Lineage priming and cell type proportioning depends on the interplay between stochastic and deterministic factors

Lineage priming and cell type proportioning depends on the interplay between stochastic and deterministic factors eLife Assessment This important study shows how stochastic and deterministic factors are integrated in Dictyostelium discoideum to reliably drive determination of distinct cell types despite exposure to nearly identical environmental conditions. The authors present convincing evidence that gene expression variability contributes to the robustness of cell fate decisions, which reveals an unexpected role of stochasticity during cell differentiation. https://doi.org/10.7554/eLife.105512.3.sa0Important: Findings that have theoretical or practical implications beyond a single subfield - Landmark - Fundamental - Important - Valuable - Useful Convincing: Appropriate and validated methodology in line with current state-of-the-art - Exceptional - Compelling - Convincing - Solid - Incomplete - Inadequate During the peer-review process the editor and reviewers write an eLife Assessment that summarises the significance of the findings reported in the article (on a scale ranging from landmark to useful) and the strength of the evidence (on a scale ranging from exceptional to inadequate). Learn more about eLife Assessments Abstract Isogenic cells can break symmetry and adopt different fates, even when exposed to a seemingly identical environment. This deeply conserved phenomenon allows unicellular organisms to pre-empt dynamically changing environments and is central to the evolution of multicellularity. It is thought that cells are primed towards different lineages by cell-cell variation, although the underlying mechanisms are poorly understood. To address this, we exploit the tractability of the social amoeba Dictyostelium discoideum, where cell fate choice also does not depend on spatial cues. We develop and test a model to explain quantitative experimental single-cell observations of probabilistic differentiation. The model suggests that cell cycle position affects lineage choice, as previously shown but that stochastic cell-cell variation also plays a key role. Single cell sequencing reveals genes that exhibit cell type-specific expression or genes that affect fate choice exhibit extensive stochastic cell-cell expression variation. Like lineage priming genes in ESCs, they are associated with H3K4 methylation, which when perturbed affects their expression and disrupt fate choice. We suggest the integration of stochastic and deterministic inputs represents an adaptive mechanism to increase developmental robustness against perturbations that affect deterministic signals. Introduction Symmetry-breaking and cell type differentiation are fundamental features of developmental systems. The mechanisms underlying the spatial control of cell fate choice have been extensively studied (Slack, 2014). However, there are many examples of robust cell fate choice in the absence of spatial cues. Examples include embryonic stem cells (ESCs) in culture (Pauklin and Vallier, 2013), lineage choice in the mouse blastocyst (Saiz et al., 2016; Yamanaka et al., 2010) and ‘bet hedging’ strategies in microbial populations (Maamar et al., 2007; Süel et al., 2007). In these cases, differentiation is probabilistic and is thought to depend on cell-cell heterogeneity. Intrinsic variation in cell physiology, redox state, and gene expression arising from differences in cell cycle position, cell size, inheritance of cell contents upon cell division and transcriptional bursting have all been linked to fate choice (Huh and Paulsson, 2011; Raj et al., 2006). These factors can produce robust cell type proportioning if the probability of cells being in different states is predictable at the cell-population level (if the population size is sufficiently large). Despite the widespread use of heterogeneity to facilitate developmental decision making, we still have a limited understanding of the underlying mechanisms or how variation is tuned to result in robust proportioning. Work has centred around the identification of factors that ‘prime’ cells for differentiation before they commit to a particular cell fate and express genes associated with specific cell lineages. For example, genes associated with ESC differentiation exhibit histone modifications associated with both gene activation (e.g. H3K4me3) and repression (e.g. H3K27me3) simultaneously. This has been termed a bivalent state and is thought to result in a poised state that allows developmental genes to be rapidly activated or repressed in response to differentiation cues (Azuara et al., 2006; Bernstein et al., 2006). H3K4Me3 deposition has also been shown to be sensitive to redox state, thus providing a potential explanation for the link between reactive oxygen species and ESC differentiation (Ulfig and Jakob, 2024). It has also been suggested that the level of stochasticity in the expression of lineage-associated genes could influence the number of cells that are in the primed state and thus the number of differentiating cells (Desai et al., 2021). Finally, deterministic differences between cells, such as cell cycle position have been shown to influence the response to differentiation cues and lineage choice (Pauklin and Vallier, 2013). The social amoeba Dictyostelium discoideum provides a uniquely tractable model system to study the mechanisms underlying lineage priming and the control of robust probabilistic differentiation. In response to starvation D. discoideum cells undergo a multicellular developmental programme to build a fruiting body consisting of hardy spore cells and dead stalk cells that aid dispersal from deteriorating environments. There is assumed to be selective pressure to ensure that the ‘fittest’ or most energy rich cells are chosen as spores, which requires mechanisms that bias differentiation. Furthermore, there is assumed to be strong selective pressure to ensure robust output of ‘optimal’ cell type proportioning. Excess stalk cell production is costly because it reduces the number of viable spores available for dispersal, while underproduction of stalk can compromise fruiting body architecture, limiting the success of spore dispersal (Buttery et al., 2009; Madgwick et al., 2018; Rodrigues and Gardner, 2022; Wolf et al., 2015). Symmetry breaking and initial cell type differentiation in D. discoideum does not depend on spatial cues. Instead, it is generally assumed that D. discoideum cells experience similar levels of a stalk-inducing factor, such as DIF-1. DIF-1 is easily diffusible and the rapid movement of cells within an aggregation results in a well-mixed population. Furthermore, levels of DIF-1 are regulated by negative feedback that can buffer perturbations in DIF-1 synthesis (Insall et al., 1992). Instead, cell fate choice has been associated with differences in cell cycle position at the time of starvation (Gomer and Ammann, 1996; Gomer and Firtel, 1987; Gruenheit et al., 2018; Thompson and Kay, 2000). Cell cycle position affects the threshold of responsiveness to DIF-1 (even though all cells experience the same amount of each signal) (Chattwood et al., 2013; Gruenheit et al., 2018). Under this scenario, stochastic variation in cell cycle length generates a steady-state distribution of cell cycle positions. Optimal proportioning of stalk and spore cells is presumably reached because cell fate propensity has been evolutionarily tuned through the cell cycle when a sufficiently large number of cells is randomly sampled. It is likely that this provides an adaptive mechanism to select the least fit cells to differentiate as stalk (Zahavi et al., 2018). Cells that have just divided are primed to become stalk and are more sensitive to stalk-inducing signals (and less sensitive to spore-inducing signals). Post-mitotic cells have just divided their cytoplasm and are likely to be energy poor compared to cells in G2. This idea is supported by the finding that glucose depletion causes cells to arrest around mitosis and differentiate as stalk cells (Gruenheit et al., 2018; Thompson