On Arithmetic Functions in Actin Filament Networks

Abstract

This paper is devoted to actin filament networks as a computation medium. The point is that actin filaments are sensitive to outer cellular stimuli (attractants as well as repellents) and they appear and disappear at different places of the cell to change the cell structure, e.g. its shape. Due to assembling and disassembling actin filaments, Amoeba proteus can move in responses to different stimuli. As a result, Amoeba proteus can be considered a simple reversible logic gate, where outer cellular signals are its inputs and the amoeba motions are its outputs. In this way, we can implement the FREDKIN logic gate on the amoeba behaviours. The actin filament networks have the same basic properties as neural networks: lateral inhibition; lateral activation; recurrent inhibition; recurrent excitation; feedforward inhibition; feedforward excitation; convergence/divergence. These networks can embody arithmetic functions defined recursively and corecursively within p-adic valued logic. Furthermore, within these networks we can define the so-called diagonalization for deducing undecidable arithmetic functions.

Towards the Definition of Logical Competence

“…Therefore these proteins can be considered a medium implementing different logical and arithmetic functions. So, some networks of these proteins such as actin filament networks can be presented as a logic or computation medium, too Alonso-Sanz & Adamatzky, 2016;Schumann, 2016Schumann, , 2017Siccardi & Adamatzky, 2015, 2016. Hence, these studies of actin filament networks and behaviors of unicellular organisms are being carried out in order to find out what specific logical and mathematical problems can be encoded in the biochemical processes of living organisms, thus presenting the organisms themselves in the form of computers -in other words, "the logical competence" of unicellular beings is studied (Schumann, 2018).…”

Decidable and undecidable arithmetic functions in actin filament networks

“…At these ends there are different rates of actin filament growth, so that monomers are added five to ten times faster to the plus end than to the slowgrowing minus end. Reproduced with permission from [68].…”

“…The idea of this paper was first presented at the Workshop on Logics for Unconventional Computing, 10th EAI International Conference on Bio-inspired Information and Communications Technologies (formerly BIONETICS), see [68]. This research is supported by FP7 Information and Communication Technologies: FP7-ICT-2011-8.…”