What’s luck got to do with it? Single cells, multiple fates, and biological non-determinism

Abstract

The field of single cell biology has morphed from a philosophical digression at its inception to a playground for quantitative biologists, to a major area of biomedical research. The last several years have witnessed an explosion of new technologies, allowing us to apply ever more of the modern molecular biology toolkit to single cells. Conceptual progress, however, has been comparatively slow. Here, we provide a framework for classifying both the origins of the differences between individual cells and the consequences of those differences. We discuss how the concept of “random” differences is context dependent, and propose that rigorous definitions of inputs and outputs may bring clarity to the discussion. We also categorize ways in which probabilistic behavior may influence cellular function, highlighting studies that point to exciting future directions in the field.

Introduction

There is a fairly broad appreciation in the biological community that the behavior of individual cells may vary from the population average, giving rise to an entire field of “single cell biology” (Balázsi et al., 2011; Eldar and Elowitz, 2010; Raj and van Oudenaarden, 2008; Trapnell, 2015). Early, pioneering work in bacteria (Benzer, 1953; Novick and Weiner, 1957) and mammalian cells (Ko et al., 1990) provided convincing demonstrations that cell-to-cell variability is indeed a fact of life. These studies are all the more remarkable given the limited experimental tools available at the time, which often required making inferences based on clever experimental design and specifics of the system in question. Fast forward a few decades and we can make measurements in single cells those researchers probably could not even have dreamed of–live cell imaging of transcription with single molecule resolution, measuring the entire transcriptome of thousands of single cells, and who knows what two years from now. Yet while those early years were marked with considerable theoretical discussion of the basis and consequences of the life of a single cell (Arkin et al., 1998; Peccoud and Ycart, 1995; Schrodinger, n.d.; Spudich and Koshland, 1976), such discussions have fallen by the wayside as our drive for quantification has far outpaced our justification for making those measurements to begin with. As single cell biology has recently joined the trend towards industrialization that is sweeping through molecular biology in general, we feel the time is ripe for returning to some of these fundamental questions before we embark on massive data-gathering exercises. Here, our goal is to discuss a potential framework for classifying studies of single cell biology.

Where to begin with such a framework? We think it instructive to consider that many biologists, especially those of the developmental variety, might be forgiven for saying “Single cell biology? Isn’t that what we’ve been calling ‘biology’ for decades?” Certainly, the fact that individual cells, different tissue types and even multicellular organisms can do different things with the same genome is hardly news (see examples in Figure 1). A potential starting point for a more useful discussion is to develop a conceptual classification of ways in which we think about differences between single cells. To make this concrete, let’s consider a side by side comparison between two cells. Much of the focus of the field has been on listing how these two cells may be different at the molecular level. In particular, our tools now enable us to measure the differences in the molecular state of a cell with extraordinary breadth and accuracy (though perhaps not both simultaneously), as has been reviewed thoroughly elsewhere (Itzkovitz and van Oudenaarden, 2011; Raj and van Oudenaarden, 2009; Trapnell, 2015).

Figure 1. Variable phenotypic interpretations of genomic information.

(A) Position-effect variegation gives rise to red and white patches in the Drosophila eye. The phenotype is due to imperfect spreading of pericentric heterochromatin, the white gene (red box) is silenced in some cells (white patches), but remains expressed in others (red patches). (B) Calico cats have patches on differently coloured fur (in this case black and orange, on a white background). The animals are heterozygous for a gene, with one one allele causing the orange tabby and the other the black colour. Random inactivation of either one or the other copy of the X chromosome in individual cells gives Calico cats their characteristic patches of colour. (C) Nine-banded armadillos are a polyembryonic species, with a single fertilised egg typically giving rise to quadruplets. While these genetically identical individuals seem very similar at first glance, some traits, such as the patterning of the head shield (h, with two different patterns shown in the red circles) and the banded shield (b) can be highly variable.

Sources:

(A) Image of eye from Elgin and Reuter: Position effect variegation, heterochromatin formation, and gene silencing in drosophila. Cold Spring Harb Perspect Biol 2013 Aug 1; 5(8):a017780 - http://cshperspectives.cshlp.org/cgi/pmidlookup?view=long&pmid=23906716

(B) Picture of Calico cat from Flickr, public domain dedication: https://www.flickr.com/photos/136594255@N06/24275144860/in/photolist-CZ7sQm-8hm5EF-9dVtJS-5QBizK-pqgXVF-9rYbVz-jWJT9X-8f7gz1-7R8ofB-8YS77x-nZpe8r-7Q4jpi-7HerfD-8i9WKU-7oyZxC-fwdnBA-oowW96-4jfk89-8q2j1o-8y3GUC-8UuXFw-nSSooh-8U9Yty-8BUSAK-8vMXzr-aX9Jwc-dUs5n4-7BfkNn-dML6tc-znkqQy-9KdnuE-83qdTU-czSjnY-5uEAin-7RTp6C-7wZXGY-6JatrC-p5i6vt-8MZ2Uo-9fLKRk-7S88pj-7Rrk5Q-8SNP4h-8PWpJT-9wRby8-gYD1U9-bcBNyk-m7fUdC-gKJLzf-8MhTDP/

(C) Image of Armadillos from Vogt: Stochastic developmental variation, an epigenetic source of phenotypic diversity with far-reaching biological consequences, J. Biosci. 40(1), March 2015, 159–204 http://link.springer.com/article/10.1007%2Fs12038-015-9506-8

Perhaps more interesting is to consider why these two cells are different. Broadly, there are two, non-exclusive reasons why two cells could be different from each other: deterministic, in which the cells receive different instructions, leading to different outcomes, and probabilistic, in which cells receiving the same instructions can have different outcomes. The latter has often been termed “random” or “stochastic”, and we believe that has led to some conceptual difficulties arising from defining what it means to truly be random. For any given difference between cells, say, the expression of a particular gene, one must assume that difference arises–deterministically–from some other difference between the cells in the past, say, the spatial configuration of transcription factors regulating the gene. This “cellular butterfly effect” makes the very word random difficult to rigorously justify. We will later propose instead a framework centered around more concrete operational definitions based on mappings between inputs and outputs (Figure 2). For example, inputs could be defined as the abundances of all transcriptional regulators, the output could be defined as the the abundance of the target gene’s mRNA, and the mapping would then be process of transcription itself. A deterministic mapping is one in which the values of a particular input will always give the same output. A probabilistic mapping is one in which a given set of inputs yield different outputs–in the example of gene expression, different abundances of the target gene’s mRNA. We will discuss various mappings in biology and how various submappings within those mappings reveal the ways in which probabilistic behavior is generated and controlled.

