Fluctuations and Control in Cells

生物系统在各个层面上都表现出异质性。即使是基因相同、暴露在相同环境中的细胞，其化学成分也可能不同。根本原因是分子以一种不可预测的方式反弹，就像扔到桌子上的骰子一样，当它们随机碰撞时会做出反应。这个项目将从数学上描述这种随机性。具体地说，它将探索波动和控制之间的一般联系，即控制系统的某些部分如何在其他部分创造异质性，就像天气的微小变化必须转化为散热器温度的巨大变化以保持室温恒定一样。它将采取一种更通用的方法来捕捉复杂系统的广泛原则，而不是对特定的系统进行建模。这使得这一结果广泛适用于其他学科--无论是在概念上类似挑战出现的健康和医学、生态学或基础设施问题上。该项目将在科学学科之间的接口上培训学生，并产生将在本科教育中有用的范例和原则。细胞的随机描述历来依赖于必须猜测许多系统细节的详细计算机模拟，或者只包括几个反应的简化玩具模型。相反，这个项目将专注于推导足够普遍的定理，以适用于大家族的过程，以严格理解更广泛的生物系统设计原则。具体地说，该项目将专注于推导作为其他系统属性函数的方差的界限，以展示例如，选择最大的合成代谢或酶效率如何不可避免地导致巨大的波动。同样，该项目将得出波动权衡，显示抑制某些组件中的噪音如何不可避免地增加其他组件中的波动。在数学上，这依赖于马尔可夫过程和非马尔可夫过程、信息论和涨落-耗散关系，以推导出开放模型族的统计矩。

Biological systems display heterogeneity at every level. Even cells that are genetically identical and exposed to the same environments can have different chemical composition. The fundamental reason is that molecules bounce around in an unpredictable way, much like dice do when thrown on a table, and react when they randomly collide. This project will describe the randomness mathematically. Specifically, it will explore the general connection between fluctuations and control, that is, how controlling some parts of a system creates heterogeneity in others, much as small variations in the weather must be translated into large variations in the temperature of radiators to keep the room temperature constant. Rather than model specific systems, it will take a more general approach to capture broad principles of complex systems. That makes the results widely applicable in other disciplines - whether in health and medicine, ecology, or infrastructure problems where conceptually similar challenges arise. The project will train students at the interface between scientific disciplines, as well as generate examples and principles that will be useful in undergraduate education. Stochastic descriptions of cells have historically relied on detailed computer simulations that must guess many of the system details, or simplified toy models that only include a few reactions. This project will instead focus on the derivation of theorems of sufficient generality to hold for large families of processes, to rigorously understand broader design principles of biological systems. Specifically, the project will focus on deriving bounds on variances as a function of other system properties, to show, for example, how selection for maximal anabolic or enzymatic efficiency inevitably leads to large fluctuations. Similarly, the project will derive fluctuation trade-offs showing how suppressing noise in some components inevitably increases fluctuations in others. Mathematically this relies on both Markov and non-Markov processes, information theory, and fluctuation-dissipation relations, to derive statistical moments for open ended families of models.