Bacteriophage and Antibiotic Resistance: a Mathematical and Imaging Approach

人们普遍认为，医学科学正面临着一个对人类健康的未来具有重大影响的问题。由于耐药细菌的进化和传播以及合成新的抗生素产品的难度越来越大，我们需要找到治疗细菌感染的新方法。当我们着手设计利用工程细菌及其病毒噬菌体的合成疗法时，我们需要更好地了解如何使用我们拥有的抗菌剂。找到“最佳的抗生素治疗方法”可能是一个遥远的目标，但研究人员最近开始考虑将抗生素结合起来的新方法，以尽量减少抗生素耐药性的演变。这是提案的重点：我们如何超越药效的药代动力学测量来寻找最佳治疗的新原理？解决这个问题的方法必须包含不同的领域。我们需要系统生物学的工具来告诉我们如何模拟单个细胞内复杂过程的行为，但我们也需要模型来描述抗生素如何抑制这些细胞过程并导致细菌死亡：抗生素的系统生物学。为了检验理论，我们需要实证工作，因为如果我们声称不同抗生素的组合可以制成一种有效的鸡尾酒，我们就应该在实验室里测试这一说法的真实性。提案中解决的研究问题类型的实验范式是“实验微生物系统”，可以在体外创建进化的微观世界，并观察和重复它们的进化。事实上，抗生素耐药性的演变可能如此之快，以至于可以在持续几天的实验中观察到。这种经验方法的效用在于可以迅速地检验假设。我们很快就会看到，理论上创造的观念在实践中是否有效。但我们如何得出这样的理论预测呢？通过采用实验系统的数学模型，并询问“可控性”的形式。也就是说，我们首先要问一个特定的结果是否可以在数学模型中实现。这一结果可能意味着，例如，使用抗生素将细菌从其宿主中移除，方法是将其密度降至最低，同时防止该细菌产生抗生素耐药性；我们认为这类问题很适合系统和控制方法。尽管基因组技术进步很快，但众所周知，生物系统很难建模，数据也很稀少，因此我们需要努力控制它们。然而，我们提出的工作的一个基本特征是概括性原则，这可能有助于超越数据。这个想法是一种常见的数学技术，它是寻找识别具有相同结构的不同系统的原理，这些结构可以用数学工具抽象地处理。例如，在治疗大肠杆菌或假单胞菌感染时，最好的抗生素鸡尾酒有什么共同的原则吗？及时循环使用不同抗生素的治疗方法总是比将抗生素混合成单一鸡尾酒的治疗方法更好吗？细胞内特定的抗生素蛋白靶点重要吗？数学可以帮助阐明像这样的一般问题。由于其中一些问题是困难和雄心勃勃的，提出了更可行的目标。例如，我们是否可以使用成像技术来观察细菌菌落在不同抗生素培养基中的生长，并预测和测量不同鸡尾酒的效力？这种实验本身是新颖的，将为更多的理论部分的工作提供基础。简而言之，结合数学，生物学和物理学的工具，我们的目标是了解简单系统中最佳的抗生素治疗方法，并了解这些治疗方法是否对更复杂的生物系统仍然是最佳的。

There is general agreement that medical science is facing a problem of grave importance with implications for the future of human health.Due to the evolution and spread of antibiotic resistant bacteria and the increasing difficulty of synthesising new antibiotic products,we need to find new ways of treating bacterial infections. As we embark upon the design of synthetictherapies that exploit engineered bacteria and their viral bacteriophages, we need to better understand how to use the antimicrobial agents in our possession.Locating 'the optimal antibiotic treatment' may be a distant goal, but researchers have recently begun to consider new ways in whichantibiotics should be combined to minimise the evolution of resistance to antibiotics. This is the focus of the proposal: how do wego beyond pharmacokinetic measures of efficacy to find new rationales for the optimal treatment?An approach to this question must encompass different fields. We need tools from systems biology thattell us how to model the behaviour of the complex processes within a single cell, but we also need modelsdescribing how antibiotics inhibit those cellular processes and lead to death in bacteria: the systems biology of antibiotics. To test theory we need empirical work, for if we claim that a combination of different antibiotics makes a potent cocktail, we should then test the veracity of this claim in the lab.The experimental paradigm for the type of research questions tackled in the proposal are 'experimental microbial systems', evolving microcosms that can be created in vitro and their evolution observed and repeated. Indeed, the evolution of antibiotic resistance can be so rapid that it may be observed in experiments lasting a handful of days. The utility of this empirical device is the rapidity with which hypotheses can be tested, we will soon see whether ideas created in theory have any validity in practise.But how do we derive such theoretical predictions? By taking mathematical models of experimental systems and asking fora form of 'controllability'. That is, we first ask whether a particular outcome can be achieved within the mathematical model. This outcome might mean, for example, using antibiotics to removal a bacterium from its host by minimising its density while, at the same time, preventing that bacterium from evolving antibiotic resistance; we claim that this kind of problem fits nicely into a systems and control approach.Despite very rapid advances in genomic technologies, biological systems are notoriously hard to model and data can be sparse so we will need to work hard to control them. However, a fundemental feature of the work we propose is the principle of generality that may help see beyond data. The idea, a common mathematical technique, is to look for principles that identify different systems as having identical structures that can be dealt with abstractly using mathematical tools. For example, are there any principles common to the best antibiotic cocktails when treating both E.coli or Pseudomonas infections? Are treatments that cycle different antibiotics in time always better than ones that mix antibiotics into a single cocktail? Is the particular antibiotic protein target within the cell important? Mathematics can help elucidate general problems like these.As some of these problems are difficult and ambitious, more feasible goals are presented. For example, can we use imaging to watch bacterial colonies grow in different antibiotic media and predict and measure the potency of different cocktails? This kind of experiment is novel in itself and will provide a foundation for more theoretical parts of the work.In short, with a combination of tools from mathematics, biology and physics our aim is to understand what the optimalantibiotic treatments are in simple systems and to understand whether those treatments remain optimal for more complex biological systems.