The attempt to elucidate biological pathways and classify genes has led to the development of numerous clustering approaches to gene expression. All these approaches use a single metric to identify genes with similar expression levels. Until now, the correlation between the expression levels of such genes has been based on phenomenological and heuristic correlation functions, rather than on biological models. In this paper, we derive six distinct correlation functions based on explicit thermodynamic modeling of gene regulatory networks. We then combine these correlation functions with novel biclustering algorithms to identify functionally enriched groups. The statistical significance of the identified groups is demonstrated by precision-recall curves and calculated p-values. Furthermore, comparison with chromatin immunoprecipitation data indicates that the performance of the derived correlation functions depends on the specific regulatory mechanisms. Finally, we introduce the idea of multi-class biclustering and with the help of support vector machines we demonstrate its improved classification performance in a microarray dataset.