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Thesis advisor: Charles Hoffman / The second messenger cyclic 3’-5’ adenosine monophosphate (cAMP) signaling pathway plays an important physiological role in many organisms. Cyclic nucleotide phosphodiesterases (PDEs) regulate signal transduction by catalyzing the hydrolysis of cAMP and cGMP allowing for the downregulation of cyclic nucleotide levels. Human PDEs are encoded by 21 genes grouped into 11 families. The biological role of the most recently discovered PDE family (PDE11) remains poorly understood partly due to the lack of selective inhibitors. Mutations in the PDE11A gene have been linked to a wide range of diseases, such as Cushing Syndrome, which is a result of inactivating mutations expressed in adrenocortical tumors. Meanwhile, PDE11 levels are seen to increase in the ventral hippocampus as a function of aging, and is associated with a loss of social memory. Thus, the development of a selective PDE11 inhibitor could provide a potential therapeutic benefit to patients receiving long-term corticosteroid treatment by stimulating cortisol production by the adrenal gland, as well as to aging adults to maintain social memory. To address these needs, candidate PDE11 inhibitors related to a compound discovered by the Hoffman lab in a high throughput screen for PDE11 inhibitors are being synthesized by the Rotella laboratory. I have been evaluating these compounds using two fission yeast-based growth assays in complement with in vitro enzyme assays carried out by Dr. Jeremy Eberhard. Here I describe my role in the project, leading to the identification of a compound, SMQ2-57, which is a selective inhibitor of the PDE11 enzyme whose potency has been confirmed through both yeast-based assays and in vitro enzyme assays. In addition, I have taken both a forward and reverse genetic approach to identify PDE11A4 mutant alleles that confer resistance to inhibitor compounds as such knowledge could guide a rational drug design approach to produce more effective PDE11 inhibitors. Based on our results, SMQ2-57 could serve as a useful tool in understanding the biological role of PDE11. Meanwhile, data from my study of compound resistant mutant PDE11 alleles should allow for the characterization of the physical interaction between PDE11 and its inhibitors in an effort to guide a medicinal chemistry program to develop a more potent and drug-like PDE11 inhibitor. / Thesis (BS) — Boston College, 2023. / Submitted to: Boston College. College of Arts and Sciences. / Discipline: Scholar of the College. / Discipline: Biology.

In this two-part study, I investigated whether the cyclic-adenosine monophosphate response element-binding (CREB) protein has the potential to be clinically modulated as a therapeutic target for the treatment of neurodegenerative diseases. Part one consisted of a systematic review that was conducted on select articles gathered through a stepwise method to explore (1) the relationship between diseased, neurodegenerative brains and levels of active, phosphorylated CREB (pCREB), (2) increased activation of CREB as a treatment for neurodegenerative symptoms, and (3) a potential therapeutic drug for neurodegenerative diseases that can target CREB signaling. The results of the systematic review showed evidence that suggested excitotoxic concentrations of N-methyl-D-aspartate (NMDA) results in decreased pCREB levels, while decreased pCREB levels were associated with impaired cognition and behavior, increased cell death, as well as decreased CRE-gene transcription and long-term potentiation (LTP). Part two consisted of a systematic review and meta-analysis on clinical trials that used the phosphodiesterase type IV inhibitor, roflumilast, on healthy and schizophrenic patients. It was found that 100 µM roflumilast was able to improve verbal learning in healthy and schizophrenic subjects (ES = 64). Initial evidence indicates that future research on neurodegenerative diseases should further investigate CREB’s potential to be clinically modulated and research investigating PDE4 inhibitor drug therapy for the treatment of neurodegeneration should be expanded upon further in subsequent studies.

