Towards a mathematical theory of development

生物学已进入精密测量的新时代。单细胞 RNA 测序等技术已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群体发展和亚群体分化而移动的轨迹，我们就可能了解控制胚胎发育的遗传力量、细胞类型如何在整个成年过程中保持稳定，以及它们如何随着年龄的增长或在癌症等疾病中不稳定。然而，这对于当前的测量技术来说是不可能的，因为它们具有破坏性：必须先杀死细胞，然后才能测量其表达谱。 该提案开发了一个数学框架，用于基于时间过程中的静态快照来理解动态变化的异质群体中细胞的轨迹。我们提出了一种新的发育原理，称为最佳运输假说，它催生了发育生物学的新数学理论。通过实验合作，我们在不同的生物环境中测试了该理论，包括免疫学、小鼠皮层发育、人类干细胞重编程以及海胆和秀丽隐杆线虫胚胎的发育。受该理论的启发，我们提出了一种实验程序来收集具有数千个时间点的胚胎发育的 scRNA-seq 时间过程。最后，我们开发了新颖的数学方法来分析这种前所未有的时间过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与麻省理工学院和哈佛大学博德研究所的同事合作开发的数学框架的基础上，以便分析小鼠干细胞重编程的时间过程。关键思想是使用一种称为最佳运输的经典数学技术将细胞与其在下一个时间点的潜在后代连接起来，其具体形式是在拿破仑军队中开发的，用于重新分配土堆。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，并使我们能够推断控制该过程的转录因子。例如，我们的分析预测转录因子 Obox6 和细胞因子 GDF9 在多能性的建立中发挥作用，并且我们通过实验验证了这些预测，证明添加这些因子中的任何一个都可以提高 iPSC 重编程的效率。我们还通过保留中间时间点的数据并对细胞分布进行插值来证明了我们的模型的计算预测能力；我们的插值本质上与保留数据的独立复制一样好。这为以下假设提供了证据：真正的发育耦合与短时间范围内的最佳运输一致。

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.