Predicting single-cell transcription dynamics even when the central limit theorem fails

Mechanistic modeling is more predictive in engineering than in biology, but the reason for this discrepancy is poorly understood. The difference extends beyond randomness and complexity in biological systems. Statistical tools exist to disentangle such issues in other disciplines, but these assume normally distributed fluctuations or enormous datasets, which don’t apply to the discrete, positive and non-symmetric distributions that characterize single-cell and single-molecule dynamics. Our approach captures discrete, non-normal effects within finite datasets and enables biologically significant predictions. Using transcription regulation as an example, we discover quantitatively precise, reproducible, and predictive understanding of diverse transcription regulation mechanisms, including gene activation, polymerase initiation, elongation, mRNA accumulation, transport, and degradation. Our model-data integration approach extends to any discrete dynamic process with rare events and realistically limited data.