Search for: All records

In this paper, we present convergent numerical algorithms for P-area minimizing surfaces in the Heisenberg group under Dirichlet boundary conditions. 

Early stages of metastasis depend on the collective behavior of cancer cells and their interaction with the extracellular matrix (ECM). Cancer cell clusters are known to exhibit higher metastatic potential than single cells. To explore clustering dynamics, we developed a calibrated computational model describing how motile cancer cells biochemically and biomechanically interact with the ECM during the initial invasion phase, including ECM degradation and mechanical remodeling. The model reveals that cluster formation time, size, and shape are influenced by ECM degradation rates and cellular compliance to external stresses (durotaxis). The results align with experimental observations, demonstrating distinct cell trajectories and cluster morphologies shaped by biomechanical parameters. The simulations provide valuable insights into cancer invasion dynamics and may suggest potential therapeutic strategies targeting early-stage invasive cells. 

Tracking plant cells in three-dimensional (3D) tissue captured through light microscopy presents significant challenge due to the large number of densely packed cells, non-uniform growth patterns, and variations in cell division planes across different cell layers. In addition, images of deeper tissue layers are often noisy, and systemic imaging errors further exacerbate the complexity of the task. In this paper, we propose a novel learning-based method DEGAST3D: Learning Deformable 3D GrAph Similarity to Track Plant Cells in Unregistered Time Lapse Images exploits the tightly packed 3D cell structure of plant cells to create a three-dimensional graph for accurate cell tracking. We also propose a novel algorithm for cell division detection and an effective three-dimensional registration, improving state-of-the-art algorithms. On a public dataset, our novel cell pair matching method outperforms the baseline by 6.83%, 5.96%, 6.40% in precision, recall, and F-1 score, respectively. On the same dataset, our proposed novel cell division technique improves the results of the baseline method by 15.38% and 14.78% in terms of recall and Fl-score, respectively. 

Understanding the mechanisms of the cellular aging processes is crucial for attempting to extend organismal lifespan and for studying age-related degenerative diseases. Yeast cells divide through budding, providing a classical biological model for studying cellular aging. With their powerful genetics, relatively short cell cycle, and well-established signaling pathways also found in animals, yeast cells offer valuable insights into the aging process. Recent experiments suggested the existence of two aging modes in yeast characterized by nucleolar and mitochondrial declines, respectively. By analyzing experimental data, this study shows that cells evolving into those two aging modes behave differently when they are young. While buds grow linearly in both modes, cells that consistently generate spherical buds throughout their lifespan demonstrate greater efficacy in controlling bud size and growth rate at young ages. A three-dimensional multiscale chemical-mechanical model was developed and used to suggest and test hypothesized impacts of aging on bud morphogenesis. Experimentally calibrated model simulations showed that during the early stage of budding, tubular bud shape in one aging mode could be generated by locally inserting new materials at the bud tip, a process guided by the polarized Cdc42 signal. Furthermore, the aspect ratio of the tubular bud could be stabilized during the late stage as observed in experiments in this work. The model simulation results suggest that the localization of new cell surface material insertion, regulated by chemical signal polarization, could be weakened due to cellular aging in yeast and other cell types, leading to the change and stabilization of the bud aspect ratio.