Department of Chemical Engineering, Institute of Chemical Technology, Prague, 16628 Prague 6, Czech Republic.
J Chem Phys. 2013 Oct 28;139(16):164108. doi: 10.1063/1.4825379.
We study a model system of three diffusively coupled reaction cells arranged in a linear array that display Turing patterns with special focus on the case of equal coupling strength for all components. As a suitable model reaction we consider a two-variable core model of glycolysis. Using numerical continuation and bifurcation techniques we analyze the dependence of the system's steady states on varying rate coefficient of the recycling step while the coupling coefficients of the inhibitor and activator are fixed and set at the ratios 100:1, 1:1, and 4:5. We show that stable Turing patterns occur at all three ratios but, as expected, spontaneous transition from the spatially uniform steady state to the spatially nonuniform Turing patterns occurs only in the first case. The other two cases possess multiple Turing patterns, which are stabilized by secondary bifurcations and coexist with stable uniform periodic oscillations. For the 1:1 ratio we examine modular spatiotemporal perturbations, which allow for controllable switching between the uniform oscillations and various Turing patterns. Such modular perturbations are then used to construct chemical computing devices utilizing the multiple Turing patterns. By classifying various responses we propose: (a) a single-input resettable sensor capable of reading certain value of concentration, (b) two-input and three-input memory arrays capable of storing logic information, (c) three-input, three-output logic gates performing combinations of logical functions OR, XOR, AND, and NAND.
我们研究了一个由三个扩散耦合反应单元组成的线性阵列的模型系统，该系统呈现出特殊的图灵模式，特别关注所有组件耦合强度相等的情况。作为一个合适的模型反应，我们考虑了一个双变量核心糖酵解模型。我们使用数值连续和分岔技术，分析了系统稳态对变化的回收步骤的速率系数的依赖关系，而抑制剂和激活剂的耦合系数固定在 100:1、1:1 和 4:5 的比值。我们表明，在所有三种情况下都会出现稳定的图灵模式，但正如预期的那样，从空间均匀的稳态到空间非均匀的图灵模式的自发转变仅在第一种情况下发生。其他两种情况存在多个图灵模式，这些模式由次分岔稳定，并与稳定的周期振荡共存。对于 1:1 的比值，我们研究了模块化时空扰动，这些扰动允许在均匀振荡和各种图灵模式之间进行可控切换。然后，使用这种模块化扰动来构建利用多种图灵模式的化学计算设备。通过对各种响应进行分类，我们提出了：（a）单输入可重置传感器，能够读取特定浓度值，（b）具有存储逻辑信息的双输入和三输入存储阵列，（c）执行逻辑函数 OR、XOR、AND 和 NAND 的组合的三输入、三输出逻辑门。
