MATHEMATICAL ANALYSIS OF WEST NILE VIRUS MODEL WITH DISCRETE DELAYS

The paper presents the basic model for the transmission dynamics of West Nile virus (WNV). The model, which consists of seven mutually-exclusive compartments representing the birds and vector dynamics,...     

Mathematical Analysis of West Nile Virus Model with Discrete Delays

The paper presents the basic model for the transmission dynamics of West Nile virus (WNV). The model, which consists of seven mutually-exclusive compartments representing the birds and vector dynamics, has a locally-asymptotically stable disease-free equilibrium whenever the associated reproduction number (?₀) is less than unity. As reveal in [3, 20], the analyses of the model show the existence of the phenomenon of backward bifurcation (where the stable disease-free equilibrium of the model co-exists with a stable endemic equilibrium when the reproduction number of the disease is less than unity). It is shown, that the backward bifurcation phenomenon can be removed by substituting the associated standard incidence function with a mass action incidence. Analysis of the reproduction number of the model shows that, the disease will persist, whenever ?₀ > 1, and increase in the length of incubation period can help reduce WNV burden in the community if a certain threshold quantities, denoted by Δ_b and Δ_v are negative. On the other hand, increasing the length of the incubation period increases disease burden if Δ_b > 0 and Δ_v > 0. Furthermore, it is shown that adding time delay to the corresponding autonomous model with standard incidence (considered in [2]) does not alter the qualitative dynamics of the autonomous system (with respect to the elimination or persistence of the disease).     

Computational chemistry in drug lead discovery and design

The main contributions of our group during the last 15 years developing and using biomolecular simulation tools in drug lead discovery and design, in close collaboration with experimental researchers, are presented. Special emphasis has been given to methodological improvements in the following areas: (1) target homology modeling incorporating knowledge about known ligands to accurately characterize the binding site; (2) designing alternative strategies to account for protein flexibility in high-throughput docking; (3) development of stochastic- and normal-mode-based methods to de novo design structurally diverse protein conformers; (4) development and validation of quantum mechanical semi-empirical linear-scaling calculations to correctly estimate ligand binding free energy. Several successful cases of computer-aided drug discovery are also presented, especially our recent work on viral targets.     

Dye Sensitization Offers a Brighter Afterglow Nanoparticle Future for in vivo Recharged Luminescent Imaging

While concerns about improving recharged afterglow intensity in vivo still motivate further exploration, afterglow nanoparticles (AGNP) offer unique optical merit for autofluorescence-free biological imaging. Apart from efforts enhancing the afterglow emission properties of AGNP, improving afterglow excitation response to visible or near infrared light is important but has lacked success. Dye sensitization has been used to improve the optical response of photovoltaic nanomaterials and to enhance upconversion luminescence efficiency. This concept has recently been expanded and applied to AGNPs. As a new multifunctional nanoprobe, such dye-sensitized AGNP takes advantage of both high spatial resolution fluorescence imaging and sensitive afterglow imaging. This Concept introduces the background, the concept, mechanism, and related imaging application, as well as reviewing existing challenges and proposing future developmental directions for the dye-sensitized AGNPs.     

Transient and Persistent Room‐Temperature Mechanoluminescence from a White‐Light‐Emitting AIEgen with Tricolor Emission Switching Triggered by Light

Persistent luminescence from purely organic materials is basically triggered by light and electricity, which largely confines its practical applications. A purely organic AIEgen exhibits not only persistent photoluminescence, but also transient and persistent room‐temperature mechanoluminescence. By simply turning on and off a UV lamp, tricolor emission switching between blue, white, and yellow was achieved. The data from single‐crystal structure analysis and theoretical calculation suggest that mechanism of the observed persistent mechanoluminescence (pML) is correlated with the strong spin–orbit coupling of the bromine atom, as well as the formation of H‐aggregates and restriction of intramolecular motions in noncentrosymmetric crystal structure. These results outline a fundamental principle for the development of new pML materials, providing an important step forward in expanding the application scope of persistent luminescence.     

Evaluation of multiple alternative instrument platforms for targeted and non‐targeted dioxin and furan analysis

The use of gas chromatography coupled to high‐resolution magnetic sector mass spectrometers (GC‐HRMS) is well established for dioxin and furan analysis. However, the use of gas chromatography coupled to triple quadrupole (MS/MS) and time of flight (TOF) mass spectrometers with atmospheric pressure ionization (API) and traditional electron ionization (EI) for dioxin and furan analysis is emerging as a viable alternative to GC‐HRMS screening. These instruments offer greater versatility in the lab for a wider range of compound identification and quantification as well as improved ease of operation. The instruments utilized in this study included 2 API‐MS/MS, 1 traditional EI‐MS/MS, an API‐quadrupole time of flight mass spectrometer (API‐QTOF), and a EI‐high‐resolution TOF (EI‐HRTOF). This study compared these 5 instruments to a GC‐HRMS using method detection limit (MDLs) samples for dioxin and furan analysis. Each instrument demonstrated acceptable MDL values for the 17 chlorinated dioxin and furans studied. The API‐MS/MS instruments provide the greatest overall improvement in MDL value over the GC‐HRMS with a 1.5 to 2‐fold improvement. The API‐QTOF and EI‐TOF demonstrate slight increases in MDL value as compared with the GC‐HRMS with a 1.5‐fold increase. The 5 instruments studied all demonstrate acceptable MDL values with no MDL for a single congener greater than 5 times that for the GC‐HRMS. All 5 instruments offer a viable alternative to GC‐HRMS for the analysis of dioxins and furans and should be considered when developing new validated methodologies.     

Exact sequences for the homology of the matching complex

Building on work by Bouc and by Shareshian and Wachs, we provide a toolbox of long exact sequences for the reduced simplicial homology of the matching complex Mn, which is the simplicial complex of matchings in the complete graph Kn. Combining these sequences in different ways, we prove several results about the 3-torsion part of the homology of Mn. First, we demonstrate that there is nonvanishing 3-torsion in whenever , where . By results due to Bouc and to Shareshian and Wachs, is a nontrivial elementary 3-group for almost all n and the bottom nonvanishing homology group of Mn for all n≠2. Second, we prove that is a nontrivial 3-group whenever . Third, for each k?0, we show that there is a polynomial fk(r) of degree 3k such that the dimension of , viewed as a vector space over Z₃, is at most fk(r) for all r?k+2.     

CH/pi hydrogen bonds determine the selectivity of the Src homology 2 domain to tyrosine phosphotyrosyl peptides: an ab initio fragment molecular orbital study

The CH/pi hydrogen bond is a weak molecular force occurring between CH groups (soft acids) and pi-systems (soft bases), and has been recognized to be important in the interaction of proteins with their specific ligands. For instance, it is well known that Src homology-2 protein (SH2) recognizes its specific pTyr peptide in two key regions, pTyr-binding region and specificity-determining region, by the use of attractive molecular forces, including the CH/pi hydrogen bond. We hypothesized that the CH/pi hydrogen bond plays a key role in determining the selectivity of SH2 proteins, and studied this issue by the ab initio fragment molecular orbital (FMO) method. The FMO calculations were carried out, at the HF/6-31G* and MP2/6-31G* level, for SH2 domains of Src, Grb2, P85alpha(N), Syk, and SAP, in complex with corresponding pTyr peptides. CH/pi hydrogen bonds have in fact been found to be important in stabilizing the structure of the complexes. We conclude that the CH/pi hydrogen bond plays an indispensable role in the recognition of SH2 domains with their specific pTyr peptides, thus playing a vital role in the signal transduction system.