Matching Items (2)
Description
Advances in experimental techniques have allowed for investigation of molecular dynamics at ever smaller temporal and spatial scales. There is currently a varied and growing body of literature which demonstrates the phenomenon of \emph{anomalous diffusion} in physics, engineering, and biology. In particular many diffusive type processes in the cell have been observed to follow a power law $\left \propto t^\alpha$ scaling of the mean square displacement of a particle. This contrasts with the expected linear behavior of particles undergoing normal diffusion. \emph{Anomalous sub-diffusion} ($\alpha<1$) has been attributed to factors such as cytoplasmic crowding of macromolecules, and trap-like structures in the subcellular environment non-linearly slowing the diffusion of molecules. Compared to normal diffusion, signaling molecules in these constrained spaces can be more concentrated at the source, and more diffuse at longer distances, potentially effecting the signalling dynamics. As diffusion at the cellular scale is a fundamental mechanism of cellular signaling and additionally is an implicit underlying mathematical assumption of many canonical models, a closer look at models of anomalous diffusion is warranted. Approaches in the literature include derivations of fractional differential diffusion equations (FDE) and continuous time random walks (CTRW). However these approaches are typically based on \emph{ad-hoc} assumptions on time- and space- jump distributions. We apply recent developments in asymptotic techniques on collisional kinetic equations to develop a FDE model of sub-diffusion due to trapping regions and investigate the nature of the space/time probability distributions assosiated with trapping regions. This approach both contrasts and compliments the stochastic CTRW approach by positing more physically realistic underlying assumptions on the motion of particles and their interactions with trapping regions, and additionally allowing varying assumptions to be applied individually to the traps and particle kinetics.
ContributorsHoleva, Thomas Matthew (Author) / Ringhofer, Christian (Thesis advisor) / Baer, Steve (Thesis advisor) / Crook, Sharon (Committee member) / Gardner, Carl (Committee member) / Taylor, Jesse (Committee member) / Arizona State University (Publisher)
Created2014
Description
The goal of this theoretical study of infrared spectra was to ascertain to what degree molecules may be identified from their IR spectra and which spectral regions are best suited for this purpose. The frequencies considered range from the lowest frequency molecular vibrations in the far-IR, terahertz region (below ~3 THz or 100 cm-1) up to the highest frequency vibrations (~120 THz or 4000 cm-1). An emphasis was placed on the IR spectra of chemical and biological threat molecules in the interest of detection and prevention. To calculate IR spectra, the technique of normal mode analysis was applied to organic molecules ranging in size from 8 to 11,352 atoms. The IR intensities of the vibrational modes were calculated in terms of the derivative of the molecular dipole moment with respect to each normal coordinate. Three sets of molecules were studied: the organophosphorus G- and V-type nerve agents and chemically related simulants (15 molecules ranging in size from 11 to 40 atoms); 21 other small molecules ranging in size from 8 to 24 atoms; and 13 proteins ranging in size from 304 to 11,352 atoms. Spectra for the first two sets of molecules were calculated using quantum chemistry software, the last two sets using force fields. The "middle" set used both methods, allowing for comparison between them and with experimental spectra from the NIST/EPA Gas-Phase Infrared Library. The calculated spectra of proteins, for which only force field calculations are practical, reproduced the experimentally observed amide I and II bands, but they were shifted by approximately +40 cm-1 relative to experiment. Considering the entire spectrum of protein vibrations, the most promising frequency range for differentiating between proteins was approximately 600-1300 cm-1 where water has low absorption and the proteins show some differences.
ContributorsMott, Adam J (Author) / Rez, Peter (Thesis advisor) / Ozkan, Banu (Committee member) / Shumway, John (Committee member) / Thorpe, Michael (Committee member) / Vaiana, Sara (Committee member) / Arizona State University (Publisher)
Created2012