Figure 2. Mappings of inputs to outputs can either be deterministically specified, diversity generating, or buffering.

A. Illustration of the three types of mappings. B. Illustration of revealing hidden variables that explain a seemingly probabilistic mapping, with an example of cell size as a hidden variable (from Padovan-Merhar et al. Mol. Cell 2015). C. Diagram of layers of specification in the retinal mosaic in Drosophila melanogaster (adapted from Wernet et al. Nature 2006). Individual ommatidia contain R7 and R8 cells, which either express Rh3 and Rh5, respectively (pale ommatidia) or Rh4 and Rh6, respectively (yellow ommatidia). The specification results from stochastic expression of the spineless transcription factor. Ultimately, the organismal phenotype is ~30% pale vs. ~70% yellow ommatidia.

With this framework, the question of what differences actually matter for the cell becomes easier to conceptualize. Here, one can define the output of a mapping may be, say, a phenotype of interest. For a given set of inputs, does one get a probabilistic output? In that case, such a mapping would be considered a diversity generating mapping (Figure 2A). For example, if we consider the mapping between genotype and phenotype, a probabilistic phenotype would be an example of a diversity generating map. Conversely, a mapping that takes multiple inputs to a single, reliable output would be considered a buffering mapping (Figure 2A). For example, consider induced pluripotent stem cells: our increasingly comprehensive molecular assays have revealed that they often differ remarkably from the embryonic stem cells they are meant to mimic, but the bottom line is that you can use these cells to generate a full mouse (Takahashi and Yamanaka, 2006).

We will highlight a number of examples that point to interesting new types of mappings, suggesting that many biological processes consist of layers of both determinism and non-determinism. We hope that viewing single cell biology through this lens may reinvigorate debates around the concepts at the core of this still rapidly evolving field.

How cells are different from each other: let me count the ways

Researchers have known for decades that genetically identical cells can differ from each other: as early as 1961, Mary Lyon (Lyon, 1961) reported mosaic inactivation of the X chromosome in female mice, and in 1989–using the then newly developed technique of PCR –scientists showed the presence of extremely lowly expressed tissue-specific genes in bulk RNA from other tissues, which they inferred to be ‘illegitimate’ transcripts that were present in only one or few cells (Chelly et al., 1989). Further refinement of molecular techniques has unearthed a new world of cellular diversity, and over the last several years, researchers have developed a plethora of new tools that have revealed how cells are different from each other with an unprecedented level of depth, breadth and variety. A number of excellent reviews discussing these tools and their findings already exist (Crosetto et al., 2015; Itzkovitz and van Oudenaarden, 2011) and therefore we only provide an overview here to give context for our further discussion.

One of the first areas in which people measured cell-to-cell variability was in gene expression by measuring the levels of mRNA and proteins. Initially, researchers measured expression levels by simply quantifying the amount of GFP in the cell via fluorescence microscopy or flow cytometry (Elowitz et al., 2002; Ozbudak et al., 2002; Raser and O’Shea, 2004). Rapidly, these techniques evolved to measure variability in GFP levels across panels of genes (Bar-Even et al., 2006) or even across all genes (Newman et al., 2006), revealing, amongst other things, that stress-response genes tended to be more variable than housekeeping genes.

In parallel, the development of single molecule microscopy techniques enabled new science-fiction-like levels of accuracy, enabling us to measure cellular differences with incredible quantitative precision by counting individual molecules in single cells. One thread has evolved around the visualisation of individual mRNAs in single cells, both in fixed (Femino et al., 1998; Levsky et al., 2002; Raj et al., 2008, 2006; Zenklusen et al., 2008) and living cells (Bertrand et al., 1998; Chubb et al., 2006; Coulon et al., 2014; Golding et al., 2005; Larson et al., 2011a). Over the years, these methods have matured in terms of the types of processes that one can measure, including now sensitive measurements of the transcriptional process itself (Levesque and Raj, 2013; Levsky et al., 2002; Little et al., 2013), nuclear export (Grünwald and Singer, 2010) and allele-specific expression (Ginart et al., 2016; Hansen and van Oudenaarden, 2013; Levesque et al., 2013). The advent of new probing strategies have also greatly increased the breadth of measurements, enabling on the one hand the measurement of 1000s of genes - one at a time - across very large numbers of cells (Battich et al., 2013), and on the other hand allowing measurements of transcript abundance of 10s to 100s or even 1000s of genes simultaneously in individual cells (Chen et al., 2015; Levesque and Raj, 2013; Lubeck et al., 2014; Lubeck and Cai, 2012), with direct in situ sequencing on the horizon (Ke et al., 2013; Lee et al., 2014).

Single protein measurements present a greater technical challenge, but clever combinations of different technologies has allowed the absolute quantification of protein numbers, pioneered in large part by the Xie and Xiao labs (Cai et al., 2006; Choi et al., 2008; Hensel et al., 2012; Yu et al., 2006), even parallelized to measure thousands of genes in E. coli (Taniguchi et al., 2010). Techniques such as mass cytometry enable the detection of protein levels by flow cytometry for dozens of proteins at a time, allowing also for the detection of protein modifications that are essential parts of cell signaling (Bendall et al., 2012). Spatial localization of signaling molecules in single cells, such as nuclear translocation (Cai et al., 2008; Tay et al., 2010), can also reveal signaling behavior in single cells.

