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A mathematical model for simulating biological field effect transistor (Bio-FET) experiments is introduced. It takes the form of a nonlinear equation that describes evolution of reacting species co...

A partial differential equation (PDE) was developed to describe time-dependent ligand-receptor interactions for applications in biosensing using field effect transistors (FET). The model describes biochemical interactions at the sensor surface (or biochemical gate) located at the bottom of a solution-well, which result in a time-dependent change in the FET conductance. It was shown that one can exploit the disparate length scales of the solution-well and biochemical gate to reduce the coupled PDE model to a single nonlinear integrodifferential equation (IDE) that describes the concentration of reacting species. Although this equation has a convolution integral with a singular kernel, a numerical approximation was constructed by applying the method of lines. The need for specialized quadrature techniques was obviated and numerical evidence strongly suggests that this method achieves first-order accuracy. Results reveal a depletion region on the biochemical gate, which non-uniformly alters the surface potential of the semiconductor.

One may measure the kinetic rate constants associated with biochemical reactions using an optical biosensor: an instrument in which ligand molecules are convected through a flow cell over a surface to which receptors are immobilized. If there are multiple reactants, one is faced with the problem of fitting multiple kinetic rate constants to one signal, since data from all of the reacting species is lumped together. Even in the presence of ambiguous data, one may use a series of experiments to accurately determine the rate constants. Moreover, the true set of rate constants may be identified by either postprocessing the signals or adjusting the ligand inflow concentrations.

Optical biosensors are often used to measure kinetic rate constants associated with chemical reactions. Such instruments operate in the \textit{surface-volume} configuration, in which ligand molecules are convected through a fluid-filled volume over a surface to which receptors are confined. Currently, scientists are using optical biosenors to measure the kinetic rate constants associated with DNA translesion synthesis--a process critical to DNA damage repair. Biosensor experiments to study this process involve multiple interacting components on the sensor surface. This multiple-component biosensor experiment is modeled with a set of nonlinear integrodifferential equations (IDEs). It is shown that in physically relevant asymptotic limits these equations reduce to a much simpler set of Ordinary Differential Equations (ODEs). To verify the validity of our ODE approximation, a numerical method for the IDE system is developed and studied. Results from the ODE model agree with simulations of the IDE model, rendering our ODE model useful for parameter estimation.

The increased interest in using monoclonal antibodies (mAbs) as a platform for biopharmaceuticals has led to the need for new analytical techniques that can precisely assess physicochemical properties of these large and very complex drugs for the purpose of correctly identifying quality attributes (QA). One QA, higher order structure (HOS), is unique to biopharmaceuticals and essential for establishing consistency in biopharmaceutical manufacturing, detecting process-related variations from manufacturing changes and establishing comparability between biologic products. To address this measurement challenge, two-dimensional nuclear magnetic resonance spectroscopy (2D-NMR) methods were introduced that allow for the precise atomic-level comparison of the HOS between two proteins, including mAbs. Here, an inter-laboratory comparison involving 26 industrial, government and academic laboratories worldwide was performed as a benchmark using the NISTmAb, from the National Institute of Standards and Technology (NIST), to facilitate the translation of the 2D-NMR method into routine use for biopharmaceutical product development. Two-dimensional 1H,15N and 1H,13C NMR spectra were acquired with harmonized experimental protocols on the unlabeled Fab domain and a uniformly enriched-15N, 20%-13C-enriched system suitability sample derived from the NISTmAb. Chemometric analyses from over 400 spectral maps acquired on 39 different NMR spectrometers ranging from 500 MHz to 900 MHz demonstrate spectral fingerprints that are fit-for-purpose for the assessment of HOS. The 2D-NMR method is shown to provide the measurement reliability needed to move the technique from an emerging technology to a harmonized, routine measurement that can be generally applied with great confidence to high precision assessments of the HOS of mAb-based biotherapeutics.

Scientists measure rate constants associated with biochemical reactions in an optical biosensor—an instrument in which ligand molecules are convected through a flow cell over a surface to which receptors are immobilized. We quantify transport effects on such reactions by modeling the associated convection-diffusion equation with a reaction boundary condition. In experimental situations, the full PDE model reduces to a set of unwieldy integrodifferential equations (IDEs). Employing common physical assumptions, we may reduce the system to an ODE model, which is more useful in practice, and which can be easily adapted to the inverse problem of finding rate constants. The results from the ODE model compare favorably with numerical simulations of the IDEs, even outside its range of validity.

