Fluctuations and Control in Cells

生物系统在各个层面上都表现出异质性。即使是基因相同且暴露在相同环境中的细胞也可能具有不同的化学成分。最根本的原因是分子以不可预测的方式弹跳，就像扔在桌子上的骰子一样，当它们随机碰撞时发生反应。这个项目将用数学方法描述随机性。具体来说，它将探讨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产生异质性，就像天气的小变化必须转化为散热器温度的大变化以保持室温恒定一样。它将采用更通用的方法来捕获复杂系统的广泛原理，而不是为特定的系统建模。这使得结果广泛适用于其他学科——无论是在卫生和医学、生态学，还是在出现概念上类似挑战的基础设施问题上。该项目将培养学生在科学学科之间的界面，并产生将在本科教育有用的例子和原则。对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，或者只包括少数反应的简化玩具模型。相反，这个项目将集中于定理的推导，这些定理具有足够的通用性，可以适用于大的过程家族，从而严格理解生物系统的更广泛的设计原则。具体而言，该项目将侧重于推导方差作为其他系统特性的函数的界限，例如，如何选择最大的合成代谢或酶效率不可避免地导致大波动。同样，该项目将得出波动权衡，显示抑制某些组件中的噪声如何不可避免地增加其他组件的波动。数学上，这依赖于马尔可夫过程和非马尔可夫过程、信息论和波动-耗散关系，来推导开放式模型族的统计矩。

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.