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--- examples:multiscale [14:49 30.07.2013] – [Time scales] Walter
+++ examples:multiscale [17:19 18.08.2021] (current) – Moved to GitLab Pages Diego Jahn
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-~~NOTOC~~
-===== Multiscale models =====
-==== Coupling spatial models: Autocrine chemotaxis ====
-[{{ :example-cpm_pde.png?direct&200|Cell cluster due to chemotaxis towards self-produced chemoattractant}}]
-{{vimeo>47176046?small }}
-=== Introduction ===
-This example models a cellular Potts model for autocrine chemotaxis by coupling a CPM to a diffusive chemoattractant.
-=== Model description ===
-It exemplifies the combination of a ''CPM'' with a ''PDE'' through the chemotaxis towards a diffusive chemoattractant produced by cells. The ''CellType'' has a ''Property'' p (production rate) which is positive within biological cells, and is zero in the medium 'cell type'. The symbol p can than be used in the ''PDE'' as the production term for species or ''Layer'' U. In this way, U is produced in each lattice node that is occupied by a cell, and is not produced outside of cells. At the same time, cells perform ''Chemotaxis'' towards the chemoattractant U.
-The simulation is visualized using some advances ''Gnuplotter'' feature. Cells are ''superimposed'' on the PDE and appear as transparent domains (see ''opacity''). Moreover, the concentration gradient of the PDE is emphasized by the use of ''isolines'' that draws contours as positions with equal concentration.
-=== Model ===
-<code xml |h AutocrineChemotaxis.xml |h>
-extern>
-http://imc.zih.tu-dresden.de/morpheus/examples/Multiscale/AutocrineChemotaxis.xml
-</code>
-In Morpheus GUI: ''File -> Examples -> Multiscale -> AutocrineChemotaxis.xml''
-----
-==== Coupling CPM and PDE: Vascular patterning ====
-{{vimeo>47171670?small }}
-[{{ :example-vascularpatterning.png?direct&200|Cells organize into networks due to matrix-anchorage of chemoattractant}}]
-=== Introduction ===
-This example shows a model of vascular network formation by paracrine signaling ([[http://dx/doi.org/10.1371/journal.pone.0024175|Köhn-Luque et al., 2011]]) and employs a coupled CPM and reaction-diffusion model.
-=== Model description ===
-The model defines a ''CPM'' as well as a ''PDE''. These models are coupled by two processes:
-  - Cells, specified in ''CellTypes'', respond chemotactically to a ''Layer'' (or species) in the ''PDE''
-  - Conversely, the production term of one ''PDE Layer'' is coupled to the presence/absence of cell.
-=== Model ===
-<code xml |h VascularPatterning.xml |h>
-extern>http://imc.zih.tu-dresden.de/morpheus/examples/Multiscale/VascularPatterning.xml
-</code>
-In Morpheus GUI: ''File -> Examples -> Multiscale -> VascularPatterning.xml''
-=== Reference ===
-Köhn-Luque A, de Back W, Starruß J, Mattiotti A, Deutsch A, et al. [[http://dx/doi.org/10.1371/journal.pone.0024175|Early Embryonic Vascular Patterning by Matrix-Mediated Paracrine Signalling: A Mathematical Model Study]]. //PLoS ONE// 6(9): e24175, 2011
-----
-==== ODEs in CPM cells: Cell cycle and proliferation ====
-[{{ :examples:example-cellcycle.png?direct&200|Cells divide according to an oscillatory ODE model representing the early cell cycle in Xenopus.}}]
-=== Introduction ===
-This multiscale model example shows
-  - how to define a coupled system of continuous ODEs in discrete CPM cells
-  - how to specify and change time scales between these model formalisms
-=== Model description ===
-This model specifies an oscillatory ODE model representing the cell cycle in Xenopus oocytes using three components (CDK1, Plk1, APK) (Ferrell et al., Cell, 2011) (see ''CellTypes->CellType->System''). This ODE model is coupled to 2D shaped CPM cells that perform divide based on the concentration of these components (see ''CellTypes->CellType->Proliferation->Condition''). As in the early Xenopus cell cleavage, this leads to exponential growth of the number of cells, without increase of total cell volume.
-=== Time scales ===
-Time scales are defined in the following fashion: \\
-  * The so-called global time scheme is defined in ''Time'' and here runs from ''0'' to ''1'' arbitrary time units. All models and plugins specify their updating scheme in terms this global time scheme (e.g. ''Analysis->Gnuplotter->interval''). \\
-  * The CPM time scale for cell motility and behaviors is defined in ''CPM->MCSDuration''. This specifies the time that a single Monte Carlo step in the CPM lasts, in terms of the 'global time'. Here, the ''MCSDuration'' is $1.0\cdot10^{-4}$ which means the CPM is executed 10.000 times during this simulation. \\
-  * For setting time of ODEs, one has to distinguish the (1) how often the ODEs are evaluated from (2) controlling the time scale of the ODE dynamics:
-    - The time scale of the ODE dynamics can be changed using ''System->time-scaling'' which, when larger or smaller than $1.0$, speeds up or slows down make the dynamics, without influencing the accuracy of the approximation.
