Mathematical Methods to Infer Biological Mechanisms From Single Cell Data

活细胞表现出很大的异质性，即使它们具有相同的基因，并在几乎相同的环境中生长。其根本原因是细胞中的分子四处弹跳并相互碰撞，有时会随机反应。这个过程是不可预测的，就像掷骰子的结果是不可预测的一样。因此，细胞的行为可能存在很大差异，这是它们对药物的反应如此不同的主要原因，并且亚群通常在癌症或抗生素治疗中存活。最近的技术发展现在可以测量单个细胞中的成分水平，而不仅仅是细胞群体的平均水平。这提供了大量的信息，但也迫使数据分析在试图解释数据时处理更多的复杂性。该项目将开发分析这些数据的方法。具体来说，它将开发工具来解释生物机制方面的数据，同时对间接影响系统动力学的所有过程保持不可知论，而不是将解释建立在可能有效也可能无效的大大简化的假设基础上。在以前的处理中，这些间接影响会完全混淆解释，而本项目中的方法完全消除了这些问题。该方法是广泛适用的，该项目在基础细胞和分子生物学，健康和医学，生态学和人口生物学方面具有广泛的影响。此外，该项目将在科学学科之间的界面上培训学生，并产生对本科教育有用的原则和方法。 丰度波动的单细胞数据包含了大量关于潜在机制的信息。分析这些数据的传统方法依赖于对特定模型的拟合，这些模型试图对所有对观察到的波动产生重大影响的过程做出正确的假设。无论是使用简单的玩具模型还是详细的模拟，这都带来了一个很大的问题，因为许多间接效应尚未知道，这些效应可能会极大地影响感兴趣的过程。研究还表明，模型的唯一性是这一领域的一个大问题，非常不同的可行模型会产生相同的拟合，但会产生关于潜在生物学的非常不同的具体结论。事实上，从机械上解释最简单的生物体中最简单的单细胞过程是极其困难的，这表明解释更复杂的系统（如嵌入组织中的人类细胞）的希望渺茫。通过这个项目的研究解决了这一挑战，考虑大类的过程集体，允许模型在所有间接影响中任意不同。这是可能的，通过考虑边际分布的属性，可以证明不受许多模型假设的影响，并使其能够严格剖析复杂和稀疏特征的网络，这些网络受到不断变化的环境输入，非线性反馈回路和未知的波动来源的影响，尽管只能访问快照而不是时间序列。由于所提出的方法是分析性的，并且边际性质可以直观地表示在几个明确的机械假设方面，该方法在概念上也是透明的。此外，由于该理论产生的可检验关系对间接效应是严格不变的，因此它们特别适合于分析特征稀疏的复杂系统或药物效应，即使后者是复杂的和占主导地位的，也可以将直接效应与间接效应分开。

Living cells show a great deal of heterogeneity, even when they have the same genes and grow in virtually identical environments. The underlying reason is that molecules in the cell bounce around and collide with each other, and sometimes randomly react. This process is unpredictable in much the same way that the outcome is unpredictable when throwing dice. Cells can therefore differ greatly in their behavior, which is a main reason that they respond so differently to drugs and that sub-populations often survive e.g. cancer or antibiotic treatments. Recent technological developments now make it possible to measure the levels of components in individual cells, rather than just the average level over a population of cells. This provides an incredible amount of information, but also forces the data analyses to deal with many more complications when trying to interpret the data. This project will develop methods to analyze such data. Specifically, rather than basing the interpretations on greatly simplified assumptions, which may or may not be valid, it will develop tools to interpret data in terms of biological mechanisms while remaining agnostic about all the processes that indirectly affect the system dynamics. In previous treatments those indirect effects would completely confound interpretations, whereas the approaches in this project eliminate such problems entirely. The approach is broadly applicable and the project has broad consequences in basic cell and molecular biology, in health and medicine, and in ecology and population biology. Further, the project will train students at the interface between scientific disciplines, and generate principles and approaches that will be useful in undergraduate education. Single cell data for fluctuations in abundances contain a great deal of information about the underlying mechanisms. Conventional approaches to analyze such data have relied on fits to specific models that try to make correct assumptions about all processes that substantially affect the observed fluctuations. Whether using simple toy models or detailed simulations, this poses a great problem because so many indirect effects are not yet known that can greatly affect the process of interest. It has also been shown that model uniqueness is a great problem in this field, where very different feasible models produce the same fit, yet produce very different concrete conclusions about the underlying biology. In fact it has been exceedingly difficult to mechanistically interpret the simplest single cell processes in the simplest organisms, suggesting that there is little hope of interpreting more complex systems, such as human cells embedded in tissue. Research through this project addresses this challenge by considering large classes of processes collectively, allowing the models to differ arbitrarily in all indirect effects. This is possible by considering properties of marginal distributions that are provably unaffected by many model assumptions, and makes it possible to rigorously dissect complex and sparsely characterized networks subject to changing environmental inputs, nonlinear feedback loops and unknown sources of fluctuations, despite only having access to snapshots rather than time-series. Because the presented approaches are analytical, and the marginal properties can be intuitively expressed in terms of the few explicit mechanistic assumptions, the approach is also conceptually transparent. Further, because the testable relations produced by the theory are rigorously invariant of indirect effects, they are particularly well suited for the analysis of sparsely characterized complex systems or the effects of drugs, separating direct from indirect effects even when the latter are complicated and dominant.