Using phase-space localized basis functions to obtain vibrational energies of molecules

For decades scientists have attempted to use ideas of classical mechanics to choose basis functions for calculating spectra. The hope is that a classically-motivated basis set will be small because it covers only the dynamically important part of phase space. One popular idea is to use phase space localized (PSL) basis functions. This thesis improves on previous efforts to use PSL functions and examines the usefulness of these improvements. Because the overlap matrix, in the matrix eigenvalue problem obtained by using PSL functions with the variational method, is not an identity, it is costly to use iterative methods to solve the matrix eigenvalue problem. We show that it is possible to circumvent the orthogonality (overlap) problem and use iterative eigensolvers. We also present an altered method of calculating the matrix elements that improves the performance of the PSL basis functions, and also a new method which more efficiently chooses which PSL functions to include. These improvements are applied to a variety of single well molecules. We conclude that for single minimum molecules, the PSL functions are inferior to other basis functions. However, the ideas developed here can be applied to other types of basis functions, and PSL functions may be useful for multi-well systems.

3D considerations for motion perception and visuomotor transformations

Moving through a stable, three-dimensional world is a hallmark of our motor and perceptual experience. This stability is constantly being challenged by movements of the eyes and head, inducing retinal blur and retino-spatial misalignments for which the brain must compensate. To do so, the brain must account for eye and head kinematics to transform two-dimensional retinal input into the reference frame necessary for movement or perception. The four studies in this thesis used both computational and psychophysical approaches to investigate several aspects of this reference frame transformation. In the first study, we examined the neural mechanism underlying the visuomotor transformation for smooth pursuit using a feedforward neural network model. After training, the model performed the general, three-dimensional transformation using gain modulation. This gave mechanistic significance to gain modulation observed in cortical pursuit areas while also providing several testable hypotheses for future electrophysiological work. In the second study, we asked how anticipatory pursuit, which is driven by memorized signals, accounts for eye and head geometry using a novel head-roll updating paradigm. We showed that the velocity memory driving anticipatory smooth pursuit relies on retinal signals, but is updated for the current head orientation. In the third study, we asked how forcing retinal motion to undergo a reference frame transformation influences perceptual decision making. We found that simply rolling one's head impairs perceptual decision making in a way captured by stochastic reference frame transformations. In the final study, we asked how torsional shifts of the retinal projection occurring with almost every eye movement influence orientation perception across saccades. We found a pre-saccadic, predictive remapping consistent with maintaining a purely retinal (but spatially inaccurate) orientation perception throughout the movement. Together these studies suggest that, despite their spatial inaccuracy, retinal signals play a surprisingly large role in our seamless visual experience. This work therefore represents a significant advance in our understanding of how the brain performs one of its most fundamental functions.

Investigating the Role of PDE4D1/2 in Vascular Smooth Muscle Cell Desensitization

Vascular smooth muscle cell (VSMC) behaviour and phenotypic modulation is critical to vessel repair following damage, and the progression of various cardiovascular diseases. The second messenger cyclic adenosine monophosphosphate (cAMP) plays a key role in VSMC function under the synthetic/activated phenotype, which is typically associated with unhealthy cell behaviour. Consequently, cAMP signaling is often targeted in attempts to impact several pathological diseases, including atherosclerosis, restenosis, and pulmonary arterial hypertension (PAH). The cyclic nucleotide phosphodiesterases (PDEs) catalyze hydrolysis of cAMP to an inactive form, and therefore directly regulate cAMP signaling. The PDE4D family dominates in synthetic VSMCs, and there is considerable interest in determining how distinct PDE4D isoforms affect cell function. Specifically, we are interested in the potential link between short isoforms of PDE4D and VSMC desensitization to pharmacological agents that impact cardiovascular disease via cAMP signaling. This study extends on previous work that assessed the expression of PDE4D splice variants in rat aortic VSMCs following prolonged challenge with cAMP-elevating agents. It was determined that PDE4D1 and PDE4D2 were uniquely expressed in synthetic VSMCs incubated with these agents, and that this upregulation impacted PDE activity and cAMP accumulation in these cells. Here, we report that PDE4D1 and PDE4D2 are markedly upregulated in synthetic human aortic smooth muscle cells (HASMCs) following prolonged challenge with cAMP-elevating agents. Using a combination of RNAi-based and pharmacological approaches, we establish that this upregulation is reflected in levels of cAMP PDE activity, and restricted to the cytosolic sub-cellular compartment. Our results suggest a role for localized PDE4D1 and PDE4D2 activity in regulating cAMP-mediated desensitization in HASMCs, and highlight their therapeutic potential in treating various cardiovascular diseases.