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Convergent extension of epithelial tissue is a key motif of animal morphogenesis. On a coarse scale, cell motion resembles laminar fluid flow; yet in contrast to a fluid, epithelial cells adhere to each other and maintain the tissue layer…
Proteins control many vital functions in living cells, such as cell growth and cell division. Reliable coordination of these functions requires the spatial and temporal organizaton of proteins inside cells, which encodes information about…
Gene expression represents a fundamental interface between genes and environment in the development and ongoing plasticity of the human organism. Individual differences in gene expression are likely to underpin much of human diversity,…
A blood cell lineage consists of several consecutive developmental stages from the pluripotent or multipotent stem cell to a particular stage of terminally differentiated cells. There is considerable interest in identifying the key…
The lung airway tree modeling is essential to work for the diagnosis of pulmonary diseases, especially for X-Ray computed tomography (CT). The airway tree modeling on CT images can provide the experts with 3-dimension measurements like wall…
Systemic properties of living cells are the result of molecular dynamics governed by so-called genetic regulatory networks (GRN). These networks capture all possible features of cells and are responsible for the immense levels of adaptation…
Identifying key driver genes governing biological processes such as development and disease progression remains a challenge. While existing methods can reconstruct cellular trajectories or infer static gene regulatory networks (GRNs), they…
The Turing patterning mechanism is believed to underly the formation of repetitive structures in development, such as zebrafish stripes and mammalian digits, but it has proved difficult to isolate the specific biochemical species…
Branched actin networks at the leading edge of a crawling cell evolve via protein-regulated processes such as polymerization, depolymerization, capping, branching, and severing. A formulation of these processes is presented and analyzed to…
The Unfolded Protein Response is the cell mechanism for maintaining the balance of properly folded proteins in the endoplasmic reticulum , the specialized cellular compartment. Although it is largely studied from a biological point of view,…
Advances in imaging technology now provide us with detailed 3D data on gene expression patterns in developing embryos. This information can be used to build predictive mathematical models of embryogenesis. Current modelling approaches are,…
Cells receive a wide variety of cellular and environmental signals, which must be processed combinatorially to generate specific and timely genetic responses. We present here a theoretical study on the combinatorial control and integration…
Plasma membrane tubes are ubiquitous in cellular membranes and in the membranes of intracellular organelles. They play crucial roles in trafficking, ion transport, and cellular motility. The formation of plasma membrane tubes can be due to…
Turing's reaction-diffusion theory of morphogenesis has been very successful in understanding macroscopic patterns within complex objects ranging from biological systems to sand dunes. However, this mechanism was never tested against…
We present a general methodology in order to build mathematical models of genetic regulatory networks. This approach is based on the mass action law and on the Jacob and Monod operon model. The mathematical models are built symbolically by…
The formation of protein patterns inside cells is generically described by reaction-diffusion models. The study of such systems goes back to Turing, who showed how patterns can emerge from a homogenous steady state when two reactive…
Transformers have become the dominant architecture in modern machine learning, yet the theoretical understanding of their training dynamics remains limited. This paper develops a rigorous mathematical framework for analyzing gradient-based…
Regulatory networks consist of interacting molecules with a high degree of mutual chemical specificity. How can these molecules evolve when their function depends on maintenance of interactions with cognate partners and simultaneous…
We consider a simplified model for gene regulation, where gene expression is regulated by transcription factors (TFs), which are single proteins or protein complexes. Proteins are in turn synthesised from expressed genes, creating a…
The regulatory mechanisms driving progression of the yeast cell cycle appears to be comprised of an interacting network of transcription factors (TFs), cyclin-dependent kinases (CDK) and ubiquitin ligases. From a systems perspective the…