Towards a mathematical theory of development

生物学已经进入了精密测量的新时代。像单细胞RNA测序这样的技术已经成为以前所未有的分辨率观察生物过程的强大工具。如果我们能够分析细胞随着种群的发展和亚群的分化而移动的轨迹，我们可能会了解控制胚胎发育的遗传力量，细胞类型在整个成年生活中是如何稳定的，以及它们如何随着年龄或癌症等疾病而不稳定。然而，这在目前的测量技术中是不可能的，因为它们是破坏性的：细胞必须在其表达谱被测量之前被杀死。 这一建议开发了一个数学框架，用于基于沿时间进程的静态快照来理解动态变化的、不同种类的种群中细胞的轨迹。我们提出了一种新的发育原理，称为最优运输假说，这导致了一种新的发育生物学的数学理论。通过实验合作，我们在不同的生物学环境中测试了这一理论，包括免疫学、小鼠皮质发育、人类干细胞重新编程以及海胆和线虫胚胎的发育。在这一理论的启发下，我们提出了一种收集数千个时间点的胚胎发育时间过程的scRNA-seq实验程序。最后，我们开发了新的数学方法来分析这种史无前例的时间进程数据，并恢复复杂的基因调控模型。 这项工作建立在我最近开发的一个数学框架上，以便与麻省理工学院和哈佛大学的博德研究所的同事合作，分析小鼠干细胞重新编程的时间过程。关键的想法是在下一个时间点使用一种名为最优运输的经典数学技术将细胞与它们潜在的后代连接起来，这种技术的具体形式是拿破仑的军队为重新分配成堆的泥土而开发的。我们发现，应用最佳运输思想来重新分配细胞的分布很容易重新发现已知的生物学特征，发现新的替代细胞命运，并允许我们推断控制这一过程的转录因子。例如，我们的分析预测转录因子Obox6和细胞因子GDF9在建立多能性中发挥作用，我们通过实验验证了这些预测，证明添加这两个因子中的任何一个都可以提高对IPSCs重新编程的效率。我们还通过在中间时间点保留数据和对细胞分布进行内插，在计算上证明了我们模型的预测能力；我们的内插基本上与保持数据的独立复制一样好。这为以下假设提供了证据，即真正的发展耦合与短时间尺度上的最优运输相一致。

Biology has entered a new era of precision measurement. Techniques like single-cell RNA sequencing have emerged as powerful tools to observe biological processes at unprecedented resolution. If we could analyze the trajectories cells traverse as populations develop and subpopulations differentiate, we might understand the genetic forces that control embryonic development, how cell types are stabilized throughout adult life, and how they destabilize with age or in diseases like cancer. However, this is not possible with current measurement technologies because they are destructive: a cell must be killed before its expression profile can be measured. This proposal develops a mathematical framework for understanding the trajectories of cells in a dynamically changing, heterogeneous population based on static snapshots along a time-course. We propose a new principle of development called the optimal-transport hypothesis, which leads to a new mathematical theory of developmental biology. Through experimental collaboration, we test the theory in diverse biological settings including immunology, mouse cortex development, human stem cell reprogramming, and development of sea urchin and C. elegans embryos. Motivated by the theory, we propose an experimental procedure to collect scRNA-seq time-courses of embryonic development with thousands of time-points. Finally, we develop novel mathematical methods to analyze this unprecedented time-course data and recover intricate models of gene regulation. This work builds on a mathematical framework I developed recently in order to analyze a time-course of mouse stem cell reprogramming, in collaboration with colleagues at the Broad Institute of MIT and Harvard. The key idea is to connect cells to their potential descendants at the next time-point using a classical mathematical technique called optimal transport, whose concrete form was developed in Napoleon's army to redistribute piles of earth. We found that applying optimal transport ideas to redistribute the distribution of cells readily rediscovers known biological features, uncovers new alternative cell fates, and allows us to infer transcription factors that control the process. For example, our analysis predicted that the transcription factor Obox6 and the cytokine GDF9 play a role in the establishment of pluripotency, and we validated these predictions experimentally by demonstrating that adding either of these factors increases the efficiency of reprogramming to iPSCs. We've also demonstrated the predictive power of our model computationally by withholding data at intermediate time points and interpolating the distribution of cells; our interpolation is essentially as good as an independent replicate of the held-out data. This provides evidence for the hypothesis that the true developmental coupling agrees with optimal transport over short time-scales.