Sharmistha Dhatt

Single-substrate enzyme kinetics: the quasi-steady-state approximation and beyond

We analyze the standard model of enzyme-catalyzed reactions at various substrate-enzyme ratios by adopting a different scaling scheme and computational procedure. The regions of validity of the quasi-steady-state approximation are noted. Certain prevalent conditions are checked and compared against the actual findings. Efficacies of a few other measures, obtained from the present work, are highlighted. Some recent observations are rationalized, particularly at moderate and high enzyme concentrations.

Infinite square well with a sinusoidal bottom: a candidate for the Klauder phenomenon?

In contrast to a recent observation, we notice that a particle in a box with any cosine bottom does not show up the Klauder phenomenon when the perturbation is gradually reduced to zero. Both perturbative and variational approaches have been pursued. The case of a harmonic oscillator perturbed by a similar potential is additionally studied. No peculiarity is observed anywhere in this case too. Possible reasons behind the phenomenon are sought to rationalize our findings.

Concurrent multiple-state analytic perturbation theory via supersymmetry

Conventional nondegenerate perturbation theory for some nth state starts with the corresponding unperturbed state. The present formulation yields recursively perturbation expansions for any bound state using the sole information of the unperturbed ground state. Logarithmic perturbation theory is exploited along with supersymmetric quantum mechanics to achieve this end. As the method involves ground-state perturbations of a series of supersymmetric Hamiltonians, concern about nodal shifts of targeted excited states arises only at the ultimate step, thus, minimizing considerably the labor of clumsy computations involved in dealing with excited states.

Immune Activation and Immunodeficiency: A Model Reduction Strategy

Motivated by the recent medical experiments on vectored immunoprophylaxis for protection against HIV infection and the success of some theoretical models in simulating the observed behavior, a simple kinetic model is proposed to explain both the T cell and viral dynamics after pathogenic attack. The model, described through a system of just three coupled differential equations, is successful in faithfully simulating the autocatalytic augmentations of both T-cells and auto-inhibition of virions. A long-time coexistence of both virions and T-cells, either with damping or growing, or with sustained oscillations, as evidences of some complicated dynamical behavior is observed in the proposed model. The possible physiological consequences that can account for a variety of in vivo experimental data related to viral attacks is thoroughly assessed. Paradoxical situations showing a fall off of T-cell count in spite of enhanced immune activity is highlighted over a wide range of values of system parameters.

Indicators for suicide substrate inactivation: A kinetic investigation

Suicide substrate kinetic pathway and a proposed set of indicators, some theoretical and a few practical ones, that can decisively conclude enzyme inactivation are considered. Steady-state approximation is assumed not only when a catalytic amount of enzyme is used but also for any substrate-enzyme ratio. In each situation, adequacy of the approximation is numerically tested. An equation for the rate of inactivation of the enzyme has been derived and employed under suitable approximations to estimate various indicators. Progressive curves for such indicators via numerical simulation are shown that decide impromptu inactivation too. The scheme though is a traditional one, the findings are novel.Graphical AbstractSynopsis. A few new indicators to identify enzyme inactivation in ‘suicide - substrate inhibition’ are studied. Validity of the indicators over a wide range of enzyme substrate ratio was investigated. The major pitfalls in prevalent indicators in prior articles their shortcomings were identified. The proposed indicators were justified with analytical and probabilistic arguments. Experimental relevance of the indicators is highlighted.

Accurate estimates of asymptotic indices via fractional calculus

We devise a three-parameter random search strategy to obtain accurate estimates of the large-coupling amplitude and exponent of an observable from its divergent Taylor expansion, known to some desired order. The endeavor exploits the power of fractional calculus, aided by an auxiliary series and subsequent construction of Padé approximants. Pilot calculations on the ground-state energy perturbation series of the octic anharmonic oscillator reveal the spectacular performance.