An economic air pollution control model-application : photochemical smog in Los Angeles County in 1975

An economic air pollution control model, which determines the least cost of reaching various air quality levels, is formulated. The model takes the form of a general, nonlinear, mathematical programming problem. Primary contaminant emission levels are the independent variables. The objective function is the cost of attaining various emission levels and is to be minimized subject to constraints that given air quality levels be attained.

The model is applied to a simplified statement of the photochemical smog problem in Los Angeles County in 1975 with emissions specified by a two-dimensional vector, total reactive hydrocarbon, (RHC), and nitrogen oxide, (NO_x), emissions. Air quality, also two-dimensional, is measured by the expected number of days per year that nitrogen dioxide, (NO₂), and mid-day ozone, (O₃), exceed standards in Central Los Angeles.

The minimum cost of reaching various emission levels is found by a linear programming model. The base or "uncontrolled" emission levels are those that will exist in 1975 with the present new car control program and with the degree of stationary source control existing in 1971. Controls, basically "add-on devices", are considered here for used cars, aircraft, and existing stationary sources. It is found that with these added controls, Los Angeles County emission levels [(1300 tons/day RHC, 1000 tons /day NO_x) in 1969] and [(670 tons/day RHC, 790 tons/day NO_x) at the base 1975 level], can be reduced to 260 tons/day RHC (minimum RHC program) and 460 tons/day NO_x (minimum NO_x program).

"Phenomenological" or statistical air quality models provide the relationship between air quality and emissions. These models estimate the relationship by using atmospheric monitoring data taken at one (yearly) emission level and by using certain simple physical assumptions, (e. g., that emissions are reduced proportionately at all points in space and time). For NO₂, (concentrations assumed proportional to NO_x emissions), it is found that standard violations in Central Los Angeles, (55 in 1969), can be reduced to 25, 5, and 0 days per year by controlling emissions to 800, 550, and 300 tons /day, respectively. A probabilistic model reveals that RHC control is much more effective than NO_x control in reducing Central Los Angeles ozone. The 150 days per year ozone violations in 1969 can be reduced to 75, 30, 10, and 0 days per year by abating RHC emissions to 700, 450, 300, and 150 tons/day, respectively, (at the 1969 NO_x emission level).

The control cost-emission level and air quality-emission level relationships are combined in a graphical solution of the complete model to find the cost of various air quality levels. Best possible air quality levels with the controls considered here are 8 O₃ and 10 NO₂ violations per year (minimum ozone program) or 25 O₃ and 3 NO₂ violations per year (minimum NO₂ program) with an annualized cost of $230,000,000 (above the estimated $150,000,000 per year for the new car control program for Los Angeles County motor vehicles in 1975).

Neural Prosthetics and Parietal Cortex

In the last decade, research efforts into directly interfacing with the neurons of individuals with motor deficits have increased. The goal of such research is clear: Enable individuals affected by paralysis or amputation to regain control of their environments by manipulating external devices with thought alone. Though the motor cortices are the usual brain areas upon which neural prosthetics depend, research into the parietal lobe and its subregions, primarily in non-human primates, has uncovered alternative areas that could also benefit neural interfaces. Similar to the motor cortical areas, parietal regions can supply information about the trajectories of movements. In addition, the parietal lobe also contains cognitive signals like movement goals and intentions. But, these areas are also known to be tuned to saccadic eye movements, which could interfere with the function of a prosthetic designed to capture motor intentions only. In this thesis, we develop and examine the functionality of a neural prosthetic with a non-human primate model using the superior parietal lobe to examine the effectiveness of such an interface and the effects of unconstrained eye movements in a task that more closely simulates clinical applications. Additionally, we examine methods for improving usability of such interfaces.

The parietal cortex is also believed to contain neural signals relating to monitoring of the state of the limbs through visual and somatosensory feedback. In one of the world’s first clinical neural prosthetics based on the human parietal lobe, we examine the extent to which feedback regarding the state of a movement effector alters parietal neural signals and what the implications are for motor neural prosthetics and how this informs our understanding of this area of the human brain.

Designing conformational control of human tissue transglutaminase

Understanding the mechanisms of enzymes is crucial for our understanding of their role in biology and for designing methods to perturb or harness their activities for medical treatments, industrial processes, or biological engineering. One aspect of enzymes that makes them difficult to fully understand is that they are in constant motion, and these motions and the conformations adopted throughout these transitions often play a role in their function.

