Effect of thermal lag and measurement precision in differential scanning calorimetry: theoretical guidelines for enzyme-substrate reactions by the method of orthogonal collocation

Abstract

A simplified model of a differential scanning calorimeter (DSC) with large (40-120 pL) aqueous enzyme sample was simulated digitally by the mathematical technique called orthogonal collocation in order to observe the errors due to thermal lag (temperature and concentration gradients) in calculating the first-order Arrhenius kinetic parameters Zand AE. Only two dimensionless parameters were found to Influence the determinate errors in the data, one related to the scan rate and the other related to the rate of diffusion relative to the rate of chemical reaction. The errors were independent of AH, C", and Dm and also the parameters Z, AE, and T0 as long

Thermotropic Phase Transitions in Butyltrimethylammonium Bis(trifluoromethylsulfonyl)imide Ionic Liquids are Dependent on Heat Flux

“…These complete melting (Figure a) and partial melting (Figure b) features show relatively small increases in the peak temperatures (<5 °C) across the entire range of heating rates examined. This may partially be ascribed to thermal lag, as observed previously at fast heating or cooling rates, and therefore the negligible change due to temperature change rate reveals the melting phase transitions to be in stable thermodynamic equilibria. , However, the variations are not uniform for the multiple phase transitions observed here. Specifically, the peak temperatures for solid–solid (Figure c) and cold crystallization (Figure d) phase transitions decrease until reaching an inflection point, at a “critical rate”, beyond which the peak temperature no longer changes.…”

“…The peak temperatures for each melting phase transition show relatively small decrease with increasing heating rates, which is likely due to thermal lag, but otherwise the melting transitions are stable thermodynamic processes with respect to cooling/heating rate. In direct contrast, the larger change in peak temperature for the cold crystallization and solid–solid transition indicate a significantly larger heating rate effect on these phase transtions. , The cold crystallization and solid–solid transition exhibit two linear regions, an initial range that rapidly decreases in peak temperature and a second more constant peak temperature range. We define the point each linear range meets the critical heating rate, after which the peak temperature does not change with respect to the heating rate.…”

Theoretical evaluation of the steady-state response of potentiometric enzyme electrodes

“…Detailed treatments of the mass transport equation that results from the enzyme electrode, assuming Michaelis-Menton kinetics, have been frustrated by the inefficiency of the numerical methods suitable for the resulting nonlinear differential equation. Numerical solutions of complicated heat and mass transfer problems have been successfully and efficiently accomplished by the method of orthogonal collocation (8)(9)(10)(11)(12)(13). Noting the power this method has shown in problems of a similar and more complex nature, a simulation of the steady-state response of the potentiometric enzyme electrode was attempted here in order to better establish the theoretical, steady-state behavior of enzyme electrodes.…”

“…In the region of high enzyme loading (a > 1), the limiting bulk substrate concentration is governed by the relationship C* = 0.16 a1'25 (11) Km which is obtained as at least squares fit to the data from a = 3 to a = 100. Combining Equation 3 and the definition of enzyme activity (18), one obtains an equation for the minimum required enzyme activity per unit volume of membrane at a specified limiting bulk substrate concentration 2.60 X 105KM0-2DS £(units/cm3) = ---(C's)0-8 (12) Lz where C's is the limiting substrate concentration in molarity and the other symbols are as previously defined. The expression shows a positive fifth root dependence on KM, a result which is superficially surprising when one considers that it Z Figure 5.…”

Simulation of electrochemical processes by orthogonal collocation. Spherical electrode geometry

“…Orthogonal collocation techniques for the simulation of second order partial differential equations have been demonstrated for a variety of problems in electrochemistry (1-7), chemical engineering (8-ll), differential scanning calorimetry (12), and other fields (13). The advantages over other methods have been described, but noteworthy is generally increased accuracy for decreased computational effort (1)(2)(3)(4)(5)(6)(7).…”