Synthetic biology seeks to envision living cells as a matter of engineering. However, increasing evidence suggests that the genetic load imposed by the incorporation of synthetic devices in a living organism introduces a sort of unpredictability in the design process. As a result, individual part characterization is not enough to predict the behavior of designed circuits and thus, a costly trial-error process is eventually required. In this work, we provide a new theoretical framework for the predictive treatment of the genetic load. We mathematically and experimentally demonstrate that dependences among genes follow a quantitatively predictable behavior. Our theory predicts the observed reduction of the expression of a given synthetic gene when an extra genetic load is introduced in the circuit. The theory also explains that such dependence qualitatively differs when the extra load is added either by transcriptional or translational modifications. We finally show that the limitation of the cellular resources for gene expression leads to a mathematical formulation that converges to an expression analogous to the Ohm's law for electric circuits. Similitudes and divergences with this law are outlined. Our work provides a suitable framework with predictive character for the design process of complex genetic devices in synthetic biology.