Non-genetic heterogeneity from stochastic partitioning at cell division

Abstract

Gene expression involves inherently probabilistic steps that create fluctuations in protein abundances. The results from many in-depth analyses and genome-scale surveys have suggested how such fluctuations arise and spread, often in ways consistent with stochastic models of transcription and translation. But fluctuations also arise during cell division when molecules are partitioned stochastically between the two daughters. Here we mathematically demonstrate how stochastic partitioning contributes to the non-genetic heterogeneity. Our results show that partitioning errors are hard to correct, and that the resulting noise profiles are remarkably difficult to separate from gene expression noise. By applying these results to common experimental strategies and distinguishing between creation versus transmission of noise, we 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 propose experiments to separate between these two types of fluctuations and discuss future directions.

Figure 1. Growing and dividing cells

(a) Cartoon of an individual cell line and segregating units (dots) followed through rounds of growth and division. (b) Sample time trace of copy number per cell (gray) and their average (black). Random changes are due to births and deaths during the cell cycle, and segregation at cell division (time T).

Figure 2. Partitioning errors mimic gene expression noise

(a) The CV in protein numbers per cell half-way through the cell cycle as a function of average protein level for different mechanisms of gene expression and segregation. The solid line (−) corresponds to the gene expression model above with probabilistic births and deaths but no cell cycle or division. For all other scenarios, mRNAs are made at constant intensities, degraded exponentially, and independently partitioned at cell division, while a stable protein is produced with constant intensity per transcript. Circles (○) correspond to an average burst size of 4.4 and independent protein segregation. Squares (□) correspond to clustered protein segregation with an average of 13 proteins per vesicle and a Poisson distributed number of vesicles with an average value proportional to the number of proteins, while all other reactions are modeled as deterministic. Triangles (△) correspond to independent partitioning of proteins and deterministic reactions during cell growth. (b) Bars correspond to a model in which mRNAs and proteins are made deterministically during the cell cycle, then discretized and independently partitioned at cell division. The distribution is fitted to a negative binomial (line) that is expected from commonly used stochastic gene expression models. (c) Protein time-series for a simplistic model including a protein, its unsaturated protease, and the two corresponding mRNAs. All synthesis and degradation reactions are approximated as deterministic and discretized, and heterogeneity is only created through independent partitioning errors (Methods), that eventually are transmitted to protein levels. The assumptions about deterministic effects in a–c are of course physically unrealistic and included only to demonstrate the fits even in extreme cases.

Figure 3. Partitioning errors are difficult to effectively correct during the cell cycle

(a) Negative feedback can exacerbate the effect of partitioning errors. Here we consider an open loop system where component w is synthesized at a constant rate, components x and y are synthesized at constant rates per w and x molecule respectively, and all three components are degraded exponentially. Synthesis and degradation reactions are modeled as deterministic and independent partitioning of each component is the only source of randomness. The negative feedback model system is identical except that the synthesis rate of w is down-regulated by y according to a negative Hill function with a Hill coefficient of three (Method). As the half-life of y relative to the cell cycle time increases, the closed loop system exhibits noisier behavior of x than the open loop. The average abundances of each species are kept the same for the open and the closed loop system, and for all half-lives, by changing the synthesis rate constant of w. (b) The total effect of random segregation can increase with shorter half-lives of the components. The mRNA noise originating from segregation, assuming a stable TF is made at a constant intensity and that the mRNA birth rate is proportional to the number of TF molecules, where both TF and mRNA molecules segregate independently. The CV is evaluated half-way through the cell cycle, with 5 TFs and 25 mRNAs per average newborn cell. As the mRNA half-life relative to the cell cycle time increases, the randomizing effect of its own segregation (green) increases, but the transmitted fluctuations from random TF segregation (red) instead goes through a maximum and then decreases. Shorter lifetimes can thus increase the contribution of random segregation to the population heterogeneity (purple). See Methods for derivations and details.