A new application of the phasefield method for un

Authors: S Seirin Lee S Tashiro A Awazu R Kobayashi

Publish Date: 2016/05/30

Volume: 74, Issue: 1-2, Pages: 333-354

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Abstract

Specific features of nuclear architecture are important for the functional organization of the nucleus and chromatin consists of two forms heterochromatin and euchromatin Conventional nuclear architecture is observed when heterochromatin is enriched at nuclear periphery and it represents the primary structure in the majority of eukaryotic cells including the rod cells of diurnal mammals In contrast to this inverted nuclear architecture is observed when the heterochromatin is distributed at the center of the nucleus which occurs in the rod cells of nocturnal mammals The inverted architecture found in the rod cells of the adult mouse is formed through the reorganization of conventional architecture during terminal differentiation Although a previous experimental approach has demonstrated the relationship between these two nuclear architecture types at the molecular level the mechanisms underlying longrange reorganization processes remain unknown The details of nuclear structures and their spatial and temporal dynamics remain to be elucidated Therefore a comprehensive approach using mathematical modeling is required in order to address these questions Here we propose a new mathematical approach to the understanding of nuclear architecture dynamics using the phasefield method We successfully recreated the process of nuclear architecture reorganization and showed that it is robustly induced by physical features independent of a specific genotype Our study demonstrates the potential of phasefield method application in the life science fieldsIn eukaryotes the genome where the genetic information is stored in the DNA molecule shows a hierarchical structure and this information is integrated into the chromosome of a cell nucleus Although DNA is a long molecule that can be compacted forming a highly condensed chromatin structure in the nucleus the transcription of DNA represents a dynamic process Studies showed that DNA represents a part of an ordered folded structure in the cell nucleus and that the formation of this structure is most likely tightly regulated Chromatin fibers are formed when DNA molecule is wrapped around the histones and transcriptionally inactivated and condensed DNA region is known as heterochromatin while the more transcriptionally active and less condensed region is called euchromatin Chromatin fibers consist of alternating euchromatin and heterochromatin structures that can interact with each other depending on the alterations in the cellular processes In the interphase nuclei the chromatin fibers of each chromosome are highly compartmentalized and none of the domain structures interact and this is called a chromosome territory Chubb et al 2002 Cremer and Cremer 2010The organization of the rod cell nucleus during postnatal development P0–P28 and in a 9monthold mouse 9 m a Left panel FISH using probes for L1rich heterochromatin red euchromatin green and chromocenters blue Right panel euchromatin distribution of histone H3K4me3 histone modifications green nucleoli blue arrowheads and nuclear counterstaining red b Reorganization of the nuclear architecture The nuclei of mouse retinas dissected at birth P0 6 14 21 and 28 days after birth P6 P14 P21 P28 respectively and at 9 months 9 m When a mouse is born the rod cell has conventional architecture However a few days later the heterochromatin domains close to nuclear envelope move and fuse with neighboring heterochromatin domains which consequently leads to the inverted architecture with a single cluster of heterochromatin domain c Distribution of chromosome subregions in the nuclei with the conventional left and inverted right architecture euchromatin green white heterochromatin red gray chromocenters blue nucleolus yellow The chromosomes in the nucleus with the conventional architecture relocate during the reorganization and form the inverted architecture The diagrams in a–c and the descriptions are adapted from Solovei et al 2009 colour figure onlineSolovei et al 2009 demonstrated that these different types of nuclear architecture are associated with different mammalian lifestyles eg diurnal versus nocturnal and are determined by the epigenetic changes For example the nuclear architecture of rod photoreceptor cells in the retina of diurnal mammals is typically conventional while that in nocturnal animals is typically inverted Solovei et al 2013 The inverted nuclear architecture of the mouse retina rod cells is determined by the transformation of the conventional architecture as shown in Fig 1b This process is accompanied by the relocation of chromosomes from their position observed in the conventional nuclear organization like slices of pizza and the creation of a single heterochromatin cluster heterocluster in the inverted nuclear architecture as shown by 2D imaging Fig 1c At the time of birth the nuclei of the rod cells in mice exhibit conventional nuclear architecture However the distribution of chromosomes and heterochromatic clusters changes slowly and the inverted architecture is formed during terminal differentiation The relationships between the different types of nuclear architecture and nuclear functions are not clear However a previous study suggested that different types of nuclear architecture may result in the different rates of light collection efficiency and that the inverted architecture is more suitable for this process in comparison with the conventional nuclear architecture Solovei et al 2009Detailed analyses of this reorganization process showed that the conventional architecture is reorganized through the transformation of the nuclear shape from elliptical to circular which is accompanied by a decrease in nuclear volume by approximately 40  Fig 1b Solovei et al 2009 Furthermore structural differences between the conventional and inverted architectures can be attributed to the activity of the nuclear envelope proteins lamin B receptor LBR and lamin A Lmna which sequentially tether peripheral heterochromatin Solovei et al 2013 The conventional architecture is associated with LBR or lamin A/C expression while the expression of these molecules was not found in the cells with the inverted architecture However specific mechanisms mediating these events are still poorly understood and the factors involved in the association between nuclear architecture changes and other events such as the alterations in nuclear size or shape are unknown It remains unclear how the same inverted structure is consistently created in the nuclei of rod cellsSome theoretical studies have described the spatial organization of nuclear chromatin Finan et al 2011 Heermann 2011 Awazu 2014 Ganai et al 2014 The approach used in these studies is based on a model in which chromatin is represented as loops or strings and the heterochromatin and euchromatin states are described by the differences in entropic forces or mobility at the protein structure level These studies showed that chromatin fibers can create chromosome territories and longrange structures composed of heterochromatin and euchromatin domains within the nucleus However these studies were not able to explain the specific mechanisms responsible for the formation of the conventional and inverted types of architecture String models Finan et al 2011 Awazu 2014 Ganai et al 2014 have shown that the heterochromatic domain is distributed at the nuclear periphery and not at the center of the nucleus when no relationship between the nuclear envelope and heterochromatin is assumed which is in contrast to the previously observed inverted architecture Solovei et al 2009 2013 This indicates that the string model may not be appropriate for the determination of chromatin structure details using macroscopic models Further macroscopic descriptions should be included in the model in order to integrate the longrange dynamics of chromatin and its molecular characteristics and facilitate the elucidation of the key mechanisms involved in the reorganization processTherefore we chose an approach that involves a higher macroscopic description by capturing chromatin as a domain and subsequently describes the overall dynamics of chromatin based on the variations in the domain structures since the previously described string models have shown that chromatin fibers occupy discrete territories and that the movement of each chromatin fiber is confined within a domain The phasefield method has been applied to a wide range of problems related to the complex dynamics of the domain interface especially in the materials science Provatas and Elder 2010 Takagi and Yamanaka 2012 Recently it was used for the numerical simulation of vesicles and their biomechanical properties Maitre et al 2009 Wang and Du 2008 and was applied in cell dynamics investigations because it simulates the complex domains of higher dimensions such as cell shape Akiyama et al 2010 Shao et al 2010 A novel method using multiphasefields applied to the studies of cell and tissue dynamics has been proposed as well leading to the investigations of cell division cell adhesion and cell sorting in higher dimensions Nonomura 2012 Here we chose to use the multiphasefield method proposed by Nonomura 2012 and we developed a novel application of this method for the analysis of chromatin dynamics Capturing chromatin within a domain can yield the information about the distribution of heterochromatin domains as shown by the image analysis data Solovei et al 2009 This allowed us to focus on the elucidation of the mechanisms underlying the reorganization process in nocturnal mammals

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