However, while most of the examples cited above were mostly limited to the study of one or a few genes at a time through microscopy, much of the recent interest in single cell biology has been driven by the massive increase in the scale of measurements, primarily advances in sequencing. Single cell RNA-sequencing has allowed us to probe the entire transcriptome of individual cells, and while technical questions about accuracy remain (Grün et al., 2014; Marinov et al., 2014; Wu et al., 2014), the ability to measure even coarse transcriptomes from large numbers of cells (Klein et al., 2015; Macosko et al., 2015) is poised to transform the sophistication of the questions we can ask. Developments in mass spectrometry suggest that single-cell proteomics (Bjornson et al., 2013) and metabolomics (Zenobi, 2013) may be on the verge of a revolution akin to that of the RNA field. Analysis of the protein content of single cells is likely to provide us with a far richer and more comprehensive picture of cellular variability in the near future.

Despite our now rather mature ability to measure RNA and protein at the single cell level, a host of open questions remain. It will be increasingly important to integrate different types of measurements and simultaneously monitor regulatory activity, RNA and protein levels, as well as the metabolic and signalling state of individual cells to fully capture the relationship between these processes and their relative importance for biological function. For example, simultaneous measurements of RNA and protein levels in single cells (Albayrak et al., 2016; Raj et al., 2006; Taniguchi et al., 2010) has shown that depending on half-lives, mRNA and protein levels may or may not correlate strongly between cells, and new tools have even enabled the visualization of the initial rounds of translation (Halstead et al., 2015; Katz et al., 2016; Wu et al., 2015). At the same time, recent work has also attempted to link transcription factor localization and binding to transcription. Using cutting edge microscopy (Elf et al., 2007; Hammar et al., 2012) and probing technology (Shah and Tyagi, 2013), efforts to relate the binding of transcription factors to transcription itself are just now shedding light on these relationships (Larson et al., 2011b; Sepúlveda et al., 2016; Shah and Tyagi, 2013; Xu et al., 2015), and single cell reporters of methylation are on the horizon as well (Stelzer et al., 2015). The advent of genome-wide techniques for measuring transcription factor binding provide a glimpse of what the future holds in this regard (Buenrostro et al., 2015; Cusanovich et al., 2015).

The integration of spatial information to understand the relationship between cells in space and time is another frontier in the field that will be critical for linking single cell phenomena to organismal behavior. Imaging studies are a natural starting point, and RNA hybridization studies have already begun to assess the degree of heterogeneity directly in tissue (Bahar Halpern et al., 2015a, 2015b; Bahar Halpern and Itzkovitz, 2015). Exciting new developments augmenting sequencing-based transcriptomics with spatial information have led to the development of spatial transcriptomics (Achim et al., 2015; Junker et al., 2014; Satija et al., 2015), and as mentioned, in situ sequencing may ultimately provide an even more direct spatial picture of expression (Lee et al., 2014). Spatial information can provide not just context, but by proxy, information on cell lineage, showing that, for instance, expression profiles of closely related (e.g., sister) cells tend to be more correlated (Bai et al., 2010; Cote et al., 2016; Duffy et al., 2012). Furthermore, combining time-lapse microscopy with subsequent transcriptional analysis can explicitly demonstrate how cells inherit expression patterns through cell divisions (Cote et al., 2016).

Why are cells different from each other?

As the single cell toolkit expands, the question of how to parse all these data remains largely unanswered, however. Even if we could count every molecule in the cell, would that necessarily lead to more understanding of the biology of single cells? Just as Tycho Brahe’s comprehensive star charts were not the key to understanding the motion of heavenly bodies, we think that more careful conceptual thought must go into understanding exactly why cells are different from each other, otherwise we will continue with quantification sans justification ad infinitum (Mellis and Raj, 2015).

Gene expression provides an excellent case study to examine the reasons why cells are different: the landmark studies of Elowitz et al. and Ozbudak et al. (Elowitz et al., 2002; Ozbudak et al., 2002) clearly demonstrated using fluorescent proteins that expression levels can vary between otherwise identical-seeming cells. These papers in many ways marked the beginning of the current era of quantitative single cell biology.

The variability identified by these studies raised the fundamental question: why are these cells different from each other? A priori, there are a number of possibilities. Perhaps the most aesthetically pleasing is the chemical one, in which the small numbers of molecules and their random collisions–in this case, say, RNA polymerases with DNA and ribosomes with RNA (Arkin et al., 1998; Kepler and Elston, 2001; McAdams and Arkin, 1997; Paulsson, 2005; Thattai and van Oudenaarden, 2001)–leads to variability in transcription and translation. Yet implicit in this explanation is the notion that each cell is otherwise completely equivalent to the next one.What if there were other “hidden variables” explaining why the expression of the cells differed, i.e., if not all inputs to the mapping had been fully defined (Figure 2B)? The beauty of the Elowitz experiment was that it not only revealed cell-to-cell variability, but that it also provided an explicit demonstration of a probabilistic mapping that takes hidden variables into account. Experimentally, they constructed two almost identical but experimentally distinguishable copies of a gene in the cell, and any deviations between these two genes were interpreted as “intrinsically random” variability, whereas deviations shared between the two genes, but different in one cell and another cell, were deemed “extrinsic” variability, i.e., variability due to hidden or not-considered factors. Elowitz et al. found that both types of variability exist.

The demonstration that hidden factors exist provides an imperative to more carefully define the inputs to the gene expression mapping. Indeed, consider the case of lambda-phage: seminal theoretical work demonstrated that pure chemical noise could generate the divergent cell fates of lysis and lysogeny (Arkin et al., 1998), but subsequent experimental work has shown that much of this diversity is actually the result of variability in “hidden factors” (St-Pierre and Endy, 2008; Zeng et al., 2010), such as cell size, position in cell cycle, and even the subcellular localization of virus infection. Other studies have revealed a host of hidden factors in other systems as well. For example, in mammalian cells, even the simple fact that larger cells have more RNA in them overall (Kempe et al., 2015; Padovan-Merhar et al., 2015a) show that many hidden variables may lay in plain sight. (Importantly, Padovan-Merhar et al. followed up by experiments to explicitly demonstrate that this results from a global volume-dependent transcriptional control mechanism to maintain transcript concentration rather than just count.) Additional factors influencing variability in expression include cell cycle (Buettner et al., 2015; Zopf et al., 2013), mitochondrial variability (Guantes et al., 2015; Johnston et al., 2012), heterogeneity in cell culture medium (Guo et al., 2016), temperature (Arnaud et al., 2015) and a plethora of other factors (Battich et al., 2015).

