Mathematical Analysis of Reaction–Diffusion Equations Modeling the Michaelis–Menten Kinetics in a Micro-Disk Biosensor

In this study, we have investigated the mathematical model of an immobilized enzyme system that follows the Michaelis–Menten (MM) kinetics for a micro-disk biosensor. The film reaction model under steady state conditions is transformed into a couple differential equations which are based on dimensionless concentration of hydrogen peroxide with enzyme reaction (H) and substrate (S) within the biosensor. The model is based on a reaction–diffusion equation which contains highly non-linear terms related to MM kinetics of the enzymatic reaction. Further, to calculate the effect of variations in parameters on the dimensionless concentration of substrate and hydrogen peroxide, we have strengthened the computational ability of neural network (NN) architecture by using a backpropagated Levenberg–Marquardt training (LMT) algorithm. NNs–LMT algorithm is a supervised machine learning for which the initial data set is generated by using MATLAB built in function known as “pdex4”. Furthermore, the data set is validated by the processing of the NNs–LMT algorithm to find the approximate solutions for different scenarios and cases of mathematical model of micro-disk biosensors. Absolute errors, curve fitting, error histograms, regression and complexity analysis further validate the accuracy and robustness of the technique.     

The use of contact angle measurements to estimate the adhesion propensity of calcium carbonate to solid substrates in water

We have studied a series of solids using contact angle measurements; stainless steel, gold, aluminium, titanium nitride and PTFE that are frequently used in domestic water environments. It was found the influence of electron-donor (γ⁻) and electron-acceptor (γ⁺) free energies on material scaling rate was dominated by water wetting angles, providing materials exhibit an average roughness below 100 nm. The γ⁻ component had the greatest influence on theoretical adhesion, while γ^LW, (Lifshitz-van der Waals) γ⁺ and γ^AB (acid-base) had little effect. From the materials analysed, amorphous carbon coatings were least adhesive, while ‘kettle coating’ and highly roughened steel the most adhesive. The size and distribution of asperities also influenced the polar free energies and subsequent adhesion due to fluctuations in the wetting angle. The results obtained indicate works of adhesion can be used as a complementary technique with Lewis acid-base theory to deliver useful information about the propensity of scale to deposit on solids.     

Visible regime application of zone plate coded incoherent holography

Unlike conventional optical holography which requires coherent radiation, zone plate coded holography (ZPCH) offers the possibility of encoding 3D information of an incoherent radiation source. But ZPCH with its coherent optical reconstruction (COR) is unsuitable to be used in the visible regime. However, proposed digital ZPCH scheme for visible regime uses digital decoding instead of COR and overcomes this limitation. This paper discusses the issues of visible regime ZPCH and presents experimental results of applying the modified scheme to encode and successfully decode a visible source, for the first time, to our knowledge. In addition to imaging of incoherent radiation sources, visible regime incoherent holography may find use in constructing holograms of live cells or objects, like retina, where coherent illumination can be detrimental.     

Structural basis of the inhibition of Golgi alpha-mannosidase II by mannostatin A and the role of the thiomethyl moiety in ligand-protein interactions

The X-ray crystal structures of mannose trimming enzyme drosophila Golgi alpha-mannosidase II (dGMII) complexed with the inhibitors mannostatin A (1) and an N-benzyl analogue (2) have been determined. Molecular dynamics simulations and NMR studies have shown that the five-membered ring of mannostatin A is rather flexible occupying pseudorotational itineraries between 2T3 and 5E, and 2T3 and 4E. In the bound state, mannostatin A adopts a 2T1 twist envelope conformation, which is not significantly populated in solution. Possible conformations of the mannosyl oxacarbenium ion and an enzyme-linked intermediate have been compared to the conformation of mannostatin A in the cocrystal structure with dGMII. It has been found that mannostatin A best mimics the covalent linked mannosyl intermediate, which adopts a 1S5 skew boat conformation. The thiomethyl group, which is critical for high affinity, superimposes with the C-6 hydroxyl of the covalent linked intermediate. This functionality is able to make a number of additional polar and nonpolar interactions increasing the affinity for dGMII. Furthermore, the X-ray structures show that the environment surrounding the thiomethyl group of 1 is remarkably similar to the arrangements around the methionine residues in the protein. Collectively, our studies contradict the long held view that potent inhibitors of glycosidases must mimic an oxacarbenium ion like transition state.     

