The logic of receptor-ligand interactions in the Notch signaling pathway

The Notch signaling pathway enables neighboring cells to coordinate developmental fates in diverse processes such as angiogenesis, neuronal differentiation, and immune system development. Although key components and interactions in the Notch pathway are known, it remains unclear how they work together to determine a cell's signaling state, defined as its quantitative ability to send and receive signals using particular Notch receptors and ligands. Recent work suggests that several aspects of the system can lead to complex signaling behaviors: First, receptors and ligands interact in two distinct ways, inhibiting each other in the same cell (in cis) while productively interacting between cells (in trans) to signal. The ability of a cell to send or receive signals depends strongly on both types of interactions. Second, mammals have multiple types of receptors and ligands, which interact with different strengths, and are frequently co-expressed in natural systems. Third, the three mammalian Fringe proteins can modify receptor-ligand interaction strengths in distinct and ligand-specific ways. Consequently, cells can exhibit non-intuitive signaling states even with relatively few components.

In order to understand what signaling states occur in natural processes, and what types of signaling behaviors they enable, this thesis puts forward a quantitative and predictive model of how the Notch signaling state is determined by the expression levels of receptors, ligands, and Fringe proteins. To specify the parameters of the model, we constructed a set of cell lines that allow control of ligand and Fringe expression level, and readout of the resulting Notch activity. We subjected these cell lines to an assay to quantitatively assess the levels of Notch ligands and receptors on the surface of individual cells. We further analyzed the dependence of these interactions on the level and type of Fringe expression. We developed a mathematical modeling framework that uses these data to predict the signaling states of individual cells from component expression levels. These methods allow us to reconstitute and analyze a diverse set of Notch signaling configurations from the bottom up, and provide a comprehensive view of the signaling repertoire of this major signaling pathway.

Model predictive control for deferrable loads scheduling

Real-time demand response is essential for handling the uncertainties of renewable generation. Traditionally, demand response has been focused on large industrial and commercial loads, however it is expected that a large number of small residential loads such as air conditioners, dish washers, and electric vehicles will also participate in the coming years. The electricity consumption of these smaller loads, which we call deferrable loads, can be shifted over time, and thus be used (in aggregate) to compensate for the random fluctuations in renewable generation.

In this thesis, we propose a real-time distributed deferrable load control algorithm to reduce the variance of aggregate load (load minus renewable generation) by shifting the power consumption of deferrable loads to periods with high renewable generation. The algorithm is model predictive in nature, i.e., at every time step, the algorithm minimizes the expected variance to go with updated predictions. We prove that suboptimality of this model predictive algorithm vanishes as time horizon expands in the average case analysis. Further, we prove strong concentration results on the distribution of the load variance obtained by model predictive deferrable load control. These concentration results highlight that the typical performance of model predictive deferrable load control is tightly concentrated around the average-case performance. Finally, we evaluate the algorithm via trace-based simulations.

Convex model predictive control for vehicular systems

In this work, the author presents a method called Convex Model Predictive Control (CMPC) to control systems whose states are elements of the rotation matrices SO(n) for n = 2, 3. This is done without charts or any local linearization, and instead is performed by operating over the orbitope of rotation matrices. This results in a novel model predictive control (MPC) scheme without the drawbacks associated with conventional linearization techniques such as slow computation time and local minima. Of particular emphasis is the application to aeronautical and vehicular systems, wherein the method removes many of the trigonometric terms associated with these systems’ state space equations. Furthermore, the method is shown to be compatible with many existing variants of MPC, including obstacle avoidance via Mixed Integer Linear Programming (MILP).

A Model For Residential Adoption of Photovoltaic Systems

The rapid rise in the residential photo voltaic (PV) adoptions in the past half decade has created a need in the electricity industry for a widely-accessible model that estimates PV adoption based on a combination of different business and policy decisions. This work analyzes historical adoption patterns and finds fiscal savings to be the single most important factor in PV adoption, with significantly greater predictive power compared to all other socioeconomic factors including income and education. We can create an application available on Google App Engine (GAE) based on our findings that allows all stakeholders including policymakers, power system researchers and regulators to study the complex and coupled relationship between PV adoption, utility economics and grid sustainability. The application allows users to experiment with different customer demographics, tier structures and subsidies, hence allowing them to tailor the application to the geographic region they are studying. This study then demonstrates the different type of analyses possible with the application by studying the relative impact of different policies regarding tier structures, fixed charges and PV prices on PV adoption.

A model for energy and morphology of crystalline grain boundaries with arbitrary geometric character

It has been well-established that interfaces in crystalline materials are key players in the mechanics of a variety of mesoscopic processes such as solidification, recrystallization, grain boundary migration, and severe plastic deformation. In particular, interfaces with complex morphologies have been observed to play a crucial role in many micromechanical phenomena such as grain boundary migration, stability, and twinning. Interfaces are a unique type of material defect in that they demonstrate a breadth of behavior and characteristics eluding simplified descriptions. Indeed, modeling the complex and diverse behavior of interfaces is still an active area of research, and to the author's knowledge there are as yet no predictive models for the energy and morphology of interfaces with arbitrary character. The aim of this thesis is to develop a novel model for interface energy and morphology that i) provides accurate results (especially regarding "energy cusp" locations) for interfaces with arbitrary character, ii) depends on a small set of material parameters, and iii) is fast enough to incorporate into large scale simulations.

In the first half of the work, a model for planar, immiscible grain boundary is formulated. By building on the assumption that anisotropic grain boundary energetics are dominated by geometry and crystallography, a construction on lattice density functions (referred to as "covariance") is introduced that provides a geometric measure of the order of an interface. Covariance forms the basis for a fully general model of the energy of a planar interface, and it is demonstrated by comparison with a wide selection of molecular dynamics energy data for FCC and BCC tilt and twist boundaries that the model accurately reproduces the energy landscape using only three material parameters. It is observed that the planar constraint on the model is, in some cases, over-restrictive; this motivates an extension of the model.

In the second half of the work, the theory of faceting in interfaces is developed and applied to the planar interface model for grain boundaries. Building on previous work in mathematics and materials science, an algorithm is formulated that returns the minimal possible energy attainable by relaxation and the corresponding relaxed morphology for a given planar energy model. It is shown that the relaxation significantly improves the energy results of the planar covariance model for FCC and BCC tilt and twist boundaries. The ability of the model to accurately predict faceting patterns is demonstrated by comparison to molecular dynamics energy data and experimental morphological observation for asymmetric tilt grain boundaries. It is also demonstrated that by varying the temperature in the planar covariance model, it is possible to reproduce a priori the experimentally observed effects of temperature on facet formation.

Finally, the range and scope of the covariance and relaxation models, having been demonstrated by means of extensive MD and experimental comparison, future applications and implementations of the model are explored.