It is tempting, then, to imagine that a proper determination of intrinsic, random variability would require factoring out all other hidden factors, and indeed many studies try to “control” for as many of these factors as possible. Ultimately, though, this quixotic endeavor would leave us empty-handed, because factoring out all possible hidden variables would also remove all randomness. After all, setting aside quantum mechanical considerations for now, if we could measure the locations and trajectories of every molecule, and could then (with sufficient simulation power) predict why one copy of Elowitz’s gene produced more fluorescent protein than the other–would the differences then be considered truly random? Although these philosophical musings are worth debating, the point is that there are always more hidden factors, and so the motivation for the mapping concept we have introduced is to sidestep these discussions and allow for a framework to practically discuss the origins of cellular variability. In particular, the concept of submappings that reflects both our increased ability to measure various inputs and outputs and our theoretical considerations of what layers of abstraction are most important, provides a practical means by which to classify the origins of cellular variability. For instance, now that we are able to measure transcription factor concentration and transcription directly in single cells (Sepúlveda et al., 2016), we can decompose the original Elowitz mapping (from cellular concentrations of all potential regulators to fluorescent protein levels) into two submappings: first, from cellular concentrations of a particular regulator to transcription, and second, from transcript abundance to protein abundance. Being explicit about such decompositions (and the definitions of inputs and outputs) allow us to precisely describe what the sources of probabilistic behavior are.

Probabilistic gene expression

Gene expression provides perhaps the most well-studied set of examples of probabilistic mappings and submappings. These submappings involve a plethora of molecular processes, including transcription, translation, RNA degradation, binomial partitioning upon cell division (Rosenfeld et al., 2005), alternative splicing (Waks et al., 2011) and nuclear trafficking (Bahar Halpern et al., 2015a; Battich et al., 2015). Yet, for most genes, the root source of probabilistic expression levels is most likely the low copy number of the gene itself, combined with the fact that in many instances, the transcription of genes is itself pulsatile, with transcription occurring in “bursts” (Bahar Halpern et al., 2015b; Chubb et al., 2006; Golding et al., 2005; Levsky et al., 2002; Raj et al., 2006; Suter et al., 2011). How do we know these bursts are a manifestation of the probabilistic execution of the transcriptional mapping? To the extent that we believe the intracellular milieu is the input to the mapping, then an Elowitz-style experiment would reveal probabilistic behavior. In mammalian cells, imaging studies have revealed that bursts from the two alleles are largely uncoordinated (Levesque and Raj, 2013), thus showing that bursts themselves are a major source of non-determinism in gene expression. Similarly, multiple independent studies that used gene expression measurements from a collection of cell lines where a transgene was positioned at different genomic locations, has shown that the difference in gene expression variance is rooted in the locus-dependent pattern of transcriptional bursts (Dey et al., 2015; Singh et al., 2010; Viñuelas et al., 2013).

A major remaining gap is disentangling the sub-mappings between the transcriptional regulators and the bursts themselves; i.e., between the biochemical underpinnings of transcription and the phenomenology of bursts. In the case of bacteria, the work of Chong et al. has shown that DNA supercoiling can result in bursts of transcription (Chong et al., 2014), while other work measuring binding of transcription factors simultaneously with transcription revealed that transcription factor occupancy was too rapid to in and of itself lead to bursts (Sepúlveda et al., 2016)(Jones et al., 2014). In eukaryotes, and particularly higher eukaryotes, the situation is considerably more murky. The most intuitive candidate for bursting is the binding of a transcription factor; however, the timescales of transcription factor binding and unbinding is considerably faster than that of transcriptional bursts, and most strikingly, variability in transcription factor concentration and binding does not seem to propagate to the level of transcriptional bursts (Shah and Tyagi, 2013; Xu et al., 2015). Thus, the mapping between transcription factor milieu and instantaneous transcriptional activation seems highly probabilistic.

Looking elsewhere, evidence supports some role for nucleosome positioning (Brown et al., 2013; Raser and O’Shea, 2004), promoter structure (Dadiani et al., 2013; Suter et al., 2011) and transcription factor concentration (Octavio et al., 2009; Senecal et al., 2014) in regulating transcriptional bursting. In addition, numerous studies have pointed to chromatin modifiers, particularly histone deacetylases, as modulators of bursting behavior (Batenchuk et al., 2011; Dar et al., 2012; Raj et al., 2010; Suter et al., 2011; Weinberger et al., 2012), although the pleiotropic nature of these perturbations makes the case more suggestive than definitive. Another possibility is that spatial organisation of nuclear chromatin may influence bursting, either by providing a scaffold for stochastic interactions between cis-regulatory elements and proteins, or through the probabilistic interaction between regulatory elements and promoters (Hacisuleyman et al., 2014; Maamar et al., 2013; Misteli, 2007; Schoenfelder et al., 2010; Splinter and de Laat, 2011). While simultaneous measurement of three-dimensional organisation, transcription-factor occupancy and bursting at the single-cell level is not yet possible due to technical limitations, indirect data already supports links between individual elements of this hypothesis (Amano et al., 2009; Liu et al., 2014; Noordermeer et al., 2011), although we are not sure how general these findings may be.

It is important to note that transcriptional bursts are not purely non-deterministic–to the extent that transcription is itself regulated, that mapping must in fact work through bursts in some way. Recent work has shown that the two “dials” provided by transcriptional bursts (i.e., transcriptional burst size and frequency) can be tuned independently, and may represent different ways to tune gene expression (Batenchuk et al., 2011; Dar et al., 2012; Octavio et al., 2009; Padovan-Merhar et al., 2015b; Raj et al., 2006; Senecal et al., 2014; Suter et al., 2011; Weinberger et al., 2012).

