what we should measure in experiments to make the comparison with the model's assumptions and predictions.
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Affiliation(s)
- Kana Fuji
- Universal Biology Institute, Graduate School of Science, the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Sakurako Tanida
- Research Center for Advanced Science and Technology, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo, Japan
| | - Masaki Sano
- Institute of Natural Sciences, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Makiko Nonomura
- Department of Mathematical Information Engineering, College of Industrial Technology, Nihon University, 1-2-1 Izumicho, Narashino-shi, Chiba 275-8575, Japan
| | - Daniel Riveline
- Laboratory of Cell Physics IGBMC, CNRS, INSERM and Université de Strasbourg, Strasbourg, France
| | - Hisao Honda
- Division of Cell Physiology, Department of Physiology and Cell Biology, Graduate School of Medicine Kobe University, Kobe, Hyogo, Japan
| | - Tetsuya Hiraiwa
- Mechanobiology Institute, Singapore, National University of Singapore, 117411, Singapore.
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Numerical Study on Dynamics of Blood Cell Migration and Deformation in Atherosclerotic Vessels. MATHEMATICS 2022. [DOI: 10.3390/math10122022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
A phase field model is used to study the effect of atherosclerotic plaque on hemodynamics. The migration of cells in blood flows is described by a set of multiple phase field equations, which incorporate elastic energies and the interacting effects of cells. Several simulations are carried out to reveal the influences of initial velocities of blood cells, cellular elasticity and block rates of hemodynamic vessels. The results show that the cell deformation increases with the growth of the initial active velocity and block rate but with the decrease of the cellular elasticity. The atherosclerotic plaque not only affects the deformation and migration of cells but also can promote the variation in hemodynamic properties. The atherosclerotic plaque causes a burst in cell velocity, and the greater the block rate and cellular elasticity, the more dramatic the variation of instantaneous velocity. The present work demonstrates that the phase field method could be extended to reveal formation atherosclerosis at the microscopic level from the perspective of hemodynamics.
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Seirin-Lee S, Yamamoto K, Kimura A. The extra-embryonic space and the local contour are crucial geometric constraints regulating cell arrangement. Development 2022; 149:275369. [PMID: 35552395 PMCID: PMC9148568 DOI: 10.1242/dev.200401] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Accepted: 03/23/2022] [Indexed: 12/29/2022]
Abstract
In multicellular systems, cells communicate with adjacent cells to determine their positions and fates, an arrangement important for cellular development. Orientation of cell division, cell-cell interactions (i.e. attraction and repulsion) and geometric constraints are three major factors that define cell arrangement. In particular, geometric constraints are difficult to reveal in experiments, and the contribution of the local contour of the boundary has remained elusive. In this study, we developed a multicellular morphology model based on the phase-field method so that precise geometric constraints can be incorporated. Our application of the model to nematode embryos predicted that the amount of extra-embryonic space, the empty space within the eggshell that is not occupied by embryonic cells, affects cell arrangement in a manner dependent on the local contour and other factors. The prediction was validated experimentally by increasing the extra-embryonic space in the Caenorhabditis elegans embryo. Overall, our analyses characterized the roles of geometrical contributors, specifically the amount of extra-embryonic space and the local contour, on cell arrangements. These factors should be considered for multicellular systems. Summary: The local contour and the extra-embryonic space, the empty space within the eggshell not occupied by embryonic cells, are important geometric constraints in cell arrangement of nematode embryos.
