In the aftermath of large-scale disasters, such as earthquakes or hurricanes, existing communication infrastructures are often critically impaired, preventing timely information exchange between the survivors, responders, and the coordination center. Smart devices, movable base stations, easily deployable WiFi routers, and unimpaired communication towers can be used to set up temporary networks, called disaster response networks (DRNs). However, such networks are challenged by rapid energy depletion of smart devices as well as component failures. To address these issues, in this paper we propose a novel energy-efficient yet robust DRN topology, termed Bio-DRN, that mimics the inherent robustness of a biological network of living organisms, called gene regulatory network (GRN). Specifically, the Bio-DRN is a subgraph of the DRN topology generated by one-to-one mapping between the structurally similar genes and DRN components, i.e., survivors, points of interest like shelter points, and the coordination center. We first formulate the construction of Bio-DRN topology as an integer linear programming optimization problem, and show that it is NP-hard. Then, we present a sub-optimal heuristic that constructs the Bio-DRN topology as a common subgraph of both GRN and DRN topologies. Our experimental study on a real disaster prone region in Bhaktapur, Nepal, shows that Bio-DRN preserves the topological properties of GRN, such as low graph density and motif abundance, and achieves both energy efficiency and network robustness, while ensuring timely message delivery.