166DETERMINATION OF COMPLEX REACTION MECHANISMS
11.5Limits of Stoichiometric Network Analysis
As this example shows, stoichiometric network analysis yields only possibilities of reaction mechanisms, it does not lead to the determination of which of many possible reaction pathways corresponds to experiments. We need to know the rate coefficients of the system to determine paths in the system by which reactants proceed to form products. This distinction has been overlooked in a number of studies on complex biochemical reaction mechanisms (see Schilling et al. [82] and references therein).
Acknowledgments This chapter is based mainly on work published in refs. [1–9], where the ideas of the stoichiometric network analysis [10] were utilized to identify several distinct topological features in chemical networks that provide oscillatory instabilities and from that derive a classification system for chemical oscillators and species taking part in these oscillations.
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12
Lifetime and Transit Time
Distributions and Response
Experiments in Chemical Kinetics
We discussed some aspects of the responses of chemical systems, linear or nonlinear, to perturbations on several earlier occasions. The first was the responses of the chemical species in a reaction mechanism (a network) in a nonequilibrium stable stationary state to a pulse in concentration of one species. We referred to this approach as the “pulse method” (see chapter 5 for theory and chapter 6 for experiments). Second, we studied the time series of the responses of concentrations to repeated random perturbations, the formulation of correlation functions from such measurements, and the construction of the correlation metric (see chapter 7 for theory and chapter 8 for experiments). Third, in the investigation of oscillatory chemical reactions we showed that the responses of a chemical system in a stable stationary state close to a Hopf bifurcation are related to the category of the oscillatory reaction and to the role of the essential species in the system (see chapter 11 for theory and experiments). In each of these cases the responses yield important information about the reaction pathway and the reaction mechanism.
In this chapter we focus on the design of simple types of response experiments that make it possible to extract mechanistic and kinetic information from complex nonlinear reaction systems. The main idea is to use “neutral” labeled compounds (tracers), which have the same kinetic and transport properties as the unlabeled compounds. In our previous work [1–12] we have shown that by using neutral tracers a class of response experiments can be described by linear response laws, even though the underlying kinetic equations are highly nonlinear. The linear response is not the result of a linearization procedure, but it is due to the use of neutral tracers. As a result the response is linear even for large perturbations, making it possible to investigate global nonlinear kinetics by making use of linear mathematical techniques. Moreover, the susceptibility functions from the response law are related to the probability densities of the lifetimes and transit
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