Stochasticity versus determinism in development: a false dichotomy?Gene expression noise can suggest a role for stochasticity during development. But Magdalena Zernicka-Goetz and Sui Huang argue that care should be taken in data interpretation and language use before labelling developmental events as ‘random’.

‘Stochastic’ does not mean ‘disorganized’, ‘unpredictable’ or ‘unbiased’

Many biologists divide animals into two groups with dif-ferent developmental principles: either developmental events are ‘tightly regulated’ by molecular determinants, as in flies, or they exhibit flexibility that is attributed to randomness (stochasticity1), as in mammals. Recently there has been renewed interest in ‘gene expression noise’, and it is now cited in support of a stochastic view of mam-malian development. However, can we really distinguish lawful regulatory action, which is ultimately necessary for ordered development, from lawless stochastic processes, or are the two groups part of a continuum? We suggest that two main problems cause difficulties in thinking about these issues: events often seem to be random even if they are not because of a lack of information (regula-tory mechanisms may be obscured by complex layers of control), and there are disparities in the conceptualiza-tion of stochasticity. Here we illustrate these difficulties by discussing the first cell fate decisions in mouse devel-opment and offer a conceptual framework and semantic clarification to facilitate discussion in this field.

Is the dualism between deterministic regulation and randomness as black and white as it is often perceived? Obviously, they are not mutually exclusive: determin-istic control can suppress fluctuations stemming from gene expression noise2, and gene expression noise can be exploited for cell type diversification3, as in embryonic stem (ES) cell cultures4. However, noise is susceptible to bias by a deterministic influence which, however weak, can be amplified to promote a particular outcome. From where is the bias? The developing mammalian embryo differs from a structure-less culture of ES cells in a uni-form microenvironment as it must develop a definite pat-tern within a limited period of time. Thus, if cells play dice3, geometric and temporal constraints as well as the cells’ developmental history and cell–cell communication can weight the dice, thus disrupting perfect randomness to convert noise into orchestrated sounds.

Recent debate about the principles of early mammalian development offers an instructive case of semantic and conceptual misunderstanding regarding stochasticity5. The first cell fate decision in the mouse embryo is whether to become an inner-cell mass (ICM) cell or a

trophectoderm (TE) cell. Like many binary cell fate deci-sions, it is controlled by a pair of mutually repressive tran-scription factors: CDX2 promotes a TE fate and OCT4 promotes an ICM fate6. The metastable ‘undecided’ state of bipotent precursors is maintained by balanced expression of these factors. Small perturbations can tilt the balance7, and an imbalance can self-amplify by feedback loops until the stable expression pattern of a committed fate is reached. Dynamical systems theory of such regulatory circuits accommodates a stochastic component.

The ‘salt-and-pepper’ appearance of cells expressing different fate-specifying factors in snapshot observa-tions of fixed embryos generated a climate of thinking in which it was tacitly assumed that the first fate decisions in mouse development occurred at random, beyond any regulatory bias8,9. Specifically, a cell’s decision to divide either symmetrically to generate two TE progenitors or asymmetrically to produce one TE and one ICM daughter was believed to occur at random. Subsequent decision events in which ICM cells develop into either cells of the pluripotent epiblast or primitive endoderm (PE) could be assumed random on the same basis — imaging showed a ‘salt-and-pepper’ picture of the two cell types. Although this seemed to fit the notion of gene expres-sion noise, it pre-judged the origin of individual cells with their particular gene expression patterns as random despite the lack of experimental evidence. Apparently lawless distribution does not warrant the assumption of stochasticity without careful scrutiny to exclude any departure from chance events.

