Mathematical Foundations of Information and Decisions in Dynamic Cell Signalling

由于DNA是由a、T、C和G碱基对组成的线性字符串，因此，经典信息理论很好地描述了基因组中存储的信息的性质。然而，这些信息通过分子相互作用转化为细胞内的动态过程，正是这些过程决定了细胞的最终状态，比如最终的细胞类型，或者它是否会杀死自己或决定分裂。这些过程用随机动力系统的数学模型来模拟。它们对细胞内外产生的信号作出反应，并利用动态相互作用将这些信号中的信息传递给处理单元，如基因网络，用于细胞决策。然而，当人们谈论DNA或RNA中由有限字母组成的字符串时，信息内容的概念是明确的，一旦基因组信息被传递到动态过程中，目前还没有明确的概念框架。该项目的一个关键目标是通过提供数学基础，在动态信号系统的背景下开发这样一个概念框架。我们的新方法背后的一个关键思想是将细胞决策与信息传输相结合。在这种方法中，信号系统中信息的价值取决于它能在多大程度上用于做出“正确”的决策。我们不去问传输了多少信息，而是问信息的数量和质量是否足以在单个细胞水平或细胞群体水平上做出可靠的决策。决策将在类似于假设检验和歧视分析的背景下进行。基本的想法是，细胞利用信号系统提供的信息来检验多种假设，或在多种选择之间进行区分，每种选择决定一个特定的细胞结果。为此，我们研究基因反应的概率分布随着输入信号的变化而变化的方式。细胞接收到许多关于外部环境和内部状态的信号。这些信号通过相互作用的蛋白质组成的信号系统传递到细胞核，通常通过提高细胞核中转录因子（TF）的水平。这些转录因子调节基因。通过这种方式，输入信号S引起基因的反应R。然而，这个过程是高度随机的，因此响应R有一个分布P(R|S)，我们非常感兴趣的是，随着S的变化，它是如何变化的。基因网络可以被设计成反应R编码一个决定。例如，R可能是导致细胞分裂或杀死自己的基因水平。我们将确定这种决策背后的原则，并将了解支配它的一般原则。特别是，我们将开发工具来了解其有效性。要做到这一点，我们需要分析信号系统的详细模型。我们已经开发了新的方法，并将在项目中进一步开发这些方法。这些模型表明，当S是多维的时候，P（R|S）的依赖性对S具有惊人的依赖性——响应在比输入S低得多的维度空间中移动，这意味着这样的系统将很难做出复杂的决策。我们将研究这是否在通常观察到的调节基因的tf修饰背后，因为我们假设，虽然紧耦合振荡系统允许比平衡系统更复杂的决策，但由于上述低维性，多路复用受到严重限制。当这些修饰状态被包括在模型中时，它可以大大生长，因为TF被其他可以动态调节的蛋白质修饰或结合的能力允许TF动态改变其功能。

Because DNA is a linear string of the base pairs A, T, C and G, the nature of information stored in the genome is well-described by classical information theory. However, this information is translated by molecular interactions into dynamical processes in the cell and it is these processes that determine the end-states of the cell such as its final cell type or whether it will kill itself or decide to divide. These processes are modelled mathematically by stochastic dynamical systems. They respond to signals generated both inside and outside the cell and can use the dynamical interactions to pass information in these signals to processing units, such as networks of genes, to be used for cellular decision-making. However, while the notion of information content is clear when one is talking about strings formed from a finite alphabet as in DNA or RNA, there is currently no clear conceptual framework once the genomic information has been passed into the dynamic processes.A key aim of this project is to develop such a conceptual framework in the context of dynamic signalling systems by providing the mathematical foundations. A key idea behind our approach which is novel is the integration of cellular decision-making with information transmission. In this approach the value of the information in the signalling system is defined by how well it can be used to make the "correct" decisions. Rather than asking how much information is being transmitted, we ask whether the amount and quality of the information is adequate for reliable decision-making either at the single cell level or at the level of populations of cells. Decision-making will be viewed in a context similar to hypothesis testing and discrimination analysis. The basic idea will be that the cell is using the information provided by the signalling system to test multiple hypotheses or discriminate between multiple choices each of which determines a particular cellular outcome.To do this we study the way that the probability distribution of gene responses changes as the input signal changes. Cells receive many signals informing them about the external environment and their internal state. These signals are communicated by signalling systems made up of interacting proteins into the nucleus of the cell typically by raising the level of a transcription factor (TF) in the nucleus. These transcription factors regulate genes. In this way the input signal S causes a response R by the genes. However, the process is highly stochastic and therefore the response R has a distribution P(R|S) and we are very interested in how this changes as S changes.Gene networks can be designed so that the response R encodes a decision. For example, R might be the level of a gene that causes the cell to divide or kill itself. We will determine the principles behind such decision making and will understand the general principles governing it. In particular we will develop tools to understand its effectiveness.To do this we will need to analyse detailed models of signalling systems. We have developed new approaches to this and will be further developing these in the project. These models indicate that the dependence of P(R|S) has a surprising dependence on S when S is multi-dimensional - the response moves in a much lower-dimensional space than the input S which implies that such systems will find complex decision making difficult. We will investigate whether this is behind the commonly observed modifications of the TFs that regulate genes because we hypothesise that while tightly coupled oscillating systems allow more complex decisions than equilibrium systems, the multiplexing is severely limited because of the above low-dimensionality. It can grow greatly when these modification states are included in the model because the ability of the TF to be modified or bound by other proteins that can be dynamically regulated allows the TF to change its function dynamically.