ODE

‘How can I specify time scales?’

Introduction This model is a simple three-species ODE model of the Xenopus embryonic cell cycle (Ferrell et al., 2011). It exhibits sustained limit cycle oscillations. Time plots of ODE model of Xenopus embryonic cell cycle.

Derived from the seminal Hodgkin-Huxley and FitzHugh-Nagumo models, the Barkley model is probably the simplest continuous model for excitable media. It replaces the cubic term in the FitzHugh-Nagumo model with a piece-wise linear term as a simplification that enables fast simulation.

Examples Menu To explore the potential and modeling features, it is the best to learn by example. Morpheus comes with a range of fully functional example models showcasing a number of model formalism and modeling features.

To show SBML support in Morpheus as of version 2.1 in practice, we give a step-by-step example of how to download, import and extend an SBML model. 1. Get an SBML Model from BioModels First, we browse the BioModels model repository and select a model.

Introduction This model has been imported and automatically converted from SBML format by Morpheus. It shows oscillations in the MAPK signaling cascade (Kholodenko, 2000). Time plots of oscillations in MAPK signaling (Kholodenko, 2000).

Introduction This model is a two-species version of the Xenopus embryonic cell cycle shown above that uses delay differential equations (Ferrell et al., 2011). It exhibits sustained limit cycle oscillations.

Introduction This example model cell fate decisions during early patterning of the pancreas (de Back et al., 2012). The simple gene regulatory network of each cell is coupled to adjacent cells by lateral (juxtacrine) signaling.

A Word on the Word ‘Multiscale’ First, let’s clarify what we mean by the somewhat hyped term ‘multiscale’. Generally, the term refers to mathematical and computational models that simultaneously describe processes at multiple time and spatial scales.

Introduction This model implements an extension of the well-known Lotka-Volterra system. It illustrates how to create a simple ODE model and log and plot data as time course. Output of predator-prey example model.