Traditionally, it has been difficult to isolate a protein in a particular conformation to determine what role each form plays in the reaction or biology of that enzyme. A new technology, computational protein design, makes the isolation of various conformations possible, and therefore is an extremely powerful tool in enabling a fuller understanding of the role a protein conformation plays in various biological processes.

One such protein that undergoes large structural shifts during different activities is human type II transglutaminase (TG2). TG2 is an enzyme that exists in two dramatically different conformational states: (1) an open, extended form, which is adopted upon the binding of calcium, and (2) a closed, compact form, which is adopted upon the binding of GTP or GDP. TG2 possess two separate active sites, each with a radically different activity. This open, calcium-bound form of TG2 is believed to act as a transglutaminse, where it catalyzes the formation of an isopeptide bond between the sidechain of a peptide-bound glutamine and a primary amine. The closed, GTP-bound conformation is believed to act as a GTPase. TG2 is also implicated in a variety of biological and pathological processes.

To better understand the effects of TG2’s conformations on its activities and pathological processes, we set out to design variants of TG2 isolated in either the closed or open conformations. We were able to design open-locked and closed-biased TG2 variants, and use these designs to unseat the current understanding of the activities and their concurrent conformations of TG2 and explore each conformation’s role in celiac disease models. This work also enabled us to help explain older confusing results in regards to this enzyme and its activities. The new model for TG2 activity has immense implications for our understanding of its functional capabilities in various environments, and for our ability to understand which conformations need to be inhibited in the design of new drugs for diseases in which TG2’s activities are believed to elicit pathological effects.

Control mechanisms in the human binocular oculomotor system

A study of human eye movements was made in order to elucidate the nature of the control mechanism in the binocular oculomotor system.

We first examined spontaneous eye movements during monocular and binocular fixation in order to determine the corrective roles of flicks and drifts. It was found that both types of motion correct fixational errors, although flicks are somewhat more active in this respect. Vergence error is a stimulus for correction by drifts but not by flicks, while binocular vertical discrepancy of the visual axes does not trigger corrective movements.

Second, we investigated the non-linearities of the oculomotor system by examining the eye movement responses to point targets moving in two dimensions in a subjectively unpredictable manner. Such motions consisted of hand-limited Gaussian random motion and also of the sum of several non-integrally related sinusoids. We found that there is no direct relationship between the phase and the gain of the oculomotor system. Delay of eye movements relative to target motion is determined by the necessity of generating a minimum afferent (input) signal at the retina in order to trigger corrective eye movements. The amplitude of the response is a function of the biological constraints of the efferent (output) portion of the system: for target motions of narrow bandwidth, the system responds preferentially to the highest frequency; for large bandwidth motions, the system distributes the available energy equally over all frequencies. Third, the power spectra of spontaneous eye movements were compared with the spectra of tracking eye movements for Gaussian random target motions of varying bandwidths. It was found that there is essentially no difference among the various curves. The oculomotor system tracks a target, not by increasing the mean rate of impulses along the motoneurons of the extra-ocular muscles, but rather by coordinating those spontaneous impulses which propagate along the motoneurons during stationary fixation. Thus, the system operates at full output at all times.

Fourth, we examined the relative magnitude and phase of motions of the left and the right visual axes during monocular and binocular viewing. We found that the two visual axes move vertically in perfect synchronization at all frequencies for any viewing condition. This is not true for horizontal motions: the amount of vergence noise is highest for stationary fixation and diminishes for tracking tasks as the bandwidth of the target motion increases. Furthermore, movements of the occluded eye are larger than those of the seeing eye in monocular viewing. This effect is more pronounced for horizontal motions, for stationary fixation, and for lower frequencies.

Finally, we have related our findings to previously known facts about the pertinent nerve pathways in order to postulate a model for the neurological binocular control of the visual axes.

