Amoebic Foraging Model of Metastatic Cancer Cells

Daiki Andoh,Yukio-Pegio Gunji

doi:10.3390/sym13071140

Abstract

The Lévy walk is a pattern that is often seen in the movement of living organisms; it has both ballistic and random features and is a behavior that has been recognized in various animals and unicellular organisms, such as amoebae, in recent years. We proposed an amoeba locomotion model that implements Bayesian and inverse Bayesian inference as a Lévy walk algorithm that balances exploration and exploitation, and through a comparison with general random walks, we confirmed its effectiveness. While Bayesian inference is expressed only by P(h) = P(h|d), we introduce inverse Bayesian inference expressed as P(d|h) = P(d) in a symmetry fashion. That symmetry contributes to balancing contracting and expanding the probability space. Additionally, the conditions of various environments were set, and experimental results were obtained that corresponded to changes in gait patterns with respect to changes in the conditions of actual metastatic cancer cells.

Highlights

It is known that many patterns of animal foraging are characterized by the Lévy walk.A Lévy walk is characterized by a non-Gaussian, heavy-tailed, power law distribution [1]of consistent step size, and its exponent μ is 1 < μ < 3; typically, μ = 2 [2]
An amoebic foraging model implementing random walks, Bayes and Bayesian and inverse Bayesian inference (BIB) was evaluated for each foraging pattern and step length distribution
In the Bayes and BIB models, amoebae forage randomly τ times to give the likelihood of prior probability

Summary

Introduction

It is known that many patterns of animal foraging are characterized by the Lévy walk. Lévy walk consists of many short step lengths and a few long step lengths. A high transfer efficiency [3] enables predators to obtain more resources, and it is known that many plant and animal foraging patterns, including those of insects, birds, fish, and humans, follow the Lévy walk. Metastatic cancer cells are experimentally indicated to show a scale-free Lévy walk [9]. This can be considered a valid strategy for cancer cell transitions to search more widespread areas. T cells searching for parasite-infected cells [10], bacteria [9,11], and even molecular motors within cells [12] show Lévy walks

Methods

Results

Discussion

Conclusion