Entropy as a measure of variability and stemness in single-cell transcriptomics

Gandrillon, Olivier; Gaillard, Mathilde; Espinasse, Thibault; Garnier, Nicolas; Dussiau, Charles; Kosmider, Olivier; Sujobert, Pierre

doi:10.1016/j.coisb.2021.05.009

Cited by 15 publications

(13 citation statements)

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“…It is noteworthy that the use of Shannon entropy to analyze the scRNA-seq data can be equivocal. Some authors measure the variability of gene expression in a single cell (what we called intracellular entropy) which has been shown to be a proxy for stemness [38,39]. With this approach, the differentiation process is associated with a continuous decrease in entropy, because the transcriptional program is getting more and more specialized as cells undergo differentiation.…”

Section: Discussionmentioning

confidence: 99%

Hematopoietic differentiation is characterized by a transient peak of entropy at a single-cell level

et al. 2022

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Background Mature blood cells arise from hematopoietic stem cells in the bone marrow by a process of differentiation along one of several different lineage trajectories. This is often represented as a series of discrete steps of increasing progenitor cell commitment to a given lineage, but as for differentiation in general, whether the process is instructive or stochastic remains controversial. Here, we examine this question by analyzing single-cell transcriptomic data from human bone marrow cells, assessing cell-to-cell variability along the trajectories of hematopoietic differentiation into four different types of mature blood cells. The instructive model predicts that cells will be following the same sequence of instructions and that there will be minimal variability of gene expression between them throughout the process, while the stochastic model predicts a role for cell-to-cell variability when lineage commitments are being made. Results Applying Shannon entropy to measure cell-to-cell variability among human hematopoietic bone marrow cells at the same stage of differentiation, we observed a transient peak of gene expression variability occurring at characteristic points in all hematopoietic differentiation pathways. Strikingly, the genes whose cell-to-cell variation of expression fluctuated the most over the course of a given differentiation trajectory are pathway-specific genes, whereas genes which showed the greatest variation of mean expression are common to all pathways. Finally, we showed that the level of cell-to-cell variation is increased in the most immature compartment of hematopoiesis in myelodysplastic syndromes. Conclusions These data suggest that human hematopoietic differentiation could be better conceptualized as a dynamical stochastic process with a transient stage of cellular indetermination, and strongly support the stochastic view of differentiation. They also highlight the need to consider the role of stochastic gene expression in complex physiological processes and pathologies such as cancers, paving the way for possible noise-based therapies through epigenetic regulation.

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Section: Discussionmentioning

confidence: 99%

Hematopoietic differentiation is characterized by a transient peak of entropy at a single-cell level

et al. 2022

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“…Shannon entropy is defined for a probability distribution and measures the extent of departure from the uniform distribution - the flatter the distribution, the greater the entropy and the greater the degree of uncertainty ( MacArthur and Lemischka, 2013 ). In particular, the Shannon entropy can be computed per cell (intracellular entropy) or per gene (intercellular entropy), where the latter aims to capture the gene expression variability of genes across an entire cellular population ( Gandrillon et al., 2021 ). In our analysis of the NMp population, we compute both I c and the intercellular entropy of the NM index distribution to examine the gene expression variability of the NM population.…”

Section: Introductionmentioning

confidence: 99%

Zebrafish neuromesodermal progenitors undergo a critical state transition in vivo

et al. 2022

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“…It is noteworthy that the use of Shannon entropy to analyze scRNA-seq data can be equivocal. Some authors measure the variability of gene expression in a single cell (what we called intracellular entropy) which was shown to be a proxy for stemness ( 35, 36 ). With this approach, the differentiation process is associated with a continuous decrease in entropy, because the transcriptional program is getting more and more specialized as cells progress in the differentiation.…”

Section: Discussionmentioning

confidence: 99%

Hematopoietic differentiation is characterized by a transient peak of entropy at a single cell level

Dussiau

Boussaroque

Gaillard³

et al. 2021

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Hematopoietic differentiation has been considered as a multistep process which is metaphorically represented as linear trajectories with discrete steps from hematopoietic stem cells to mature cells. While the transcriptional state of cells at the beginning or at the end of these trajectories are relatively well described from bulk analysis, what happens in the intermediate states has remained elusive until the use of single cell approaches allowed to capture the dynamic changes of transcriptomic states.Applying Shannon entropy to measure cell-to-cell variability among cells at the same stage of differentiation, we observed a transient peak of gene expression variability in all the hematopoietic differentiation pathways. Strikingly, genes with the highest entropy variation in a given differentiation pathway matched genes known as pathway-specific, whereas genes with the highest expression variation were common to all pathways. Finally, we showed that the level of cell-to-cell variation is increased in the most immature compartment of hematopoiesis in myelodysplastic syndromes.These data suggest that differentiation may not be as deterministic and linear as previously thought, but could be better conceptualized as a dynamical stochastic process with a transient stage of cellular indetermination.

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Entropy as a measure of variability and stemness in single-cell transcriptomics

Cited by 15 publications

References 94 publications

Hematopoietic differentiation is characterized by a transient peak of entropy at a single-cell level

Hematopoietic differentiation is characterized by a transient peak of entropy at a single-cell level

Zebrafish neuromesodermal progenitors undergo a critical state transition in vivo

Hematopoietic differentiation is characterized by a transient peak of entropy at a single cell level

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