The open metabolic cycles (OMC) can be considered as systems, with a permanent entry and exit of substrates (metabolites); in spite of this dynamic state they tend to maintain, between physiological ranges, the concentration of their components. The OMC cycles can be studied with different and complementary approaches, among others by measuring the level of their components and analyzing potential changes in their concentration in different metabolic or nutritional conditions. However, these are cumbersome procedures and sometimes difficult to be implemented [1] - [3] . The advances in computational techniques have allowed a more comprehensive understanding of open metabolic cycles [1] [4] - [7] .

Part of the experimental work from our laboratory had been lately centered on the mechanism of action of enzymes ligases [8] , and more particularly on the ubiquitin-activating enzyme. In this last case, experimental and theoretical aspects were carried out in parallel, with the help of the Mathematica Program [9] ; the occurrence of 19 hypothetical intermediate enzyme forms (EFs) and 22 different reactions were then contemplated [9] .

These previous studies directed us to apply the Mathematica Program to the analysis of several biochemical processes, such as:

a) Simulation of linear pathways exploring the effect of changing Vmax and/or Km values of one or more enzymes of the pathway; the reservoir model for enzyme kinetics previously developed in our laboratory was adapted to visualize the effect of the retro-inhibition of the first enzyme of the pathway by the final product; the time needed to achieve half of the total synthesis of the final product was also addressed [10] ;

b) Simulation of metabolic cycles, usually composed of a number of interconnected substrates and the same number of enzymes. Two different types of cycles can be theoretically considered, depending on whether i) substrates and enzymes form a separate entity in itself, with no entry or exit of material (a closed metabolic cycle, or CMC) or ii) a continuous interchange of material (input and/or output) between the substrates of the inner core cycle and other related metabolites takes place (open metabolic cycles, or OMC). For reasons of simplicity we have firstly approached a peculiar type of closed metabolic cycle (or pre-CMC) which reaches equilibrium, starting from a unique initial substrate [9] - [13] .

In this work, the changes in the substrate profiles of a closed metabolic cycle (CMC) promoted by the input and/or output of material are shown, and a new correlation between CMC and OMC is obtained. Although by definition the metabolic cycles tend permanently to equilibrium, the time needed to get that situation has been mathematically explored in theoretical situations in which the time needed to get the equilibrium was measured in cycles starting with only one of its substrates(a) at a fixed concentration (of 12 mM or 1 mM).