and Kay, 2000). These observations provide insights into the effects of cell cycle position heterogeneity on cell fate at a population level. However, we still have a poor understanding of how single cells interpret heterogeneity to result in probabilistic decision making or how heterogeneity is tuned to result in robust cell type proportions. To understand how cell-cell variation can be exploited to control fate choice and generate robust proportioning in the absence of cell-cell communication, we have used a combination of mathematical modelling and experimentation. The model is based on observations of probabilistic differentiation in D. discoideum. We find that quantitative behaviour can only be explained by a model that not only encompasses deterministic cell cycle effects, but also the effects of stochastic cell-cell variation on the responsiveness of cells to differentiation-inducing signals. Experimental observations, using single-cell RNA-seq, reveal a set of genes that show extensive stochastic gene expression variation at the time of starvation. These genes show many hallmarks of lineage priming genes. They are upregulated as cells undergo a programme of differentiation and exhibit cell-type-specific gene expression. A genome-wide screen reveals that these genes, together with cell cycle-associated genes, are also more likely to be required for cell type differentiation. Stochastically expressed genes also exhibit differential H3K4 methylation. Perturbation of H3K4 methylation preferentially affects the level of their expression (and thus cell-cell variation), as well as cell type proportioning during development. These observations suggest that deterministic variation in cell cycle position acts together with stochastic variation in developmental genes to control probabilistic cell fate choice. Finally, we suggest this system is evolutionarily advantageous because it allows the use of deterministic information on the status or quality of cells (e.g. their energetic state), yet protects against potentially catastrophic effects of large-scale perturbations that cause cells to exhibit inadequate variation in deterministic properties. These studies provide further evidence supporting the key role of stochastic variation in developmental gene expression and cellular decision making. Results A combination of stochastic and deterministic variation explains lineage priming and fate choice in D. discoideum To understand the mechanisms underlying lineage priming and fate choice, we first reassessed an earlier deterministic model designed to explain cell cycle-dependent fate propensity in D. discoideum (Gruenheit et al., 2018). The model proposes that a cell cycle-associated factor (CCAF) rapidly accumulates at mitosis and increases stalk propensity (Gruenheit et al., 2018). Following mitosis, the level of CCAF decays, resulting in a decreasing propensity of cells to adopt stalk cell fate (and increasing spore propensity) as the cell cycle progresses. This model provides a relatively good fit to observed population level cell fate proportions. However, a deterministic factor governing cell fate would be expected to drive cells in the same state towards the same fate. Instead, experimental observations show cells at the same cell cycle position can adopt different fates (Gruenheit et al., 2018). Furthermore, a truly deterministic model would be expected to result in a discrete change from stalk to spore fate at the point in the cell cycle where CCAF level drops below the threshold that results in stalk fate (see Figure 1 parts A.i and A.ii). Instead, there is a gradual decrease in stalk propensity after mitosis. To develop a model that generates the sort of probabilistic differentiation observed in D. discoideum we first incorporated the deterministic influence of the cell cycle on responsiveness or sensitivity to stalk-inducing factors (CCAF) (Figure 1Ai): where is the starting level of CCAF, β is its rate of decay, and is the amount of time after the end of the previous mitosis. CCAF is measured on the scale of its biological effect rather than in terms of its molecular concentration. In theory, the decay in the level of CCAF could show a range of shapes (e.g. exponential/convex, linear, or parabolic/concave), which depends both on how the underlying factor(s) decay at the molecular level and how molecular concentrations translate into biological effects. We assume linear decay both for simplicity, and because fitting alternative models to experimental data indicate that it is the best fit model (see Supplementary text). Cells with a CCAF level above a threshold value (denoted ) adopt stalk cell fate (in response to stalk-inducing factors). As a result, stalk propensity at time after the end of the previous mitosis () is determined by the proportion of cells with a value of CCAF (given by ) above . This model would produce the step-like pattern of cell fate through the cell cycle (as described above), where all cells adopt stalk cell fate during the period of the cell cycle where CCAF levels are above the threshold () and switch to spore cell fate when CCAF levels decay below the threshold () (Figure 1Aii). This steplike pattern will occur irrespective of how CCAF levels change through the cell cycle (i.e. regardless of whether it is linear or nonlinear) since cells in the same cell-cycle state can only be above or below the CCAF threshold that results in stalk fate. A purely deterministic model clearly does not recapitulate the quantitative shift in cell fate propensity observed experimentally (Figure 1Aiii). We next reasoned that, for the system to show a deterministic change through the cell cycle, but result in a probabilistic output (i.e. stalk propensity), it must integrate another source of cell-cell variation that is independent of the cell cycle (along with a deterministic cell-cycle dependent factor, CCAF). We, therefore, hypothesised that there is also a stochastically variable cell-cycle independent factor (CCIF) contributing to sensitivity to stalk-inducing factors (e.g. CCAF accumulation or breakdown). The addition of such intrinsic variability makes cell fate probabilistic by allowing otherwise identical cells to adopt a distribution of possible responsiveness to stalk-inducing factors. Protein levels can vary widely between cells because it is regulated at multiple levels, including transcription, translation, and stability. The position of the noisiest step in a pathway affects the overall noise dramatically, because each step usually amplifies noise in the previous steps (Alon, 2007). Consistent with this idea, theory and single-cell experiments have shown that a major contributor to cell-cell variation is the bursty expression of low-copy mRNAs. We, therefore, hypothesised that this noisiness across cells arises from stochastic expression of a set of genes contributing to CCIF levels. For this, we adapt the logic of the telegraph model of gene expression (Peccoud and Ycart, 1995). A given gene is either expressed () or not expressed () in any given time interval being examined, where the probability that it is expressed () is a Bernoulli process with probability . Although genes might logically vary in the value of , such variability does not impact our results, so we simply consider the average probability of being expressed across all genes: . When gene is expressed, it contributes to the total value of CCIF, making its realised contribution and expected contribution in any time interval . We assume that genes vary in their contribution to CCIF according to (i.e. is normally distributed with mean and variance ). The expected level of CCIF overall all genes at time is the sum of the values (i.e. the realised level of expression) for the set of stochastically expressed genes. This expectation gives the mean level of CCIF: , with (following the law of total variance; Cornell and Benjamin, 1970) an expected variance of . This scenario results in a normal distribution of CCIF levels, CCIF , which we use to model the properties of the aggregate effect of all stochastically expressed genes on CCIF. Although this