Graph-based Complexity and Computational Capabilites of Proteinoid Spike Systems

Proteinoids, as soft matter fluidic systems, are computational substrates that have been recently proposed for their analog computing capabilities. Such systems exhibit oscillatory electrical activity because of cationic and anionic exchange inside and outside such gels. It has also been recently shown that this (analog) electrical activity, when sampled at fixed time intervals, can be used to reveal their underlying information-theoretic, computational code. This code, for instance, can be expressed in the (digital) language of Boolean gates and QR codes. Though, this might seem as a good evidence that proteinoid substrates have computing abilities when subjected to analog-to-digital transition, the leap from their underlying computational code to computing abilities is not well demonstrated. In this work, we analyse the electrical activity patterns of proteinoid substrates using computational methods including deep ReLU networks. Our findings suggest intriguing parallels between these patterns and certain computational frameworks, hinting at the possibility that such chemical systems might possess inherent information-processing and computational capabilities. To demonstrate the computational ability, we construct a prediction algorithm which acts as a binary classification model and extract 16-dimensional vector data from the proteinoid spike, in order to perform predictions with 70.41% accuracy. This model in its core has a unique transformation modality, inspired from number-theoretic sieve theory, and is combination of two functions: spiral sampling F1 and significant digit extraction F2 functions. The complexity of the transformed data is measured using eight distinct metrics, and effectively, using a single meta-metric.