This article presents a few methods for generating Sudoku puzzles. These methods are developed based on the concepts of matrix, permutation, and modular functions, and therefore can be used to form application examples or student projects when teaching various mathematics courses. Mathematical properties of these methods are studied, connections between the methods are investigated, and student projects are suggested. Since most students tend to enjoy games, studies like this may help raising students’ interests and enhance their problem-solving skills.

Avian influenza viruses of H5 subtype can cause highly pathogenic disease in poultry. In March 2014, a new reassortant H5N6 subtype highly pathogenic avian influenza virus emerged in Lao People’s Democratic Republic. We have assessed the pathogenicity, pathobiology and immunological responses associated with this virus in chickens. Infection caused moderate to advanced disease in 6 of 6 chickens within 48 h of mucosal inoculation. High virus titers were observed in blood and tissues (kidney, spleen, liver, duodenum, heart, brain and lung) taken at euthanasia. Viral antigen was detected in endothelium, neurons, myocardium, lymphoid tissues and other cell types. Pro-inflammatory cytokines were elevated compared to non-infected birds. Our study confirmed that this new H5N6 reassortant is highly pathogenic, causing disease in chickens similar to that of Asian H5N1 viruses, and demonstrated the ability of such clade 2.3.4-origin H5 viruses to reassort with non-N1 subtype viruses while maintaining a fit and infectious phenotype. Recent detection of influenza H5N6 poultry infections in Lao PDR, China and Viet Nam, as well as six fatal human infections in China, demonstrate that these emergent highly pathogenic H5N6 viruses may be widely established in several countries and represent an emerging threat to poultry and human populations.

In this paper we consider a class of partial integro-differential equations of fractional order, motivated by an equation which arises as a result of modeling surface-volume reactions in optical biosensors. We solve these equations by employing techniques from fractional calculus; several examples are discussed. Furthermore, for the first time, we encounter an order of the fractional derivative other than $\frac{1}{2}$ in an applied problem. Hence, in this paper we explore the applicability of fractional calculus in real-world applications, further strengthening the true nature of fractional calculus., Comment: 19 pages, 2 figures, Preprint submitted for publication

Background: A third of all known freshwater mollusk extinctions worldwide have occurred within a single medium-sized American drainage. The Mobile River Basin (MRB) of Alabama, a global hotspot of temperate freshwater biodiversity, was intensively industrialized during the 20 th century, driving 47 of its 139 endemic mollusk species to extinction. These include the ancylinid limpet Rhodacmea filosa, currently classified as extinct (IUCN Red List), a member of a critically endangered southeastern North American genus reduced to a single known extant population (of R. elatior) in the MRB. Methodology/Principal Findings: We document here the tripling of known extant populations of this North American limpet genus with the rediscovery of enduring Rhodacmea filosa in a MRB tributary and of R. elatior in its type locality: the Green River, Kentucky, an Ohio River Basin (ORB) tributary. Rhodacmea species are diagnosed using untested conchological traits and we reassessed their systematic and conservation status across both basins using morphometric and genetic characters. Our data corroborated the taxonomic validity of Rhodacmea filosa and we inferred a within-MRB cladogenic origin from a common ancestor bearing the R. elatior shell phenotype. The geographically-isolated MRB and ORB R. elatior populations formed a cryptic species complex: although overlapping morphometrically, they exhibited a pronounced phylogenetic disjunction that greatly exceeded that of within-MRB R. elatior and R. filosa sister species. Conclusions/Significance: Rhodacmea filosa, the type species of the genus, is not extinct. It persists in a Coosa River tributary and morphometric and phylogenetic analyses confirm its taxonomic validity. All three surviving populations of the genus Rhodacmea merit specific status. They collectively contain all known survivors of a phylogenetically highly distinctive North American endemic genus and therefore represent a concentrated fraction of continental freshwater gastropod biodiversity. We recommend the establishment of a proactive targeted conservation program that may include their captive propagation and reintroduction.