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Throughout the 19th and 20th centuries, aided by advances in medical imaging, discoveries in physiology and medicine have added nearly 25 years to the average life expectancy. This resounding success brings with it a need to understand a broad range of age-related health conditions, such as dementia. Today, mathematics, neuroimaging and scientific computing are being combined with fresh insights, from animal models, to study the brain and to better understand the etiology and progression of Alzheimer's disease, the most common cause of age-related dementia in humans. In this manuscript, we offer a brief primer to the reader interested in engaging with the exciting field of mathematical modeling and scientific computing to advance the study of the brain and, in particular, human AD research. 

DNA carries more than the list of biochemical ingredients that drive the basic functions of living systems. The sequence of base pairs includes a multitude of structural and energetic signals, which determine the degree to which the long, threadlike molecule moves and how it responds to proteins and other molecules that control its processing and govern its packaging. The chemical composition of base pairs directs the spatial disposition and fluctuations of successive residues. The observed arrangements of these moieties in high-resolution protein–DNA crystal structures provide one of the best available estimates of the natural, sequence-dependent structure and deformability of the double-helical molecule. Here, we update the set of knowledge-based elastic potentials designed to describe the observed equilibrium structures and configurational fluctuations of the ten unique base-pair steps. The large number of currently available structures makes it possible to characterize the configurational preferences of the DNA base-pair steps within the context of their immediate neighbors, i.e., tetrameric context. Use of these knowledge-based potentials shows promise in accounting for known effects of sequence in long chain molecules, e.g., the degree of curvature reported in classic gel mobility studies and the recently reported sequence-dependent responses of supercoiled minicircles to nuclease cleavage.