Interpretable and tractable models of transcriptional noise for the rational design of single-molecule quantification experiments

Abstract

The question of how cell-to-cell differences in transcription rate affect RNA count distributions is fundamental for understanding biological processes underlying transcription. We argue that answering this question requires quantitative models that are both interpretable (describing concrete biophysical phenomena) and tractable (amenable to mathematical analysis). This enables the identification of experiments which best discriminate between competing hypotheses. As a proof of principle, we introduce a simple but flexible class of models involving a stochastic transcription rate coupled to a discrete stochastic RNA transcription and splicing process, and compare and contrast two biologically plausible hypotheses about transcription rate variation. One assumes variation is due to DNA experiencing mechanical strain, while the other assumes it is due to regulator number fluctuations. Although biophysically distinct, these models are mathematically similar, and we show they are hard to distinguish without comparing whole predicted probability distributions. Our work illustrates the importance of theory-guided data collection, and introduces a general framework for constructing and solving mathematically nontrivial continuous–discrete stochastic models.Significance StatementThe interpretation of transcriptomic observations requires detailed models of biophysical noise that can be compared and fit to experimental data. Models of intrinsic noise, describing stochasticity in molecular reactions, and extrinsic noise, describing cell-to-cell variation, are particularly common. However, integrating and solving them is challenging, and previous results are largely limited to summary statistics. We examine two mechanistically grounded stochastic models of transcriptional variation and demonstrate that (1) well-known regimes naturally emerge in limiting cases, and (2) the choice of noise model significantly affects the RNA distributions, but not the lower moments, offering a route to model identification and inference. This approach provides a simple and biophysically interpretable means to construct and unify models of transcriptional variation.