Plasmonic artificial virus nano-particles for probing virus-host cell interactions

Targeting of key events in viral infection pathways creates opportunities for virus disease prevention and therapy. Nanoparticles with well-defined surfaces are promising tools for the direct visualization of biological processes and for interrogating virus behavior that is usually determined by the synergistic interplay of multiple factors and involves various transient signaling steps. Smart nanoparticles mimicking enveloped viral particles are thus developed and tested in this work with the aim to de-couple key steps in human immune-deficiency virus HIV-1 trans-infection with an engineerable viral model system. Uni-lamellar liposomes resemble biological lipid bilayer membrane structures with tunable particle size, surface charge, and composition. Pretreatment with ganglioside-GM3-containing liposomes inhibited the binding of HIV-1 by dendritic cells, indicating an essential role for GM3 in virus binding. To equip the liposome based model systems with strong non bleaching optical properties, the membranes were in the next step assembled around noble metal nanoparticle core. Noble metal nanoparticles with a size of 20nm-100nm have extraordinarily large scattering cross-sections and enable prolonged tracking of even individual particles with high temporal and spatial resolutions. The plasmon resonance peak of near-field coupled gold nanoparticles red-shifts within decreasing interparticle separation. The distance dependent optical properties of noble metal nanoparticles were utilized for characterizing clustering levels of breast cancer cell marker protein CD24 and CD44 on immortalized cancer cell lines. These encouraging results supported the choice of gold nanoparticles as core for multi-modal artificial virus nanoparticles. Artificial virus nanoparticles combine the biological versatility of a self-assembled membrane with the unique optical properties of a nanoparticle core. We developed these hybrid materials specifically for the purpose of elucidating key steps of the glycoprotein independent binding and uptake of HIV-1 during trans-infection. Systematic validation experiments revealed that GM3 containing artificial virus nanoparticles (AVNs) recapitulate the initial capture and uptake of viruses by sialoadhesin CD169 presenting cells. The AVNs also reproduced the tendency of the virus to re-distribute into confined cluster spots in cell peripheral areas. Upon contact formation between T cell and DC, the AVNs developed a polarized distribution in which they enriched at the interface between DC and CD4+ T cells. The multimodality of the AVNs was instrumental in determining the detailed location and kinetics of the nanoparticles during the trans-infection process, proving the AVN system to be a unique model system to address key mechanistic questions in the infection pathway of enveloped virus particles

Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation

In this article we apply the technique proposed in Deng-Hou-Yu (Comm. PDE, 2005) to study the level set dynamics of the 2D quasi-geostrophic equation. Under certain assumptions on the local geometric regularity of the level sets of $\theta$, we obtain global regularity results with improved growth estimate on $| \nabla^{\bot} \theta |$. We further perform numerical simulations to study the local geometric properties of the level sets near the region of maximum $| \nabla^{\bot} \theta |$. The numerical results indicate that the assumptions on the local geometric regularity of the level sets of $\theta$ in our theorems are satisfied. Therefore these theorems provide a good explanation of the double exponential growth of $| \nabla^{\bot} \theta |$ observed in this and past numerical simulations.Comment: 25 pages, 10 figures. Corrected a few typo

Logarithmic improvement of regularity criteria for the Navier-Stokes equations in terms of pressure

XY is partially supported by a grant from NSERC.In this article we prove a logarithmic improvement of regularity criteria in the multiplier spaces for the Cauchy problem of the incompressible Navier-Stokes equations in terms of pressure. This improves the main result in [S. Benbernou, A note on the regularity criterion in terms of pressure for the Navier-Stokes equations, Applied Mathematics Letters 22 (2009) 1438–1443].PostprintPeer reviewe

Numerical Analysis for Real-time Nonlinear Model Predictive Control of Ethanol Steam Reformers

The utilization of renewable energy technologies, particularly hydrogen, has seen a boom in interest and has spread throughout the world. Ethanol steam reformation is one of the primary methods capable of producing hydrogen efficiently and reliably. This paper provides an in-depth study of the reformulated system both theoretically and numerically, as well as a plan to explore the possibility of converting the system into its conservation form. Lastly, we offer an overview of several numerical approaches for solving the general first-order quasi-linear hyperbolic equation to the particular model for ethanol steam reforming (ESR). We conclude by presenting some results that would enable the usage of these ODE/PDE solvers to be used in non-linear model predictive control (NMPC) algorithms and discuss the limitations of our approach and directions for future work.Comment: Canadian Undergraduate Mathematics Conference 202