Gene expression involves many inherently probabilistic steps that create fluctuations in protein abundances between cells. A collection of in-depth analyses and genome-scale surveys have suggested how such noise arises and spreads through genetic networks, often as expected from stochastic models that predict statistical properties in terms of the rates of gene activation, transcription and translation. But noise also arises at cell division when molecules are partitioned stochastically between the two daughter cells. Here we mathematically demonstrate how such partitioning errors contribute to the non-genetic heterogeneity in a population. Our results show that partitioning errors are hard to correct, and that the resulting noise profiles closely mimic those of gene expression noise, making it remarkably difficult to separate between the two. By applying the results to previous experimental studies and distinguishing between actual creation versus mere transmission of noise we surprisingly hypothesize that much of the cell-to-cell heterogeneity that has been attributed to various aspects of gene expression instead comes from random segregation at cell division. We also propose experiments to separate between the two types of noise, and discuss future directions.

Many RNAs, proteins, and organelles are present in such low numbers per cell that random segregation of individual copies causes large "partitioning errors" at cell division. Even symmetrically dividing cells can then by chance produce daughters with very different composition. The size of the errors depends on the segregation mechanism: Control systems can reduce low-abundance errors, but the segregation process can also be subject to upstream sources of randomness or spatial heterogeneities that create large errors despite high abundances. Here we mathematically demonstrate how partitioning errors arise for different types of segregation mechanisms and how errors can be greatly increased by upstream heterogeneity but remarkably hard to avoid through controlled partitioning. We also show that seemingly straightforward experiments cannot be straightforwardly interpreted because very different mechanisms produce identical fits and present an approach to deal with this problem by adding binomial counting noise and testing for convexity or concavity in the partitioning error as a function of the binomial thinning parameter. The results lay a conceptual groundwork for more effective studies of heterogeneity among growing and dividing cells, whether in microbes or in differentiating tissues.A t balanced growth the abundances of cellular components are on average doubled during each cell cycle and then halved at cell division. But individual cells can deviate greatly from the average. Stochastic chemical reactions create fluctuations during the cell cycle and stochastic partitioning of components creates further fluctuations at cell division (1-4). This process perturbs concentrations and indirectly shapes molecular mechanisms by placing evolutionary constraints on reaction rates and network topologies.The variation coming from stochastic production has been closely studied in the last decade (5-13), emphasizing how it could be much greater than expected from Poisson statistics due to upstream sources of randomness (5-7), how it could be controlled (8, 9) or exploited (10, 11) depending on selective pressures, and how fluctuations can reveal properties of the underlying mechanisms (12, 13). Partitioning errors can contribute just as much to the overall heterogeneity and recent results suggest that much of the noise attributed to, e.g., gene expression may in fact originate in stochastic partitioning (14). But not even the basic guiding principles of partitioning have been identified: how partitioning errors depend on upstream spatial heterogeneity or self-control, how they affect the observable cell heterogeneity, or what they can teach us about mechanisms.The goal of this study is to provide a mathematical understanding of these principles by quantitatively modeling the heterogeneity introduced by various types of segregation mechanisms. We compare simple independent segregation where each segregating unit has a constant and independent probability of ending up in either daughter cell, to disordered segregation where...