We here consider the genetic network model depicted in figure 1. We start with the matrix notition for connectivity theorems for concentration control coefficients in a modified form. The modifications could be made due to the special stochiometry of genetic networks. Instead of considering both transcription and mRNA degradation we consider a production rate which is equal to the magnitude of the steady state flux through each mRNA(thus equal to both the transcription and the degradation rate). The special control coefficients in C^* are defined as the normalized effect of a change in these rates on the steady state concentration of them RNAs. The elasticities are now aggragations of the effects on transcription and degradation steps. Actually, E^* is the scaled Jacobian matrix.

Matrix C^* is multiplied by the inverse of its diagonal and E^* by the diagonal of C^*. Since D^-1D=I,

Multiplication of -C^* with D^-1 gives a matrix O with ratios between control coefficients, which are the co-control coefficients. Multiplication of E^* with D gives a matrix Rd with products of control coefficients and elasticity coefficients, which are regulatory strengths. These regulatory strengths are a subset of the total number of regulatory strengths and we consider these 'direct' regulatory strengths, because they are products of an (aggragated) elasticity on a certain rate and a control coefficient of that rate on the mRNA that it produces.

Using this relation one can be obtained by inverting the other. We propose to calculate the co-control matrix from microarray data and obtaining the regulatory strength matrix, Rd, by inversion. This regulatory strength matrix contains all direct regulatory strengths, therefore defining the gene network structure unambigiously.

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