The first part of this talk is focused on 3D structure determination and analysis at molecular and cellular scales using image processing and cryo-electron microscopy (cryo-EM) imaging techniques. In particular, I shall talk about the structure analysis of large bio-molecular complexes (LBC's), such as ribosomes and viruses that are assemblies of dozens or even thousands of structural/functional bio-molecular units (e.g., proteins, RNAs). The cryo-EM technique, coupled with 3D image reconstruction, has been applied to reveal the structures of LBC's at medium to subnanometer resolutions (20-5Å). While numerous LBC structures have been solved, little efforts had been made towards automatic and quantitative interpretations of the reconstructed 3D maps. To this end, I shall present computational approaches on structural analysis of reconstructed 3D virus maps, including symmetry detection, subunit segmentation and alignment, secondary structure identification, and quasi-atomic structure modeling.

In the second part of this talk, I shall present our recent work on mathematical modeling and numerical simulation of calcium signaling, buffering, and diffusion in cardiac muscle cells. A tight coupling between cell structure, ionic fluxes and intracellular Ca2+ transients underlies the regulation of cardiac muscle functions. Alterations in the cell geometry, Ca2+ channel distribution and pathways involved in these coupled processes are now recognized to be primary mechanisms of cardiac dysfunctions. We developed 3D continuum models in cardiac muscle cells to investigate how the distribution of Ca2+-related membrane proteins (L-type Ca2+ channel clusters, Na+/Ca2+ exchangers, membrane Ca2+ leaks) might affect Ca2+ signals in terms of amplitude, time-course and spatial features. As part of our future work, I shall also introduce how the molecular and cellular structures will be used to construct and sophisticate the geometric models of cardiac muscle cells in order to achieve more realistic simulations.