Information Persistence Theory: A Mathematical and Computational Framework for Biologically Meaningful Information.

Biological systems can maintain their function and organization even when individual molecular components change. We propose Information Persistence Theory (IPT) to describe this idea and introduce the Meaningful Functional Organization Score (MFOS) as an estimator of coordinated biological organization. MFOS was developed using single-cell RNA-sequencing data from mouse pancreatic endocrinogenesis (GSE132188). From an initial pool of 169 candidate genes, differential-expression, functional, regulatory, protein-protein interaction, and feature-prioritization analyses were used to develop a 16-gene panel. Gene expression was scaled independently for each gene and combined with equal weights to produce a dataset-relative score ranging from 0 to 1. In the pancreatic dataset, the MFOS panel showed stronger group-associated organization than matched random gene panels, and leave-one-gene-out analysis showed that the result was not substantially dependent on any single gene. The estimator was also examined in an independent human kidney dataset (GSE131685), where the historical kidney implementation retained measurable information associated with annotated cell groups and exceeded the majority-class and label-permutation accuracy baselines. These findings indicate that MFOS can capture measurable patterns of coordinated biological organization in the datasets examined. However, MFOS is not a direct measure of information persistence, and the present datasets contain no experimental persistence labels. Longitudinal, perturbation-based, and multi-omic studies will be needed to test the proposed framework more directly.