On discovering functions in actin filament automata.

Andrew Adamatzky

doi:10.1098/rsos.181198

Abstract

We simulate an actin filament as an automaton network. Every atom takes two or three states and updates its state, in discrete time, depending on a ratio of its neighbours in some selected state. All atoms/automata simultaneously update their states by the same rule. Two state transition rules are considered. In semi-totalistic Game of Life like actin filament automaton atoms take binary states ‘0’ and ‘1’ and update their states depending on a ratio of neighbours in the state ‘1’. In excitable actin filament automaton atoms take three states: resting, excited and refractory. A resting atom excites if a ratio of its excited neighbours belong to some specified interval; transitions from excited state to refractory state and from refractory state to resting state are unconditional. In computational experiments, we implement mappings of an 8-bit input string to an 8-bit output string via dynamics of perturbation/excitation on actin filament automata. We assign eight domains in an actin filament as I/O ports. To write True to a port, we perturb/excite a certain percentage of the nodes in the domain corresponding to the port. We read outputs at the ports after some time interval. A port is considered to be in a state True if a number of excited nodes in the port's domain exceed a certain threshold. A range of eight-argument Boolean functions is uncovered in a series of computational trials when all possible configurations of eight-elements binary strings were mapped onto excitation outputs of the I/O domains.

Highlights

Ideas of information processing on a cytoskeleton network have been proposed by Hameroff and Rasmussen in late 1980s in their designs of tubulin microtubules automata [1] and a general framework of cytoskeleton automata as sub-cellular information processing networks [2,3]
Projection of actin filament on z-plane is shown in grey; projection of nodes being in state w by the moment of recording inputs are shown in red
We demonstrated an implementation of logical functions on automaton models of actin filaments

Summary

Andrew Adamatzky

Every atom takes two or three states and updates its state, in discrete time, depending on a ratio of its neighbours in some selected state. All atoms/automata simultaneously update their states by the same rule. In semi-totalistic Game of Life like actin filament automaton atoms take binary states ‘0’ and ‘1’ and update their states depending on a ratio of neighbours in the state ‘1’. In excitable actin filament automaton atoms take three states: resting, excited and refractory. We implement mappings of an 8-bit input string to an 8-bit output string via dynamics of perturbation/excitation on actin filament automata. A port is considered to be in a state True if a number of excited nodes in the port’s domain exceed a certain threshold. A range of eight-argument Boolean functions is uncovered in a series of computational trials when all possible configurations of eight-elements binary strings were mapped onto excitation outputs of the I/O domains

Introduction

Examples of excitation dynamics

Game of

Discussion