Experimental protein structure determination methods make up a fundamental part of our understanding of biological systems. Manual interpretation of the output from these methods has been made obsolete by the sheer size and complexity of the acquired data. Instead, computational methods are becoming essential for this task and with the advent of high-throughput methods the efficiency and robustness of these methods are a major concern. This work focuses on the computational challenge of efficiently extracting statistically supported information from noisy or significantly reduced experimental data.

Small-angle X-ray scattering (SAXS) is a method capable of probing structural information with many experimental benefits compared to alternative methods. However, the acquired data is a noisy reduction of a large set of structural features into a low-dimensional signal-mixture, which significantly limits its interpretability. Due to this SAXS has this far been limited to conclusions about large-scale structural features, like radius of gyration or the oligomeric state of the sample. In this thesis I present an approach where SAXS data is used to guide molecular dynamics simulations to explore experimentally relevant conformational states. The experimental data is fed into the simulations through a metadynamics protocol, which explores the experimental data through conformational sampling subject to thermodynamic restraints. I show how this approach makes it possible to use SAXS to produce atomic-resolution models and make further-reaching conclusions about the underlying biological system, in particular by showcasing de novo folding of a small protein.

Another experimental method that generates noisy and reduced data is cryogenic electron microscopy (cryo-EM). Due to recent development in the field, the computational burden has become a considerable bottleneck, which greatly limits the throughput of the method. I present computational techniques to alleviate this burden through the use of specialized algorithms capable of efficient execution on graphics processing units (GPUs). This work improves the computational efficiency of the entire pipeline by several orders of magnitude and significantly advances the overall efficiency and applicability of the method. I show how this enables the development of improved algorithms with increased capabilities for extracting relevant biological information form the data. Several such improvements are presented that significantly increase the resolution of the refinement results and provide additional information about the dynamics of the system. Additionally, I present an application of these methods to data collected on a biogenesis intermediate of the mitochondrial ribosome. The new structures provide insights into the timing of the rRNA folding and protein incorporation as well as the role of two previously unknown assembly factors during the final stages of ribosome maturation.