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The atomic force microscope (AFM) is a widespread tool for the study of surfaces, as it allows for the unobtrusive measurement of nanoscale topography. AFM is also versatile, with variants that allow for the measurement of other quantities such as the local surface potential and Young’s modulus. A hurdle to the use of AFM systems is that interpretation of force probe data is nontrivial due to non-idealities of experimental systems including noise and artifacts. This thesis covers two computational techniques to overcome the limitations of AFM systems. First, finite element method simulations are used in conjunction with KPFM studies of vapor-liquid-solid grown silicon nanowires. The nanowires are studied with a variable electric bias applied across them, analogous to a field-effect transistor in operation. Then, batch analysis is applied to extract mechanical information from large amounts of AFM force spectroscopy data from tethered lipid bilayer membrane systems, which are important model systems for studying the mechanics of cell membranes.

Protein folding is a fundamental life process with many implications throughout biology and medicine. Consequently, there have been enormous efforts to understand how proteins fold. Almost all of this effort has focused on water-soluble proteins, however, leaving membrane proteins largely wandering in the wilderness. The neglect has not occurred because membrane proteins are unimportant, but rather because they present many theoretical and technical complications. Indeed, quantitative membrane protein folding studies are generally restricted to a handful of well-behaved proteins. Single-molecule methods may greatly alter this picture, however, because the ability to work at or near infinite dilution removes aggregation problems, one of the main technical challenges of membrane protein folding studies.