During development, precise cellular patterning is essential for the formation of functional tissues and organs. These patterns arise from conserved signaling networks that regulate communication both within between cells. Here, we develop present a model-independent ordinary differential equation (ODE) framework analyzing pattern in homogeneous cell array. In con trast to traditional approaches focus on specific equations, our method relies solely general assumptions about global...

Centrosomes are critical organelles associated with the nucleus, consisting of a pair centrioles surrounded by cloud pericentriolar material. They serve as key nucleation sites for microtubule arrays and essential positioning nucleus prior to cell division, but mechanisms ensuring proper centrosome not well understood. Previous research has identified asymmetries in nucleated centrosomes including during first cycle Caenorhabditis elegans, playing role positioning, however origin this...

Cortical actin networks are highly dynamic and play critical roles in shaping the mechanical properties of cells. The cytoskeleton undergoes significant reorganization many different contexts, including during directed cell migration over course cycle, when cortical can transition between configurations such as open patched meshworks, homogeneous distributions, aligned bundles. Several types myosin motor proteins, characterized by kinetic parameters, have been involved this filaments. Given...

Positioning of microtubule-organizing centers (MTOCs) incorporates biochemical and mechanical cues for proper alignment the mitotic spindle cell division site. Current experimental theoretical studies in early Caenorhabditis elegans embryo assume remarkable changes origin polarity forces acting on MTOCs. These must occur over a few minutes, between initial centration rotation pronuclear complex entry into mitosis, models do not replicate vivo timing rotation. Here we propose model that...

Pollen provides an excellent system to study pattern formation at the single-cell level. surface is covered by pollen wall exine, whose deposition excluded from certain areas, apertures, which vary between species in their numbers, positions, and morphology. What determines aperture patterns not understood. Arabidopsis thaliana normally develops three equally spaced along equator. However, mutants has higher ploidy larger volume develop four or more apertures. To explore possible mechanisms...

Many cells rearrange proteins and other components into spatially distinct domains in a process called polarization. This asymmetric patterning is required for number of biological processes including division, cell migration, embryonic development. Proteins involved polarization are highly conserved include members the Par Rho protein families. Despite importance these polarization, it not yet known how they interact regulate each to produce localization patterns associated with In this...

Virtually all forms of life, from single-cell eukaryotes to complex, highly differentiated multicellular organisms, exhibit a property referred as symmetry. However, precise measures symmetry are often difficult formulate and apply in meaningful way biological systems, where symmetries asymmetries can be dynamic transient, or visually apparent but not reliably quantifiable using standard mathematics physics. Here, we present illustrate novel measure that draws on concepts information theory...

Intracellular polarization, where a cell specifies spatial axis by segregation of specific factors, is fundamental biological process. In the early embryo nematode worm Caenorhabditis elegans (C. elegans), polarization often accompanied deformations cortex, highly contractile structure consisting actin filaments cross-linked motor protein myosin (actomyosin). It has been suggested that eggshell surrounding plays role in although its function not understood. Here we develop mathematical model...

Improvements in experimental and computational technologies have led to significant increases data available for analysis. Topological analysis (TDA) is an emerging area of mathematical research that can identify structures these sets. Here we develop a TDA method detect physical cell persist over time. In most cells, protein filaments (actin) interact with motor proteins (myosins) organize into polymer networks higher-order structures. An example are ring channels maintain constant...

Alterations to only specific parameters in a model including EGF, Wnt and Notch lead cell behavior differences.

Mathematical models of complex systems rely on parameter values to produce a desired behavior. As mathematical and computational increase in complexity, it becomes correspondingly difficult find that satisfy system constraints. We propose Markov Chain Monte Carlo (MCMC) approach for the problem constrained model generation by designing chain efficiently explores model's space. demonstrate use our proposed methodology analyze responses newly constructed bistability-constrained protein...

A time series is an extremely abundant data type arising in many areas of scientific research, including the biological sciences. Any method that compares relies on a pairwise distance between trajectories, and choice measure determines accuracy speed comparison. This paper introduces optimal transport for comparing trajectories are allowed to lie spaces different dimensions and/or with differing numbers points possibly unequally spaced along each trajectory. The construction based modified...