Palmer Michael L, Williams Richard A, Gatherer Derek
Division of Biomedical & Life Sciences, Faculty of Health & Medicine, Lancaster University, Lancaster LA14YW, UK.
Department of Management Science, Management School, Lancaster University, Lancaster LA1 4YW, UK.
J Theor Biol. 2016 Nov 7;408:97-104. doi: 10.1016/j.jtbi.2016.08.007. Epub 2016 Aug 9.
Robert Rosen's (M,R) system is an abstract biological network architecture that is allegedly both irreducible to sub-models of its component states and non-computable on a Turing machine. (M,R) stands as an obstacle to both reductionist and mechanistic presentations of systems biology, principally due to its self-referential structure. If (M,R) has the properties claimed for it, computational systems biology will not be possible, or at best will be a science of approximate simulations rather than accurate models. Several attempts have been made, at both empirical and theoretical levels, to disprove this assertion by instantiating (M,R) in software architectures. So far, these efforts have been inconclusive. In this paper, we attempt to demonstrate why - by showing how both finite state machine and stream X-machine formal architectures fail to capture the self-referential requirements of (M,R). We then show that a solution may be found in communicating X-machines, which remove self-reference using parallel computation, and then synthesise such machine architectures with object-orientation to create a formal basis for future software instantiations of (M,R) systems.
罗伯特·罗森的（M，R）系统是一种抽象的生物网络架构，据称它既不能简化为其组成状态的子模型，也不能在图灵机上进行计算。（M，R）对系统生物学的还原论和机械论表述都构成了障碍，主要是由于其自我参照结构。如果（M，R）具有其所宣称的特性，那么计算系统生物学将不可能实现，或者充其量只是一门近似模拟的科学，而非精确模型的科学。在经验和理论层面都已经进行了几次尝试，通过在软件架构中实例化（M，R）来反驳这一断言。到目前为止，这些努力尚无定论。在本文中，我们试图通过展示有限状态机和流X机形式架构如何无法满足（M，R）的自我参照要求来证明原因。然后我们表明，在通信X机中可能找到解决方案，通信X机使用并行计算消除自我参照，然后将这种机器架构与面向对象相结合，为（M，R）系统未来的软件实例化创建一个形式基础。
