Continuous space parameterisation and intracellular fields
Motivation
Continuous space parameterization
Parameterisation in scenario units
Preserve control on time and space discretization
Provide support for other model standards
Standardisation efforts
OpenVT — transferable model components
SBML spatial
MultiCellML
Continuous surface mechanics
[Magno et al., 2015] introduced a scaling of CPM parameters for the different node sizes.
Scalable Cell Motility
recap
Naïve modelling assumptions
Composable taxis and persistence
Continuous space time parameterization
Node length $\eta$ and CPM time scale $\tau$ define discretization
Limited energy budget for cell motility
CPM temperature T shall be a technical parameter
Motility System Dynamics
Energy bias for a displacement $\Delta C$ of a cell with volume $v$ and an intrinsic orientation $\vec{p}$:
$$ \Delta H = - \mu v (\vec{\Delta C} \cdot \vec{p})$$
Every Monte Carlo step, angular noise $\xi$ is applied:
$$ \Delta\theta(\vec{p}) = \xi $$
time scaling $j$
$\mu'=j\mu, \,\, \xi'=\sqrt{j} \xi$
$$ \Delta H = - \mu v (\vec{\Delta C} \cdot \vec{p}), \,\, \Delta\theta(\vec{p}) = \xi $$
space scaling scaling $k$
$$ \mu'=\mu/k^2, \,\, \xi'=\xi/\sqrt{k}, \,\, \tau'= k \tau $$
runtime considerations
Open VT
transferable model components
Persistent random walk
Reimplementations in CompuCell3D, PhysiCell, ...
Potential basis for all models involving cell motility
Spatial molecular transport processes
Molecular spatial transport processes
Advection / Diffusion
Cell-Cell transport / reactions
Intracellular transport
Intracellular fields
Inhomogeneous cytosolic diffusives
Cytosceleton giving rise to cell motility
Cross-cellular transport processes (plants)
SBML spatial
Intracellular field reshaping solver
Adaptive spatial sub-domain per cell
Track mass gain/loss due to copy operations
Regular rescaling
Shape change and displacement tracking
Velocity field generation
Perform advection
Mass conserving non-advective
Mass conserving advective
Morpheus ML 3.0
Continuous space parametrization on all scales
Representing reactions explicitly will allow mass-conserving, precission guided solver schemes
Interplay with other standards and other simulators largely improved