Effect of Thermal Lag and Measurement Precision in Differential Scanning Calorimetry: Theoretical Guidelines for Enzyme-Substrate Reactions by the Method of Orthogonal Collocation

L. F. Whiting, P. W. Carr

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Abstract

A simplified model of a differential scanning calorimeter (DSC) with large (40-120 µL) 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 ΔE. 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 ΔH, C0, and Dm and also the parameters Z, ΔE, and To as long as the initial rate constant, k0, remained unchanged. Simulations also indicate that In Z and Δ can be obtained to within 5 % for an 80-µL sample at a scan rate of 5 K/min. An additional study was carried out involving the indeterminate errors incurred when one scans slowly relative to the rate of chemical reaction. Results indicate that random errors can easily be several times greater than the determinate errors related to thermal lag.

Original languageEnglish (US)
Pages (from-to)1997-2006
Number of pages10
JournalAnalytical chemistry
Volume50
Issue number14
DOIs
StatePublished - Jan 1 1978

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Differential scanning calorimetry
Substrates
Enzymes
Chemical reactions
Random errors
Calorimeters
Kinetic parameters
Rate constants
Hot Temperature
Scanning
Temperature

Cite this

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title = "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 µL) 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 ΔE. 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 ΔH, C0, and Dm and also the parameters Z, ΔE, and To as long as the initial rate constant, k0, remained unchanged. Simulations also indicate that In Z and Δ can be obtained to within 5 {\%} for an 80-µL sample at a scan rate of 5 K/min. An additional study was carried out involving the indeterminate errors incurred when one scans slowly relative to the rate of chemical reaction. Results indicate that random errors can easily be several times greater than the determinate errors related to thermal lag.",
author = "Whiting, {L. F.} and Carr, {P. W.}",
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AU - Whiting, L. F.

AU - Carr, P. W.

PY - 1978/1/1

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N2 - A simplified model of a differential scanning calorimeter (DSC) with large (40-120 µL) 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 ΔE. 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 ΔH, C0, and Dm and also the parameters Z, ΔE, and To as long as the initial rate constant, k0, remained unchanged. Simulations also indicate that In Z and Δ can be obtained to within 5 % for an 80-µL sample at a scan rate of 5 K/min. An additional study was carried out involving the indeterminate errors incurred when one scans slowly relative to the rate of chemical reaction. Results indicate that random errors can easily be several times greater than the determinate errors related to thermal lag.

AB - A simplified model of a differential scanning calorimeter (DSC) with large (40-120 µL) 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 ΔE. 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 ΔH, C0, and Dm and also the parameters Z, ΔE, and To as long as the initial rate constant, k0, remained unchanged. Simulations also indicate that In Z and Δ can be obtained to within 5 % for an 80-µL sample at a scan rate of 5 K/min. An additional study was carried out involving the indeterminate errors incurred when one scans slowly relative to the rate of chemical reaction. Results indicate that random errors can easily be several times greater than the determinate errors related to thermal lag.

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