Rapid one-pot iterative diselenide–selenoester ligation using a novel coumarin-based photolabile protecting group

The development of an iterative one-pot peptide ligation strategy is described that capitalises on the rapid and efficient nature of the diselenide–selenoester ligation reaction, together with photodeselenisation chemistry. This ligation strategy hinged on the development of a novel photolabile protecting group for the side chain of selenocysteine, namely the 7-diethylamino-3-methyl coumarin (DEAMC) moiety. Deprotection of this DEAMC group can be effected in a mild, reagent-free manner using visible light (λ = 450 nm) without deleterious deselenisation of selenocysteine residues, thus enabling a subsequent ligation reaction without purification. The use of this DEAMC-protected selenocysteine in iterative DSL chemistry is highlighted through the efficient one-pot syntheses of 60- and 80-residue fragments of mucin-1 as well as apolipoprotein CIII in just 2–4 hours.

A method for the rapid one-pot iterative assembly of proteins via diselenide–selenoester ligation (DSL) chemistry is described that capitalises on a novel coumarin-based photolabile protecting group for selenocysteine.     

A quantum pseudodot system with two-dimensional pseudoharmonic oscillator in external magnetic and Aharonov-Bohm fields

Using the Nikiforov–Uvarov (NU) method, the energy levels and the wave functions of an electron confined in a two-dimensional (2D) pseudoharmonic quantum dot are calculated under the influence of temperature and an external magnetic field inside dot and Aharonov–Bohm (AB) field inside a pseudodot. The exact solutions for energy eigenvalues and wave functions are computed as functions of the chemical potential parameters, applied magnetic field strength, AB flux field, magnetic quantum number and temperature. Analytical expression for the light interband absorption coefficient and absorption threshold frequency are found as functions of applied magnetic field and geometrical size of quantum pseudodot. The temperature dependence energy levels for GaAs semiconductor are also calculated.     

Reversal of Klein reflection by magnetic barriers in bilayer graphene

Massless Dirac fermions in monolayer graphene exhibit total transmission when normally incident on a scalar potential barrier, a consequence of the Klein paradox originally predicted by O Klein for relativistic electrons obeying the 3 + 1 dimensional Dirac equation. For bilayer graphene, charge carriers are massive Dirac fermions and, due to different chiralities, electron and hole states are not coupled to each other. Therefore, the wavefunction of an incident particle decays inside a barrier as for the non-relativistic Schr?dinger equation. This leads to exponentially small transmission upon normal incidence. We show that, in the presence of magnetic barriers, such massive Dirac fermions can have transmission even at normal incidence. The general consequences of this behavior for multilayer graphene consisting of massless and massive modes are mentioned. We also briefly discuss the effect of a bias voltage on such magnetotransport.     

Relativistic New Yukawa-Like Potential and Tensor Coupling

We approximately solve the Dirac equation for a new suggested generalized inversely quadratic Yukawa potential including a Coulomb-like tensor interaction with arbitrary spin-orbit coupling quantum number ${\kappa}$ . In the framework of the spin and pseudospin (p-spin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions, in closed form, by using the parametric Nikiforov–Uvarov method. The numerical results show that the Coulomb-like tensor interaction, ?T/r, removes degeneracies between spin and p-spin state doublets. The Dirac solutions in the presence of exact spin symmetry are reduced to Schr?dinger solutions for Yukawa and inversely quadratic Yukawa potentials.     

Dopant induced morphologies of ZnS nanoparticles

We have reported the synthesis of cubic (zinc blende) phase ZnS: Ni²⁺ nanoparticles using a simple wet‐chemical method. Synthesized ZnS: Ni²⁺ nanoparticles had been characterized by X‐ray diffraction (XRD) and Energy Dispersive X‐ray (EDX) analysis. Surface morphologies were studied using Scanning Electron Microscopy (SEM). Fourier Transform Infrared (FTIR) spectra of selected samples were also carried out to confirm the presence of capping agent on the surface of the material. We have demonstrated that various morphologies like spherical, tetrapods, sheet and long‐armed multipods are emerged by simple chemical route without any vigorous reaction parameters and changing the concentration of dopant ions only. The probable mechanism for such morphologies has also been suggested.