Incorporation of Hysteretic Effects in Model-Order Reduction Analysis of Magnetic Devices

The ability to predict the properties of magnetic materials in a device is essential to ensuring the correct operation and optimization of the design as well as the device behavior over a wide range of input frequencies. Typically, development and simulation of wide-bandwidth models requires detailed, physics-based simulations that utilize significant computational resources. Balancing the trade-offs between model computational overhead and accuracy can be cumbersome, especially when the nonlinear effects of saturation and hysteresis are included in the model. This study focuses on the development of a system for analyzing magnetic devices in cases where model accuracy and computational intensity must be carefully and easily balanced by the engineer. A method for adjusting model complexity and corresponding level of detail while incorporating the nonlinear effects of hysteresis is presented that builds upon recent work in loss analysis and magnetic equivalent circuit (MEC) modeling. The approach utilizes MEC models in conjunction with linearization and model-order reduction techniques to process magnetic devices based on geometry and core type. The validity of steady-state permeability approximations is also discussed.

Analysis of Molecular Dynamics Simulations of Protein Folding

Microsecond long Molecular Dynamics (MD) trajectories of biomolecular processes are now possible due to advances in computer technology. Soon, trajectories long enough to probe dynamics over many milliseconds will become available. Since these timescales match the physiological timescales over which many small proteins fold, all atom MD simulations of protein folding are now becoming popular. To distill features of such large folding trajectories, we must develop methods that can both compress trajectory data to enable visualization, and that can yield themselves to further analysis, such as the finding of collective coordinates and reduction of the dynamics. Conventionally, clustering has been the most popular MD trajectory analysis technique, followed by principal component analysis (PCA). Simple clustering used in MD trajectory analysis suffers from various serious drawbacks, namely, (i) it is not data driven, (ii) it is unstable to noise and change in cutoff parameters, and (iii) since it does not take into account interrelationships amongst data points, the separation of data into clusters can often be artificial. Usually, partitions generated by clustering techniques are validated visually, but such validation is not possible for MD trajectories of protein folding, as the underlying structural transitions are not well understood. Rigorous cluster validation techniques may be adapted, but it is more crucial to reduce the dimensions in which MD trajectories reside, while still preserving their salient features. PCA has often been used for dimension reduction and while it is computationally inexpensive, being a linear method, it does not achieve good data compression. In this thesis, I propose a different method, a nonmetric multidimensional scaling (nMDS) technique, which achieves superior data compression by virtue of being nonlinear, and also provides a clear insight into the structural processes underlying MD trajectories. I illustrate the capabilities of nMDS by analyzing three complete villin headpiece folding and six norleucine mutant (NLE) folding trajectories simulated by Freddolino and Schulten [1]. Using these trajectories, I make comparisons between nMDS, PCA and clustering to demonstrate the superiority of nMDS. The three villin headpiece trajectories showed great structural heterogeneity. Apart from a few trivial features like early formation of secondary structure, no commonalities between trajectories were found. There were no units of residues or atoms found moving in concert across the trajectories. A flipping transition, corresponding to the flipping of helix 1 relative to the plane formed by helices 2 and 3 was observed towards the end of the folding process in all trajectories, when nearly all native contacts had been formed. However, the transition occurred through a different series of steps in all trajectories, indicating that it may not be a common transition in villin folding. The trajectories showed competition between local structure formation/hydrophobic collapse and global structure formation in all trajectories. Our analysis on the NLE trajectories confirms the notion that a tight hydrophobic core inhibits correct 3-D rearrangement. Only one of the six NLE trajectories folded, and it showed no flipping transition. All the other trajectories get trapped in hydrophobically collapsed states. The NLE residues were found to be buried deeply into the core, compared to the corresponding lysines in the villin headpiece, thereby making the core tighter and harder to undo for 3-D rearrangement. Our results suggest that the NLE may not be a fast folder as experiments suggest. The tightness of the hydrophobic core may be a very important factor in the folding of larger proteins. It is likely that chaperones like GroEL act to undo the tight hydrophobic core of proteins, after most secondary structure elements have been formed, so that global rearrangement is easier. I conclude by presenting facts about chaperone-protein complexes and propose further directions for the study of protein folding.

Analysis of the role of the transcription factor C/EBPβ in controlling uterine functions during early pregnancy

Embryo implantation into the endometrium is a complex biological process involving the integration of steroid hormone signaling, endometrial tissue remodeling and maternal- fetal communications. A successful pregnancy is the outcome of the timely integration of these events during the early stages of implantation. The involvement of ovarian steroid hormones, estrogen (E) and progesterone (P), acting through their cognate receptors, is essential for uterine functions during pregnancy. The molecular mechanisms that control the process of implantation are undergoing active exploration. Through our recent efforts, we identified the transcription factor, CCAAT Enhancer Binding Protein Beta (C/EBPb) as a prominent target of estrogen and progesterone signaling in the uterus. The development of a C/EBPb-null mouse model, which is infertile, presented us with an opportunity to analyze the role of this molecule in uterine function. We discovered that C/EBPb functions in two distinct manners: (i) by acting as a mediator of E-induced proliferation of the uterine epithelium and (ii) by controlling uterine stromal cell differentiation, a process known as decidualization, during pregnancy. My studies have delineated important mechanisms by which E regulates C/EBPb expression to induce DNA replication and prevent apoptosis of uterine epithelial cells during E-induced epithelial growth. In subsequent studies, I analyzed the role of C/EBPb in decidualization and uncovered a unique mechanism by which C/EBPb regulates the synthesis of a unique laminin-containing extracellular matrix (ECM) that supports stromal cell differentiation and embryo invasion. In order to better define the role of laminin in implantation, we developed a laminin gamma 1-conditional knockout mouse model. This is currently an area of ongoing investigation. The information gained from our analysis of C/EBPb function in the uterus provides new insights into the mechanisms of steroid hormone action during early pregnancy. Ultimately, our findings may aid in the understanding of dysregulation of hormone-controlled pathways that underlie early pregnancy loss and infertility in women.