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. In contrast to the models based on the quasi-steady state assumption that discard interactions between scales, multiscale models describe systems where processes at different scales can influence each other. Therefore, these models should not only describe multiple scales simultaneously, but also allow them to interact.

One fact that complicates this is that processes at different scales are often best formalized in different modeling formalisms. Therefore, multiscale modeling often also involves coupling different modeling formalisms that may include spatial/nonspatial models, discrete/continuous models, stochastic/deterministic models.


In short, multiscale models are, for the purpose of this post, characterized by three features:

  1. They simultaneously describe multiple time or spatial scales.
  2. They allow interaction between the scales.
  3. They typically involve coupling between model formalisms.

Multiscale Models and Middle-Out

Morpheus deals with a particular type of multiscale models for multicellular systems that consists of:

  • intracellular processes such as genetic regulatory networks, often modeled as ordinary differential equations,
  • cellular processes such as motility or cell division, modeled in terms of cellular Potts model, and
  • inter/extra-cellular processes such as production and diffusion of cytokines, modeled with reaction-diffusion systems.
Middle-out modeling of multiscale cellular systems ([Walter de Back, PhD thesis, TU Dresden, 2015](https://www.qucosa.de/api/qucosa%3A29750/attachment/ATT-0/)).
Middle-out modeling of multiscale cellular systems (Walter de Back, PhD thesis, TU Dresden, 2015).

Morpheus enables you to first model each of these systems separately as single-scale models and later flexibly combine these sub-models into multi-scale models. This allows you to include certain sub-models in a pragmatically fashion in which you start from a certain level of abstraction and work your way up and down by including crucial processes at different scales. Morpheus is designed to support this so-called middle-out modeling strategy.