Extensive variation in early gap gene expression in the Drosophila blastoderm is reduced over time because of gap gene cross regulation. This phenomenon is a manifestation of canalization, the ability of an organism to produce a consistent phenotype despite variations in genotype or environment. The canalization of gap gene expression can be understood as arising from the actions of attractors in the gap gene dynamical system. In order to better understand the processes of developmental robustness and canalization in the early Drosophila embryo, we investigated the dynamical effects of varying spatial profiles of Bicoid protein concentration on the formation of the expression border of the gap gene hunchback. At several positions on the anterior-posterior axis of the embryo, we analyzed attractors and their basins of attraction in a dynamical model describing expression of four gap genes with the Bicoid concentration profile accounted as a given input in the model equations. This model was tested against a family of Bicoid gradients obtained from individual embryos. These gradients were normalized by two independent methods, which are based on distinct biological hypotheses and provide different magnitudes for Bicoid spatial variability. We showed how the border formation is dictated by the biological initial conditions (the concentration gradient of maternal Hunchback protein) being attracted to specific attracting sets in a local vicinity of the border. Different types of these attracting sets (point attractors or one dimensional attracting manifolds) define several possible mechanisms of border formation. The hunchback border formation is associated with intersection of the spatial gradient of the maternal Hunchback protein and a boundary between the attraction basins of two different point attractors. We demonstrated how the positional variability for hunchback is related to the corresponding variability of the basin boundaries. The observed reduction in variability of the hunchback gene expression can be accounted for by specific geometrical properties of the basin boundaries. We clarified the mechanisms of gap gene expression canalization in early Drosophila embryos. These mechanisms were specified in the case of hunchback in well defined terms of the dynamical system theory.

Human pluripotent stem cells are promising for a wide range of research and therapeutic purposes. Their maintenance in culture requires the deep control of their pluripotent and clonal status. A non-invasive method for such control involves day-to-day observation of the morphological changes, along with imaging colonies, with the subsequent automatic assessment of colony phenotype using image analysis by machine learning methods. We developed a classifier using a convolutional neural network and applied it to discriminate between images of human embryonic stem cell (hESC) colonies with “good” and “bad” morphological phenotypes associated with a high and low potential for pluripotency and clonality maintenance, respectively. The training dataset included the phase-contrast images of hESC line H9, in which the morphological phenotype of each colony was assessed through visual analysis. The classifier showed a high level of accuracy (89%) in phenotype prediction. By training the classifier on cropped images of various sizes, we showed that the spatial scale of ~144 μm was the most informative in terms of classification quality, which was an intermediate size between the characteristic diameters of a single cell (~15 μm) and the entire colony (~540 μm). We additionally performed a proteomic analysis of several H9 cell samples used in the computational analysis and showed that cells of different phenotypes differentiated at the molecular level. Our results indicated that the proposed approach could be used as an effective method of non-invasive automated analysis to identify undesirable developmental anomalies during the propagation of pluripotent stem cells.

The ability of human pluripotent stem cells for unlimited proliferation and self-renewal promotes their application in the fields of regenerative medicine. The morphological assessment of growing colonies and cells, as a non-invasive method, allows the best clones for further clinical applications to be safely selected. For this purpose, we analyzed seven morphological parameters of both colonies and cells extracted from the phase-contrast images of human embryonic stem cell line H9, control human induced pluripotent stem cell (hiPSC) line AD3, and hiPSC line HPCASRi002-A (CaSR) in various passages during their growth for 120 h. The morphological phenotype of each colony was classified using a visual analysis and associated with its potential for pluripotency and clonality maintenance, thus defining the colony phenotype as the control parameter. Using the analysis of variance for the morphological parameters of each line, we showed that selected parameters carried information about different cell lines and different phenotypes within each line. We demonstrated that a model of classification of colonies and cells by phenotype, built on the selected parameters as predictors, recognized the phenotype with an accuracy of 70–75%. In addition, we performed a qRT-PCR analysis of eleven pluripotency markers genes. By analyzing the variance of their expression in samples from different lines and with different phenotypes, we identified group-specific sets of genes that could be used as the most informative ones for the separation of the best clones. Our results indicated the fundamental possibility of constructing a morphological portrait of a colony informative for the automatic identification of the phenotype and for linking this portrait to the expression of pluripotency markers.

We consider a model of gap gene expression during the early development of Drosophilaembryo. Parameter values in the model have been obtained by fitting to experimental patterns under an additional...

We consider a mathematical formulation of the problem of protein production during segment determination in the Drosophila blastoderm, together with some preliminary results of its analytical study. We reformulate the spatial difference equations as a set of nonlinear partial differential equations and obtain their dimensionless form in the continuum limit. Using previous results obtained by the gene circuit method, we find an asymptotic statement of the problem with a small parameter. Some results of the comparison method applied to the model are obtained, and exact stationary upper solutions are derived. They exhibit distinctive features of localized bell-shaped structures.