AUTÔMATOS CELULARES EM BIOFÍSICA

Abstract

In this thesis we considered cellular automaton model with time delay. Time delay included in this model reflects the delay between the time in which the site is affected and the time in which its variable is updated. Firstly, we studied the growth of cancer considering the infiltration of cancer cells in normal tissues. It was used a simple cellular automaton that models a biological system, which is classified in spatio-temporal classes using the Hamming distance as a form of diagnosis. With this diagnosis it was possible to observe the suppression of cancerous cells, varying the system parameters. We also studied the relation between the time delay in the cell cycle and the time to start the metastasis, using suitable numerical diagnostics. Moreover, we study the firing rate properties of a cellular automaton model for a neuronal network with chemical synapses. We propose a simple mechanism in which the nonlocal connections are included, through electrical and chemical synapses. In the latter case, we introduce a time delay which produces selfsustained activity. Nonlocal connections, or shortcuts, are randomly introduced according to a specified connection probability. There is a range of connection probabilities for which neuron firing occurs, as well as a critical probability for which the firing ceases in the absence of time delay. The critical probability for nonlocal shortcuts depends on the network size according to a power-law. We also compute the firing rate amplification factor by varying both the connection probability and the time delay for different network sizes. A issue that would be interesting to explore in future works is the influence of cancerous cells on the firing rate in a neuronal network considering cellular automaton.