Response of Systems to Pulse Perturbations

In chapter 5, we studied the responses of chemical species in a reaction system to pulse perturbations and showed the deduction of direct, causal connectivities by chemical reactions—the reaction pathway—and the reaction mechanism from such measurements. The causal connectivites give the information on how the chemical species are connected by chemical reactions. In this chapter we turn to another source of information about chemical species in a reaction system, that of correlations among the species. 

There exists meanwhile a variety of frequency selective experiments still using the conventional CW irradiation as the ID NOE experiment, or upgraded with one or more selective pulses, as the ID TOCSY or the ID COSY experiment. These experiments and their many variants are probably the best choice in such cases as long as the response of a spin system to the perturbation of only one single spin or one single group of equivalent spins is of interest. If, however, and this is the most common situation, informations on several rather than only one spin-spin interaction is needed. 

Oscillatory reactions require a separate analysis, which is presented in detail. Responses of nonlinear systems to pulses or other perturbations are treated in some generality. The concluding chapter gives a brief introduction to bioinformatics, including several methods for determining reaction mechanisms. 

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. 

Transient measurements have often been used in electrochemical studies as a means of obtaining deeper insight into reaction mechanisms and estimating quantitatively kinetic parameters. Transient measurements have been obtained by applying a rectangular pulse or sinusoidal polarization to the electrode, which has previously reached a certain open-circuit or polarization steady state. The response of the system to these perturbations, recorded oscillographically, may then be analyzed and interpreted. 

Figure 11 shows typical CL oscillating responses of this system as perturbed by vitamin B6 pulses, which decrease the oscillation amplitude. Arrowheads indicate the times at which analyte pulses were introduced. Zone A corresponds to the oscillating steady state zone B to the response of the oscillating system to vitamin B6 perturbations and zone C to the recovery following each perturbation (second response cycle), which was the measured parameter. This... 

In a typical pulse experiment, a pulse of known size, shape and composition is introduced to a reactor, preferably one with a simple flow pattern, either plug flow or well mixed. The response to the perturbation is then measured behind the reactor. A thermal conductivity detector can be used to compare the shape of the peaks before and after the reactor. This is usually done in the case of non-reacting systems, and moment analysis of the response curve can give information on diffusivities, mass transfer coefficients and adsorption constants. The typical pulse experiment in a reacting system traditionally uses GC analysis by leading the effluent from the reactor directly into a gas chromatographic column. This method yields conversions and selectivities for the total pulse, the time coordinate is lost. 

The most convenient means of making time-resolved SH measurements on metallic surfaces is to use a cw laser as a continuous monitor of the surface during a transient event. Unfortunately, in the absence of optical enhancements, the signal levels are so low for most electrochemical systems that this route is unattractive. A more viable alternative is to use a cw mode-locked laser which offers the necessary high peak powers and the high repetition rate. The experimental time resolution is typically 12 nsec, which is the time between pulses. A Q-switched Nd YAG provides 30 to 100 msec resolution unless the repetition rate is externally controlled. The electrochemical experiments done to date have involved the application of a fast potential step with the surface response to this perturbation followed by SHG [54, 55,116, 117]. Since the optical technique is instantaneous in nature, one has the potential to obtain a clearer picture than that obtained by the current transient. The experiments have also been applied to multistep processes which are difficult to understand by simple current analysis [54, 117]. 

The title of this review can be shortened to a consideration of the transient method, as in two earlier reviews (i, 2) in 1976 and 1982. In the simplest version of the method, the composition of a stream in steady flow to an open heterogeneous catalytic reactor is perturbed (step function, pulse, sine or square wave, etc.) and the response of the system to the signal is measured, as manifested by the composition of the outlet stream as a function of time. Of particular interest is the measurement by appropriate spectroscopies of the response during the transient period of the intermediates adsorbed on the surface of the catalyst. 

Under resting conditions, CRH and AVP are released from the hypothalamus in a pulsatile fashion with a frequency of 2-3 episodes per hour (Engler et al., 1989). The amplitude of the neuropeptide pulses normally increases in the morning, resulting in a circadian fluctuation in ACTH and cortisol levels. This daily rhythm is modulated by feeding and activity schedules, but is particularly perturbed by stressful stimuli originating internally (e.g., anxiety or systemic infection) or externally (e.g., threatening situations). Thus, acute stressors lead to activation of the stress response. 

As explained earlier, in transient electrochemical methods an electrical perturbation (potential, current, charge, and so on) is imposed at the working electrode during a time period 0 (usually less than 10 s) short enough for the diffusion layer 8 (2D0) to be smaller than the convection layer (S onv imposed by natural convection. Thus the electrochemical response of the system investigated depends on the exact perturbation as well as on the elapsed time. This duality is apparent when one considers a double-pulse potentiostatic perturbation applied to the electrode as in the double-step chronoampero-metric method. 

Fig. 5.31. Relay of cAMP signals. Starting from a stable steady state, the system is perturbed by an increase in y by 0.3 unit (which corresponds to the addition of a 3 X 10 M pulse of extracellular cAMP for a dissociation constant /lr -10" M see tables 5.2 and 5.3). The curve for p shows the amplification of this perturbation, in the form of synthesis of a peak of intracellular cAMP. A second stimulus of similar magnitude applied in r = 10 min produces a response of smaller amplitude, while the response to a third, identical stimulus in t = 17.5 min is even weaker. The curve showing the corresponding evolution of the fraction of active receptor is also given. The curves are obtained by integration of eqns (5.12) for cr = 0.57 min", = 3.58 min k-, = 0.958 min, e = 0.108 the values of the other parameters are as in table 5.3 (Martiel Goldbeter, 1987a).

Many reaction sequences consist of converging and diverging chains an example of converging irreversible reactions is shown in fig. 5.5. Calculations of the response of this system to a pulse perturbation of Xi and Xg are plotted in figs. 5.6(a) and (b), respectively. The plots indicate the convergence of two chains at the species X3. 

For the application of the pulse method to an unknown reaction system we would of course use all information available, which we resisted in this test example. The pulse method does not require the pulsing of each reactant species. We did not perturb F6P but showed its connectivities from pulses of G6P and F1,6BP. Further, we did not measure NADH (although it is easy to do so spectroscopically), but pulses of this species showed its connectivities in the reaction system. Reactions that are fast compared with others may be difficult to detect because responses of more than one species may occur... 

---