Workflows for the acquisition and analysis of data in the natural sciences exhibit a growing degree of complexity and heterogeneity, are increasingly performed in large collaborative efforts, and often require the use of high-performance computing (HPC). Here, we explore the reasons for these new challenges and demands and discuss their impact, with a focus on the scientific domain of computational neuroscience. We argue for the need for software platforms integrating HPC systems that allow scientists to construct, comprehend and execute workflows composed of diverse processing steps using different tools. As a use case we present a concrete implementation of such a complex workflow, covering diverse topics such as HPC-based simulation using the NEST software, access to the SpiNNaker neuromorphic hardware platform, complex data analysis using the Elephant library, and interactive visualizations. Tools are embedded into a web-based software platform under development by the Human Brain Project, called Collaboratory. On the basis of this implementation, we discuss the state-of-the-art and future challenges in constructing large, collaborative workflows with access to HPC resources.