Objective. The advent of high-performance computing (HPC) in recent years has led to its increasing use in brain studies through computational models. The scale and complexity of such models are constantly increasing, leading to challenging computational requirements. Even though modern HPC platforms can often deal with such challenges, the vast diversity of the modeling field does not permit for a homogeneous acceleration platform to effectively address the complete array of modeling requirements. Approach. In this paper we propose and build BrainFrame, a heterogeneous acceleration platform that incorporates three distinct acceleration technologies, an Intel Xeon-Phi CPU, a NVidia GP-GPU and a Maxeler Dataflow Engine. The PyNN software framework is also integrated into the platform. As a challenging proof of concept, we analyze the performance of BrainFrame on different experiment instances of a state-of-the-art neuron model, representing the inferior-olivary nucleus using a biophysically-meaningful, extended Hodgkin-Huxley representation. The model instances take into account not only the neuronal-network dimensions but also different network-connectivity densities, which can drastically affect the workload's performance characteristics. Main results. The combined use of different HPC technologies demonstrates that BrainFrame is better able to cope with the modeling diversity encountered in realistic experiments while at the same time running on significantly lower energy budgets. Our performance analysis clearly shows that the model directly affects performance and all three technologies are required to cope with all the model use cases. Significance. The BrainFrame framework is designed to transparently configure and select the appropriate back-end accelerator technology for use per simulation run. The PyNN integration provides a familiar bridge to the vast number of models already available. Additionally, it gives a clear roadmap for extending the platform support beyond the proof of concept, with improved usability and directly useful features to the computational-neuroscience community, paving the way for wider adoption.