Ordinary Differential Equation

How is the right islet size established during zebrafish pancreas development? Introduction Beta cells in the developing pancreas of zebrafish divide rapidly between 5 and 30 days post fertilization (dpf) and additional beta cells are recruited to the islet.

Hepatocyte–sinusoid alignment (HSA) supports the coordination of hepatocytes during liver regeneration after damage by carbon tetrachloride. Introduction The regenerative capacity of the mammalian liver did already inspire the fate of Prometheus in Greek Myth but it still poses many questions today that call for spatio-temporal multicellular modeling.

Autoregulatory multicellular incoherent feedforward loop (mIFFL) that generates the 7-stripe even-skipped (eve) expression pattern in Drosophila melanogaster embryogenesis Introduction This model demonstrates the influence of maternal effect genes and gap genes on the even-skipped (eve) gene.

Multiscale model of epithelial-mesenchymal transition (EMT) with intracellular TGFβ signaling circuit Introduction The growth factor TGFβ regulates the snail-zeb intracellular circuit that affects EMT by controlling the levels of E and N-cadherin expression.

Multiple models in epithelial-mesenchymal transitions (EMT) Introduction We model epithelial-mesenchymal transition (EMT) by first assembling an ODE model for intracellular Yes-associated protein (YAP) signalling and then embedding this single cell model within individual cells in a multiscale simulation.

Simulated sheet morphology for YAP knockdown (KD) and overexpression (OE) Introduction We model epithelial-mesenchymal transition (EMT) by first assembling an ODE model for intracellular Yes-associated protein (YAP) signalling and then embedding this single cell model within individual cells in a multiscale simulation.

Multiscale simulation of EMT by minimal signaling circuit Introduction We model epithelial-mesenchymal transition (EMT) by first assembling an ODE model for intracellular Yes-associated protein (YAP) signalling and then embedding this single cell model within individual cells in a multiscale simulation.

Pattern formation is robust to noise. Introduction Morpheus can also simulate ODE and PDE models with noise. One example (in the GUI menu Examples → ODE → LateralSignaling.xml) with coupled noisy ODE systems is explained in M0004.

Simple model for neuronal firing Introduction This is one of the simplest models used to depict neuronal firing. Description A simple model for neuronal firing consists of the basic ‘integrate-and-fire’ system ODE:

ODEs for the FitzHugh–Nagumo well-mixed system Introduction The FitzHugh–Nagumo (FN) model is commonly used as a toy model for neuronal excitation. Description Everything is well-mixed and two ODEs are solved for two variables, $u$ (voltage) and $v$ (recovery variable).