With cancer rates increasing at an alarming rate, many traditional methods for cancer treatment begin to feel outdated. This is where engineering nanomaterials, such as Graphene Quantum Dots (GQDs), offer a promising approach to making chemotherapy a more targeted treatment and therefore minimizing the side effects. This study focuses on optimizing drug delivery mechanisms using GQDs, specifically Reduced Graphene Quantum Dots (RGQDs) synthesized via a top-down approach from reduced graphene oxide, and Hyaluronic Acid Graphene Quantum Dots (HAGQDs) synthesized bottom-up from hyaluronic acid. The process is done by loading chemotherapeutics Gemcitabine, Paclitaxel, and Doxorubicin (DOX) HCl onto GQDs through sonication, this is followed by a centrifugal purification which isolates properly drug-loaded GQDs. To evaluate their controlled release, photothermal properties of GQDs are utilized. Samples are excited with an 808 nm laser at 1, 5, and 10 minutes, and they are later compared to a control group. This analysis provides insights into how laser stimulation affects drug release efficiency, paving the way for advancements in GQD based cancer treatments.

We introduce a structural method used for quantifying the spatial heterogeneity(or clumpiness) of viral syncytial cells in a transfection bioassay. The solution lies in an inter-disciplinary process based on simplicial topology being applied to a biological system. Our method revolves around using topological theories including Delaunay tessellations and Voronoi graphs to signify cell-cell interaction probability. The main emphasis is the subset of Delaunay tessellation called Alpha shapes. By applying a filtration to the overall Delaunay tessellation, we can obtain unique Alpha Shapes that have cell-cell interactions removed. The emphasis of the filtration is to find the correct shape where there were no connection crossing syncytia, only between healthy neighborhoods of cells. The process allows for the associated alpha number to be assigned to the clumpiness. Alpha numbers can then be used to separate different bioassays, or quantify temporal changes found in a single viral transfection due to syncytia.

In virology, mathematical models are often deployed to examine and test various behaviors of viruses. For example, one for the flu it is speculated that lethality is linked to the virus’s ability to propagate down the trachea, specifically in how ciliated cells push virus up through mucous layers in a process known as advection. We propose a model for this process, believing that this model can reveal links and critical points between lethality and advection. To solve this model, we utilize three techniques: Laplacian transform, non-linear analysis, and quasi-state analysis. We discuss the findings of each method.

Our neighboring galaxies, the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC), interact with each other as they move through the hot, outer region of the Milky Way. This interaction can pull and sweep away gas from the edges of the galaxies, forming large, stretched-out clouds of gas. The LMC has two gas filaments that resemble arms, which connect to a region where stars are formed, possibly hinting toward their origin or their final destination. In this study, we used radio observations and data from the Hubble Space Telescope to search for signs of these gas arms near the star-forming region. We find a continuous stream of gas that could be the arms located at least partially in front of the LMC. The positioning of these arms raises two competing questions: 1) Is the gas flow fueling new star formation in the LMC, or 2) Is gas from exploded stars in the LMC flowing out into these arms? While the inflow of gas makes sense for these gas flows, we also conducted simulations of outflows from the starburst region. Our results suggest that it is possible for debris from exploded stars to be swept into the arms. Future observations will help us better reconstruct the arms’ evolutionary history.

Some viruses have the ability to form syncytia. Syncytia are multi-nucleated cells formed via membrane fusion. Syncytia formation allows viruses to spread infection to other cells without entering the extracellular space where it could be exposed to antiviral drugs or immune responses such as antibodies. This project explores how syncytia formation can help viruses avoid antiviral drugs. Drug efficacy parameters are applied to a mathematical model of differential equations to explore the impact of antiviral drugs on cell infection, cell fusion, and viral production to model respiratory syncytial virus. The models show that as syncytia formation increases the drugs become less effective. This information will help physicians treat patients with syncytia forming viruses.