Exploration of new drug delivery pathways: I. Mechanism of folate uptake in cultured human cells. II. Role of nuclear localization signal peptides in the delivery of oligonucleotide into reconstituted nuclei

The roles of the folate receptor and an anion carrier in the uptake of 5- methyltetrahydrofolate (5-MeH_4folate) were studied in cultured human (KB) cells using radioactive 5-MeH_4folate. Binding of the 5-MeH_4folate was inhibited by folic acid, but not by probenecid, an anion carrier inhibitor. The internalization of 5-MeH_4folate was inhibited by low temperature, folic acid, probenecid and methotrexate. Prolonged incubation of cells in the presence of high concentrations of probenecid appeared to inhibit endocytosis of folatereceptors as well as the anion carrier. The V_(max) and K_M values for the carrier were 8.65 ± 0.55 pmol/min/mg cell protein and 3.74 ± 0.54µM, respectively. The transport of 5-MeH4folate was competitively inhibited by folic acid, probenecid and methotrexate. The carrier dissociation constants for folic acid, probenecid and methotreate were 641 µM, 2.23 mM and 13.8 µM, respectively. Kinetic analysis suggests that 5-MeH_4folate at physiological concentration is transported through an anion carrier with the characteristics of the reduced-folate carrier after 5-MeH_4folate is endocytosed by folate receptors in KB cells. Our data with KB cells suggest that folate receptors and probenecid-sensitive carriers work in tandem to transport 5-MeH_4folate to the cytoplasm of cells, based upon the assumption that 1 mM probenecid does not interfere with the acidification of the vesicle where the folate receptors are endocytosed.

Oligodeoxynucleotides designed to hybridize to specific mRNA sequences (antisense oligonucleotides) or double stranded DNA sequences have been used to inhibit the synthesis of a number of cellular and viral proteins (Crooke, S. T. (1993) FASEB J. 7, 533-539; Carter, G. and Lemoine, N. R. (1993) Br. J. Cacer 67, 869-876; Stein, C. A. and cohen, J. S. (1988) Cancer Res. 48, 2659-2668). However, the distribution of the delivered oligonucleotides in the cell, i.e., in the cytoplasm or in the nucleus has not been clearly defined. We studied the kinetics of oligonucleotide transport into the cell nucleus using reconstituted cell nuclei as a model system. We present evidences here that oligonucleotides can freely diffuse into reconstituted nuclei. Our results are consistent with the reports by Leonetti et al. (Proc. Natl. Acad. Sci. USA, Vol. 88, pp. 2702-2706, April 1991), which were published while we were carrying this research independently. We also investigated whether a synthetic nuclear localization signal (NLS) peptide of SV40 T antigen could be used for the nuclear targeting of oligonucleotides. We synthesized a nuclear localization signal peptide-conjugated oligonucleotide to see if a nuclear localization signal peptide can enhance the uptake of oligonucleotides into reconstituted nuclei of Xenopus. Uptake of the NLS peptide-conjugated oligonucleotide was comparable to the control oligonucleotide at similar concentrations, suggesting that the NLS signal peptide does not significantly enhance the nuclear accumulation of oligonucleotides. This result is probably due to the small size of the oligonucleotide.

Characterization of the neural mechanisms supporting the implementation of cognitive control in human decision making

Humans are particularly adept at modifying their behavior in accordance with changing environmental demands. Through various mechanisms of cognitive control, individuals are able to tailor actions to fit complex short- and long-term goals. The research described in this thesis uses functional magnetic resonance imaging to characterize the neural correlates of cognitive control at two levels of complexity: response inhibition and self-control in intertemporal choice. First, we examined changes in neural response associated with increased experience and skill in response inhibition; successful response inhibition was associated with decreased neural response over time in the right ventrolateral prefrontal cortex, a region widely implicated in cognitive control, providing evidence for increased neural efficiency with learned automaticity. We also examined a more abstract form of cognitive control using intertemporal choice. In two experiments, we identified putative neural substrates for individual differences in temporal discounting, or the tendency to prefer immediate to delayed rewards. Using dynamic causal models, we characterized the neural circuit between ventromedial prefrontal cortex, an area involved in valuation, and dorsolateral prefrontal cortex, a region implicated in self-control in intertemporal and dietary choice, and found that connectivity from dorsolateral prefrontal cortex to ventromedial prefrontal cortex increases at the time of choice, particularly when delayed rewards are chosen. Moreover, estimates of the strength of connectivity predicted out-of-sample individual rates of temporal discounting, suggesting a neurocomputational mechanism for variation in the ability to delay gratification. Next, we interrogated the hypothesis that individual differences in temporal discounting are in part explained by the ability to imagine future reward outcomes. Using a novel paradigm, we imaged neural response during the imagining of primary rewards, and identified negative correlations between activity in regions associated the processing of both real and imagined rewards (lateral orbitofrontal cortex and ventromedial prefrontal cortex, respectively) and the individual temporal discounting parameters estimated in the previous experiment. These data suggest that individuals who are better able to represent reward outcomes neurally are less susceptible to temporal discounting. Together, these findings provide further insight into role of the prefrontal cortex in implementing cognitive control, and propose neurobiological substrates for individual variation.

