On the embryonic cell division beyond the contractile ring mechanism: experimental and computational investigation of effects of vitelline confinement, temperature and egg size

Linel2D-Net: A deep learning approach to solving 2D linear elastic boundary value problems on image domains

Efficient solution of physical boundary value problems (BVPs) remains a challenging task demanded in many applications. Conventional numerical methods require time-consuming domain discretization and solving techniques that have limited throughput capabilities. Here, we present an efficient data-driven DNN approach to non-iterative solving arbitrary 2D linear elastic BVPs. Our results show that a U-Net-based surrogate model trained on a representative set of reference FDM solutions can accurately emulate linear elastic material behavior with manifold applications in deformable modeling and simulation.

FDM data driven U-Net as a 2D Laplace PINN solver

Efficient solution of partial differential equations (PDEs) of physical laws is of interest for manifold applications in computer science and image analysis. However, conventional domain discretization techniques for numerical solving PDEs such as Finite Difference (FDM), Finite Element (FEM) methods are unsuitable for real-time applications and are also quite laborious in adaptation to new applications, especially for non-experts in numerical mathematics and computational modeling. More recently, alternative approaches to solving PDEs using the so-called Physically Informed Neural Networks (PINNs) received increasing attention because of their straightforward application to new data and potentially more efficient performance. In this work, we present a novel data-driven approach to solve 2D Laplace PDE with arbitrary boundary conditions using deep learning models trained on a large set of reference FDM solutions. Our experimental results show that both forward and inverse 2D Laplace problems can efficiently be solved using the proposed PINN approach with nearly real-time performance and average accuracy of 94% for different types of boundary value problems compared to FDM. In summary, our deep learning based PINN PDE solver provides an efficient tool with various applications in image analysis and computational simulation of image-based physical boundary value problems.

Classical and Emerging Regulatory Mechanisms of Cytokinesis in Animal Cells

The primary goal of cytokinesis is to produce two daughter cells, each having a full set of chromosomes. To achieve this, cells assemble a dynamic structure between segregated sister chromatids called the contractile ring, which is made up of filamentous actin, myosin-II, and other regulatory proteins. Constriction of the actomyosin ring generates a cleavage furrow that divides the cytoplasm to produce two daughter cells. Decades of research have identified key regulators and underlying molecular mechanisms; however, many fundamental questions remain unanswered and are still being actively investigated. This review summarizes the key findings, computational modeling, and recent advances in understanding of the molecular mechanisms that control the formation of the cleavage furrow and cytokinesis.

Unite to divide - how models and biological experimentation have come together to reveal mechanisms of cytokinesis

Cytokinesis is the fundamental and ancient cellular process by which one cell physically divides into two. Cytokinesis in animal and fungal cells is achieved by contraction of an actomyosin cytoskeletal ring assembled in the cell cortex, typically at the cell equator. Cytokinesis is essential for the development of fertilized eggs into multicellular organisms and for homeostatic replenishment of cells. Correct execution of cytokinesis is also necessary for genome stability and the evasion of diseases including cancer. Cytokinesis has fascinated scientists for well over a century, but its speed and dynamics make experiments challenging to perform and interpret. The presence of redundant mechanisms is also a challenge to understand cytokinesis, leaving many fundamental questions unresolved. For example, how does a disordered cytoskeletal network transform into a coherent ring? What are the long-distance effects of localized contractility? Here, we provide a general introduction to 'modeling for biologists', and review how agent-based modeling and continuum mechanics modeling have helped to address these questions.

Asymmetric Flows in the Intercellular Membrane during Cytokinesis

Eukaryotic cells undergo shape changes during their division and growth. This involves flow of material both in the cell membrane and in the cytoskeletal layer beneath the membrane. Such flows result in redistribution of phospholipid at the cell surface and actomyosin in the cortex. Here we focus on the growth of the intercellular surface during cell division in a Caenorhabditis elegans embryo. The growth of this surface leads to the formation of a double-layer of separating membranes between the two daughter cells. The division plane typically has a circular periphery and the growth starts from the periphery as a membrane invagination, which grows radially inward like the shutter of a camera. The growth is typically not concentric, in the sense that the closing internal ring is located off-center. Cytoskeletal proteins anillin and septin have been found to be responsible for initiating and maintaining the asymmetry of ring closure but the role of possible asymmetry in the material flow into the growing membrane has not been investigated yet. Motivated by experimental evidence of such flow asymmetry, here we explore the patterns of internal ring closure in the growing membrane in response to asymmetric boundary fluxes. We highlight the importance of the flow asymmetry by showing that many of the asymmetric growth patterns observed experimentally can be reproduced by our model, which incorporates the viscous nature of the membrane and contractility of the associated cortex.