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Cellular automaton models for time-correlated random walks: derivation and analysis
J M Nava-Sedeño1, H Hatzikirou2,3, R Klages4
1Technische Universität Dresden, Center for Information Services and High Performance Computing, Nöthnitzer Straße 46, 01062, Dresden, Germany. nava@mail.zih.tu-dresden.de.
Scientific Reports
|December 7, 2017
Summary
This study introduces data-driven cellular automata models to simulate anomalous diffusion in biological cell migration. These models incorporate memory effects, offering new insights into collective cell behaviors like clustering.
Area of Science:
- Physics
- Biophysics
- Computational Biology
Background:
- Many natural and societal diffusion processes deviate from standard Brownian motion, exhibiting anomalous diffusion.
- Biological cell migration is a key example, characterized by memory effects due to slowly decaying velocity autocorrelation functions.
Purpose of the Study:
- To construct non-Markovian lattice-gas cellular automata models for agents with memory.
- To investigate anomalous diffusion and memory effects in collective cell dynamics.
Main Methods:
- Deriving agent reorientation probabilities from a priori specified velocity autocorrelation functions.
- Utilizing a data-driven approach where correlations dictate agent behavior.
- Employing cellular automata for computational efficiency.
Main Results:
- Successfully modeled anomalous diffusion using velocity correlations decaying as power laws.
- Demonstrated that exponential decay of velocity correlations leads to different diffusion patterns.
- The models effectively integrate memory effects into agent-based simulations.
Conclusions:
- The developed models provide a framework for studying memory and anomalous diffusion in interacting cell populations.
- This approach facilitates exploration of phenomena like confluent cell monolayers and cell clustering.
- Computational efficiency enables large-scale simulations of complex biological dynamics.
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