The lack of sufficient training data is the limiting factor for many Machine Learning applications in Computational Biology. If data is available for several different but related problem domains, Multitask Learning algorithms can be used to learn a model based on all available information. However, combining information from several tasks requires careful consideration of the degree of similarity between tasks. We propse to use the recently published q-Norm Multiple Kernel Learning algorithm to simultaneously learn or refine the similarity matrix between tasks along with the Multitask Learning classifier by formulating the Multitask Learning problem as Multiple Kernel Learning. We demonstrate the performance of our method on two problems from Computational Biology. First, we show that our method is able to improve performance on a splice site dataset with given hierarchical task structure by refining the task relationships. Second, we consider an MHC-I dataset, for which we assume no knowledge about the degree of task relatedness. Here, we are able to learn the task similarity ab initio. Our framework is very general as it allows to incorporate prior knowledge about tasks relationships if available, but is also able to identify task similarities in absence of such prior information. Both variants show promising results in applications from Computational Biology.