derivation implicitly assumes that stochastically expressed genes are independent, this assumption is not strictly required for the distribution of CCIF to be approximately normal. If stochastically expressed genes show clustered co-expression owing to shared regulation, then the sum across these co-expressed blocks is still expected to be approximately normally distributed (as long as there are a reasonably large number of co-expressed clusters) (Diananda, 1955; Hoeffding and Robbins, 1994; Rosén, 1967). In this case, the variance would differ from the form above and instead depend on the properties of the co-expressed blocks (where the blocks of co-expressed genes would simply replace the individual genes in the derivation above). If we were to only consider the contribution of this stochastic variation, the proportion of cells adopting stalk fate () would be determined by the proportion of the distribution that exceeds the threshold value () that leads to stalk fate (Figure 1Bi), which is given by the complementary cumulative distribution of CCIF values above the threshold : where erf is the Gauss error function, defined as . Under this scenario, the proportion of prestalk cells would remain constant throughout the cell cycle (Figure 1Bii), which does not follow the observed progressive shift in stalk fate probability after mitosis (Figure 1Biii). We integrate the deterministic influence of cell-cycle state and noisy gene expression by considering that the total level of sensitivity to stalk-inducing factors is the sum of the value of CCAF and CCIF. We achieve this integration by assuming that the mean sensitivity across cells has a constant component (CCIF) given by (Equation 2), and a cell-cycle dependent component (CCAF) given by (Equation 1). This produces an expression for mean sensitivity at time () that is analogous to Equation 1: , where (i.e. is the sum of the mean CCIF value and starting CCAF value). Note that the change in average sensitivity through the cell cycle depends solely on changes in CCAF levels (), but the change in the average stalk propensity does not change linearly through the cell cycle because it depends on the proportion of cells with a value above (see Figure 1Ci). Using this expression, we can rewrite the overall stalk propensity () at time by replacing in Equation 2 with (see Figure 1Ci): (which represents the integral over the distribution of sensitivity values above the value at time t). This ‘stochastic-deterministic’ model generates a non-linear change in stalk propensity through time (Figure 1Cii) that matches the probabilistic nature of cell stalk fate after mitosis (Figure 1Ciii). The model is also flexible in that, at its limits, it can produce anywhere from the step function (Figure 1A) expected for a purely deterministic process (i.e. as ) and the constant proportioning (Figure 1B) expected for a purely stochastic process (i.e. as ) (see Appendix 1). To facilitate fitting of the model in Equation 3 to experimental data, we can reduce the parameter space by combining the three constants (, , and ) into a single term, denoted , which represents a sort of reference point for the model. This rescaling is achieved by assuming that the parameters are all measured in standard deviation units and that sensitivity is measured as a distance from the threshold that leads to stalk cell fate (), such that . This results in a two-parameter version of Equation 3, , that can be fitted to the stalk propensity data (see below) to estimate the two parameters ( and ), where the parameter estimates are in standard deviation units (meaning represents how far mean sensitivity is from the threshold, measured as a Z-score). To test this model empirically, we started by fitting the model to existing data on stalk propensity through the cell cycle (see Supplementary file 1 for the original raw data and adjusted values used in the analysis). These data come from an experiment (Gruenheit et al., 2018) where time-lapse microscopy was used to group cells according to their cell cycle position at the time of starvation. The fate of each cell was monitored using live cell reporter genes. For our analysis, we used the measures of relative stalk propensity over 6 hr (after which cells stochastically re-enter mitosis). We find that the stochastic-deterministic model provides an excellent fit to the data (adjusted R-squared=0.92, AIC = −56.37), yielding estimates of = 0.57 and = 0.41 (Figure 1Ciii) that correspond to an expected steady-state stalk propensity of 0.35 and an expected starting propensity of 0.72. Moreover, the stochastic deterministic model provides a significantly better fit to the data than the previously proposed model for exponential decay of CCAF (Gruenheit et al., 2018) (it is 98 times more likely; see Appendix 1 and Figure 1—figure supplement 1). We also evaluated the support for our model assumptions by comparing the fit of other models derived using alternative assumptions. We evaluated the assumption of linear decay in CCAF by comparison to models with exponential, quadratic, and cubic decay functions (which together capture a broad range of possible shapes), and the assumption of Gaussian variation in CCIF by fitting a model based on gamma-distributed variation (which can capture a diversity of distributions, including ones approximating normality). These model comparisons all support our model assumptions (see Appendix 1 for the methods and results of these comparisons). Stochastic gene expression variation is extensive in growing cells The stochastic-deterministic model suggests that cell fate choice in D. discoideum should not only depend on deterministic cell cycle-dependent cell-cell variation, but also stochastic effects on the expression of genes associated with fate choice. Cell cycle position-dependent gene expression variation has been observed in single-cell RNA-seq (scRNA-seq) data from D. discoideum cells isolated prior to starvation and exposure to differentiation-inducing signals (Gruenheit et al., 2018). Because these data are from a relatively small number of cells, but sequenced to high depth, we reasoned they could also be used to identify stochastic expression variation. We first determined the coefficient of variation (CV2) of expression for all genes. As expected, this tends to decrease as average expression level increases (Figure 2—figure supplement 1). When this trend is accounted for, genes with greater cell-cell variability than expected for their level of expression (FDR 0.65) allowed even those genes that show a weak association with cell cycle position to be identified. When these were removed, many genes remain that exhibit variation that cannot be explained by differences in cell cycle position (Figure 2B). Unlike cell cycle genes, principal component analysis does not result in cell groupings (Figure 2C). This variation is, therefore, consistent with stochastic influences on gene expression rather than a consequence of hitherto unknown extrinsic cues. This approach was extended to determine whether cell cycle-associated genes are also influenced by stochastic effects. For this, the CV2 of each gene was recalculated within groups of cells from each of the different cell cycle stages. Most cell cycle dependent genes were found to exhibit greater within group variation than expected (Figure 2D). This is not due to the low level of expression at specific cell cycle stages, as variation is higher at all stages, including when they are maximally expressed (Figure 2—figure supplement 2). These results thus reveal that stochastic effects on gene expression variation are widespread in growing cells. Stochastically expressed genes are associated with cell fate determination In D. discoideum, growing cells undergo a development cycle that begins with the aggregation of thousands of cells and ends with the formation of a fruiting body consisting of terminally differentiated stalk and spore cells. To test whether genes that exhibit variability in their expression are associated with cell fate choice, we first compared the timing of expression of stochastically expressed