Deterministic Kinetics in Chemistry and Systems Biology: The Dynamics of Complex Reaction Networks

This bookgives a concise overview of the mathematical foundations of kinetics used in chemistry and systems biology. The analytical and numerical methods used to solve complex rate equations with the widely used deterministic approach will be described, with primary focus on practical aspects important in designing experimental studies and the evaluation of data. The introduction of personal computers transformed scientific attitudes in the last two decades considerably as computational power ceased to be a limiting factor. Despite this improvement, certain time-honored approximations in solving rate equations such as the pre-equilibrium or the steady-state approach are still valid and necessary as they concern the information content of measured kinetic traces. The bookshows the role of these approximations in modern kinetics and will also describe some common misconceptions in this field

[1]  Kinetics of irreversible consecutive processes with first order second steps: analytical solutions , 2015, Journal of Mathematical Chemistry.

[2]  H. A. C. MCKAY,et al.  Kinetics of Exchange Reactions , 1938, Nature.

[3]  C. Gardner Swain,et al.  Quantitative Correlation of Relative Rates. Comparison of Hydroxide Ion with Other Nucleophilic Reagents toward Alkyl Halides, Esters, Epoxides and Acyl Halides1 , 1953 .

[4]  A. Robinson Non-standard analysis , 1966 .

[5]  M. Smoluchowski Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen , 1918 .

[6]  Robert W. Taft,et al.  Polar and Steric Substituent Constants for Aliphatic and o-Benzoate Groups from Rates of Esterification and Hydrolysis of Esters1 , 1952 .

[7]  R. Marcus Theory of electron transfer reactions , 1994 .

[8]  H. Mckay Kinetics of Some Exchange Reactions of the Type RI + I*-⇄ RI*+ I-in Alcoholic Solution , 1943 .

[9]  Louis Guttman,et al.  Statistical Adjustment of Data , 1944 .

[10]  Richard M. Noyes,et al.  Effects of diffusion rates on chemical kinetics , 1961 .

[11]  C F Curtiss,et al.  Integration of Stiff Equations. , 1952, Proceedings of the National Academy of Sciences of the United States of America.

[12]  G. Lente Stochastic mapping of first order reaction networks: a systematic comparison of the stochastic and deterministic kinetic approaches. , 2012, The Journal of chemical physics.

[13]  I. Fábián,et al.  Effect of dissolved oxygen on the oxidation of dithionate ion. Extremely unusual kinetic traces. , 2004, Inorganic chemistry.

[14]  G. G. Stokes On the Effect of the Internal Friction of Fluids on the Motion of Pendulums , 2009 .

[15]  C. Runge,et al.  Vorlesungen über Numerisches Rechnen , 1924 .

[16]  C. W. Gear,et al.  The automatic integration of ordinary differential equations , 1971, Commun. ACM.

[17]  Péter Érdi,et al.  Stochastic Chemical Kinetics: Theory and (Mostly) Systems Biological Applications , 2014 .