Summary Individual mammalian cells exhibit large variability in cellular volume even with the same absolute DNA content and so must compensate for differences in DNA concentration in order to maintain constant concentration of gene expression products. Using single molecule counting and computational image analysis, we show that transcript abundance correlates with cellular volume at the single cell level due to increased global transcription in larger cells. Cell fusion experiments establish that increased cellular content itself can directly increase transcription. Quantitative analysis shows that this mechanism measures the ratio of cellular volume to DNA content, mostly likely through sequestration of a transcriptional factor to DNA. Analysis of transcriptional bursts reveals a separate mechanism for gene dosage compensation after DNA replication that enables proper transcriptional output during early and late S-phase. Our results provide a framework for quantitatively understanding the relationships between DNA content, cell size and gene expression variability in single cells.

Non-genetic factors can cause individual cells to fluctuate substantially in gene expression levels over time. Yet it remains unclear whether these fluctuations can persist for much longer than the time for a single cell division. Current methods for measuring gene expression in single cells mostly rely on single time point measurements, making the time of a fluctuation of gene expression or cellular memory difficult to measure. Here, we report a method combining Luria and Delbrück's fluctuation analysis with population-based RNA sequencing (MemorySeq) for identifying genes transcriptome-wide whose fluctuations persist for several cell divisions. MemorySeq revealed multiple gene modules that express together in rare cells within otherwise homogeneous clonal populations. Further, we found that these rare cell subpopulations are associated with biologically distinct behaviors in multiple different cancer cell lines, for example, the ability to proliferate in the face of anti-cancer therapeutics. The identification of non-genetic, multigenerational fluctuations has the potential to reveal new forms of biological memory at the level of single cells and suggests that non-genetic heritability of cellular state may be a quantitative property. Main text:Cellular memory in biology, meaning the persistence of a cellular or organismal state over time, occurs over a wide range of timescales and can be induced by a variety of mechanisms. Genetic differences are one form of memory, encoding variation between organisms on multi-generational timescales. Within an organism, epigenetic mechanisms encode the differences between cell types in different tissues, with cells retaining memory of their state over a large number of cell divisions ( 1 ) . In contrast, recent measurements suggest that expression of many genes in single cells may have very little memory, displaying highly transient .

Ploidy and size phenomena are observed to be correlated across several biological scales, from subcellular to organismal. Two kinds of ploidy change can affect plants. Whole-genome multiplication increases ploidy in whole plants and is broadly associated with increases in cell and organism size. Endoreduplication increases ploidy in individual cells. Ploidy increase is strongly correlated with increased cell size and nuclear volume. Here, we investigate scaling relationships between ploidy and size by simultaneously quantifying nuclear size, cell size, and organ size in sepals from an isogenic series of diploid, tetraploid, and octoploid Arabidopsis thaliana plants, each of which contains an internal endopolyploidy series. We find that pavement cell size and transcriptome size increase linearly with whole-organism ploidy, but organ area increases more modestly due to a compensatory decrease in cell number. We observe that cell size and nuclear size are maintained at a constant ratio; the value of this constant is similar in diploid and tetraploid plants and slightly lower in octoploid plants. However, cell size is maintained in a mutant with reduced nuclear size, indicating that cell size is scaled to cell ploidy rather than to nuclear size. These results shed light on how size is regulated in plants and how cells and organisms of differing sizes are generated by ploidy change.

Genetically identical cell populations exhibit considerable intercellular variation in the level of a given protein or mRNA. Both intrinsic and extrinsic sources of noise drive this variability in gene expression. More specifically, extrinsic noise is the expression variability that arises from cell-to-cell differences in cell-specific factors such as enzyme levels, cell size and cell cycle stage. In contrast, intrinsic noise is the expression variability that is not accounted for by extrinsic noise, and typically arises from the inherent stochastic nature of biochemical processes. Two-color reporter experiments are employed to decompose expression variability into its intrinsic and extrinsic noise components. Analytical formulas for intrinsic and extrinsic noise are derived for a class of stochastic gene expression models, where variations in cell-specific factors cause fluctuations in model parameters, in particular, transcription and/or translation rate fluctuations. Assuming mRNA production occurs in random bursts, transcription rate is represented by either the burst frequency (how often the bursts occur) or the burst size (number of mRNAs produced in each burst). Our analysis shows that fluctuations in the transcription burst frequency enhance extrinsic noise but do not affect the intrinsic noise. On the contrary, fluctuations in the transcription burst size or mRNA translation rate dramatically increase both intrinsic and extrinsic noise components. Interestingly, simultaneous fluctuations in transcription and translation rates arising from randomness in ATP abundance can decrease intrinsic noise measured in a two-color reporter assay. Finally, we discuss how these formulas can be combined with single-cell gene expression data from two-color reporter experiments for estimating model parameters.

The inherent stochastic nature of biochemical processes can drive differences in gene expression between otherwise identical cells. While cell-to-cell variability in gene expression has received much attention, randomness in timing of events has been less studied. We investigate event timing at the single-cell level in a simple system, the lytic pathway of the bacterial virus phage l. In individual cells, lysis occurs on average at 65 min, with an s.d. of 3.5 min. Interestingly, mutations in the lysis protein, holin, alter both the lysis time (LT) mean and variance. In our analysis, LT is formulated as the first-passage time (FPT) for cellular holin levels to cross a critical threshold. Exact analytical formulae for the FPT moments are derived for stochastic gene expression models. These formulae reveal how holin transcription and translation efficiencies independently modulate the LT mean and variation. Analytical expressions for the LT moments are used to evaluate previously published single-cell LT data for l phages with mutations in the holin sequence or its promoter. Our results show that stochastic holin expression is sufficient to account for the intercellular LT differences in both wild-type phages, and phage variants where holin transcription and the threshold for lysis have been experimentally altered. Finally, our analysis reveals regulatory motifs that enhance the robustness of lysis timing to cellular noise.