Inside individual cells, expression of genes is inherently stochastic and manifests as cell-to-cell variability or noise in protein copy numbers. Since proteins half-lives can be comparable to the cell-cycle length, randomness in cell-division times generates additional intercellular variability in protein levels. Moreover, as many mRNA/protein species are expressed at low-copy numbers, errors incurred in partitioning of molecules between two daughter cells are significant. We derive analytical formulas for the total noise in protein levels when the cell-cycle duration follows a general class of probability distributions. Using a novel hybrid approach the total noise is decomposed into components arising from i) stochastic expression; ii) partitioning errors at the time of cell division and iii) random cell-division events. These formulas reveal that random cell-division times not only generate additional extrinsic noise, but also critically affect the mean protein copy numbers and intrinsic noise components. Counter intuitively, in some parameter regimes, noise in protein levels can decrease as cell-division times become more stochastic. Computations are extended to consider genome duplication, where transcription rate is increased at a random point in the cell cycle. We systematically investigate how the timing of genome duplication influences different protein noise components. Intriguingly, results show that noise contribution from stochastic expression is minimized at an optimal genome-duplication time. Our theoretical results motivate new experimental methods for decomposing protein noise levels from synchronized and asynchronized single-cell expression data. Characterizing the contributions of individual noise mechanisms will lead to precise estimates of gene expression parameters and techniques for altering stochasticity to change phenotype of individual cells.

MOTIVATION: Stochastic promoter switching between transcriptionally active (ON) and inactive (OFF) states is a major source of noise in gene expression. It is often implicitly assumed that transitions between promoter states are memoryless, i.e. promoters spend an exponentially distributed time interval in each of the two states. However, increasing evidence suggests that promoter ON/OFF times can be non-exponential, hinting at more complex transcriptional regulatory architectures. Given the essential role of gene expression in all cellular functions, efficient computational techniques for characterizing promoter architectures are critically needed. RESULTS: We have developed a novel model reduction for promoters with arbitrary numbers of ON and OFF states, allowing us to approximate complex promoter switching behavior with Weibull-distributed ON/OFF times. Using this model reduction, we created bursty Monte Carlo expectation-maximization with modified cross-entropy method ('bursty MCEM(2)'), an efficient parameter estimation and model selection technique for inferring the number and configuration of promoter states from single-cell gene expression data. Application of bursty MCEM(2) to data from the endogenous mouse glutaminase promoter reveals nearly deterministic promoter OFF times, consistent with a multi-step activation mechanism consisting of 10 or more inactive states. Our novel approach to modeling promoter fluctuations together with bursty MCEM(2) provides powerful tools for characterizing transcriptional bursting across genes under different environmental conditions. AVAILABILITY AND IMPLEMENTATION: R source code implementing bursty MCEM(2) is available upon request. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.