genes, cell cycle-associated genes, and non-variable genes. The average expression of each gene was compared during growth and development to generate a developmental index (where 0 is exclusive to growth and 1 is exclusive to development) (de Oliveira et al., 2019). Stochastic genes were greatly enriched (p≤0.001, binomial test) for developmental genes (index ≥ 0.9), whereas cell cycle and non-variable genes showed no enrichment compared to the genome-wide expectation (p>0.5, binomial test) (Figure 3A). Next, we tested whether any of these groups of genes were associated with stalk or spore cell fate. Precursors of stalk and spore cells can be identified in the multicellular slug. First, RNA-seq data from prestalk and prespore cells was analysed to identify genes that exhibit cell-type-specific gene expression (where 0 is exclusive to prespore cells and 1 is exclusive to prestalk cells). Again, stochastic genes were significantly enriched in cell-type-specific genes (p≤0.001), with both prestalk (p≤0.001, binomial test) and prespore genes (p=0.013) contributing to this enrichment (Figure 3B). Finally, we determined whether stochastic genes are more likely to be required for fate choice. We performed an unbiased large scale REMI-seq forward genetic screen (Gruenheit et al., 2021) to identify genes required for stalk cell differentiation. REMI-seq technology permits the abundance of thousands of mutants to be simultaneously quantified before or after a selection regime, such as selection imposed by the ability to undergo prestalk cell differentiation. The REMI-seq library was plated at low cell density and treated with cAMP to induce competence to differentiate followed by treatment with DIF-1 to induce prestalk cell differentiation (Figure 3C). Prestalk cells terminally differentiate as dead stalk cells after prolonged DIF-1 incubation, and thus surviving mutants with defects in prestalk cell differentiation can be enriched. After 2 and 6 rounds of growth and selection, gDNA was prepared from each biological replicate for sequencing and quantitative analysis. In order to ensure that enrichment was due to a failure to respond to DIF-1, rather than increased growth rate, we compared these mutants to a control selection in which cells were simply taken through an equivalent number of generations of growth (Gruenheit et al., 2021). An additional control screen was performed to identify mutants that are incompetent to differentiate at all (as either stalk or spore) because they fail to respond to cAMP. Cells were incubated in the presence of the cAMP analogue, 8-Br-cAMP, which triggers spore cell differentiation. Cells that cannot differentiate as spores were killed by detergent treatment, thus reducing their frequency in the population. After these mutants were removed, 244 mutants remained that have likely been enriched due to defects in stalk cell differentiation (Figure 3D, Supplementary file 1). A subset of these mutants was recreated in the parental strain and tested in stalk cell induction assays and most mutants (8/9) exhibited defects in stalk cell differentiation (Figure 3E), illustrating the quantitative success of the REMI-seq approach. This allowed us to test whether genes required for differentiation are more likely to exhibit cell-to-cell gene expression variation. REMI mutants were assigned to 199 genes with intragenic insertions, or mutations where the REMI insertion lay within upstream promoter sequences (within 500 bp of the transcription start site). These genes were significantly enriched for genes with variable expression (p≤0.001, binomial test) (Figure 3F). This is due to both cell cycle-associated and stochastically expressed genes, as the relative number of genes identified in each class does not vary significantly from expected (chi-square, p=0.77). Genes that affect fate choice also exhibit greater variability than expected when the CV2 was normalised to their expression (***p≤0.001, t-test) (Figure 3F). These results suggest gene expression variation is a feature of genes associated with fate choice and cell type proportioning. Stochastically expressed developmental genes exhibit differential patterns of H3K4 methylation Fate choice in D. discoideum shares features with lineage priming in embryonic stem cells, including extensive cell-cell variation of genes associated with differentiation (Chang et al., 2008). In embryonic stem cells, these genes are also associated with specific patterns of epigenetic marks, including the co-occurrence of H3K4me3 and H3K27me3. The role of these modifications is not fully understood due to the difficulty with which epigenetic marks can be altered at a genome-wide scale in higher organisms. However, recent studies have linked histone modifications to the control of transcriptional burst frequency (Weinberger et al., 2012; Wu et al., 2017), which will in turn affect the level of cell-cell variation in transcription. The apparent absence of polycomb-like proteins in D. discoideum suggests H3K27me3 modification is unlikely to play any role (Kaller et al., 2006). However, H3K4 mono, di, or tri-methylation (H3K4Me1-3), which is dependent on Set1/COMPASS, is present (Chubb et al., 2006). H3K9/K14 acetylation is present, which is consistent with the idea that H3K4me3 targets the Gcn5 H3K9/K14 histone acetyl-transferase to specific loci (Huang et al., 2021). We, therefore, tested whether genes that exhibit cell-cell variation in expression in D. discoideum also show hallmarks of differential regulation by H3K4 methylation. Analysis of ChIP-seq data (Wang et al., 2021) revealed that H3K4 methylation exhibits a characteristic gene expression level-dependent pattern around the transcription start site and gene body (Barski et al., 2007; Soares et al., 2017; Figure 4A). To compare patterns in variable and non-variable genes, it was thus necessary to divide genes into bins with similar gene expression levels. Ten random samples of non-variable genes with the same distribution of expression levels as those seen in variable genes were used to compare the profile and number of genes with H3K4 methylation (Figure 4—figure supplement 1). This revealed variably expressed genes exhibit different profiles around the gene promoter and gene body (Figure 4B). In addition, when these were divided into stochastic and cell cycle genes, both groups were enriched for H3K4Me1 (binomial test p10,000 mutants (Gruenheit et al., 2021) was grown to log phase. Cells were plated in triplicate at 2×105 cells/ml in stalk medium in 10 cm diameter tissue culture dishes with 5 mM cAMP for 24 hr. Cells were then washed twice with KK2 before 24 hr incubation with 10 nM DIF. Stalk medium was then removed and replaced with growth medium (HL5) and cells were allowed to grow until reaching confluency. Genomic DNA was prepared from the mutant library following 2 and 6 rounds of this selection and processed for sequencing. To control for mutants that are unable to differentiate in response to cAMP, an 8-Br-cAMP monolayer assay screen was performed. Cells from the mutant library were seeded in triplicate at 2×105 cells/ml in stalk medium supplemented with 10 mM 8-Br-cAMP. After 48 hr, detergent was added (0.1% NP40, 10 mM EDTA) to remove cells that had not formed spores. Stalk medium was then removed and replaced with growth medium (HL5) and the cells were grown until reaching confluency. Genomic DNA was prepared from the mutant library following 1 round of this selection and processed for sequencing (Gruenheit et al., 2021). Analysis of mutant pools was carried out as previously reported (Gruenheit et al., 2021) using Z-score thresholds of >1.5 for enriched mutants and 8 using an Illumina TruSeq kit and sequencing was undertaken on a HiSeq-4000 (Illumina) using 100 bp pair-end chemistry. Sequences were trimmed of TruSeq adapters and quality controlled (Trimmomatic) by discarding reads shorter than 20 bp or those where the average quality score dropped below an average of 15 in a sliding four base pair window. Leading and trailing bases of reads below a phred score of 30 were also removed from tags. Reads were aligned (Bowtie2) to