that Hypercycle with translation A hypercycle with translation consists of polynucleotides Ii (with concentration xi) and polypeptides Ei (with concentration yi). It is assumed that the kinetics of nucleotide synthesis follows a Michaelis–Menten-type reaction scheme in which the concentration of complexes cannot be neglected. During replication, molecules form complexes IiEi-1 (occurring with concentration zi). Thus, the total concentration of molecules (xi0 and yi0) will be the sum of free molecules and molecules involved in a complex: The dynamics of the hypercycle with translation can be described using a system of differential equations modelling the total number of molecules: where In the above equations, cE and cI are total concentrations of all polypeptides and all polynucleotides, φx and φy are dilution fluxes, ki is the production rate of polypeptide Ei translated from the polynucleotide Ii, and fi is the production rate of polynucleotide Ii synthesised by the complex IiEi-1 (through replication and polymerization). Coupling nucleic acids with proteins in such a model of hypercycle with translation demanded the proper model for the origin of translation code as a necessary condition for the origin of hypercycle organization. At the time of hypercycle theory formulation, two models for the origin of translation code were proposed by Crick and his collaborators. These were models stating that the first codons were constructed according to either an RRY or an RNY scheme, in which R stands for the purine base, Y for pyrimidine, and N for any base, with the latter assumed to be more reliable. Nowadays, it is assumed that the hypercycle model could be realized by utilization of ribozymes without the need for a hypercycle with translation, and there are many more theories about the origin of the genetic code. Evolution Formation of the first hypercycles Eigen made several assumptions about conditions that led to the formation of the first hypercycles. Some of them were the consequence of the lack of knowledge about ribozymes, which were discovered a few years after the introduction of the hypercycle concept and negated Eigen's assumptions in the strict sense. The primary of them was that the formation of hypercycles had required the availability of both types of chains: nucleic acids forming a quasispecies population and proteins with enzymatic functions. Nowadays, taking into account the knowledge about ribozymes, it may be possible that a hypercycle's members were selected from the quasispecies population and the enzymatic function was performed by