While no overarching rules for regulation of transcriptional bursts have emerged, our suspicion is that trans factors largely regulate transcriptional burst size and cis regulatory factors largely regulate transcriptional burst frequency (and that much of the confusion arises from the fact that the line between cis and trans regulation can be a bit blurry). Circumstantially, it seems that burst frequency varies depending on chromosomal context (Becskei et al., 2005; Raj et al., 2006). In a more direct example, a recent study from our lab has demonstrated that changes to looping of the enhancer to the promoter, when appropriately isolated from other regulatory effects, affect burst frequency specifically (Bartman et al., 2016). At the same time, phenomenological studies show that the cell may turn specific dials to solve particular biological problems, such as dosage compensation during DNA replication (Padovan-Merhar et al., 2015a; Skinner et al., 2016; Yunger et al., 2010) or dosage compensation for cell size (Padovan-Merhar et al., 2015a). Elucidating the mappings between mechanisms of gene regulation, transcriptional bursts, and consequences of this random firing remains a major challenge in the field, and will ultimately be critical to understanding this important source of probabilistic behavior in gene expression.

Probabilistic cellular identity

In the case of gene expression, the framework of deterministic vs. probabilistic maps looks rather similar to the experiments from Elowitz et al. Conceptually, however, the mapping framework can encompass many other processes and aspects of single cell biology. Consider cell-type determination in multicellular organisms, a topic that has gained renewed excitement after single cell RNA-sequencing experiments revealed the presence of new cell types and cell states, including new intermediates (Trapnell, 2015). Let’s say we measure the transcriptome profiles of two cells and find a set of genes with differential expression. Often, these differences are assumed to be part of a cell-type specification program, and many algorithms to reconstruct cell differentiation trajectories make this assumption implicitly (Bendall et al., 2014; Trapnell, 2015; Trapnell et al., 2014). Yet, it is possible that many of the differences between these cells are probabilistic rather than deterministic. As we will discuss, rigorous demonstration of this fact is difficult, and many seemingly probabilistic mappings become more deterministic as hidden variables are exposed, but we will also highlight examples in which we think the case for probabilistic mappings is strong, describing how the definition of inputs allows one to make that inference. We also point to results that hint that the relative homogeneity we typically observe may mask hidden underlying probabilistic behavior, suggesting that cell-fate specification may be composed of layers of diversity generating and subsequent buffering mappings. A major challenge for the field will be to settle on the appropriate levels of abstraction for these mappings to enable practical application.

As an illustration of the difficulties associated with definitively showing that cellular behavior is probabilistic as opposed to deterministic, consider the case of embryonic stem cells. When grown in culture, these cells often exhibit variable levels of expression of key regulators such as Nanog. The question is what the status of the cells with low levels of Nanog is. Are they intermediate states of cells on their (deterministic) way to differentiation? Or, given the signals and other inputs they receive, are they in a probabilistic, transient (and hence reversible) “primed” state in which they are exploring several potential lineages (Abranches et al., 2014; Kalmar et al., 2009; Singer et al., 2014)? One means by which to argue for transient (and thus potentially probabilistic) intermediates is to sort out high and low Nanog populations of cells and then see if these subpopulations will eventually revert to the original population’s distribution; similar experiments have also been done in cancer (Gupta et al., 2011) and hematopoiesis (Chang et al., 2008). On the face of it, such experiments confirm state reversion and thus a probabilistic process, though careful analyses of population dynamics both in stem cells (Nair et al., 2015) and hematopoiesis (Pina et al., 2012) raise the possibility that such effects are mostly due to differential growth dynamics. At the same time, observations of variability in Nanog expression levels in vivo raise the possibility that such variability is not just an artifact of cell culture (Smith, 2013). The difficulty of confirming probabilistic behavior in vivo, however, is verifying that the inputs to the mapping (e.g., signaling pathways, regulatory milieu) are indeed constant and not predetermined by some developmental pathway. The ongoing controversy serves to highlight some of the difficulties in establishing whether behavior is truly probabilistic. Such studies could have immense practical implications: one major barrier to the therapeutic use of stem cells is their seemingly probabilistic tendency to differentiate into multiple different lineages, often resulting in poor performance (Cote et al., 2016). If we can specify a layer of mapping at which the lineage chosen is deterministic, then that layer may hold the key to directing stem cells towards more homogeneous fates.

As researchers have delved deeper into regulatory mechanisms, other examples of probabilistic behavior have been revealed to be far more deterministic than initially thought, much as was the case for lambda phage. For instance, in mouse blastocyst development, work on gene expression and cell fate decisions initially suggested that early genes have a seemingly stochastic gene expression pattern, which later stabilise and define cell lineages through signal reinforcement (Dietrich and Hiiragi, 2007; Ohnishi et al., 2014; Plusa et al., 2008). This is in contrast with new data, which suggests not only that clear differences can already be identified between cells (Biase et al., 2014), but that Sox2 (and Oct4) expression and binding predicts cell fate (Goolam et al., 2016; White et al., 2016) much earlier than previously suggested. Another example of a hidden variable is that of mice that can have either 5 or 6 lumbar vertebrae. While seemingly a probabilistic choice, a clever set of embryo transfer experiments showed that the maternal environment can influence the seemingly random decision of the progeny (McLAREN and Michie, 1958).

Stem cell division provides us with another example of potentially probabilistic behavior, this time the maintenance of tissue-specific stem cells. Tissue specific stem cells are responsible for maintaining and replacing adult tissues, but the correct balance between maintaining the stem cell population and differentiation of cells is critical for tissue function. Recent work (reviewed by Krieger and Simonis (Krieger and Simons, 2015)) has shown that in addition to the classic model of differentiation, wherein this balance is achieved through asymmetric cell divisions, the maintenance of adult stem cell can also be determined at the population level, with probabilistic loss and replacement of individual stem cells. Thus, while inputs exist that can deterministically dictate the fate of daughter cells in some cases (Inaba and Yamashita, 2012), experiments using time-lapse microscopy, lineage tracing and modelling have shown that in other situations the stem cell population is dynamically being turned over, with individual clones constantly being lost and replaced by others (Doupé et al., 2012). However, while this behaviour is probabilistic at the population level, it is still unclear precisely what - if any - cues influence these changes in cell state, and so the details of the mappings from one cell’s state to the states of its progeny (and back) is fertile ground for further study.

