# Background The statistical thermodynamics based approach provides a promising framework for

Background The statistical thermodynamics based approach provides a promising framework for construction of the genotype-phenotype map in many biological systems. to formulate and study such models under different modeling assumptions. Results We elaborate a two-layer model for the of a TFBS: quantifies the input of the TFBS in the solution. To explore how the regulatory weight depends on the context (either the solution quality assessment or the modeling assumptions) we analyze its values for all model variants is the statistical weight (relative probability) of configuration of all TFs as parameters and are concentrations of mRNA and protein respectively for target gene and are the maximum synthesis rates and are the diffusion coefficients and and are the decay rates for protein and mRNA of gene for the case when for the case when and and protein concentrations for each DAPT gene for mRNA or for protein while the corresponding data are denoted as ri with its maximum level rmax. Correctly predicted amount of expression that can be defined for each nuclei as min(pi ri) is weighted by the predicted expression level ri and ‘rewarded’ that is subtracted from the Error. The incorrect predictions defined as |pi ? ri| are weighted by the extent of incorrect expression (rmax ? ri) and added to the Error i.e. ‘penalized’. The third component in the combined objective function penalizes the squared values of the regulatory parameters Tab:

$Penalty=∑?a b(Tab)2$
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