Submitted to the faculty of Indiana University in partial fulfillment of the requirements for the degree Master of Science in the Department of Bioinformatics in the School of Informatics of, Indiana University December, 2004 / Electrostatic modeling was done with Delphi of insight II to explain and predict protein aggregation, measured here for β-lactoglobulin and insulin using turbidimetry and stopped flow spectrophotometry. The initial rate of aggregation of β-Lactoglobulin was studied between pH 3.8 and 5.2 in 4.5mM NaCl; and for ionic strengths from 4.5 to 500mM NaCl at pH 5.0. The initial slope of the turbidity vs. time curve was used to define the initial rate of aggregation. The highest initial rate was observed near pH < pI i.e., 4.6 (< 5.2). The decrease in aggregation rate when the pH was increased from 4.8 to 5.0 was large compared to its decrease when the pH was reduced from 4.4 to 4.2; i.e., the dependence of initial rate on pH was highly asymmetric. The initial rate of aggregation at pH 5.0 increased linearly with the reciprocal of ionic strength in the range I = 0.5 to 0.0045M. Protein electrostatic potential distributions are used to understand the pH and ionic strength dependence of the initial rate of aggregation. Similar studies were done with insulin. In contrast to BLG, the highest initial aggregation rate for insulin was observed at pH = pI. Electrostatic computer modeling shows that these differences arise from the distinctly different surface charge distributions of insulin and BLG.

Piezoceramic fiber composite (PFC) actuators and sensors offer many advantages over conventional monolithic piezoceramic devices. Conformable, durable and, when equipped with interdigitated electrodes (IDEs), more responsive than regular monolithic devices, PFCs promise to revolutionize the application of piezoelectric materials. Developed by the NASA-Langley Research Center, the Macro-Fiber Composite (MFC) actuator and sensor is the most sophisticated PFC device yet invented. With superior qualities among PFCs in performance, behavior repeatability and manufacturability, the MFC has spawned great interest in the commercial and academic community as a tool in multitudinous engineering applications. While the MFC's characteristics render it a singularly useful device, limited characterization and modeling research on the MFC exists. Empirically designed and assembled, the MFC is poorly understood, especially in terms of its underlying operating principles, its dependence on design parameters and its electrical properties. The majority of published MFC studies focus on experimental quantification of MFC mechanical and actuation properties, and the research that attempts to model the MFC relies totally on finite element analysis. Published works widely assume that analytical models of the MFC are totally impossible. Rectifying gaps in the current body of MFC research, this study presents the first accurate analytical model of the static electrical field properties of the MFC. Implementing the techniques of conformal mapping, a branch of complex analysis, the following chapters derive a closed-form, exact analytical solution describing the electrical potential field and electrical field of the MFC's dual-IDE structure. Based on the conformal mapping solution for the MFC's electrical field, the electrical field of the commercially available MFC is examined and analyzed, introducing an intuitive knowledge of the MFC's operation. Demonstrating the utility of this solution in modeling the MFC, this work also predicts the capacitance and induced strain properties of a continuum of potential MFC designs and offers final suggestions on improving the current commercial MFC design. After establishing the theoretical underpinnings of the analytical MFC model, this report derives the conformal mapping solutions for the MFC, discusses the computational application of the resulting equations and then presents the results of numerical analyses executed using the new analytical model. / Master of Science