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Defiant daughters and coordinated cousins

Nature volume 519, pages 422423 (26 March 2015) | Download Citation

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Genetically identical cells can have many variable properties. A study of correlations between cells in a lineage explains paradoxical inheritance laws, in which mother and daughter cells seem less similar than cousins. See Letter p.468

During the winter holidays, many of us are reminded of the complexities and challenges of family dynamics. Some traits, such as table manners or verbal tics, may run in the family; others, such as a passion for science or the law, might generate rebellion in the next generation. Repeated defiance could even cause behavioural traits to skip a generation, so that a child's apparent rebellion turns out to be an unconscious copying of a grandparent. Rebellious cells are harder to imagine, but in this issue, Sandler et al.1 (page 468) demonstrate that pairs of cousins (cells with a common 'grandparent') are more similar to one another than are mothers and daughters, in terms of the time it takes them to grow and divide.

Intuitively, if one cell in a population has more or less of a particular component than the population average, levels of that component will tend to deviate in the same direction in that cell's daughters. Owing to subsequent random fluctuations, these deviations will decorrelate over time, such that compositions of genetically identical cells should become less correlated with each generation. Contrary to this expectation, observations2,3 indicate that the time it takes one cell to become two — its doubling time — can show a stronger correlation between cousins than between mother–daughter pairs (Fig. 1). It has been unclear whether this surprising result reflects the fact that cells born at different times are exposed to different conditions, just as the teenagers of the 1980s behaved differently from those of the 1990s. But the current study demonstrates that, under tightly controlled conditions, the phenomenon persists.

Figure 1: Family values.
Figure 1

When considering cellular inheritance, an intuitive model implies that each generation will display the previous generation's behaviour plus some stochastic variation. The entire family tree can then be reconstructed from the correlation coefficient ρ, which describes how much each generation decorrelates from its predecessor. For example, correlations between sisters and between grandmother–granddaughter pairs, which are both separated by two generations, are ρ2. Similarly, cousin–cousin correlations are ρ4 because, to go from one cousin to another, we have to move two generations up in the family tree and two down again, connecting cousins through the common grandmother. Sandler et al.1 report that the time each cell takes to divide strongly violates this model, because these times are, on average, more similar between pairs of cousins than between mothers and daughters.

Simple inheritance laws seem to imply that this is impossible: if doubling times become uncorrelated in a single generation, how can they persist between cousins, which are separated by four generations of growth? Sandler and colleagues propose that an unknown factor that affects doubling times oscillates periodically in cells, such that cousins tend to be born in a similar phase, but mothers and daughters usually are not. A computational model showed this simple explanation to be consistent with the authors' findings in a mammalian cell type called a lymphoblast. Sandler et al. then analysed their data using measures borrowed from chaos theory4, a field of mathematics that predicts seemingly random variation using non-random (deterministic) equations that merely amplify tiny changes in initial conditions. The results of this work further support the researchers' hypothesis that the variation they observed arises from a simple dynamical system, rather than from a random process. Finally, they reanalysed published data5 for cyanobacteria, in which growth is coupled to circadian rhythms, and showed that cousins were indeed substantially more positively correlated than mothers and daughters.

Much of the variation in doubling times thus seems to reflect differences in the phase of an as-yet-unidentified internal oscillator, rather than stochastic factors, such as 'noisy' gene expression. A few decades ago, such a deterministic scenario might even have been the first guess. Differences between genetically identical cells were then often explained by nonlinear models, for example oscillations, chaos, or bistable switches. Noise was invoked only to explain infinitesimal perturbations that might eventually cause systems to diverge. Now the pendulum has swung the other way, and physiological heterogeneity is explained by random bursts of gene expression almost by default.

The problem is that both no-noise and all-noise views ignore the interconnectedness of random fluctuations and average dynamical tendencies. In ballistics, the trajectories of projectiles can be considered in the absence of random gusts of wind, but in small chemical systems such as cells, randomness is a consequence of the basic mechanisms by which the system changes. For example, exponential decay at the level of population averages typically reflects exponentially distributed times of individual reaction steps. However, the term 'random' in this context does not imply an absence of patterns — the magnitude and time correlations of fluctuating concentrations always depend strongly on the underlying interactions. Processes in single cells are thus always shaped by both chemical noise and average dynamical tendencies, and the question is how to use the information hidden in population averages to understand more about both factors.

One lesson from previous work6 is how tricky it can be to interpret variation mechanistically. In fact, even Sandler and colleagues' cell data could in principle be explained by noise. In a multicomponent network, the fact that one component or property shows no correlation between two time points does not imply that the process as a whole has become uncorrelated. For example, systems in which two random factors affect cell doubling times in opposite ways and decorrelate on different timescales can produce negligible correlations between mother and daughter cells, but substantial correlations between cousins. The tools from chaos theory must then be used very carefully, because they can make random processes seem deterministic depending on the sampling intervals used7,8,9. There is no particular reason to suspect that this type of behaviour occurs in mammalian cells, but such effects would also be hard to rule out. One of the most promising ways of analysing these effects may in fact be extensions of Sandler and co-workers' lineage-correlation analysis. By monitoring more properties and longer lineages, a wealth of extra correlation patterns becomes available without introducing further model parameters.

The authors' approach cannot be used for human family trees because, to be effective, conditions must be constant, and parents must reproduce asexually and thus 'disappear' to form the next generation. Such conditions would be a mixed blessing for adolescents — no parental oversight, but no sexual reproduction to pine for either — but a dream for cell biologists, because the assays are non-perturbative and yet provide more handles on complex dynamics. Given the explosion of microfluidics approaches, which allow tracking of cells for many generations in tightly controlled conditions, the types of lineage-correlation analysis introduced by Sandler et al. will probably bring many more important insights in the future.

Notes

References

  1. 1.

    et al. Nature 519, 468–471 (2015).

  2. 2.

    J. Gen. Microbiol. 18, 382–417 (1958).

  3. 3.

    Exp. Cell Res. 35, 415–419 (1964).

  4. 4.

    & Physica D 9, 189–208 (1983).

  5. 5.

    , , , & Science 327, 1522–1526 (2010).

  6. 6.

    & Nature Genet. 43, 95–100 (2011).

  7. 7.

    J. Opt. Soc. Am. A 7, 1055–1073 (1990).

  8. 8.

    Scholarpedia 2, 3043, rev. 91330; (2007).

  9. 9.

    & Nonlinear Time Series Analysis (Cambridge Univ. Press, 2003).

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  1. Andreas Hilfinger and Johan Paulsson are in the Department of Systems Biology, Harvard Medical School, Boston, Massachusetts 02115, USA.

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Correspondence to Johan Paulsson.

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https://doi.org/10.1038/nature14210

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