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Affiliation(s)
- Sungrim Seirin-Lee
- Institute for the Advanced Study of Human Biology (ASHBi), Kyoto University Institute for Advanced Study, Kyoto University, Kyoto 606-8315, Japan.,JST CREST, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
| | - Kazunori Yamamoto
- Department of Applied Bioscience, Faculty of Applied Bioscience, Kanagawa Institute of Technology, Atsugi 243-0292, Japan
| | - Akatsuki Kimura
- Cell Architecture Laboratory, Department of Chromosome Science, National Institute of Genetics, Mishima 411-8540, Japan.,Department of Genetics, The Graduate University for Advanced Studies, Sokendai, Mishima 411-8540, Japan
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Laghmach R, Di Pierro M, Potoyan D. A Liquid State Perspective on Dynamics of Chromatin Compartments. Front Mol Biosci 2022; 8:781981. [PMID: 35096966 PMCID: PMC8793688 DOI: 10.3389/fmolb.2021.781981] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2021] [Accepted: 12/22/2021] [Indexed: 12/11/2022] Open
Abstract
The interior of the eukaryotic cell nucleus has a crowded and heterogeneous environment packed with chromatin polymers, regulatory proteins, and RNA molecules. Chromatin polymer, assisted by epigenetic modifications, protein and RNA binders, forms multi-scale compartments which help regulate genes in response to cellular signals. Furthermore, chromatin compartments are dynamic and tend to evolve in size and composition in ways that are not fully understood. The latest super-resolution imaging experiments have revealed a much more dynamic and stochastic nature of chromatin compartments than was appreciated before. An emerging mechanism explaining chromatin compartmentalization dynamics is the phase separation of protein and nucleic acids into membraneless liquid condensates. Consequently, concepts and ideas from soft matter and polymer systems have been rapidly entering the lexicon of cell biology. In this respect, the role of computational models is crucial for establishing a rigorous and quantitative foundation for the new concepts and disentangling the complex interplay of forces that contribute to the emergent patterns of chromatin dynamics and organization. Several multi-scale models have emerged to address various aspects of chromatin dynamics, ranging from equilibrium polymer simulations, hybrid non-equilibrium simulations coupling protein binding and chromatin folding, and mesoscopic field-theoretic models. Here, we review these emerging theoretical paradigms and computational models with a particular focus on chromatin’s phase separation and liquid-like properties as a basis for nuclear organization and dynamics.
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Affiliation(s)
- Rabia Laghmach
- Department of Chemistry, Iowa State University, Ames, IA, United States
| | - Michele Di Pierro
- Department of Physics, Northeastern University, Boston, MA, United States
| | - Davit Potoyan
- Department of Chemistry, Iowa State University, Ames, IA, United States
- *Correspondence: Davit Potoyan,
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10
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Kuang X, Guan G, Wong MK, Chan LY, Zhao Z, Tang C, Zhang L. Computable early Caenorhabditis elegans embryo with a phase field model. PLoS Comput Biol 2022; 18:e1009755. [PMID: 35030161 PMCID: PMC8794267 DOI: 10.1371/journal.pcbi.1009755] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2021] [Revised: 01/27/2022] [Accepted: 12/14/2021] [Indexed: 01/11/2023] Open
Abstract
Morphogenesis is a precise and robust dynamic process during metazoan embryogenesis, consisting of both cell proliferation and cell migration. Despite the fact that much is known about specific regulations at molecular level, how cell proliferation and migration together drive the morphogenesis at cellular and organismic levels is not well understood. Using Caenorhabditis elegans as the model animal, we present a phase field model to compute early embryonic morphogenesis within a confined eggshell. With physical information about cell division obtained from three-dimensional time-lapse cellular imaging experiments, the model can precisely reproduce the early morphogenesis process as seen in vivo, including time evolution of location and morphology of each cell. Furthermore, the model can be used to reveal key cell-cell attractions critical to the development of C. elegans embryo. Our work demonstrates how genetic programming and physical forces collaborate to drive morphogenesis and provides a predictive model to decipher the underlying mechanism. Embryonic development is a precise process involving cell division, cell-cell interaction, and cell migration. During the process, how each cell reaches its supposed location and be in contact with the right neighbors, and what roles genetic factors and physical forces play are important and fascinating questions. Using the worm Caenorhabditis elegans as a model system, we build a phase field model to simulate early morphogenesis. With a few physical inputs, the model can precisely reproduce the early morphological development of the worm. Such an accurate simulator can not only teach us how physical forces work together with genetic factors to shape up the complex process of development, but also make predictions, such as key cell-cell attractions critical in the process.
