Graph-based complexity and computational capabilities of proteinoid spike systems

Abstract Proteinoid microspheres exhibit oscillatory electrical dynamics that encode rich temporal structure. We analyse five proteinoid spike-train datasets using a two-step nonlinear transformation based on spiral sampling and significant-digit extraction, producing a multi-nodal graph representation of the electrical activity. Eight graph-theoretic metrics are combined into a meta-metric to quantify computational complexity across datasets. We further construct a 16-dimensional feature space capturing temporal, statistical and spectral characteristics, enabling a binary spike-prediction model based on a deep rectified linear unit (ReLU) network that achieves 70.41% accuracy. The analysis reveals structured computational signatures and suggests parallels between proteinoid activity and computational frameworks such as the Kolmogorov–Arnold (KA) representation. These results support the view of proteinoids as proto-cognitive substrates with measurable information-processing properties.