Sum over Histories Representation for Kinetic Sensitivity Analysis: How Chemical Pathways Change When Reaction Rate Coefficients Are Varied

2015 ◽  
Vol 119 (45) ◽  
pp. 11039-11052 ◽  
Author(s):  
Shirong Bai ◽  
Michael J. Davis ◽  
Rex T. Skodje
Keyword(s):  
Sensitivity Analysis ◽  
Reaction Rate ◽  
Rate Coefficients

Spreadsheet Method for Evaluation of Biochemical Reaction Rate Coefficients and Their Uncertainties by Weighted Nonlinear Least-Squares Analysis of the Integrated Monod Equation

1998 ◽  
Vol 64 (6) ◽  
pp. 2044-2050 ◽  
Author(s):  
Laurence H. Smith ◽  
Perry L. McCarty ◽  
Peter K. Kitanidis
Keyword(s):  
Least Squares ◽  
Mixed Culture ◽  
Substrate Concentration ◽  
Reaction Rate ◽  
Initial Rate ◽  
Weighted Least Squares ◽  
Nonlinear Least Squares ◽  
Rate Coefficients ◽  
Monod Equation ◽  
Best Fit

ABSTRACT A convenient method for evaluation of biochemical reaction rate coefficients and their uncertainties is described. The motivation for developing this method was the complexity of existing statistical methods for analysis of biochemical rate equations, as well as the shortcomings of linear approaches, such as Lineweaver-Burk plots. The nonlinear least-squares method provides accurate estimates of the rate coefficients and their uncertainties from experimental data. Linearized methods that involve inversion of data are unreliable since several important assumptions of linear regression are violated. Furthermore, when linearized methods are used, there is no basis for calculation of the uncertainties in the rate coefficients. Uncertainty estimates are crucial to studies involving comparisons of rates for different organisms or environmental conditions. The spreadsheet method uses weighted least-squares analysis to determine the best-fit values of the rate coefficients for the integrated Monod equation. Although the integrated Monod equation is an implicit expression of substrate concentration, weighted least-squares analysis can be employed to calculate approximate differences in substrate concentration between model predictions and data. An iterative search routine in a spreadsheet program is utilized to search for the best-fit values of the coefficients by minimizing the sum of squared weighted errors. The uncertainties in the best-fit values of the rate coefficients are calculated by an approximate method that can also be implemented in a spreadsheet. The uncertainty method can be used to calculate single-parameter (coefficient) confidence intervals, degrees of correlation between parameters, and joint confidence regions for two or more parameters. Example sets of calculations are presented for acetate utilization by a methanogenic mixed culture and trichloroethylene cometabolism by a methane-oxidizing mixed culture. An additional advantage of application of this method to the integrated Monod equation compared with application of linearized methods is the economy of obtaining rate coefficients from a single batch experiment or a few batch experiments rather than having to obtain large numbers of initial rate measurements. However, when initial rate measurements are used, this method can still be used with greater reliability than linearized approaches.

scholarly journals New Constraints on Diffuse Interstellar Cloud Models. The Model of the ζ Ophiuchi Cloud Revisited

1987 ◽  
Vol 120 ◽  
pp. 227-233
Author(s):  
Y. P. Viala ◽  
H. Abgrall ◽  
E. Roueff
Keyword(s):  
Molecular Species ◽  
Transfer Equation ◽  
Molecular Hydrogen ◽  
Reaction Rate ◽  
Radiative Transfer Equation ◽  
Interstellar Cloud ◽  
Rate Coefficients ◽  
Cloud Models ◽  
Parallel Geometry ◽  
Simple Molecules

Using most recent observational data as well as new experimental and theoretical determinations of various reaction rate coefficients, we present a model of the ζ θphiuchus cloud. the radiative transfer equation is solved in a plane parallel geometry taking into account absorptions by both the gas and by dust. A part certain atypical molecules (CH+, CN) and neutral iron, we are able to reproduce the observed column densities of neutral atoms, and molecular species, including the rotational populations of molecular Hydrogen with a two shell model. the concentrations of other simple molecules are predicted.

scholarly journals Low temperature gas phase reaction rate coefficient measurements: Toward modeling of stellar winds and the interstellar medium

2019 ◽  
Vol 15 (S350) ◽  
pp. 382-383
Author(s):  
Niclas A. West ◽  
Edward Rutter ◽  
Mark A. Blitz ◽  
Leen Decin ◽  
Dwayne E. Heard
Keyword(s):  
Low Temperature ◽  
Interstellar Medium ◽  
Gas Phase ◽  
Low Temperatures ◽  
Reaction Rate ◽  
Rate Coefficient ◽  
Building Blocks ◽  
Rate Coefficients ◽  
Stellar Winds ◽  
Phase Reaction

AbstractStellar winds of Asymptotic Giant Branch (AGB) stars are responsible for the production of ∼85% of the gas molecules in the interstellar medium (ISM), and yet very few of the gas phase rate coefficients under the relevant conditions (10 – 3000 K) needed to model the rate of production and loss of these molecules in stellar winds have been experimentally measured. If measured at all, the value of the rate coefficient has often only been obtained at room temperature, with extrapolation to lower and higher temperatures using the Arrhenius equation. However, non-Arrhenius behavior has been observed often in the few measured rate coefficients at low temperatures. In previous reactions studied, theoretical simulations of the formation of long-lived pre-reaction complexes and quantum mechanical tunneling through the barrier to reaction have been utilized to fit these non-Arrhenius behaviours of rate coefficients.Reaction rate coefficients that were predicted to produce the largest change in the production/loss of Complex Organic Molecules (COMs) in stellar winds at low temperatures were selected from a sensitivity analysis. Here we present measurements of rate coefficients using a pulsed Laval nozzle apparatus with the Pump Laser Photolysis - Laser Induced Fluorescence (PLP-LIF) technique. Gas flow temperatures between 30 – 134 K have been produced by the University of Leeds apparatus through the controlled expansion of N2 or Ar gas through Laval nozzles of a range of Mach numbers between 2.49 and 4.25.Reactions of interest include those of OH, CN, and CH with volatile organic species, in particular formaldehyde, a molecule which has been detected in the ISM. Kinetics measurements of these reactions at low temperatures will be presented using the decay of the radical reagent. Since formaldehyde and the formal radical (HCO) are potential building blocks of COMs in the interstellar medium, low temperature reaction rate coefficients for their production and loss can help to predict the formation pathways of COMs observed in the interstellar medium.

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