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Affiliation(s)
- Xiangyu Kuang
- Center for Quantitative Biology, Peking University, Beijing, China
| | - Guoye Guan
- Center for Quantitative Biology, Peking University, Beijing, China
| | - Ming-Kin Wong
- Department of Biology, Hong Kong Baptist University, Hong Kong, China
| | - Lu-Yan Chan
- Department of Biology, Hong Kong Baptist University, Hong Kong, China
| | - Zhongying Zhao
- Department of Biology, Hong Kong Baptist University, Hong Kong, China
- State Key Laboratory of Environmental and Biological Analysis, Hong Kong Baptist University, Hong Kong, China
| | - Chao Tang
- Center for Quantitative Biology, Peking University, Beijing, China
- Peking-Tsinghua Center for Life Sciences, Peking University, Beijing, China
- School of Physics, Peking University, Beijing, China
- * E-mail: (CT); (LZ)
| | - Lei Zhang
- Center for Quantitative Biology, Peking University, Beijing, China
- Beijing International Center for Mathematical Research, Peking University, Beijing, China
- * E-mail: (CT); (LZ)
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Moreira-Soares M, Cunha SP, Bordin JR, Travasso RDM. Adhesion modulates cell morphology and migration within dense fibrous networks. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:314001. [PMID: 32378515 DOI: 10.1088/1361-648x/ab7c17] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2019] [Accepted: 03/03/2020] [Indexed: 06/11/2023]
Abstract
One of the most fundamental abilities required for the sustainability of complex life forms is active cell migration, since it is essential in diverse processes from morphogenesis to leukocyte chemotaxis in immune response. The movement of a cell is the result of intricate mechanisms, that involve the coordination between mechanical forces, biochemical regulatory pathways and environmental cues. In particular, epithelial cancer cells have to employ mechanical strategies in order to migrate through the tissue's basement membrane and infiltrate the bloodstream during the invasion stage of metastasis. In this work we explore how mechanical interactions such as spatial restriction and adhesion affect migration of a self-propelled droplet in dense fibrous media. We have performed a systematic analysis using a phase-field model and we propose a novel approach to simulate cell migration with dissipative particle dynamics modelling. With this purpose we have measured in our simulation the cell's velocity and quantified its morphology as a function of the fibre density and of its adhesiveness to the matrix fibres. Furthermore, we have compared our results to a previousin vitromigration assay of fibrosarcoma cells in fibrous matrices. The results show good agreement between the two methodologies and experiments in the literature, which indicates that these minimalist descriptions are able to capture the main features of the system. Our results indicate that adhesiveness is critical for cell migration, by modulating cell morphology in crowded environments and by enhancing cell velocity. In addition, our analysis suggests that matrix metalloproteinases (MMPs) play an important role as adhesiveness modulators. We propose that new assays should be carried out to address the role of adhesion and the effect of different MMPs in cell migration under confined conditions.
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Affiliation(s)
| | - Susana P Cunha
- CQC, Department of Chemistry, University of Coimbra, Rua Larga, 3004-535 Coimbra, Portugal
| | - José Rafael Bordin
- Department of Physics, Institute of Physics and Mathematics, Federal University of Pelotas, Rua dos Ipês, Capão do Leão, RS, 96050-500, Brazil
| | - Rui D M Travasso
- CFisUC, Department of Physics, University of Coimbra, Rua Larga, 3004-516 Coimbra, Portugal
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12
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Laghmach R, Di Pierro M, Potoyan DA. Mesoscale Liquid Model of Chromatin Recapitulates Nuclear Order of Eukaryotes. Biophys J 2019; 118:2130-2140. [PMID: 31623887 DOI: 10.1016/j.bpj.2019.09.013] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2019] [Revised: 09/04/2019] [Accepted: 09/11/2019] [Indexed: 02/01/2023] Open
Abstract
The nuclear envelope segregates the genome of Eukaryota from the cytoplasm. Within the nucleus, chromatin is further compartmentalized into architectures that change throughout the lifetime of the cell. Epigenetic patterns along the chromatin polymer strongly correlate with chromatin compartmentalization and, accordingly, also change during the cell life cycle and at differentiation. Recently, it has been suggested that subnuclear chromatin compartmentalization might result from a process of liquid-liquid phase separation orchestrated by the epigenetic marking and operated by proteins that bind to chromatin. Here, we translate these observations into a diffuse interface model of chromatin, which we named the mesoscale liquid model of nucleus. Using this streamlined continuum model of the genome, we study the large-scale rearrangements of chromatin that happen at different stages of the growth and senescence of the cell and during nuclear inversion events. In particular, we investigate the role of droplet diffusion, fluctuations, and heterochromatin-lamina interactions during nuclear remodeling. Our results indicate that the physical process of liquid-liquid phase separation, together with surface effects, is sufficient to recapitulate much of the large-scale morphology and dynamics of chromatin along the life cycle of cells.
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Affiliation(s)
- Rabia Laghmach
- Department of Chemistry, Iowa State University, Ames, Iowa
| | - Michele Di Pierro
- Center for Theoretical Biological Physics, Rice University, Houston, Texas
| | - Davit A Potoyan
- Department of Chemistry, Iowa State University, Ames, Iowa; Department of Biochemistry and Molecular Biology, Iowa State University, Ames, Iowa; Bioinformatics and Computational Biology Program, Iowa State University, Ames, Iowa.
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