These models heralded the emergence of a veritable plethora of mechanical modelling methods over the subsequent decades , though the choice of model must ultimately be informed by the questions one seeks to answer . with uniformly distributed averaging points (i.e., with only global scaling of embryos, without relative local stretching of embryo designs). = 22 overlaid and scaled embryo halves from experimental data (lines in shades of blue), and averages thereof (reddish lines), for 10 stages of inversion. Shaded areas correspond to standard deviation designs. Unsatisfactory ‘kinks’ arise in the bend region. Observe S1 Data for numerical values.(TIF) pbio.2005536.s003.tif (1.5M) GUID:?9D4B1BB1-F382-40CA-8776-7E4DCA2A380A S4 Fig: Comparison of mean shape variation for different averaging methods. Mean shape variation against imply time ?embryo from selective plane illumination imaging of chlorophyll autofluorescence. Left: maximum intensity projection of z-stacks. Right: tracing of midsagittal cross-section (Materials and methods). Scale bar: 50 m.(MP4) pbio.2005536.s005.mp4 (965K) GUID:?2EC3C825-2C8D-41DC-9AE1-BA521A10206F S2 Video: Cell rearrangement at the phialopore. Time-lapse video of the phialopore opening obtained from confocal laser scanning microscopy of chlorophyll autofluorescence and manual tracing of selected cells (Materials and methods). Scale bar: 20 m. The video shows a rearrangement of cells surrounding the phialopore.(MP4) pbio.2005536.s006.mp4 (141K) GUID:?E118E550-ED14-495A-989D-BE7B08FD99D2 S1 Data: Numerical data. Numerical values underlying the designs and graphs shown in Figs ?Figs4,4, ?,5,5, ?,7,7, ?,88 and ?and1111 in the main text; supplementary figures S2 Fig, S3 Fig, S4 Fig, and figures A1, A2, A3, A4 in S1 Text. Numerical values of the fitted parameters used to obtain Fig 7. Additional data Levofloxacin hydrate for Rabbit polyclonal to baxprotein analysis of variability.(XLSX) pbio.2005536.s007.xlsx (1.1M) GUID:?47B647DD-F59F-4AE8-A0B2-21671F5DD918 S2 Data: Raw data for random perturbations. Random perturbations of parameters, corresponding shape variations, and other statistics utilized for the analysis of variability.(GZ) pbio.2005536.s008.tar.gz (66M) GUID:?6A34192B-A994-4AC6-BC60-CE0D49B03055 S1 Code: Code for tracing embryo shapes. Elements of Python code utilized for semiautomated embryo shape tracing.(GZ) pbio.2005536.s009.tar.gz (7.7K) GUID:?2DA6C804-66FF-4F9A-8743-AA4CE21144ED S2 Code: Code for numerical calculations. Elements of Matlab (The MathWorks) code utilized for numerical answer of the equations governing the model, for aligning designs, and for fitted designs.(M) pbio.2005536.s010.m (16K) GUID:?274BDAA9-4E53-49C2-A839-B512AD8EF0D2 S1 Text: Summary statistics and geometric descriptors of inversion. Initial analysis of the variability using summary statistics. Analysis of inversion in terms of six geometric descriptors and comparison of geometric descriptors for averaged and fitted designs.(PDF) pbio.2005536.s011.pdf (264K) GUID:?6DDE98BD-9BEC-47D4-92D6-2DB98D14EC22 S2 Text: Elastic model in the contact configuration. Boundary conditions for the contact configuration. Numerical study of the contact configuration. Asymptotic analysis of a toy problem.(PDF) pbio.2005536.s012.pdf (218K) GUID:?D0979957-CF27-42B0-A444-06947FE727D7 Data Availability StatementAll relevant data are within the paper and its Supporting Information files. Abstract Variability is usually emerging as an integral part of development. It is therefore imperative to inquire how to Levofloxacin hydrate access the information contained in this variability. Yet most studies of development average their observations and, discarding the variability, seek to derive models, biological or physical, that explain these average observations. Here, we analyse this variability in a study of cell sheet folding in the green alga change themselves inside out, results from two individual mechanisms of bending and stretching (growth and subsequent contraction). Our analysis therefore uncovers a prototypical transition of developmental complexity in and the related volvocine algae, from a morphogenetic process driven by a single mechanism to one driven by two individual mechanisms. This complements the similarly prototypical transition from one cell type to two cell types that has made the volvocine algae a model system for the development of multicellularity. Introduction The phenomena are usually the same, and this is usually what matters to us, but their variations, for the greater or for the smaller, are beyond count. Thus opined Xavier Bichat in the account of his investigations into life and death  and Levofloxacin hydrate thereby spelt out how, to the present day, questions in developmental biology and cell sheet folding in particular are commonly approached: the vast majority of analyses average their experimental observations and seek to derive a model, biological or physical, that explains this average behaviour. In so doing, they discard the variability or deviations from average behaviour that are observed in experiments. A certain amount of noise is, however, unavoidable in biological systems; indeed, it may even be necessary for strong development, as demonstrated, for example, by Hong and colleagues , who showed that variability in cell growth is necessary for reproducible sepal size and shape in [5, 6], can be driven primarily by cell shape changes. In more complex.
These models heralded the emergence of a veritable plethora of mechanical modelling methods over the subsequent decades , though the choice of model must ultimately be informed by the questions one seeks to answer