Rapid Reaction Kinetics: Lessons Learnt from Ion Pumps

2011 ◽  
Vol 64 (1) ◽  
pp. 5 ◽  
Author(s):  
Ronald J. Clarke
Keyword(s):  
Data Analysis ◽  
Chemical Kinetics ◽  
Kinetic Data ◽  
Rate Equations ◽  
Differential Rate ◽  
Ion Pumps ◽  
Computing Power ◽  
Relaxation Kinetic ◽  
Rapid Reaction ◽  
Traditional Approaches

Chemical kinetics underwent a revolution in the 1950–60s with the development by Manfred Eigen of relaxation kinetic techniques and theory for the analysis of the results obtained. The techniques he introduced extended the time scale of measurable reactions into the microsecond range and beyond. Since then, computing power has increased astronomically. Some of the approximations traditionally used in the analysis of relaxation kinetic data to reduce mathematical complexity are, therefore, now no longer a necessity. Numerical integration of coupled series of differential rate equations can be performed in seconds or less on desk-top computers. In research on the mechanism of the Na+,K+-ATPase, it has been found that traditional approaches to relaxation kinetic data can sometimes lead to erroneous conclusions or to an incomplete description of the mechanism. Therefore, one needs to be flexible in one’s approach to kinetic data analysis and carefully consider the validity of any approximations used.

Kinetic data analysis with a noisy input function

1987 ◽  
Vol 32 (12) ◽  
pp. 1569-1579 ◽  
Author(s):  
R H Huesman ◽  
B M Mazoyer
Keyword(s):  
Data Analysis ◽  
Kinetic Data ◽  
Input Function ◽  
Noisy Input

Kinetic Data Analysis.

1984 ◽  
Vol 79 (386) ◽  
pp. 476
Author(s):  
Irwin Ho ◽  
L. Endrenyi
Keyword(s):  
Data Analysis ◽  
Kinetic Data

Kinetic Data Analysis: Design and Analysis of Enzyme and Pharmacokinetic Experiments.

Biometrics ◽  
1983 ◽  
Vol 39 (2) ◽  
pp. 538
Author(s):  
R. M. Cormack ◽  
L. Endrenyi
Keyword(s):  
Data Analysis ◽  
Kinetic Data ◽  
Analysis Design

scholarly journals Selected topics in statistical computing

2017 ◽  
Vol 01 (01) ◽  
pp. 1630013 ◽  
Author(s):  
Suneel Babu Chatla ◽  
Chun-Houh Chen ◽  
Galit Shmueli
Keyword(s):  
Data Analysis ◽  
Density Estimation ◽  
Statistical Methods ◽  
Kernel Smoothing ◽  
Smoothing Splines ◽  
Additive Models ◽  
Statistical Computing ◽  
Computational Statistics ◽  
Computing Power ◽  
Computationally Intensive

The field of computational statistics refers to statistical methods or tools that are computationally intensive. Due to the recent advances in computing power, some of these methods have become prominent and central to modern data analysis. In this paper, we focus on several of the main methods including density estimation, kernel smoothing, smoothing splines, and additive models. While the field of computational statistics includes many more methods, this paper serves as a brief introduction to selected popular topics.

The Y-Procedure methodology for the interpretation of transient kinetic data: Analysis of irreversible adsorption

2011 ◽  
Vol 66 (24) ◽  
pp. 6441-6452 ◽  
Author(s):  
Evgeniy A. Redekop ◽  
Gregory S. Yablonsky ◽  
Denis Constales ◽  
Palghat A. Ramachandran ◽  
Cathryn Pherigo ◽  
...  
Keyword(s):  
Data Analysis ◽  
Kinetic Data ◽  
Irreversible Adsorption

scholarly journals Combining simulation to nonlinear fitting for the determination of rate constants of elementary reactions by using Excel spreadsheets

2012 ◽  
Vol 8 (4) ◽  
Author(s):  
Ammar M. Tighezza ◽  
Daifallah M. Aldhayan ◽  
Nouir A. Aldawsari
Keyword(s):  
Experimental Data ◽  
Numerical Integration ◽  
Chemical Kinetics ◽  
Chemical Reactions ◽  
Rate Constants ◽  
Model Equation ◽  
Rate Equations ◽  
Unknown Parameters ◽  
Elementary Reactions ◽  
Nonlinear Fitting

A common problem in chemistry is to determine parameters (constants) in an equation used to represent experimental data. Examples are fitting a set of data to a model equation (straight line or curve) to obtain unknown parameters. In chemical kinetics, a set of data is usually a number of concentrations versus time, but the model equation is not well defined! Instead of a well defined model equation we have a set of coupled ODE’s (ordinary differential equations) which represent rate equations for reactants and products. The analytical integration of these ODE’s is rarely possible. The numerical integration is the alternative. In this work are combined the simulation of chemical reactions, by using numerical integration, and nonlinear regression (curve fitting) by using “Solver add-in” of Microsoft Excel to find rate constants of elementary reactions from experimental data. This method is illustrated on three complex mechanisms. The simulation of chemical reactions in Excel spreadsheets is illustrated with/without VBA programming. The automation (automatic obtaining of rate equations from mechanism: no need of chemical kinetics knowledge from the end user!) of mechanism simulation is demonstrated on many example.

scholarly journals Theory on the rate equation of Michaelis-Menten type single-substrate enzyme catalyzed reactions

2017 ◽  
Author(s):  
Rajamanickam Murugan
Keyword(s):  
Steady State ◽  
Critical Parameters ◽  
Rate Equations ◽  
Differential Rate ◽  
Single Substrate ◽  
Progress Curve ◽  
Catalyzed Reactions ◽  
Space Dynamics ◽  
Time Required ◽  
Enzyme Catalyzed Reactions

AbstractAnalytical solution to the Michaelis-Menten (MM) rate equations for single-substrate enzyme catalysed reaction is not known. Here we introduce an effective scaling scheme and identify the critical parameters which can completely characterize the entire dynamics of single substrate MM enzymes. Using this scaling framework, we reformulate the differential rate equations of MM enzymes over velocity-substrate, velocity-product, substrate-product and velocity-substrate-product spaces and obtain various approximations for both pre- and post-steady state dynamical regimes. Using this framework, under certain limiting conditions we successfully compute the timescales corresponding to steady state, pre- and post-steady states and also compute the approximate steady state values of velocity, substrate and product. We further define the dynamical efficiency of MM enzymes as the ratio between the reaction path length in the velocity-substrate-product space and the average reaction time required to convert the entire substrate into product. Here dynamical efficiency characterizes the phase-space dynamics and it would tell us how fast an enzyme can clear a harmful substrate from the environment. We finally perform a detailed error level analysis over various pre- and post-steady state approximations along with the already existing quasi steady state approximations and progress curve models and discuss the positive and negative points corresponding to various steady state and progress curve models.

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