Collectively, these studies show that the concept of probabilistic mapping between inputs and outputs likely occurs in a wide variety of single-cell contexts and layers of specification, and discriminating between deterministic and probabilistic behavior could have profound consequences. We have here chosen just a few of the many studies that illustrate the conceptual difficulties of showing a particular phenomenon is truly random. As our tools become more sophisticated, we can now often find the “cause” for a particular probabilistic-seeming event. The question that these studies raise is which of these previously hidden variables are practically relevant and which can be effectively ignored. By making those choices explicit, the mapping framework provides a way to avoid the “kick the can down the road” issue that plagues the interpretations of many such studies.

Plasticity in patterning and other organismal traits

Are there any probabilistic behaviors at practical levels of description at all, then? Consider one of the most broad mappings, namely from genotype to organismal phenotype. Depending on our definitions of inputs and outputs, this specification program would seem rather deterministic indeed: identical twins, inbred animal lines or genetic clones provide a striking demonstration of this fact, with genetic equality often leading to virtually indistinguishable physical characteristics. This is of course not to discount the many examples of phenotypic diversity in genetically identical animals (extensively reviewed in (Vogt, 2015)), including humans (Zwijnenburg et al., 2010), but in broad strokes, this mapping seems highly deterministic. Yet, this apparent homogeneity may mask layers of diversity generating and subsequent buffering mappings. As an example, consider the developmental lineage. While C. elegans is famous for its almost completely stereotypes lineage, most organisms have far more plastic lineages. As such, the precise lineage itself is not deterministic but rather likely to be probabilistic, although the ultimate “phenotype” of the organism may buffer this variability into a similar-seeming animals. Potentially, there are many layers of diversity generation and subsequent buffering.

The careful definition of inputs and outputs to submappings can make such layering effects more clear. Consider, for example, photoreceptor selection in the developing Drosophila eye (Figure 2C) (Wernet et al., 2006). Here, the fate of a particular ommatidia as being either “pale” or “yellow” light responsive depends on the expression of a particular transcription factor (spineless). Some ommatidia have cells with high levels of spineless and others do not, thus generating diversity in ommatidia fate. This example also provides a useful means of establishing probabilistic evaluation of a well-defined set of inputs—in an array of otherwise identical ommatidia, the pale ommatidia are randomly interspersed amongst the yellow ones, and such configurational randomness strongly indicates a probabilistic evaluation. It is worth mentioning, as well, that at a broader phenotypic level, the eye produces roughly the same proportion of pale and yellow ommatidia irrespective of the precise spatial configuration; thus, at that level, the functional differences between organisms is low, providing an example of masked variability.

Diversity generation and subsequent buffering may in fact prove to be the rule than the exception. Indeed, there is mounting evidence that at least some elements of embryonic patterning – while deterministic in outcome – do not require deterministic transcriptional and cellular inputs, but instead buffer variability through signalling and self-organisation. Much of embryology is focused on understanding the processes underlying this developmental robustness and some excellent reviews exist on this topic (Félix and Barkoulas, 2015; Martinez Arias et al., 2013; Umulis et al., 2008). We will therefore only highlight one case: the coordinated oscillations in gene expression that occur during vertebrate segmentation and lead to the periodic formation of new segments. These oscillations occur robustly and coordinately within embryos, but become unstable and noisy when single cells are isolated from the embryo (Masamizu et al., 2006). Oscillations can be synchronized through Delta-Notch signalling (Jiang et al., 2000), and in a recent series of experiments Tsiairis and Aulehla showed that (Tsiairis and Aulehla, 2016) coordinated behaviour can be replicated in vitro, when cells were dissociated and cultured together in a dish. Moreover, by mixing cells with different oscillation frequencies they found that they could re-establish synchronous oscillations with a new frequency that corresponded to the average of the input frequencies. These results serve as an excellent example of buffering probabilistic behavior. It will be very important to see how widespread such mechanisms are, and whether the low variability “checkpoints” revealed by genetics and development also serve to buffer probabilistic mappings.

One largely unexplored role for probabilistic behavior is, ironically enough, its use to ensure deterministic outcomes in the multicellular context. This possibility is perhaps best illustrated by Lawton et al. (Lawton et al., 2013), in which the authors study cell migration in the zebrafish tailbud. They found that cells began with relatively little angular variability, but as their motion progressed through the various zones of the embryo, the degree of angular variability increased. Indeed, their data showed a remarkable mixing of cells in this area. Surprisingly, their simulations revealed that this disorder may in fact be critical to the reliable motion of cells in these zones, since very high levels of variability led to a breakdown of orderly migration, while very low levels of disorder led to “jamming” in the cell migration patterns. Thus, a moderate level of variability provided the necessary fluidity to enable the cells to reliably move to the correct place. A similar example involves exploiting limited variability to ensure proper spacing of bristles on the Drosophila notum (Cohen et al., 2010). Other, similar cases may exist, but may remain hidden from our view because of the apparent phenotypic homogeneity masking the underlying non-deterministic behavior.

Although these studies signify the huge progress researchers have made in finding examples of probabilistic and buffering behaviors, it is worth considering that these may represent the tip of the iceberg.Indeed, there is a school of thought in which organismal development is poised at the edge of disorder, in which orderly properties emerge from a gaggle of chaotic individual actors (Peláez et al., 2015; Yuan et al., 2016). We are not sure that the evidence necessarily supports this point of view in its entirety, but we also believe it is more than just a formal possibility and warrants further exploration.

What are the benefits and detriments of probabilistic single cell variability?

