Heritable stochastic switching revealed by single-cell genealogy

Abstract

The partitioning and subsequent inheritance of cellular factors like proteins and RNAs is a ubiquitous feature of cell division. However, direct quantitative measures of how such nongenetic inheritance affects subsequent changes in gene expression have been lacking. We tracked families of the yeast Saccharomyces cerevisiae as they switch between two semi-stable epigenetic states. We found that long after two cells have divided, they continued to switch in a synchronized manner, whereas individual cells have exponentially distributed switching times. By comparing these results to a Poisson process, we show that the time evolution of an epigenetic state depends initially on inherited factors, with stochastic processes requiring several generations to decorrelate closely related cells. Finally, a simple stochastic model demonstrates that a single fluctuating regulatory protein that is synthesized in large bursts can explain the bulk of our results.

Figure 1. Cells Switch between Expressing and Nonexpressing States

Images are phase contrast micrographs (black and white) overlaid with background-subtracted fluorescent signal (purple). (A) Over 750 min, or between 4 and 5 generations, an initially ON cell of strain MA0188 develops into a small variegated colony with subpopulations of ON and OFF cells. (B) An initially OFF cell likewise grows into a mixed colony with both ON and OFF cells. The sharp interface between ON and OFF cells in both (A,B) indicates that cell-cell communication does not play a major role in defining cell expression state. a.u., arbitary units.

Figure 2. A Genealogical Switching History

We designate the first cell in each movie cell 1 and sequential daughters of that cell 1–1, 1–2, 1–3. These daughter cells bud in turn, giving rise to cells 1-1-1, 1-1-2, 1-2-1, etc. (A) As in Figure 1, an initially OFF cell grows into a variegated micro-colony. Beginning at 600 min, or 4 generations, several cells fluoresce almost simultaneously. This includes the mother-daughter pairs (1,1–2) and (1-1-1,1-1-1–1). Conspicuously, cell 1–1 does not switch for the duration of our observation, even though its mother, daughter, and closest sibling all do. (B) The family tree for colony in (A). Black lines indicate cells in the OFF state, whereas pink lines represent cells after they have switched to the ON state. (C) Fluorescent time courses for mother cell 1 and her daughter 1–2, showing each as they switch into the ON state. The marginal switch times τ₁ and τ_1–2, run from cell birth until the beginning of the increase in fluorescence and do not depend on any other cells. The period labeled τ_1|1–2 runs between the birth of cell 1–2 and the fluorescence of cell 1 and is an example of a conditional switch time.

Figure 3. Single-Cell Fate

(A) The cumulative percentage of cells that have switched is plotted against their marginal switch time. The black squares represent 251 switching cells, and the blue line is an exponential fit. The cyan dashed line is a result of our stochastic simulation (see Figure 5). Error bars are derived from a bootstrap analysis. The fits are consistent with the idea that a constant-rate process may underlie the network. The inset shows ways that mother-daughter pairs may switch, either dependently via the center route or independently of one another via the outer routes. (B) Gray circles describe the likelihood that a mother cell has switched given that its daughter cell is known to have switched before this time. The solid red line describes a two-parameter least-squares fit simultaneously to both curves with parameters described in the inset and main text. The dashed dark red line shows the fit resulting from the stochastic simulation. Black squares and blue lines are reproduced from (A) for comparison.

Figure 4. Cell-Pair Behavior

The conditional switch times for closely related cells are compared. (A) The daughter switch time is compared to the mother switch times for 141 cell pairs. For times extending past 350 min (about two cell divisions), a strong correlation in times is observed. The other cell pair relationships, shown again in (B, C), are shadowed in grey. (B, C) The more distant relationships of GM-GD (n = 55) continue to show significant correlation, while the S1-S2 relationships (n = 74) shows somewhat less. The notable asymmetry of the S1-S2 distribution reflects the tendency for older siblings to sometimes switch before the younger sibling is even born. (D) In blue, the mean squared difference of the switch times from the combined relationships in (A–C), binned according to their average switch time. In red, a computer-generated Poisson simulation sets a bound for switching correlation in the limit of correlation tends to zero. The mean cell doubling time is labeled t _doub. (E) Dark green squares show the ratio of the two curves in (D), demonstrating the persistence of a correlation for at least hundreds of minutes after cell division. In purple, the predicted fit from our stochastic simulation after fitting to the curves in Figure 3.

Figure 5. Burst-Induced Correlations

Results of our stochastic simulation. (A–C) Fluctuations of protein concentration as a function of time are shown (gray lines). Several selected realizations are highlighted for emphasis. Proteins are created in bursts of size = 12, 120, and 1,200 respectively for the three panels, with the average protein level held fixed. Thresholds (solid black lines) are chosen to result in an average switching rate equal to our experimentally measured value. When protein levels drop below a threshold, that cell is considered to have switched. (D–F) The resulting M-D scatter plots. As the burst size increases, the pattern becomes markedly more correlated. Gray circles in (F) are the experimental data reproduced from Figure 4A.