Compiling Elementary Mathematical Functions into Finite Chemical Reaction Networks via a Polynomialization Algorithm for ODEs
Compiling Elementary Mathematical Functions into Finite Chemical Reaction Networks via a Polynomialization Algorithm for ODEs
复制标题
通过常微分方程多项式化算法将基本数学函数编译为有限化学反应网络
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
S. Soliman
中科院分区：
文献类型：
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作者：
Mathieu Hemery;Franccois Fages;S. Soliman
连续化学反应网络（CRN）的Turing完整性结果表明，使用大多数双分子反应与质量作用定律动力学，CRN可以通过CRN在有限的正式分子物种上计算任何可计算的功能。该证明使用了图的完整性的先前结果，用于由多项式普通微分方程（pode）定义的功能，通过两个分子物种之间的浓度差异对真实变量的双围栏编码，以及后端四倍体化转换，以限制与基本反应，以限制为基本反应最多有两个反应物。在本文中，我们提出了一种二次时间复杂性的多项式化算法，以将基本微分方程系统转换为pode。该算法用作前端变换，以将任何时间或某些输入物种的任何基本数学功能汇编为有限的CRN。我们在数学函数指定的合成生物学中与CRN设计问题有关的基本功能的基准说明了编译器的性能。特别地，将通过订单5的山丘函数汇编获得的抽象CRN与MAPK信号网络的自然CRN结构进行了比较。
The Turing completeness result for continuous chemical reaction networks (CRN) shows that any computable function over the real numbers can be computed by a CRN over a finite set of formal molecular species using at most bimolecular reactions with mass action law kinetics. The proof uses a previous result of Turing completeness for functions defined by polynomial ordinary differential equations (PODE), the dualrail encoding of real variables by the difference of concentration between two molecular species, and a back-end quadratization transformation to restrict to elementary reactions with at most two reactants. In this paper, we present a polynomialization algorithm of quadratic time complexity to transform a system of elementary differential equations to PODE. This algorithm is used as a front-end transformation to compile any elementary mathematical function, either of time or of some input species, into a finite CRN. We illustrate the performance of our compiler on a benchmark of elementary functions relevant to CRN design problems in synthetic biology specified by mathematical functions. In particular, the abstract CRN obtained by compilation of the Hill function of order 5 is compared to the natural CRN structure of MAPK signalling networks.
DOI：
10.1073/pnas.93.19.10078
发表时间：
1996-09-17
影响因子：
11.1
作者：
Huang, CYF;Ferrell, JE
通讯作者：
Ferrell, JE