ODE

ODE Model: Cell Cycle

Morpheus Model ID: M0001 Open in Morpheus History Persistent Identifier Use this permanent link to cite or share this Morpheus model: Copy Introduction This model is a simple three-species ODE model of the Xenopus embryonic cell cycle (Ferrell et al.

1D PDE Barkley Model

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.

Try the Examples

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.

Step-by-Step Example

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.

SBML Import: MAPK Signaling

Morpheus Model ID: M0002 Open in Morpheus History Persistent Identifier Use this permanent link to cite or share this Morpheus model: Copy Introduction This model has been imported and automatically converted from SBML format by Morpheus.

Delay Differential Equations: Cell Cycle

Morpheus Model ID: M0003 Open in Morpheus History Persistent Identifier Use this permanent link to cite or share this Morpheus model: Copy Introduction This model is a two-species version of the Xenopus embryonic cell cycle shown above that uses delay differential equations (Ferrell et al.

Coupled ODE Lattice: Lateral Signaling

Morpheus Model ID: M0004 Open in Morpheus History Persistent Identifier Use this permanent link to cite or share this Morpheus model: Copy Introduction This example model cell fate decisions during early patterning of the pancreas (de Back et al.

A Multiscale Mini Model

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.

Predator-Prey Model by Rosenzweig

Morpheus Model ID: M0005 Open in Morpheus History Persistent Identifier Use this permanent link to cite or share this Morpheus model: Copy Introduction This model implements an extension of the well-known Lotka-Volterra system.

Example

Let’s go through an example. We’ll construct a model in which an intracellular cell cycle network (ODE) regulates the division of motile cells which (CPM) release a diffusive cytokine (PDE) which, in turn, controls the cell cycle (ODE).