Summary In the past decade, we have witnessed a revolutionary progress in camera technology and the attainable resolution of macromolecular assemblies via cryogenic electron microscopy (cryo-EM) and in the development of computational algorithms that relate the resulting 3D maps to atomic resolution structures. Whereas single- particle cryo-EM today is capable of directly solving atomic structures of biomolecular assemblies in isolation, electron tomography (ET) in unstained frozen-hydrated samples is widely used to capture the 3D organization of supramolecular complexes in their native (organelle, cell, or tissue) environments. We have identified three inter-related research areas where our computational modeling experience (historically rooted in pre-revolution multi-scale approaches) offers the biggest value to today's post-revolution EM community: (1) medium resolution cryo-EM modeling, (2) the segmentation and denoising of cryo-ET data, and (3) the validation of atomic models and their corresponding maps. The first aim is an extension of promising new ideas in flexible fitting as well as secondary structure prediction for medium resolution maps, which have been our key research areas in the past. medium resolution (5-10Å) maps are still widely used in EM and can be of significant biological importance. This is particularly true in the case of cryo-ET maps, which are harder to read than single particle cryo-EM maps because they often exhibit considerable noise, anisotropic resolution, and anisotropic density variations due to the low dose requirements and the missing wedge in the Fourier space. In the case of tightly packed or crowded macromolecular structures, the fusion of nearby biomolecular densities prevents an automated segmentation of geometric shapes, requiring a labor-intensive manual tracing by human experts. We are currently developing novel computational approaches to provide a more objective strategy for missing wedge correction in homogeneous specimen areas of tomograms. Our hybrid approach combines deconvolution and denoising with template matching in a unified mathematical framework that allows modeling constraints to be imposed in a least-squares optimization process. Our approach can also be extended to the flexible refinement of atomic structures using our damped dynamics flexible fitting approach by tuning the internal point-spread functions to the missing wedge of the ET data. To support these aims, we will quantitatively measure the fitness of an atomic model in local density regions and characterize the fitness of maps with reliable reference structures. The collaborative efforts supported by this grant will include the refinement of cytoskeletal filaments, molecular motors, bacterial chemoreceptor arrays, and hair cell stereocilia. The algorithmic and methodological developments will be distributed freely through the established Internet-based mechanisms used by the Situs and Sculptor packages and as plugins for the popular UCSF Chimera graphics program.