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Turbulent flows occur in various fields and are a central, yet an extremely complex, topic in fluid dynamics. Understanding the behaviour of fluids is vital for multiple research areas including, but not limited to: biological models, weather prediction, and engineering design models for automobiles and aircraft. In this thesis, we study a number of fundamental problems that arise in 2D turbulent flows, using the 2D Navier-Stokes system. Introducing optimization techniques for systems described by partial differential equations (PDE), we frame these problems such that they can be solved using computational methods. We utilize adjoint calculus to build the computational framework to be implemented in an iterative gradient flow procedure, using the "optimize-then-discretize" approach. Pseudospectral methods are employed for solving PDEs in a numerically efficient manner. The use of optimization methods together with computational mathematics in this work provides an illuminating perspective on fluid mechanics. We first apply these techniques to better understand enstrophy dissipation in 2D Navier-Stokes flows, in the limit of vanishing viscosity. By defining an optimization problem to determine optimal initial conditions, multiple branches of local maximizers were obtained each corresponding to a different mechanism producing maximum enstrophy dissipation. Viewing this quantity as a function of viscosity revealed quantitative agreement with an analytic bound, demonstrating the sharpness of this bound. We also introduce an extension of this problem, where enstrophy dissipation is maximized in the context of kinetic theory using the Boltzmann equation. Secondly, these PDE-constrained optimization techniques were used to probe the fundamental limitations on the performance of the Leith eddy-viscosity closure model for 2D Large-Eddy Simulations of the Navier-Stokes system. Obtained by solving an optimization problem with a non-standard structure, the results demonstrate the optimal eddy viscosities do not converge to a well-defined limit as regularization and discretization parameters are refined, hence the problem of determining an optimal eddy viscosity is ill-posed. Further extending the problem of finding optimal eddy-viscosity closures, we consider imposing an additional nonlinear constraint on the control variable in the problem, in the form of requiring the time-averaged enstrophy be preserved. To address this problem in a novel way, we employ adjoint calculus to characterize a subspace tangent to the constraint manifold, which allows one to approximately enforce the constraint. Not only do we demonstrate that this produces better results when compared to the case without constraints, but this also provides a flexible computational framework for approximate enforcement of general nonlinear constraints. Lastly in this thesis, we introduce an optimization problem to study the Kolmogorov-Richardson energy cascade, where a pathway towards solutions is outlined. / Thesis / Doctor of Philosophy (PhD)

Yes / Polygon, subdivision, and NURBS are three mainstream modeling techniques widely applied in commercial software packages. They require heavy manual operations, and involve a lot of design variables leading to big data, high storage costs and slow network transmissions. In this paper, we integrate the strengths of boundary-based surface creation and partial differential equation (PDE)-based geometric modeling to obtain the first analytical C continuous 4-sided PDE patches involving sculpting force-based shape creation and manipulation and use them to develop an interactive modeling technique for easy and quick creation of 3D models with small data from vertex-frames. With this modeling technique, a vertex frame is defined by eight vertices, and a C continuous 4-sided PDE patch is created from the vertex-frame through an analytical solution to a vector-valued second-order PDE subjected to the boundary conditions determined by the eight vertices of a vertex-frame. A user-friendly interface is developed from the obtained analytical solution, which enables users to interactively input and modify vertex-frame models easily and create 3D models in real time. Different surface modeling tasks are carried out to test the developed interactive tool and compare our proposed method with polygon and NURBS modeling and Coons surfaces. The results demonstrate the effectiveness of our proposed method and its advantages in reducing design variables, saving storage costs, and effective shape creation and manipulation. / European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 778035; MCIN/ AEI /10.13039/501100011033/ FEDER “Una manera de hacer Europa”

Numerical simulation is necessary to understand natural phenomena, make assessments and predictions in various research and engineering fields, develop new technologies, etc. New algorithms are needed to take advantage of the increasing computational resources and utilize the emerging hardware and software infrastructure with maximum efficiency. Adaptive numerical discretization methods can accommodate problems with various physical, scale, and dynamic features by adjusting the resolution, order, and the type of method used to solve them. In applications that simulate real systems, the numerical accuracy of the solution is typically just one of the challenges. Measurements can be included in the simulation to constrain the numerical solution through a process called data assimilation in order to anchor the simulation in reality. In this thesis we investigate adaptive discretization methods and data assimilation approaches for large-scale numerical simulations. We develop and investigate novel multirate and implicit-explicit methods that are appropriate for multiscale and multiphysics numerical discretizations. We construct and explore data assimilation approaches for, but not restricted to, atmospheric chemistry applications. A generic approach for describing the structure of the uncertainty in initial conditions that can be applied to the most popular data assimilation approaches is also presented. We show that adaptive numerical methods can effectively address the discretization of large-scale problems. Data assimilation complements the adaptive numerical methods by correcting the numerical solution with real measurements. Test problems and large-scale numerical experiments validate the theoretical findings. Synergistic approaches that use adaptive numerical methods within a data assimilation framework need to be investigated in the future. / Ph. D.

No / Parameterisation of facial expressions on PDE surface representations of human faces are presented in this work. Taking advantage of the boundary-value approach inherent to Bloor-Wilson PDE method, facial expressions are achieved by manipulating the original boundary curves. Such curves are responsible for generating a surface representation of a human face in its neutral configuration, so that regions on these curves represent a given facial expression in a fast and realistic manner. Additionally, the parameterisation proposed here is carried out by applying different mathematical transformations to the affected curves according to the corresponding facial expression. Full analytic expressions parameterising some of the most common facial expressions such as smiling and eyebrow raising are in this work. Some graphical examples of these facial expressions are used to illustrate the results obtained using Bloor-Wilson PDE method as the foundations of the parameterisation scheme proposed here. Thus, it is shown that an efficient, intuitive and realistic parameterisation of facial expressions is attainable using Bloor-Wilson PDE method in along with a suitable mathematical expression.