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A stochastic hybrid model with a fast concentration bias for chemotactic cellular attraction

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  • Ojer, Jaume
  • López, Álvaro G.
  • Used, Javier
  • Sanjuán, Miguel A.F.

Abstract

We reproduce the phenomenon of chemotaxis through a hybrid random walk model in two dimensions on a lattice. The dynamics of the chemoattractant is modelled using a partial differential equation, which reproduces its diffusion through the environment from its local sources. The cell is treated discretely and it is considered immersed in a medium with concentration gradients, so that its path is affected by these chemical anisotropies. Therefore, the direction taken in each iteration of the walk is given by a stochastic process that must be biased by the chemical concentrations, giving preference towards the highest values. For this purpose, we model the intensity of the bias by a single parameter, which is related to how much a cell is attracted to a source and, consequently, how efficient this source is with respect to the cellular capture. Since the model is intended for later hybridization with cellular automata models, a thorough quantitative analysis of the parameter space has been carried out. Finally, we also illustrate the efficiency of the cellular capture due to the concentration sources by using stochastic basins of attraction.

Suggested Citation

  • Ojer, Jaume & López, Álvaro G. & Used, Javier & Sanjuán, Miguel A.F., 2022. "A stochastic hybrid model with a fast concentration bias for chemotactic cellular attraction," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    • Handle: RePEc:eee:chsofr:v:156:y:2022:i:c:s0960077922000030
    DOI: 10.1016/j.chaos.2022.111792
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    References listed on IDEAS

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    1. Nieto, Alexandre R. & Seoane, Jesús M. & Sanjuán, Miguel A.F., 2021. "Final state sensitivity in noisy chaotic scattering," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
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    3. Muramatsu, Masakuni & Nagatani, Takashi, 2000. "Jamming transition in two-dimensional pedestrian traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 275(1), pages 281-291.
    4. Burstedde, C & Klauck, K & Schadschneider, A & Zittartz, J, 2001. "Simulation of pedestrian dynamics using a two-dimensional cellular automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 507-525.
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