In general, the invention relates to a method for designing a biological circuit. The method includes obtaining a target circuit objective for the biological circuit, determining an objective function corresponding to the target circuit objective, obtaining a number of nodes for the biological circuit, obtaining a set of possible circuit subgraphs using the number of nodes, obtaining a specific dissipation energy (SDE) for each one of the set of possible circuit subgraphs by optimizing the objective function, selecting at least one circuit subgraph from the set of possible circuit subgraphs with the lowest SDE, and designing the biological circuit using the at least one selected one circuit subgraph.