Towards a mathematical theory of development

生物学已经进入了精确测量的新时代。单细胞RNA测序等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在种群发展和亚群分化过程中的轨迹，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，这是不可能的与当前的测量技术，因为它们是破坏性的：一个细胞必须被杀死之前，其表达谱可以测量。 该建议开发了一个数学框架，用于理解细胞在动态变化的异质种群中的轨迹，该动态变化的异质种群基于沿着时间过程的静态快照。我们提出了一个新的发展原则，称为最佳运输假说，这导致了一个新的数学理论的发育生物学。通过实验合作，我们在不同的生物环境中测试了这一理论，包括免疫学，小鼠皮层发育，人类干细胞重编程，以及海胆和C。线虫胚胎受该理论的启发，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，我们开发了新的数学方法来分析这一前所未有的时间过程数据，并恢复基因调控的复杂模型。 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布罗德研究所的同事合作分析小鼠干细胞重编程的时间过程。其关键思想是使用一种称为最优运输的经典数学技术将细胞与下一个时间点的潜在后代联系起来，其具体形式是在拿破仑的军队中开发的，以重新分配成堆的泥土。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该过程的转录因子。例如，我们的分析预测转录因子Obox 6和细胞因子GDF 9在多能性的建立中起作用，并且我们通过证明添加这些因子中的任一个增加了重编程为iPSC的效率来实验验证了这些预测。我们还通过在中间时间点保留数据并对细胞分布进行插值来证明我们模型的计算预测能力;我们的插值基本上与保留数据的独立复制一样好。这提供了证据的假设，真正的发展耦合同意在短时间尺度上的最佳运输。

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.