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).

Robust Control of Evolutionary Dynamics

The application of principles from evolutionary biology has long been used to gain new insights into the progression and clinical control of both infectious diseases and neoplasms. This iterative evolutionary process consists of expansion, diversification and selection within an adaptive landscape - species are subject to random genetic or epigenetic alterations that result in variations; genetic information is inherited through asexual reproduction and strong selective pressures such as therapeutic intervention can lead to the adaptation and expansion of resistant variants. These principles lie at the center of modern evolutionary synthesis and constitute the primary reasons for the development of resistance and therapeutic failure, but also provide a framework that allows for more effective control.

A model system for studying the evolution of resistance and control of therapeutic failure is the treatment of chronic HIV-1 infection by broadly neutralizing antibody (bNAb) therapy. A relatively recent discovery is that a minority of HIV-infected individuals can produce broadly neutralizing antibodies, that is, antibodies that inhibit infection by many strains of HIV. Passive transfer of human antibodies for the prevention and treatment of HIV-1 infection is increasingly being considered as an alternative to a conventional vaccine. However, recent evolution studies have uncovered that antibody treatment can exert selective pressure on virus that results in the rapid evolution of resistance. In certain cases, complete resistance to an antibody is conferred with a single amino acid substitution on the viral envelope of HIV.

The challenges in uncovering resistance mechanisms and designing effective combination strategies to control evolutionary processes and prevent therapeutic failure apply more broadly. We are motivated by two questions: Can we predict the evolution to resistance by characterizing genetic alterations that contribute to modified phenotypic fitness? Given an evolutionary landscape and a set of candidate therapies, can we computationally synthesize treatment strategies that control evolution to resistance?

To address the first question, we propose a mathematical framework to reason about evolutionary dynamics of HIV from computationally derived Gibbs energy fitness landscapes -- expanding the theoretical concept of an evolutionary landscape originally conceived by Sewall Wright to a computable, quantifiable, multidimensional, structurally defined fitness surface upon which to study complex HIV evolutionary outcomes.

To design combination treatment strategies that control evolution to resistance, we propose a methodology that solves for optimal combinations and concentrations of candidate therapies, and allows for the ability to quantifiably explore tradeoffs in treatment design, such as limiting the number of candidate therapies in the combination, dosage constraints and robustness to error. Our algorithm is based on the application of recent results in optimal control to an HIV evolutionary dynamics model and is constructed from experimentally derived antibody resistant phenotypes and their single antibody pharmacodynamics. This method represents a first step towards integrating principled engineering techniques with an experimentally based mathematical model in the rational design of combination treatment strategies and offers predictive understanding of the effects of combination therapies of evolutionary dynamics and resistance of HIV. Preliminary in vitro studies suggest that the combination antibody therapies predicted by our algorithm can neutralize heterogeneous viral populations despite containing resistant mutations.

A nonlinear systems model for the control mechanism of free fatty acid-glucose metabolosm in normal humans

A mathematical model is proposed in this thesis for the control mechanism of free fatty acid-glucose metabolism in healthy individuals under resting conditions. The objective is to explain in a consistent manner some clinical laboratory observations such as glucose, insulin and free fatty acid responses to intravenous injection of glucose, insulin, etc. Responses up to only about two hours from the beginning of infusion are considered. The model is an extension of the one for glucose homeostasis proposed by Charette, Kadish and Sridhar (Modeling and Control Aspects of Glucose Homeostasis. Mathematical Biosciences, 1969). It is based upon a systems approach and agrees with the current theories of glucose and free fatty acid metabolism. The description is in terms of ordinary differential equations. Validation of the model is based on clinical laboratory data available at the present time. Finally procedures are suggested for systematically identifying the parameters associated with the free fatty acid portion of the model.