Biological systems, from the molecular to the organismal level, demonstrate emergent behaviors that form fundamental characteristics of the system. Many biological phenomena are difficult to observe experimentally because of technical limitations. Computational models are a useful tool for interpretation of behaviors of complex biological systems. This dissertation examines models for two different types of emergent behaviors: cortical state and RNA structure. In Chapter 2, I use a computational neural model to understand the effects of neurons with long-range projections and propagation delays. I find that propagation delays cause a local network to exhibit a variety of metastable network states. Application of transcranial alternating current stimulation enables the switching of a network to a different metastable state. These emergent behaviors of a network of modeled neurons are a simplified version of neocortical states, and the results provide a foundation for future research on the effects of stimulation on cortical behavior. In Chapter 3, I examine the structure of the 5′ UTR of the human tumor suppressor gene RB1 using an experimentally-directed RNA structural model. The 5′ UTR adopts three distinct structures with similar frequencies. Two disease-associated mutations each collapse the structural ensemble into a single structure, and also affect translation efficiency. By creating structural models of two homologous UTRs, I find that the ability to adopt multiple conformations is a conserved feature of this UTR and that RNA structure regulates this transcript. In Chapter 4, I model RNA structure in Sindbis virus (SINV). SINV is a single-stranded RNA virus, with known functional elements within its RNA genome. I created experimentally-directed structural models for highly structured portions of the genome. By disrupting these structures through systematic mutational design, I identified regulatory RNA elements within the genome. Most structures within the genome are not conserved in related species of virus, indicating that this virus is highly structurally divergent and utilizes its evolutionary space to create new structures. These three projects present three different ways of using computational models to characterize complex biological systems. Informed by biological data, computational models provide further insight into the role of these emergent behaviors within a system.