To counter the misunderstanding, let us first address the terminology used. ‘Gene expression noise’ is a physical manifestation of the mathematical concept of ‘stochasticity’, which is synonymous with ‘random’. ‘Stochastic’ does not mean ‘disorganized’, ‘unpredictable’ or ‘unbiased’, as often used by biologists. The random-ness of an event pertains to the true (not just perceived) absence of an immediate (‘deterministic’) cause that per-mits the prediction of the outcome with 100% certainty. A ‘truly’ random (‘non-deterministic’) event is funda-mentally acausal and inherently unpredictable, as can be rigorously demonstrated10. It is epitomized by the throw

Magdalena Zernicka-Goetz is at The Gurdon Institute, University of Cambridge, Tennis Court Road, Cambridge CB2 1QN, UK.Sui Huang is at the Institute for Biocomplexity and Informatics, Room # 547, Biological Sciences Building, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada.e-mails: m.zernicka-goetz@gurdon.cam.ac.uk; sui.huang@ucalgary.ca

CoMMent

nATuRE REvIEWS | Genetics vOLuME 11 | nOvEMbER 2010 | 743

© 20 Macmillan Publishers Limited. All rights reserved10

of a die. Of course, one may argue that by knowing all details (initial conditions, parameters) of how the die is thrown, one might predict the outcome. but this would bring us to the philosophical discourse about epistemo-logical versus ontological irreducibility and should not concern us here.

A ‘grey zone’ between stochasticity and determinism yields several reasons for potential misunderstanding. Firstly, multi-step processes with deterministic causation (such as gene expression) can be so complicated as to be practically (epistemologically) unpredictable because of lack of information, not because of ‘true’ (ontological) randomness. The outcome then seems lawless but may not be. Secondly, random-like behaviour can occur in fully deterministic systems that exhibit deterministic chaos11, the ‘butterfly effect’ that prevents prediction of macroscopic outcomes. Even discrete deterministic systems that consist of interacting on–off elements can generate disorder that is indistinguishable from randomness12. Thirdly, the notion of a ‘probabilistic’ process should be better delineated. Although random events cannot be predicted with absolute certainty indi-vidually, they are statistically predictable: for example, a 50% chance of heads or tails when tossing a perfect coin. Epistemological ignorance of the details needed for predicting the outcome of a complicated deterministic process also necessitates probabilistic methods. Thus, ‘probabilistic’ does not necessarily mean the same thing as ‘stochastic’, yet both stochasticity and incomplete system specification require probabilistic approaches. Finally, and in contrast to widespread assumption, a ‘lack of bias’ (a 50/50 outcome in coin tossing) is not a defining prop-erty of stochasticity. A stochastic process does not imply a symmetric, unbiased probability distribution. If a coin yields a 70/30 ratio of heads/tails, the underlying physical process can still be considered as stochastic; however, it is biased. A bias that is built into the non-perfect shape of the coin or the weighting of a die is per se deterministic.

Observations that show a balance of chance and choice in the mouse embryo5 have stimulated the debate on the role of stochasticity in development. but new techniques for tracking each cell in living embryos revealed that, despite apparent randomness, the fate of an individual cell is biased (that is, statistically predictable). Thus, the ‘salt-and-pepper’ pattern that reflects fate commitment does not develop fully at random. Instead both first and second cell fate decisions depend on the developmental history of cells. In the first decision, depending on which part of the zygote they inherit, the cells acquire different levels of a specific histone modification that affects the expres-sion of fate-determining genes, such as Cdx2 (Refs 13,14). This biases cell fate: cells with the highest levels of CDX2 preferentially divide symmetrically to contribute to TE and cells with lower levels of CDX2 preferentially divide asymmetrically to contribute to ICM15. Such bias depends on when and how cell divisions separate distinct parts of the zygote, which can differ between embryos and is dif-ficult to observe. Consequently, if embryos with differing cell division patterns are mixed together, the above rela-tionship can be missed. Similarly, in the second fate deci-sion, the ‘salt-and-pepper’ expression of fate-determining

genes is affected by cells’ history: cells that are internal-ized later have the highest levels of PE-determining factors and thus have increased proclivity to become PE rather than epiblast16. This strongly suggests that, as in other organisms, the spatiotemporal organization of the mouse embryo affects cell fate. Thus, despite the impression of stochasticity, knowledge of the history of individual cells enables a (probabilistic) prediction of developmental outcome.

