Bulletin of Mathematical Biology

, Volume 77, Issue 4, pp 660–697 | Cite as

Analysis of Individual Cell Trajectories in Lattice-Gas Cellular Automaton Models for Migrating Cell Populations

  • Carsten MenteEmail author
  • Anja Voss-Böhme
  • Andreas Deutsch
Original Article


Collective dynamics of migrating cell populations drive key processes in tissue formation and maintenance under normal and diseased conditions. Collective cell behavior at the tissue level is typically characterized by considering cell density patterns such as clusters and moving cell fronts. However, there are also important observables of collective dynamics related to individual cell behavior. In particular, individual cell trajectories are footprints of emergent behavior in populations of migrating cells. Lattice-gas cellular automata (LGCA) have proven successful to model and analyze collective behavior arising from interactions of migrating cells. There are well-established methods to analyze cell density patterns in LGCA models. Although LGCA dynamics are defined by cell-based rules, individual cells are not distinguished. Therefore, individual cell trajectories cannot be analyzed in LGCA so far. Here, we extend the classical LGCA framework to allow labeling and tracking of individual cells. We consider cell number conserving LGCA models of migrating cell populations where cell interactions are regulated by local cell density and derive stochastic differential equations approximating individual cell trajectories in LGCA. This result allows the prediction of complex individual cell trajectories emerging in LGCA models and is a basis for model–experiment comparisons at the individual cell level.


Individual cell trajectories Migrating cell populations Lattice-gas cellular automata Stochastic differential equations 



The authors thank Dr. Elisabetta Ada Cavalcanti-Adam, Max Planck Institute for Intelligent Systems, and Katrin Böttger, TU Dresden, for useful discussions and for critically reading the manuscript. This work was financially supported by the Virtual Liver initiative (, funded by the German Ministry of Education and Research (BMBF). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.


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Copyright information

© Society for Mathematical Biology 2015

Authors and Affiliations

  • Carsten Mente
    • 1
    Email author
  • Anja Voss-Böhme
    • 1
  • Andreas Deutsch
    • 1
  1. 1.Technische Universität Dresden, Zentrum für Informationsdienste und HochleistungsrechnenDresdenGermany

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