the D. discoideum genome an inverted repeat on chromosome 2 was masked, bamfiles were sorted (Samtools) and reads counted using the RPKM_count.py script (RSeQC). DESeq2 v1.26.0 was used for differential expression analyses. Thresholds for differential expression between samples were set at a p.adj2 between samples. To calculate differences in cell-type-specific gene expression, prestalk, and prespore RNA-seq data was downloaded from the SRA (PRJNA543665) (de Oliveira et al., 2019). Genes with less than 10 read counts were removed. A cell type index was calculated for the remaining 5319 genes (Cell type index = expression count in prestalk cells/expression count in prestalk cells + expression count in prespore cells). ChIP-seq analysis Bulk RNA-seq data from vegetative cells (this study) was used to rank genes based on their level of expression. Genes with detectable expression (i.e. >0 normalised reads) were divided into ten equally sized bins. ChIP-seq data for two H3K4me1 and H3K4me3 replicates was downloaded from the GEO database (accession #GSE137604 Sub-Series GSE137599) as narrowPeak files (Wang et al., 2021). Promoter regions around the TSS for each gene in each bin were identified (–2500 bp to +2500 bp up/down-stream of the TSS) and annotated. Using functions from the chIPSeeker package and custom scripts (https://github.com/WilliamSalvidge/dictyChipSeq, Salvidge, 2023) annotated regions were intersected H3K4-me1 or -me3 peaks as defined by narrowPeak files. Overlaps were averaged for each expression bin and plotted using the plotAvgProf function from the chIPSeeker R package. This accounts for differing numbers of peaks in different expression bins and allows patterns of peak density between expression bins to be compared. To compare peak distribution in variable and non-variable genes, an equal number (2024) of genes was sampled using a weighted probability based on the expression of variable genes. Identification of variable genes using single-cell RNA-sequencing Data for 81 single wild-type cells isolated using the Fluidigm C1 platform were downloaded from the SRA (SAMN07833758 - SAMN0783383). Reads were normalised (DESeq2 v1.26.0) and the coefficient of variation squared (CV2) was calculated and plotted against mean expression. A trend line was fitted to the data using non-linear least squares regression (Scran v1.15.9). Genes were defined as variable (2073 genes) based on a one-sided test assuming a normal distribution around the trend but one where deviation changed depending on the mean expression of a given gene (Scran v1.15.9 - modelGeneCV2) with a FDR of 0.65) ensured that all genes possessing weak cell cycle signature could be identified (5529 genes). This allowed variable genes to be identified that where variation is dependent on cell cycle position (1016 genes) and independent of cell cycle position (1057 genes). Single-cell sequencing of wild-type and set1- cells Actin15-GFP expressing wild-type or set1- cells were grown on tissue cultures dishes and harvested during log-growth. Cells were washed in 1 x PBS and incubated with DAPI (2.5 µg/ml). Cells were resuspended at a density of 2.8×104 cells/ml and dispensed into a SMARTer ICELL8 3’ DE Chip using the ICELL8 cx Single Cell System. Wells of the 3’ DE Chip contain pre-printed oligonucleotides possessing well-specific barcodes and UMI connected to a polydT region for hybridisation with polyadenylated transcripts. For each well of the chip, 50 nl of stained cell solution was aliquoted to maximise the number of wells containing a single cell. Cells were imaged directly dispensing into nano-wells using DAPI and FITC filters and the 3’ DE Chip was frozen at –80 °C. Images taken were analysed to identify wells containing individual cells based on DAPI and GFP fluorescence. In total, 799 wells were identified that contained single cells (399 wild-type and 400 set1-). The 3’ DE Chip was then thawed to lyse cells and loaded onto the ICELL8 cx Single Cell System, where components for reverse transcription (RT) and cDNA amplification were dispensed into chosen wells. After RT-PCR, products from separate wells were collected into a single sample, concentrated and purified according to the manufacturer’s instructions. Samples were prepared for sequencing using a Nextera XT Library Prep Kit (Illumina) and sequenced on a NextSeq 500 (Illumina) system utilising one flow cell and a NextSeq High-Output kit (2×75 bp reads). One read was used to sequence the well barcode and transcript UMI, with the second reading the 3’ end of the transcript itself. This yielded >500 million reads. FASTQ files were demultiplexed (mappa), reads were then quality controlled (reads shorter than 15 bp discarded, a minimum of 30% N’s allowed, phred score of 20) and trimmed of adapters (cutadapt). Reads were aligned (STAR) to the latest version of the D. discoideum genome (v2.7), sorted (Samtools) and tags counted (UMI-tools). Cells were quality controlled (Scater v1.14.6) and cells over 2 median associated deviations (MADs) from the median for library size, total number of features or mitochondrial reads excluded as outliers. This left 310 wild-type and 310 set1- cells. Genes with 0 reads) was determined. The normalised ratio of M/S to G2 marker gene expression was used to define the cell cycle position in each cell. Model fitting to measurements of stalk cell induction To evaluate the fit of our stochastic-deterministic model to data, we used data on stalk fate measured at different times in the progression through the cell cycle in population of cells aligned in the cell cycle (Gruenheit et al., 2018). Stalk fate propensity was measured in two genetically different sets of cells (wildtype AX3 and AX3 with a knockout of the gene gefE) grown under two conditions (‘normal’, G+, and low glucose, G−, conditions), which alter the stalk propensity of cells. We used data from the first six timepoints, corresponding to 0–5 hr after the last division, and combined the four sets of cells by adjusting the values in set such that their mean propensity matched the overall global mean propensity (and hence there is no difference in average propensity of the four sets; see Supplementary Data for the raw and adjusted values). After combining the four sets, one outlier was identified (gefE− under G− at 5 hr), which was consistent with those cells passing a checkpoint where they re-enter mitosis, and was removed, after which data were re-normalised as described above (see Appendix 1 for a comparison of the model fitting with the outlier included). To confirm that the different sets of cells behave similarly, we also fitted the model separately to each class and see no evidence of heterogeneity of model estimates. The stochastic-deterministic model was fitted to these data using the ‘NonlinearModelFit’ function in Wolfram Mathematica version 14, which uses the Levenberg–Marquardt algorithm for least-squares curve fitting. This model fitting yielded estimates of and , the Akaike Information Criterion (AIC), and of the error and total sums of squares, which were used to calculate the R-squared. The details of the alternative models that were fitted and the methods used for comparing the fit of different models to the stalk propensity data are provided in Appendix 1. STAR methods Software Trimmomatic - http://www.usadellab.org/cms/index.php?page=trimmomatic Samtools - http://samtools.sourceforge.net RSeQC - http://rseqc.sourceforge.net Takara mappa - https://takarabiousa.github.io/mappa_userguide.html Cutadapt - https://github.com/marcelm/cutadapt (Martin et al., 2026) STAR aligner manual - https://github.com/alexdobin/STAR/blob/master/doc/STARmanual.pdf (Dobin, 2024) UMI tools manual - https://github.com/CGATOxford/UMI-tools (CGATOxford, 2026) D. discoideum genome - https://protists.ensembl.org/Dictyostelium_discoideum/Info/Index Mathematica 14.0 - https://www.wolfram.com/mathematica/ (Wolfram, 2024)) R - packages DESeq2 - v1.26.0 - https://bioconductor.org/packages/release/bioc/html/DESeq2.html Scater - v1.14.6 - https://bioconductor.org/packages/release/bioc/html/scater.html Scran - v1.15.9 - https://bioconductor.org/packages/release/bioc/html/scran.html M3Drop - v1.12.0 - https://bioconductor.org/packages/release/bioc/html/M3Drop.html SC3 - v1.14.0 - https://www.bioconductor.org/packages/release/bioc/html/SC3.html Superheat - v.0.1.0 - https://rlbarter.github.io/superheat/ (Barter, 2017) Appendix 1 Expectation of the stochastic-deterministic model at its limits In the main text, we note that the stochastic-deterministic model can produce anywhere from the step-like function expected under the deterministic model (Equation 1 and Figure 1A) and the constant proportioning expected for a purely stochastic model (Equation 2 and Figure 1B). The case of the purely deterministic model can be derived by taking the limit where variation from noisy gene expression vanishes, which occurs as the variance in gene expression goes to zero (i.e. as σ→0): This expression takes on the value of 1 during the period of the cell cycle where and a value of 0 otherwise. The case of the purely stochastic model can be derived by taking the limit where the cell-cycle dependent component vanishes (i.e. as ), which yields the expression given by Equation 2, where stalk propensity depends on the properties of the stochastically expressed genes ( and ) relative to the threshold that results in stalk fate (). Comparison of model fit to the exponential-decay model of Gruenheit et al. Model fitting methods In the main text we evaluate the fit of the stochastic-deterministic model to the stalk propensity data from Gruenheit et al., 2018, and compare it to their exponential-decay model. Here, we provide further information on the exponential-decay model and the methods used to compare the fit of the two models. Like the stochastic-deterministic model, the exponential-decay model is a two-parameter model that predicts stalk propensity through the cell cycle. It treats stalk propensity as a deterministic property that changes through the cell cycle according to the equation , where represents the starting stalk propensity (just after the end of mitosis), the exponential rate of decay in stalk propensity, and, the time since the end of the last mitosis (with the tilde being used to differentiate the expectation for this model from the expectation from the stochastic-deterministic model). Although both models have two parameters that capture similar properties, they are not equivalent to each other. The stochastic-deterministic model defines a starting stalk propensity as a Z-score () that translates into the proportion of cells from a stochastically variable (Gaussian) distribution that will become stalk, whereas the exponential-decay model defines a fixed starting propensity (). Both models have decay terms, with the decay term in the exponential-decay model () giving the exponential rate of decrease in stalk propensity, while the decay term in the stochastic-deterministic model () represents the decay in the standardised mean CCAF level. The exponential-decay model was fitted to the data following the same method as that described in the text for the fitting of the stochastic-deterministic model. Briefly, the model was fitted using the ‘NonlinearModelFit’ function in Wolfram Mathematica version 14, which uses the Levenberg–Marquardt algorithm for least-squares curve fitting. This generated estimates for the two parameters, and and for the Akaike Information Criterion (AIC) of the fitted model. We used the error and corrected total sums of squares to calculate the R-squared (since it is calculated incorrectly by default in the NonlinearModelFit function). We evaluated the relative support for each model by comparing the Akaike weights (Burnham et al., 2002; Wagenmakers and Farrell, 2004), which reflect the relative likelihood of the models. To further evaluate the relative fit of the models, we used the parameter estimates to generate a set of predicted values for each model and treated these as independent variables in a single linear model where the observed (adjusted) stalk propensity values were the dependent variable, which essentially allows the two models to directly compete for the fit to the data. Model fitting results As expected based on the findings of Gruenheit et al., 2018, the exponential-decay model provides a good fit to the data (adjusted R-squared=0.88, AIC = −47.19), yielding an estimated rate of decay of = 0.351 and a starting stalk propensity of = 0.74 (Figure 1—figure supplement 1Ai), which would correspond to an overall steady-state stalk propensity of 0.35 (where all times since the end of the previous mitosis are sampled equally). As noted in the main text, although the model provides a good fit to the data, it does not offer a mechanism to translate CCAF levels into quantitative variation in stalk propensity. Hence, it provides a description of the pattern of change in stalk propensity through the cell cycle (as being approximately an exponential decline) rather than a mechanistic model for the process that produces the predicted value of stalk propensity. The ratio of the Akaike weights of the stochastic-deterministic model compared to the exponential-decay model has the value 98.35, which implies that the stochastic-deterministic model is 98.35 times more likely (in terms of Kullback–Leibler discrepancy). This result can also be interpreted as a probability of 0.990 that the stochastic-deterministic model is the better fitting model (meaning we can reject the exponential-decay model as the better fitting model with p=0.010). This conclusion is further supported by the results of the linear model that competed the two sets of predictions, which indicated that the partial fit to the predicted values from the stochastic-deterministic model is very good (F1,20 = 9.83, p=0.0052) while the fit to the predicted values from the exponential-decay model is not significant (F1,20 = 0.48, p=0.49). Evaluating the assumption of normally distributed noise To evaluate the assumption of normality for the distribution of noise in the stochastic-deterministic model, we used an approach that models noise based on the gamma distribution, which is a family of continuous distributions that vary in the values of two parameters (in our implementation, these are a shape parameter and a scale parameter ). By varying the two parameters, the gamma distribution provides probability density functions that go from a pattern of exponential decay to a pattern that approximates normality. The gamma distribution does not have a fixed mean and variance, but the shape parameters together dictate these two properties of the distribution, where the mean is given by and variance by . Using these properties, we modelled decay in CCAF by adapting the gamma distribution to a form that is directly analogous to the approach implemented in the stochastic-deterministic model: where is the Euler gamma function, and is the incomplete gamma function (which is integrated from y to ∞). Following the methods used to fit the exponential-decay and stochastic-deterministic models, we again used the ‘NonlinearModelFit’ function in Wolfram Mathematica version 14 to fit the gamma-distribution model (Equation S2) to our data, except the model includes a total of four parameters (, , , and ) instead of two parameters like the other two models. This not only allows us to evaluate whether the best fit function was consistent with the assumption of normality, but also to further evaluate the Gaussian noise model against the exponential-decay model (since the best fit gamma distribution could approximate either distribution). We find that the best fit model (=1.227, = 0.074, = 56.9, and = 0.023) has a good fit to the data (adjusted R-squared=0.91, AIC = −51.60; see Figure 1—figure supplement 1Aii), with a gamma distribution component corresponding to a distribution of noise that is approximately normal (Figure 1—figure supplement 1Bi and ii.). Hence, the additional two parameters for the gamma distribution yield a similar fit to the simpler stochastic-deterministic model that assumes Gaussian noise, meaning that gamma-distribution model will necessarily be the poorer fitting model given it has two additional