Wiesner K, Teles J, Hartnor M, Peterson C
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK.
Computational Biology and Biological Physics, Department of Astronomy and Theoretical Physics, Lund University, Lund 223 62, Sweden.
Interface Focus. 2018 Dec 6;8(6):20180040. doi: 10.1098/rsfs.2018.0040. Epub 2018 Oct 19.
The metaphor of a potential epigenetic differentiation landscape broadly suggests that during differentiation a stem cell approaches a stable equilibrium state from a higher free energy towards a stable equilibrium state which represents the final cell type. It has been conjectured that there is an analogy to the concept of entropy in statistical mechanics. In this context, in the undifferentiated state, the entropy would be large since fewer constraints exist on the gene expression programmes of the cell. As differentiation progresses, gene expression programmes become more and more constrained and thus the entropy would be expected to decrease. In order to assess these predictions, we compute the Shannon entropy for time-resolved single-cell gene expression data in two different experimental set-ups of haematopoietic differentiation. We find that the behaviour of this entropy measure is in contrast to these predictions. In particular, we find that the Shannon entropy is not a decreasing function of developmental pseudo-time but instead it increases towards the time point of commitment before decreasing again. This behaviour is consistent with an increase in gene expression disorder observed in populations sampled at the time point of commitment. Single cells in these populations exhibit different combinations of regulator activity that suggest the presence of multiple configurations of a potential differentiation network as a result of multiple entry points into the committed state.
潜在表观遗传分化景观的隐喻大致表明，在分化过程中，干细胞从较高的自由能朝着代表最终细胞类型的稳定平衡状态趋近。据推测，这与统计力学中的熵概念存在类比关系。在这种情况下，在未分化状态下，熵会很大，因为细胞的基因表达程序受到的限制较少。随着分化的进行，基因表达程序受到越来越多的限制，因此熵预计会降低。为了评估这些预测，我们在造血分化的两种不同实验设置中，对时间分辨的单细胞基因表达数据计算了香农熵。我们发现，这种熵度量的行为与这些预测相反。特别是，我们发现香农熵不是发育伪时间的递减函数，而是在再次下降之前朝着承诺时间点增加。这种行为与在承诺时间点采样的群体中观察到的基因表达紊乱增加是一致的。这些群体中的单细胞表现出调节活性的不同组合，这表明由于进入承诺状态的多个切入点，可能存在潜在分化网络的多种配置。