In the previous sections, we have argued that cell-to-cell variability (due to probabilistic gene expression programs) is prevalent and that such variability can be either propagated or buffered to higher levels of biological organisation. However, it remains a topic of heated debate whether these phenotypic manifestations are simply a consequence of inherently noisy cellular processes or whether evolution has harnessed probabilistic mappings as design strategies. Phrased differently, the question is: are probabilistic maps intrinsically useful? Conversely, what sorts of buffering maps are in place to reduce harmful variability? Considering that evolution cannot be replayed easily our response remains speculative, and undoubtedly much probabilistic behavior is just noise, but we will highlight examples that suggest that probabilistic behavior may indeed have functional importance in certain settings.

Probability as a mechanism for generating diversity

Let us begin with the ways in which probabilistic maps can be useful for biology. When considering this question a good starting point is to remember that organisms are wedged between two continuous sources of variability: on one hand they are exposed to changing and often unpredictable environments, while on the other hand mutations will unceasingly modify their genetic material, resulting in constant changes of gene expression levels and patterns. Given these conditions, it is likely that the “perfect” mapping between genotype and phenotype is a moving target. Not surprisingly, perhaps the most well-described rationale for why probabilistic execution may be helpful is the generation of diversity without having to explicitly encode a regulatory scheme for every possible (and often unforeseeable) outcome. Researchers first found examples of this sort of behavior in bacteria, with the competence circuit in B. subtilis (Maamar et al., 2007; Süel et al., 2007, 2006) and the Lac circuit in E.coli (Choi et al., 2008) being the most well-studied. In these cases the goal is to optimise fitness by committing a subpopulation of cells to a particular cell fate but not committing all the cells. In single celled organisms, one of the only ways to generate such diversity if the environment is homogeneous is to exploit probabilistic biological execution. Often these alternate cell fates can be costly to generate and reduce the the fitness of a population in a given environment, but in return maximise the fitness when the environment fluctuates, a phenomenon referred to as bet-hedging. Examples of bet hedging include bacterial persistence (Balaban et al., 2004) or sporulation of B. subtilis when nutrients are limited (Veening et al., 2008). Another intriguing recent possibility is that probabilistic gene expression can actually lead to increased genetic diversity through variable DNA repair (Uphoff et al., 2016).

In multicellular organisms, a similar phenomenon of diversifying phenotypes in adverse environments exists. Waddington’s classic experiments on flies showed that stress can reveal latent genetic variability (Waddington, 1953), and work from the Lindquist lab has shown that Hsp90 can serve as a capacitor for this variability (Queitsch et al., 2002; Rutherford and Lindquist, 1998). Studies in birds (Nussey et al., 2005) and plants (Nicotra et al., 2010) have shown that variation in phenotypic plasticity can be selected for when the environment is unfavourable. However, these examples all either rely on or cannot exclude genetic variation as a source of variability, and a role or rationale for non-deterministic execution is less clear. That said, in some instances, probabilistic behavior is a part of the normal developmental process (as discussed in the previous section), and so it remains to be seen whether probabilistic genotype-to-phenotype mapping in multicellular organisms can be linked directly to survival in changing environments.

One intriguing use for non-determinism may be the selection of the fittest (Khare and Shaulsky, 2006). Recent work in Drosophila has shown that in the imaginal wing disk, the determination of what cells live or die can hinge on whether the cells expressed higher levels of Myc, thus gaining proliferative advantages amplified by spatial interactions (Levayer et al., 2015). We consider it worth exploring whether such mechanisms for selecting cells that are for whatever reason the “best” for the particular function are widespread.

Variability as a regulatory mechanism

In addition to its potential role in tolerating different environments, probabilistic behavior may also prove to be a useful means of regulation. As a rationale, consider the difficulties complex metazoa face in specifying the large number of cellular states in the full organism. By using probability to dictate these states, one can obtain high levels of diversity without explicitly encoding all possibilities (the tradeoff being a lack of precise specification). Fascinating work on probabilistic expression and alternative splicing of clustered protocadherin genes in the mammals (Lefebvre et al., 2012) and of the Dscam gene in Drosophila (Wojtowicz et al., 2004) has demonstrated that by expressing different variants in different neurons these genes regulate the self-avoidance of cells and the specificity of neural connections. Another canonical example involves olfactory receptor neurons: each neuron expresses only one of thousands of olfactory receptor genes, and thus every odor generates a unique signature of neuron firing, allowing different smells to be distinguished (Monahan and Lomvardas, 2015). Implicit in this reasoning, however, is the notion that there is a “cost” to regulation, and that at some point, the regulatory capacity of the cell would be overwhelmed by large number of regulators required for direct specification.

A different benefit from probabilistic mappings may come from the extra knobs afforded by variability (i.e., inputs to the mapping), which the cell may use to regulate biological activity in novel ways. For example, the fact that transcription or signaling as a pulsatile process opens the possibility of regulating different aspects of these pulses, potentially leading to counterintuitive behavior. In one beautiful example, Cai et al. showed that frequency modulation of pulsatile calcium signaling allows cells to simultaneously regulate hundreds of genes with the same dose-response characteristics despite variation in individual promoter responses (Cai et al., 2008). A similar example comes from studying oscillations in NF-κB signalling. Work from Michael White’s group showed that this form of signalling involves a dual-delayed negative feedback motif, where the delay in stochastic transcription of the feedback genes is optimised to maximise cell-to-cell heterogeneity in the phasing of the oscillations. This increased temporal variability could then subsequently minimize population-level fluctuations in signalling (Ashall et al., 2009; Paszek et al., 2010). Transcriptional bursts also enable independent regulatory mechanisms to co-exist–for instance, Padovan-Merhar et al. showed that cells achieve homeostasis through the activity of two independent global regulatory mechanisms that influence transcriptional bursts: cell size affects burst size, and DNA replication affects burst frequency (Padovan-Merhar et al., 2015a). Indeed, the very existence of bursts may enable regulatory circuits that may not exist otherwise (To and Maheshri, 2010).

