Many of the continuing scientific advances achieved through computational biology are predicated on the availability of ongoing increases in computational power required for detailed simulation and analysis of cellular processes on biologically-relevant timescales. A critical challenge facing the development of future exascale supercomputer systems is the development of new computing hardware and associated scientific applications that dramatically improve upon the energy efficiency of existingsolutions, while providing increased simulation, analysis, and visualization performance. Mobile computing platforms have recently become powerful enough to support interactive molecular visualization tasks that were previously only possible on laptops and workstations, creating future opportunities for their convenient use for meetings, remote collaboration, and as head mounted displays for immersive stereoscopic viewing. We describe early experiences adapting several biomolecular simulation and analysis applications for emerging heterogeneous computing platforms that combine power-efficient system-on-chip multi-core CPUs with high-performance massively parallel GPUs. We present low-cost power monitoring instrumentation that provides sufficient temporal resolution to evaluate the power consumption of individualCPU algorithms and GPU kernels. We compare the performance and energy efficiency of scientific applications running on emerging platforms with results obtained on traditional platforms, identify hardware and algorithmic performance bottlenecks that affect the usability of these platforms, and describe avenues for improving both the hardware and applications in pursuit of the needs of molecular modeling tasks on mobile devices and future exascale computers.