[论文解读] Optimizing defence, counter-defence and counter-counter defence in parasitic and trophic interactions -- A modelling study

Stefan Schuster, Jan Ewald+2 more|arXiv (Cornell University)|Jul 10, 2019

Plant Virus Research Studies参考文献 34被引用 8

一句话总结

本研究通过酶动力学和哈伯定律，建模了宿主-寄生虫及营养级相互作用中多级防御策略的进化优化，以确定何时进化出反反防御（如抑制寄生虫解毒酶的抑制剂）具有进化优势。关键结果是确定了抑制剂的解离常数阈值：仅当结合足够强（K_i低于阈值）时，反反防御才成为最优策略，解释了为何此类机制并非普遍存在。

ABSTRACT

In host-pathogen interactions, often the host (attacked organism) defends itself by some toxic compound and the parasite, in turn, responds by producing an enzyme that inactivates that compound. In some cases, the host can respond by producing an inhibitor of that enzyme, which can be considered as a counter-counter defence. An example is provided by cephalosporins, beta-lactamases and clavulanic acid (an inhibitor of beta-lactamases). Here, we tackle the question under which conditions it pays, during evolution, to establish a counter-counter defence rather than to intensify or widen the defence mechanisms. We establish a mathematical model describing this phenomenon, based on enzyme kinetics for competitive inhibition. We use an objective function based on Haber's rule, which says that the toxic effect is proportional to the time integral of toxin concentration. The optimal allocation of defence and counter-counter defence can be calculated in an analytical way despite the nonlinearity in the underlying differential equation. The calculation provides a threshold value for the dissociation constant of the inhibitor. Only if the inhibition constant is below that threshold, that is, in the case of strong binding of the inhibitor, it pays to have a counter-counter defence. This theoretical prediction accounts for the observation that not for all defence mechanisms, a counter-counter defence exists. Our results should be of interest for computing optimal mixtures of beta-lactam antibiotics and beta-lactamase inhibitors such as sulbactam, as well as for plant-herbivore and other molecular-ecological interactions and to fight antibiotic resistance in general.

研究动机与目标

• 理解宿主在何种进化条件下应进化反反防御机制，而非强化初级防御。
• 解释为何并非所有宿主-病原体系统都表现出反反防御，尽管存在反防御机制。
• 推导出决定反反防御进化优势的抑制剂结合强度的定量阈值。
• 为临床应用中抗生素与β-内酰胺酶抑制剂的最佳组合提供指导。

提出的方法

• 基于酶动力学建立数学模型，描述毒素、酶与抑制剂之间的竞争性抑制。
• 将哈伯定律作为目标函数，其中毒效应与毒素浓度的时间积分成正比。
• 通过解析优化方法，确定宿主在初级防御与反反防御之间资源分配的最优策略。
• 推导出决定反反防御是否具有进化优势的抑制剂解离常数（K_i）的阈值。
• 解析求解描述系统的非线性微分方程，以识别在不同动力学参数下的最优策略。
• 利用已知生物系统（如头孢菌素、β-内酰胺酶和克拉维酸）验证模型。

实验结果

研究问题

• RQ1 在何种条件下，进化出反反防御相较于强化初级或次级防御具有选择优势？
• RQ2 为何一些宿主-病原体系统具备反反防御，而另一些系统在相似进化压力下却不具备？
• RQ3 决定反反防御是否为进化最优策略的关键抑制剂结合亲和力（K_i）为何值？
• RQ4 该模型的原理如何应用于设计抗生素与β-内酰胺酶抑制剂的最佳组合？
• RQ5 该模型能否预测多级防御系统在分子生态相互作用中的进化稳定性？

主要发现

• 仅当抑制剂的解离常数（K_i）低于特定阈值时，反反防御才具有进化优势，表明其结合亲和力必须足够强。
• 该阈值K_i通过解析方法推导得出，其大小取决于毒素、酶与抑制剂系统的动力学参数。
• 当K_i超过该阈值时，宿主更应增强初级或次级防御，而非投资于反反防御。
• 该模型解释了在许多生物系统（如某些抗生素耐药途径）中反反防御缺失的观察现象。
• 该框架为优化β-内酰胺类抗生素与β-内酰胺酶抑制剂（如舒巴坦）的临床组合提供了定量依据。
• 该结果可推广至植物-植食者相互作用及其他涉及多级生化防御的分子生态军备竞赛。