Cephalexin is an important β-lactam antibiotic that is enzymatically synthetized from a nucleophile (7-aminodeacetoxycephalosporanic acid – 7-ADCA) and an acyl donor (phenylglycine methyl ester – PGME). The process is catalyzed by penicillin acylase. Cephalexin is thermodynamically unstable and is typically produced in a kinetic regime. Based on our previous experimental findings and additional batch experiments intended for the estimation of kinetic constants of cephalexin synthesis, we developed a mathematical model of a microfluidic device with two aqueous phases (ATPS) for the simultaneous cephalexin production and its separation from a reaction mixture. This device operates with free enzyme dissolved in one phase and the reactants introduced in the other phase. Because of small characteristic dimensions, the reactants are intensively transported through the interface to the enzyme phase where they are converted to cephalexin. The product then easily returns into the original phase due to a high value of the partition coefficient. The transport can be enhanced by an imposed electric field as the reaction compounds are charged. We studied the effects of four well-controllable parameters on the cephalexin yield: (i) the residence time of the phase introducing the reactants, (ii) the residence time of the phase containing the enzyme, (iii) the applied voltage difference across the interface, (iv) the characteristic dimension of microfluidic chambers. The mathematical model predicts that a cephalexin yield higher than 70% can be achieved in counter-current parallel flow arrangement, which is a result comparable with those obtained in batch experiments. The applied electric field can increase the cephalexin yield by no more than several percent because of the same polarity of 7-ADCA and cephalexin charge numbers. If compared to classical batch reactors, the suggested microreactor–microseparator brings the following benefits: (i) continuous cephalexin synthesis, (ii) effective and continuous separation of cephalexin due to proper partitioning of these species in the used ATPS, (iii) the use of free and highly active enzyme with efficient recyclation. Moreover, the productivity of the suggested microreactor is solely determined by the interfacial area that can be easily provided by thin separating membranes, i.e. no technically demanding numbering up solution is necessary.

中文翻译：

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电驱动ATPS微萃取联合流式微反应器中头孢氨苄酶合成的理论研究

头孢氨苄是一种重要的β-内酰胺抗生素，由亲核试剂（7-氨基脱乙酰氧基头孢菌酸– 7-ADCA）和酰基供体（苯基甘氨酸甲酯– PGME）酶促合成。青霉素酰基转移酶催化该过程。头孢氨苄在热力学上是不稳定的，通常以动力学方式产生。基于我们先前的实验发现和旨在估计头孢氨苄合成动力学常数的其他批处理实验，我们开发了具有两个水相（ATPS）的微流控装置的数学模型，用于同时产生头孢氨苄并从反应混合物中分离。该装置在溶解于一相中的游离酶和引入另一相中的反应物的情况下运行。由于特征尺寸小，反应物通过界面集中转运到酶相，在此酶被转化为头孢氨苄。然后，由于分配系数的值很高，乘积很容易返回到原始阶段。当反应化合物带电时，可通过施加电场来增强运输。我们研究了四个可控参数对头孢氨苄收率的影响：（i）引入反应物的相的停留时间，（ii）含酶的相的停留时间，（iii）整个酶的施加电压差界面，（iv）微流体腔室的特征尺寸。该数学模型预测，在逆流平行流布置中可以达到高于70％的头孢氨苄收率，这与批量实验中获得的结果相当。由于7-ADCA的极性和头孢氨苄的电荷数相同，因此施加的电场可使头孢氨苄的产量增加不超过百分之几。如果与经典间歇式反应器相比，建议的微反应器-微分离器具有以下优点：（i）连续头孢氨苄合成，（ii）由于这些物质在使用过的ATPS中的适当分配，有效而连续地分离了头孢氨苄，（iii）使用具有高效回收利用的游离高活性酶。此外，建议的微反应器的生产率仅取决于薄薄的分离膜可以轻松提供的界面面积，如果与经典间歇式反应器相比，建议的微反应器-微分离器具有以下优点：（i）连续头孢氨苄合成，（ii）由于这些物质在使用过的ATPS中的适当分配，有效而连续地分离了头孢氨苄，（iii）使用具有高效回收利用的游离高活性酶。此外，建议的微型反应器的生产率仅取决于薄薄的分离膜可轻松提供的界面面积，如果与经典间歇式反应器相比，建议的微反应器-微分离器具有以下优点：（i）连续头孢氨苄合成，（ii）由于这些物质在使用过的ATPS中的适当分配，有效而连续地分离了头孢氨苄，（iii）使用具有高效回收利用的游离高活性酶。此外，建议的微型反应器的生产率仅取决于薄薄的分离膜可轻松提供的界面面积，即，不需要技术上苛刻的编号解决方案。