parameters (so we do not include any formal model comparisons). This conclusion is further supported by the ratio of the Akaike weights of the model with Gaussian noise compared to the model with gamma distributed noise, which has the value 10.85, meaning that, despite having two fewer parameters, the Gaussian noise model is 10.85 times more likely (corresponding to a probability of 0.92). Evaluating the assumption of linear decay in CCAF The simple version of the stochastic-deterministic model presented in the main text assumes that CCAF shows a linear decay through the cell cycle. What this means in terms of the model properties is that the mean of the distribution of stalk-inducing factors changes linearly through the cell cycle (since the level of CCAF determines the mean level of stalk-inducing factors, while CCIF adds variability around this mean). Importantly, this assumption does not necessarily imply that there is a linear change in some factor(s) at the molecular level (since the number of molecules of a signal could decay exponentially, but the effect of the signal could decay linearly if there is a non-linear relationship between signal levels and their effect, and vice versa). For many biological processes, we might expect factors to show non-linear decay, especially exponential decay (e.g. if concentrations showed a constant half-life). Therefore, to evaluate whether a model with non-linear decay provides a better fit to the data, we replaced the linear decay function in Equation 1 with an exponential decay function. Initial attempts to fit a simple two-parameter decay process (such as the exponential decay equation fitted in Gruenheit et al., which we could write as ) made it clear that there was no parameter space that would produce the pattern of change in stalk proportioning observed through the cell cycle. This issue is due to the fact that the simple exponential decay equation ties together the ‘starting value’ (which would be when ) and the effective rate of decay (e.g. the derivative of the decay function with respect to time, would be , so the linear component depends on the decay rate scaled to the starting value ). Therefore, we used a more flexible exponential decay function that allows for separation between the starting value and the rate of decay: The structure of Equation S3 is superficially similar to the linear decay equation (Equation 2). However, while is the starting level of CCAF in Equation 1 (i.e. the level of CCAF that determines stalk proportioning at the start of the cell cycle), in Equation S3, the starting level (where ) would be . The level of CCAF is eroded by an exponential process captured by the second term on the RHS, which has two parameters, , which represents the size of the CCAF pool that decays, and , which gives the rate of exponential decay. Following the same logic outlined in the main text for the case of linear decay in CCAF, we assume stalk proportion depends on the proportion of cells experiencing a value of CCAF+CCIF that is above a threshold value. Replacing linear decay with the exponential decay process in Equation S3 gives . As in the linear decay model, we can rescale the value of relative to , though the interpretation of the resulting parameter is different in this case since it does not, on its own, capture the baseline value that represents the expectation for stalk propensity at the start of the cell cycle. Instead, while gives the baseline value in the linear decay model (where ), in the exponential decay model, the baseline value (i.e. the value that determines stalk fate at the start of the cell cycle) is given by . Using this value of in place of the one for the linear model to derive the stalk propensity gives (Equation 3): Because of the more complex structure of Equation S4, this model was fitted using the ‘NMinimize’ method in the ‘NonlinearModelFit’ function in Wolfram Mathematica version 14, which forces a global search for the best fit parameters and helps avoid local minima (note that using this method for all other models fitted in our study has no impact on the estimates). The exponential decay model shows a slightly worse fit than the linear decay model (adjusted R-squared=0.920 and AIC = −56.37 for the linear decay model, while adjusted R-squared=0.916 and AIC = −54.24 for the exponential decay model), but given that the fits are almost identical, and the linear decay model shows a slightly better fit, the linear decay model is necessarily the more likely model (with the ratio of the Akaike weights being 2.90). Moreover, the two models produce very similar estimates for the starting level of CCAF (which is an estimate of in the linear decay model and in the exponential decay model), with values of 0.57 for the linear model and 0.56 in the exponential model. They also produce similar estimates for the linear rate of decay (which is given by the term in the linear model, and the first derivative of the solution with respect to in the exponential decay model), with values of 0.41 for the linear model and 0.39 for the exponential model. Importantly, the estimates from the exponential decay model produce a pattern of decay in CCAF that is almost perfectly linear (see Figure 1—figure supplement 1Ci), which reflects the fact that the quadratic change in CCAF (given by the second derivative of the solution with respect to in the to the exponential decay model), which has the value 0.01, is tiny compared to the linear change (as are all higher order relationships). Hence, the fact that the parameter estimates from the best-fit exponential decay model produce an almost perfectly linear change in CCAF through the cell cycle, while showing a model fit that is slightly worse than the linear decay model despite having an additional parameter, provides strong support in favour of the linear decay model over an exponential decay model. To further support this conclusion, we fitted two other generic models for decay of CCAF in the stochastic-deterministic model, a quadratic model of change in CCAF (i.e. where CCAF can change as a function of and ) and a cubic model of change in CCAF (i.e. where CCAF can change as a function of , and ). The quadratic model shows a similar fit to the stochastic-deterministic model with exponential decay in CCAF (adjusted R-squared=0.916 and AIC = −54.25 for the quadratic decay model, cf. above). The reason the fits of the quadratic and exponential decay models are so similar is because the best-fit parameters for both models effectively produce linear decay (Figure 1—figure supplement 1i and ii), which is reflected in the fact that the estimated quadratic term is near zero (with a value of 0.007). Like the stochastic-deterministic model with exponential decay, the model with quadratic decay is less likely than the model with linear decay because it has an additional parameter (with the ratio of the Akaike weights being 2.88). The cubic model shows a similar fit to the stochastic-deterministic model with linear decay (adjusted R-squared=0.921 and AIC = −54.64), but again, because it requires two additional parameters, it is still the less likely model (with the ratio of the Akaike weights being 2.37). Hence, although some degree of non-linearity appears in the best fit parameters for the cubic model (see Figure 1—figure supplement 1Ciii), it does not improve the fit of the model, and hence the most likely model is one with linear decay. Model fitting with the outlier value included To confirm that removal of the outlier stalk propensity value measured for gefE− under G− at 5 hr did not alter our results, we fitted the exponential-decay and stochastic-deterministic models to the full dataset. The exponential-decay model shows the same fit in terms of adjusted R-squared as the model with the outlier removed (adjusted R-squared=0.88, AIC = −50.61), yielding a similar estimated rate of decay (=0.345 compared to 0.351 for the model with the outlier removed) and an identical starting stalk propensity (=0.74 for both datasets). Likewise, the stochastic-deterministic model shows approximately the same fit in terms of adjusted R-squared