JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 78, 88-l 12 (1980) Mass Action Kinetics of Selfreplication in Flow Reactors* PETER SCHUSTER,+KARL SIGMUND,*AND ROBERT WOLFF+ Institut fiir Theoretische Chemie und Strahlenchemie, Universitiit Wien, Austria, and Institut fGr Mathematik, Universitiir Wien, Austria Submitted by S. Ulam 1. INTRODUCTION Chemical kinetics most commonly deal with reaction networks which are lacking autocatalytic steps. Autocatalysis is a rather exceptional phenomenon. Under extreme conditions it may lead to unsual types of behaviour such as explosions in the gas-phase kinetics of combustion [ 1] or chemical oscillations and dissipative structures in solution chemistry [2]. In biochemistry and biology we encounter an entirely different situation. There is one class of molecules, which appeared one day during evolution, for which selfreplication became obligatory. These molecules, of course, are the polynucleotides, the nucleic acids or, later in evolution, the genes.They owe this unique property to their particular molecular structure: due to the complementary relations of their variable constituents, the purine and pyrimidine bases adenine, guanine (hypoxanthine), uracil or thymine and cytosine (Fig. I), direct or indirect selfreplication via a negative strand became the primary and almost exclusive synthetic pathway for a whole class of biopolymers. The kinetics of selfreplication in a way are complementary to the dynamic features usually observed in mass action kinetics without autocatalysis. Because of its basic importance in prebiotic evolution, biochemistry and biology, it seems worthwhile to study selfreplication in somedetail by formal mathematical methods too. As in conventional chemical kinetics ordinary differential equations will serve perfectly well to describe the corresponding reactions in homogeneous solutions. A proper model system which is also accessible to experimental studies has been found in the evolution reactor [3] which is shown schematically in Fig. 2. The most important feature of this * This work has been supported financially by the Austrian “Fonds zur Fiirderung der wissenschaftlichen Forschung” (Project No. 3502). + lnstitut fiir Theoretische Chemie und Strahlenchemie, Universitlt Wien, Austria. * Institut fiir Mathematik, Universitlt Wien, Austria. 88 0022-247X/80/1 10088-25502.00/O Copyright .C: 1980 by Academic Press, Inc. All rights of reproduction in any form reserved.