-    - The accuracy of the numerical approximation (and is equal to the $\Delta t$ of the numerical solver) is controlled using ''System->time-step'' (and is automatically rescaled according to the time scale).
-=== Things to try ===
-  * Change the time scale of the CPM relative to the ODE dynamics: Increase ''CPM->MCSDuration'' to $1.0\cdot10^{-3}$ or decrease to $1.0\cdot10^{-5}$. This makes cells to have less resp. more motility/relaxation in between cell divisions.
-  * Change the time scale of the ODE dynamics: Increase ''CPM->MCSDuration'' to $1.0\cdot10^{-3}$ or decrease to $1.0\cdot10^{-5}$. This makes cells to have less resp. more motility/relaxation in between cell divisions.
-=== Model ===
-<code xml |h CellCycle.xml |h>
-extern>
-http://imc.zih.tu-dresden.de/morpheus/examples/Multiscale/CellCycle.xml
-</code>
-In Morpheus GUI:  ''File -> Examples -> Multiscale -> CellCycle.xml''
-----
-==== Dictyostelium ====
-[{{ :examples:example-dicty.png?direct&200|Aggregation of amoebas through chemotaxis towards waves of cAMP.}}]
-{{vimeo>57214708?small }}
-=== Introduction ===
-This model show chemotactic aggregation of Dictyostelium. It was constructed by students attending the [[http://www.math.tu-dresden.de/essim2012/|ECMI modeling week 2012]] in Dresden.
-=== Model description ===
-This model shows an interesting coupling between CPM cells and reaction-diffusion PDE. Cell state depends on the perceived concentration of cAMP, and determines whether a cell produces cAMP and whether it performs chemotaxis. The PDE is governed by a Fitzhugh-Nagumo-like model of an excitable medium, which causes traveling waves upon excitation. Chemotaxis through those waves causes cell aggregation.
-Background colors indicate the cAMP concentration. Cells are color-coded according to their phase: excitable/resting (yellow), excited/chemotactic (green), refractory/resting (red).
-=== Model ===
-<code xml |h Dictyostelium.xml |h>
-extern>
-http://imc.zih.tu-dresden.de/morpheus/examples/Multiscale/Dictyostelium.xml
-</code>
-In Morpheus GUI: ''File -> Examples -> Multiscale -> Dictyostelium.xml''
-=== References ===
-  * Savill N and Hogeweg P. [[ http://dx.doi.org/10.1006/jtbi.1996.0237|Modelling morphogenesis: from single cells to crawling slugs]]. //J. Theor. Biol//, 184:229–235, 1997.
-  * Rost F, Quintero A, Myllykoski M, Igolkina A, Rohde O’Sullivan Freltoft A, Dixit N, [[http://www.mafy.lut.fi/EcmiNL/issues.php?issueNumber=52|Morphogenesis and Dynamics of Multicellular Systems]]. //ECMI Newsletter//, 52, 2012.
-----
-==== MembraneProperties: Cell polarization and chemotaxis ====
-//Note: MembraneProperties are not available in public version of Morpheus.//
-[{{ :examples:cellpolarity0060.png?direct&200|Cell dynamically re-polarizes in response to switching external gradient}}]
-{{vimeo>60636346?small }}
-=== Aims ===
-This model show how to couple cells, PDEs on membranes and external gradients.
-=== Description ===
-This example implements two models of cell polarity: Meinhardt's substrate-depletion model and Edelstein-Keshet's wave-pinning model. The user can switch polarity model by ''Disabling''/''Enabling'' the relevant ''System''.
-The model defines a one-dimensional reaction-diffusion system (''MembraneProperty'') representing membrane-bound molecules, and is mapped to a cellular Potts model defining a discrete shaped cell. An external gradient, specified in a ''PDE'', provides a signal for the polarization of the cell. In turn, the polarity of the cell influences its ''chemotaxic'' behavior.
-After a switch in direction of the gradient, the cell re-polarizes in the new direction and starts to move up the gradient, iff the wave pinning model has been selected.
-=== Model ===
-<code xml |h CellPolarity.xml |h>
-extern>
-http://imc.zih.tu-dresden.de/morpheus/examples/Multiscale/CellPolarity.xml
-</code>