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The link between intergenic distances and controls exerted on the transcriptional regulation; an inferential approach.

The position of genes along the genome is an important evolutionary factor for organizing gene regulation. Hence, transcriptional regulatory network have been studied much more extensively from gene distributions rather than other viewpoints. The systematics of intergenic distances, therefore, should be taken into account as an important source of information on the controls exerted on gene expression by various biological mechanisms. Here we study a collection of features including, intergenic and interoperonic distances, distances between isolated genes, distances between regulatory genes and distances between isolated and regulatory genes/operons in order to provide a more informative picture of gene distributions via firstly discovering the statistical model of these features. We find that all these features significantly follow the lognormal distribution. Then we test a few important biological hypotheses particularly in relation to controls exerted in the transcriptional regulatory network in a completely inferential approach using generalized p-value based on the discovered model. We find that mean distances of isolated genes significantly is less than that of regulatory genes.  These findings are consistent with the previous evidences that many biological variables, especially in relation to systems biology, follow lognormal distribution. furthermore, our results inferentially support the crucial hypothesis on the two distinct logical types of control, namely digital control (i.e. control mediated by specific transcription factors) and analog control (i.e. control mediated by distribution of supercoiling energy and based on gene neighborhood) previously proposed by studying expression patterns.