Sharmistha Dhatt

Bio: Sharmistha Dhatt is an academic researcher from University of Calcutta. The author has contributed to research in topics: Padé approximant & Fractional calculus. The author has an hindex of 4, co-authored 21 publications receiving 52 citations.

Single-substrate Enzyme Kinetics: The Quasi-steady-state Approximation and Beyond

Abstract: We analyze the standard model of enzyme-catalyzed reactions at various substrate-enzyme ratios to identify the regions of validity of the quasi-steady-state approximation. Certain prevalent conditions are checked and compared against the actual findings. Efficacies of a few other measures are highlighted. Some very recent observations are rationalized, particularly at moderate and high enzyme concentrations.

Asymptotic response of observables from divergent weak-coupling expansions: a fractional-calculus-assisted Padé technique

Abstract: Appropriate constructions of Pade approximants are believed to provide reasonable estimates of the asymptotic (large-coupling) amplitude and exponent of an observable, given its weak-coupling expansion to some desired order. In many instances, however, sequences of such approximants are seen to converge very poorly. We outline here a strategy that exploits the idea of fractional calculus to considerably improve the convergence behavior. Pilot calculations on the ground-state perturbative energy series of quartic, sextic, and octic anharmonic oscillators reveal clearly the worth of our endeavor.

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

Abstract: 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.

Embedding scaling relations in Padé approximants: Detours to tame divergent perturbation series

Abstract: A divergent perturbation series is known to yield very unreliable results for observables even at moderate coupling strengths. One of the most popular techniques in handling such series is to express them as rational functions, but it is often faithful only for small coupling. We outline here how one can gain considerable advantages in the large-coupling regime by properly embedding known asymptotic scaling relations for selected observables during construction of the aforesaid Pade approximants. Three new bypass routes are explored in this context. The first approach involves a weighted geometric mean of two neighboring PA. The second idea is to consider series for specific ratios of observables. The third strategy is to express observables as functionals of the total energy in the form of series expansions. Symanzik's scaling relation, and the virial and Hellmann–Feynman theorems, are used at appropriate places to aid each of the strategies. Pilot calculations on the ground-state perturbation series of certain observables for the quartic anharmonic oscillator problem reveal readily the benefit and novelty. © 2012 Wiley Periodicals, Inc.

Accurate estimates of asymptotic indices via fractional calculus

Abstract: 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 Pade approximants. Pilot calculations on the ground-state energy perturbation series of the octic anharmonic oscillator reveal the spectacular performance.

Enzyme Kinetics A Modern Approach

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A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009

Abstract: (2 < p < 4) [200]. (Uq(∫u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2× 2 [185]. 3 [456, 363, 58, 18, 351]. ∗ [238]. 2 [277]. 3 [350]. p [282]. B−L [427]. α [216, 483]. α− z [322]. N = 2 [507]. D [222]. ẍ+ f(x)ẋ + g(x) = 0 [112, 111, 8, 5, 6]. Eτ,ηgl3 [148]. g [300]. κ [244]. L [205, 117]. L [164]. L∞ [368]. M [539]. P [27]. R [147]. Z2 [565]. Z n 2 [131]. Z2 × Z2 [25]. D(X) [166]. S(N) [110]. ∫l2 [154]. SU(2) [210]. N [196, 242]. O [386]. osp(1|2) [565]. p [113, 468]. p(x) [17]. q [437, 220, 92, 183]. R, d = 1, 2, 3 [279]. SDiff(S) [32]. σ [526]. SLq(2) [185]. SU(N) [490]. τ [440]. U(1) N [507]. Uq(sl 2) [185]. φ 2k [283]. φ [553]. φ4 [365]. ∨ [466]. VOA[M4] [33]. Z [550].

Michaelis-Menten equation for degradation of insoluble substrate.

Abstract: Kinetic studies of homogeneous enzyme reactions where both the substrate and enzyme are soluble have been well described by the Michaelis-Menten (MM) equation for more than a century. However, many reactions are taking place at the interface of a solid substrate and enzyme in solution. Such heterogeneous reactions are abundant both in vivo and in industrial application of enzymes but it is not clear whether traditional enzyme kinetic theory developed for homogeneous catalysis can be applied. Since the molar concentration of surface accessible sites (attack-sites) often is unknown for a solid substrate it is difficult to assess whether the requirement of the MM equation is met. In this paper we study a simple kinetic model, where removal of attack sites expose new ones which preserve the total accessible substrate, and denote this approach the substrate conserving model. The kinetic equations are solved in closed form, both steady states and progress curves, for any admissible values of initial conditions and rate constants. The model is shown to merge with the MM equation and the reverse MM equation when these are valid. The relation between available molar concentration of attack sites and mass load of substrate is analyzed and this introduces an extra parameter to the equations. Various experimental setups to practically and reliably estimate all parameters are discussed.