At present time there are several methods of expression level measuring (RNA amount) for various genes simultaneously (microchips etc). As a rule the experiments are carried out in the following way: the set of genes presumably interacting with each other is selected (genetic network), and external conditions are changing by stepping way. In response of that the levels of selected genes are changing (see figure), and reasoning from that it is possible to see which genes interact with each other.

In spite of the fact that now it is known which mechanisms are in the basis of genes interaction (activation, repression by regulatory proteins, these knowledge do not use in the analysis of expression levels, received in the experiment. Data is being proceeded usually by means of various statistical filters - received dependences of expression level on time divided into groups of curves, having similar form and conclusion which genes interact and at what times are being made. Another method – to write down empirical system of differential equations, where on the left will be derivatives of genes transcripts concentrations in time and in right part - linear function of transcripts concentrations:

x – transcript concentration, а_ij – – coefficient of j-th transcript influence on the rate of i-th formation, u_l – factor of external effect, b_il – coefficient of l-th factor influence on the rate of i-th transcript formation.

From experimental data we know both transcripts concentrations and their derivatives in various time points. Therefore it is possible to solve the system of linear equations relatively coefficients of external factors effects on genes and their expression on each other. Matrix of these coefficients gives information about genetic interactions, but ever specific experiment will have its own empirical coefficients.

Methods mentioned above do not take into account the mechanism of genes interaction and therefore use only effective parameters. We suppose that more appropriate is description of genetic interactions with the help of known mechanisms ad parameters having defined physical meaning (rate constant, dissociation rate constant). The works devoted to study of primary regulatory systems already exist. However theoretical researches as a rule are confined by primary cases (one gene, or one operator, or one regulator)

Our aim is to generalize these researches for network consisted of many genes, having made certain generalized functions describing well-known regulation mechanisms, and to estimate is it possible to define parameters of these functions on the basis of experimental data and make conclusion not only about the fact of genes interaction but also about its concrete mechanism. Such models may be applied actively for more detailed and mathematically grounded research of genetic networks.