as the model with the outlier removed (adjusted R-squared=0.91, AIC = −57.47), yielding almost identical estimates for starting sensitivity (=0.557 compared to 0.574 for the model with the outlier removed) and rate of decay in sensitivity (=0.397 compared to 0.409 for the model with the outlier removed). The ratio of the Akaike weights of the models with the outlier included is smaller than for the analysis with the outlier removed (30.91 vs 93.46), but still corresponds to a probability of 0.969 that the stochastic-deterministic model is the better fitting model (meaning we can reject the exponential-decay model as the better fitting model with p=0.031). Influence of stochastic variation on sensitivity to cell-cycle perturbations To consider how the presence of stochastic variation from noisily expressed genes can buffer against the impact of cell-cycle perturbations on stalk propensity, we developed a simple model for biased sampling across the cell cycle. In the absence of bias, we assume that cells are sampled from a continuous uniform distribution from times zero to one, so the probability density is the same for all , i.e., such that , meaning that time in the cell cycle is measured as the proportion of the cycle completed (e.g. if = ½, then cells would be halfway through the cell cycle, since ). The expected stalk propensity () at time is given by Equation (3), so the expected propensity of a population of cells sampled uniformly across the cell cycle (denoted ) is . Because our primary interest is on the impact of cell-cycle biases, and there is an unlimited range of possible ways for non-random sampling of cells from the cell cycle, we use a simple approach to capture non-random sampling across the cell cycle. We assume that bias is linear and defined by the equation , where gives the relative change in probability density caused by sampling bias, and measures the degree of sampling bias and ranges from −1 (bias towards the first half of the cell cycle) and +1 (bias towards the second half of the cell cycle). The degree of bias is translated into a bias in probability density function for sampling from the cell cycle as: (see Figure 8—figure supplement 2 for an illustration of the resulting biased probability density functions). This simple linear modification of the uniform probability density function retains the property that (and hence still represents a probability density function) because it achieves a symmetrically re-distribution of probability density across the range of from 0 to 1. This makes the expected propensity of a population of cells sampled non-uniformly across the cell cycle (denoted ): . There are a number of ways to consider the impact of this bias on the distribution of cells. For simplicity, we consider the proportion of cells that were sampled from the first or second half of the cell cycle, with the proportion of cells in the first half of the cell cycle being , meaning that, at the maximal degree of bias towards the first half of the cell cycle (), ¾ of cells would be in the first half of the cell cycle (which we denote in Figure 8—figure supplement 3 as −¾). We measured the impact of non-random sampling as the relative change in stalk proportioning: . To consider how stochastic variation impacts the relative change in stalk proportioning, we varied the value of , which gives the standard deviation of the distribution of noisy expression (see Figure 8—figure supplement 3). Data availability RNA sequence data were deposited in GEO under project codes PRJNA1034001 and PRJNA1037558. All data generated or analysed during this study are included in the manuscript and supporting files; source data files have been provided for all figures. - NCBI BioProjectID PRJNA1034001. Harnessing noise to enhance robustness of deterministic developmental signalling. - NCBI BioProjectID PRJNA1037558. Single cell sequencing of Dictyostelium discoideum AX4 and Set1 knock-out cells. References - Chromatin signatures of pluripotent cell linesNature Cell Biology 8:532–538.https://doi.org/10.1038/ncb1403 - Developmental timing in Dictyostelium is regulated by the Set1 histone methyltransferaseDevelopmental Biology 292:519–532.https://doi.org/10.1016/j.ydbio.2005.12.054 - The central limit theorem for m-dependent variablesMathematical Proceedings of the Cambridge Philosophical Society 51:92–95.https://doi.org/10.1017/S0305004100029959 - Cell cycle heterogeneity can generate robust cell type proportioningDevelopmental Cell 47:494–508.https://doi.org/10.1016/j.devcel.2018.09.023 - BookThe central limit theorem for dependent random variablesIn: Fisher NI, Sen PK, editors. The Collected Works of Wassily Hoeffding. Springer. pp. 205–213.https://doi.org/10.1007/978-1-4612-0865-5_9 - DIF-1 induces its own breakdown in DictyosteliumThe EMBO Journal 11:2849–2854.https://doi.org/10.1002/j.1460-2075.1992.tb05352.x - Epigenetics in DictyosteliumMethods in Molecular Biology 346:491–505.https://doi.org/10.1385/1-59745-144-4:491 - Markovian modeling of gene-product synthesisTheoretical Population Biology 48:222–234.https://doi.org/10.1006/tpbi.1995.1027 - Individual-level bet hedging in the bacterium Sinorhizobium melilotiCurrent Biology 20:1740–1744.https://doi.org/10.1016/j.cub.2010.08.036 - Reproductive value and the evolution of altruismTrends in Ecology & Evolution 37:346–358.https://doi.org/10.1016/j.tree.2021.11.007 - On the central limit theorem for sums of dependent random variablesZeitschrift Für Wahrscheinlichkeitstheorie Und Verwandte Gebiete 7:48–82.https://doi.org/10.1007/BF00532097 - Single-cell ChIP-seq reveals cell subpopulations defined by chromatin stateNature Biotechnology 33:1165–1172.https://doi.org/10.1038/nbt.3383 - Human but not yeast CHD1 binds directly and selectively to histone H3 methylated at lysine 4 via its tandem chromodomainsThe Journal of Biological Chemistry 280:41789–41792.https://doi.org/10.1074/jbc.C500395200 - Establishment of spatial patternWiley Interdisciplinary Reviews. Developmental Biology 3:379–388.https://doi.org/10.1002/wdev.144 - Determinants of histone H3K4 methylation patternsMolecular Cell 68:773–785.https://doi.org/10.1016/j.molcel.2017.10.013 - AIC model selection using Akaike weightsPsychonomic Bulletin & Review 11:192–196.https://doi.org/10.3758/bf03206482 - mTORC1 pathway activity biases cell fate choiceScientific Reports 14:20832.https://doi.org/10.1038/s41598-024-71298-2 - Division of labour in microorganisms: an evolutionary perspectiveNature Reviews. Microbiology 14:716–723.https://doi.org/10.1038/nrmicro.2016.111 - Fitness trade-offs result in the illusion of social successCurrent Biology 25:1086–1090.https://doi.org/10.1016/j.cub.2015.02.061 - Independent regulation of gene expression level and noise by histone modificationsPLOS Computational Biology 13:e1005585.https://doi.org/10.1371/journal.pcbi.1005585 - An individual-level selection model for the apparent altruism exhibited by cellular slime mouldsJournal of Biosciences 43:49–58. Article and author information Author details Funding Wellcome https://doi.org/10.35802/095643- Chris Thompson Natural Environment Research Council (NE/V012002/1) - Jason Wolf - Chris Thompson The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication. For the purpose of Open Access, the authors have applied a CC BY public copyright license to any Author Accepted Manuscript version arising from this submission. Acknowledgements This work was supported by a Wellcome Trust Investigator Award (WT095643AIA) to CRLT and grant from NERC (NE/V012002/1) to CRLT and JBW. Version history - Sent for peer review: - Preprint posted: - Reviewed Preprint version 1: - Reviewed Preprint version 2: - Version of Record published: Cite all versions You can cite all versions using the DOI https://doi.org/10.7554/eLife.105512. This DOI represents all versions, and will always resolve to the latest one. Copyright © 2025, Salvidge et al. This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited. Metrics - - 805 - views - - 26 - downloads - - 0 - citations Views, downloads and citations are aggregated across all versions of this paper published by eLife.