PT  - JOURNAL ARTICLE
AU  - Andreas Deutsch
AU  - Josué Manik Nava-Sedeño
AU  - Simon Syga
AU  - Haralampos Hatzikirou
TI  - BIO-LGCA: a cellular automaton modelling class for analysing collective cell migration
AID  - 10.1101/2020.10.29.360669
DP  - 2020 Jan 01
TA  - bioRxiv
PG  - 2020.10.29.360669
4099  - http://biorxiv.org/content/early/2020/10/29/2020.10.29.360669.short
4100  - http://biorxiv.org/content/early/2020/10/29/2020.10.29.360669.full
AB  - Collective dynamics in multicellular systems such as biological organs and tissues plays a key role in biological development, regeneration, and pathological conditions. Collective dynamics - understood as population behaviour arising from the interplay of the constituting discrete cells - can be studied with mathematical models. Off- and on-lattice agent-based models allow to analyse the link between individual cell and collective behaviour. Notably, in on-lattice agent-based models known as cellular automata, collective behaviour can not only be analysed through computer simulations, but predicted with mathematical methods. However, classical cellular automaton models fail to replicate key aspects of collective migration, which is a central instance of collective behaviour in multicellular systems.To overcome drawbacks of classical on-lattice models, we introduce a novel on-lattice, agent-based modelling class for collective cell migration, which we call biological lattice-gas cellular automaton (BIO-LGCA). The BIO-LGCA is characterised by synchronous time updates, and the explicit consideration of individual cell velocities. While rules in classical cellular automata are typically chosen ad hoc, we demonstrate that rules for cell-cell and cell-environment inter-actions in the BIO-LGCA can also be derived from experimental single cell migration data or biophysical laws for individual cell migration. Furthermore, we present elementary BIO-LGCA models of fundamental cell interactions, which may be combined in a modular fashion to model complex multicellular phenomena. Finally, we present a mathematical mean-field analysis of a BIO-LGCA model that allows to predict collective patterns for a particular cell-cell interaction. A Python package which implements various interaction rules and visualisations of BIO-LGCA model simulations we have developed is available at https://github.com/sisyga/BIO-LGCA.Author summary Pathophysiological tissue dynamics, such as cancer tissue invasion, and structure formation during embryonic development, emerge from individual inter-cellular interactions. In order to study the impact of single cell dynamics and cell-cell interactions on tissue behaviour, one needs to develop space-time-dependent agent-based models (ABMs), which consider the behaviour of individual cells. Typically, in agent-based models there is a payoff between biological realism and computational cost of corresponding model simulations. Continuous time ABMs are typically more realistic but computationally expensive, while rule- and lattice-based ABMs are regarded as phenomenological but computationally efficient and amenable to mathematical analysis. Here, we present the rule- and lattice-based BIO-LGCA modelling class which allows for (i) rigorous derivation of rules from biophysical laws and/or experimental data, (ii) mathematical analysis of the resulting dynamics, and (iii) computational efficiency.Competing Interest StatementThe authors have declared no competing interest.