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ODE
FAQ
Modeling
Time Scales
‘How can I specify time scales?’
Models
Built-in Examples
ODE
ODE Model: Cell Cycle
Morpheus Model ID:
M0001
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.
T. Y. Tsai
,
Q. Yang
(Authors)
Courses
From PDE to Tissue
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.
Courses
Getting Started
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.
Courses
SBML Import
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.
Models
Built-in Examples
ODE
SBML Import: MAPK Signaling
Morpheus Model ID:
M0002
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).
B. N. Kholodenko
(Author)
Models
Built-in Examples
ODE
Delay Differential Equations: Cell Cycle
Morpheus Model ID:
M0003
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.
T. Y. Tsai
,
Q. Yang
(Authors)
Models
Built-in Examples
ODE
Coupled ODE Lattice: Lateral Signaling
Morpheus Model ID:
M0004
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.
W. de Back
,
J. X. Zhou
,
L. Brusch
(Authors)
Courses
Multiscale Models
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.
Models
Built-in Examples
ODE
Predator-Prey Model by Rosenzweig
Morpheus Model ID:
M0005
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.
M. L. Rosenzweig
(Author)
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