The deterministic spatiotemporal regulatory con-straints, including the distinct histories of cells, that shape the developing organism are so complex that a snapshot of the spatial distribution of a protein can give the impres-sion of stochasticity. For decades, developmental biology may have overemphasized the reduction of macroscopic order to deterministic molecular control mechanisms, but the rediscovery of gene expression noise caused by inevitable molecular fluctuations may have tipped the balance too far to the other side. This has led to a failure to recognize the role of deterministic constraints, notably the developmental history of cells, the recording of which is not trivial. One possible explanation for the relevance of cellular history in a fluctuating system is non-ergodicity: some variables fluctuate randomly but so slowly that they stretch over multiple cell generations17 and thus can transfer (non-random) information. Conversely, those biologists who are habituated to thinking in terms of deterministic pathways should be reminded that owing to bias that may be hidden in noise, developmental history is — in a statistical sense — predictive at best. We are left with a question: to what extent is the non-deterministic ‘noisy’ component of developmental control due to true, inevitable ontological randomness and to what extent is it due to epistemological unpredictability because of missing information on the complicated history of cells? Answering this question will require technically challeng-ing studies, such as continuous cell tracking. We hope that the general principles presented here will facilitate accu-rate discussion of this fundamental problem and guide the identification of specific molecular embodiments of deterministic control in a noisy world.

1. Kupiec, J. J. Speculations Sci. Technol. 6, 471–478 (1983).2. Arias, A. M. & Hayward, P. Nature Rev. Genet. 7, 34–44 (2006).3. Enver, T., Heyworth, C. M. & Dexter, T. M. Blood 92, 348–352 (1998).4. Canham, M. A., Sharov, A. A., Ko, M. S. & Brickman, J. M. PLoS Biol.

8, e1000379 (2010).5. Zernicka-Goetz, M., Morris, S. A. & Bruce, A. W. Nature Rev. Genet.

10, 467–477 (2009).6. Niwa, H. et al. Cell 123, 917–929 (2005).7. Huang, S., Guo, Y. P., May, G. & Enver, T. Dev. Biol. 305, 695–713

(2007).8. Dietrich, J. E. & Hiiragi, T. Development 134, 4219–4231 (2007).9. Rossant, J. & Tam, P. P. Development 136, 701–713 (2009).10. Chaitin, G. in Grenzen und Grenzüberschreitungen, XIX. Deutscher

Kongress für Philosophie (eds Hogrebe, W. & Bromand, J.) 517–534 (Akademie Verlag, Berlin, 2004).

11. Gleick, J. Chaos: Making a New Science (Penguin, 1988).12. Wolfram, S. A New Kind of Science (Wolfram Media, 2002).13. Torres-Padilla, M. E., Parfitt, D. E., Kouzarides, T. & Zernicka-Goetz, M.

Nature 445, 214–218 (2007).14. Parfitt, D. E. & Zernicka-Goetz, M. Mol. Biol. Cell 21, 2649–2660

(2010).15. Jedrusik, A. et al. Genes Dev. 22, 2692–2706 (2008).16. Morris, S. A. et al. Proc. Natl Acad. Sci. USA 107, 6364–6369 (2010).17. Chang, H. H., Hemberg, M., Barahona, M., Ingber, D. E. & Huang, S.

Nature 453, 544–547 (2008).

Competing interests statementThe authors declare no competing financial interests.

a multi-step processes with deterministic causation … can be so complicated as to be practically unpredictable

744 | nOvEMbER 2010 | vOLuME 11 www.nature.com/reviews/genetics

C O M M E N T

© 20 Macmillan Publishers Limited. All rights reserved10