The downside of non-determinism

While non-determinism may have its merits, as outlined above, it is also clear that in many instances, probabilistic behavior can be detrimental. Fundamentally, this question is difficult to study because perturbations that change levels of variability typically also have other effects that make it difficult to ascribe phenotypic differences to changes in variability per se (although the emergence of “noise modulators” is an exciting development (Dar et al., 2014)). Nevertheless, there is increasing evidence suggesting that variability is itself a parameter subject to evolutionary pressures, that mechanisms exists to potentially reduce noise, and that non-genetic variability is associated with disease.

The case for selective forces acting on non-deterministic variability began with genome-wide measurements of noise in single celled organisms (Bar-Even et al., 2006; Newman et al., 2006; Taniguchi et al., 2010), which revealed that housekeeping genes exhibit less variability on average than transcription factors and other regulatory genes. High-throughput single cell imaging (Sigal et al., 2006) and sequencing approaches (Padovan-Merhar et al., 2015a) have essentially corroborated the finding that housekeeping genes are also less variable in metazoan cells, although these conclusions are mostly suggestive.

There is also ample evidence to suggest that gene regulatory networks are constructed in a manner that minimizes variability. For example, the Gregor lab has nicely shown that in Drosophila embryonic development despite probabilistic transcription, the actual transcript abundances display variability very close to theoretical limits (Gregor et al., 2007; Little et al., 2013), and there is some evidence that the topology of networks in bacteria has features that reduce variability (Kollmann et al., 2005). Furthermore, perturbing normal gene regulatory networks can reveal latent probabilistic behavior (Burga et al., 2011; Ji et al., 2013; Raj et al., 2010; Topalidou et al., 2011), indicating that (in these cases) precision and determinism are not the default mode of operation, but emerge through the presence of some buffering mechanism. Apart from the involvement of gene regulatory networks, such buffering can be achieved through the presence of redundant gene regulatory elements (such as shadow enhancers) (Boettiger and Levine, 2009) or of redundant transcription factors (Pioli and Weis, 2014; Stolt et al., 2004) . Other buffering mechanisms may be more complex: for example, mice with reduced levels of the gene Trim28 show a bistable lean-obese phenotype and accordingly also increased variability in behaviour and gene expression. These phenotypic differences are not due to genetic or environmental causes, but rather seem to the caused by the perturbation of an imprinted gene network. When and how this bistable switch is triggered, however, remains enigmatic (Dalgaard et al., 2016).

Collectively, these studies suggest that probabilistic execution of genetic programs may be deleterious for organisms and is therefore typically suppressed. Taking an even more direct approach to study this question, two recent papers explored how DNA variants and selection affect gene expression variability, with the two clever studies reaching different conclusions (Metzger et al., 2015; Wolf et al., 2015). Metzger et al. used a normal promoter altered by both random mutations and naturally occurring variants and measured the mean and variance of the expression of the resulting yeast strains. They found, interestingly, that while the distribution of mean expression levels was roughly the same between the random mutants and the natural variants, the distribution of “noise” took on larger values in the random mutants than in the natural variants. In Wolf et al., the authors took a somewhat different approach by evolving promoters, selecting only for a particular mean level of expression. Surprisingly, they found that the noise levels of these evolved promoters was actually lower than that of the natural promoters and theorize that the high levels of noise facilitate regulatory evolution. It is tempting, based on these results, to infer that variability is selected either for or against by evolution (depending on the noise requirement of a given gene), although it is worth mentioning that even if a mutation affects transcriptional variability, it may also have other effects that are the subject of selection (such as influencing mean expression levels (Ansel et al., 2008)).

Ultimately, the difficulties in specifically manipulating cellular variability make it difficult to establish phenotypic consequences of probabilistic behavior per se, and this remains a major challenge in the field.

Probability and disease

In the the previous examples we painted a general picture of the benefits and detriments of probabilistic behavior. However, understanding probabilistic phenotypes is particularly pertinent to human health, especially considering the current emphasis on personalised genome sequencing and precision medicine. t is likely that at least some cases of incomplete penetrance and variable expressivity in disease will eventually be traced to non-deterministic mutational outcomes, thus motivating the development of “cellular precision” as a complement to genetic precision. One example is the probabilistic perturbation of normal imprinting patterns that can lead to disease: in a recent study, using new, single cell allele-specific expression measurement tools in combination with epigenetic analysis Ginart et al. (Ginart et al., 2016)revealed that mutations to methylation control regions can lead to probabilistic but heritable imprinting behavior in single cells. Furthermore, this study demonstrated that manipulating methylation levels could alter the degree of imprinting heterogeneity, providing hints at the regulatory underpinnings of probabilistic behavior and how it may emerge in abnormal contexts, such as imprinting disorders (Kalish et al., 2014) or during in vitro fertilisation (de Waal et al., 2014).

Probabilistic phenotypes can also emerge in other disease setting, as in the case of resistance to therapies. The best-known examples are persister bacteria (Balaban et al., 2004), and - more recently - antibiotic resistance (El Meouche et al., 2016),(El Meouche et al., 2016)resistance of a few cells to therapeutic agents is also an enormous clinical issue in the treatment of cancer. Generally, this resistance is thought to have a genetic basis, but a mounting body of evidence suggests non-genetic mechanisms may be at play as well (Brock et al., 2009; Gupta et al., 2011; Pisco et al., 2013; Pisco and Huang, 2015; Sharma et al., 2010; Spencer et al., 2009), which may inform treatment strategies (Liao et al., 2012a, 2012b).

A few concluding remarks

Since we last surveyed the field (Raj and van Oudenaarden, 2008), it’s clear that the study of single cell biology has transformed in many ways. The tools are exponentially more powerful, bringing with them new understanding of everything from single molecule transcription factor binding events to evolutionary processes guiding variability. Nevertheless, we believe that considerable challenges lie waiting in the years ahead as we must now confront some of the same questions that have remained unanswered through the years: what are the important molecular events we should consider (and ignore) when studying cellular non-determinism? How pervasive is variability through the range of biological functions, and where does it help and where does it hinder? What are the most informative levels of abstraction? Exciting new research has laid tantalizing clues as to how we might approach these problems, and we expect the next 10 years to be very interesting indeed.