Time-course

Figure Bl.14.8. Time course study of the arrival and accumulation of labelled sucrose in the stem of a castor bean seedling. The labelled tracer was chemically, selectively edited using CYCLCROP (cyclic cross polarization). The first image in the upper left comer was taken before the incubation of the seedlmg with enriched hexoses. The time given in each image represents the time elapsed between tire start of the incubation and the acquisition. The spectmm in the lower right comer of each image shows the total intensity...

Transient, or time-resolved, techniques measure tire response of a substance after a rapid perturbation. A swift kick can be provided by any means tliat suddenly moves tire system away from equilibrium—a change in reactant concentration, for instance, or tire photodissociation of a chemical bond. Kinetic properties such as rate constants and amplitudes of chemical reactions or transfonnations of physical state taking place in a material are tlien detennined by measuring tire time course of relaxation to some, possibly new, equilibrium state. Detennining how tire kinetic rate constants vary witli temperature can further yield infonnation about tire tliennodynamic properties (activation entlialpies and entropies) of transition states, tire exceedingly ephemeral species tliat he between reactants, intennediates and products in a chemical reaction. 

How does one monitor a chemical reaction tliat occurs on a time scale faster tlian milliseconds The two approaches introduced above, relaxation spectroscopy and flash photolysis, are typically used for fast kinetic studies. Relaxation metliods may be applied to reactions in which finite amounts of botli reactants and products are present at final equilibrium. The time course of relaxation is monitored after application of a rapid perturbation to tire equilibrium mixture. An important feature of relaxation approaches to kinetic studies is that tire changes are always observed as first order kinetics (as long as tire perturbation is relatively small). This linearization of tire observed kinetics means... 

Human Extended Insulin Zinc Suspension. Ultralente Humulin U is a long-acting form of human insulin produced by recombinant DNA techniques. It is adrninistered subcutaneously and should not be given intravenously. The time course of this preparation is similar for onset of activity but shorter for maximum activity and duration of action compared with ultralente preparations of animal origin. Insulins of the lente series can be mixed in any proportion to obtain the desired dose and modified activity. 

The concentration [MB] constantly experiences tiny fluctuations, the duration of which can determine linewidths. It is also possible to adopt a traditional kinetic viewpoint and measure the time course of such spontaneous fluctuations directly by monitoring the time-varying concentration in an extremely small sample (6). Spontaneous fluctuations obey exactly the same kinetics of return to equiUbrium that describe relaxation of a macroscopic perturbation. Normally, fluctuations are so small they are ignored. The relative ampHtude of a fluctuation is inversely proportional to the square root of the number of AB entities being observed. Consequently, fluctuations are important when concentrations are small or, more usehiUy, when volumes are tiny. 

Fig. 1. Time courses of the chemiluminescence intensity from oxalate—hydrogen peroxide systems in ethyl acetate as solvent, 0.7 mM TCPO. The curves correspond to the following concentrations of triethylamine (TEA) catalyst A, 0.05 mM B, 0.10 mM and C, 0.20 mM (70).

The receptor represents the locus of dmg action. However, the pharmacokinetic processes of absorption (dmg entry), distribution, metaboHsm, and excretion play principal roles in determining in vivo time courses and concentrations of dmgs and thus modify actions initiated at receptors. 

Fig. 4. Time course for uv-irradiation of 7-dehydtocholesterol ( ) (o), previtamin D (x), lumisterol (-), tachysterol.

The reactions are carried out under first-order conditions, i.e., the stoichiometric concentration of the antioxidant, a-tocopherol, is in large excess over that of 16-ArN, such that the concentration of a-tocopherol does not change significantly throughout the time course of the reaction. The emulsion employed was prepared by mixing the non-ionic emulsifier Brij 30, octane and HCl (3 mM, pH = 2.5). The resulting emulsion is opaque, thus values were obtained electrochemically by employing Linear Sweep Voltammetry (LSV). 

It must also be recognized that adhesive interfaces are not static entities, but may deteriorate or even strengthen over time, and often it is the time course of interfacial strength or durability under different conditions and in different environments that is of greatest concern [4]. As important as durability issues are, they too will not be a direct concern of this chapter. 

In addition to the elimination rate constant, the half-life (T/i) another important parameter that characterizes the time-course of chemical compounds in the body. The elimination half-life (t-1/2) is the time to reduce the concentration of a chemical in plasma to half of its original level. The relationship of half-life to the elimination rate constant is ti/2 = 0.693/ki,i and, therefore, the half-life of a chemical compound can be determined after the determination of k j from the slope of the line. The half-life can also be determined through visual inspection from the log C versus time plot (Fig. 5.40). For compounds that are eliminated through first-order kinetics, the time required for the plasma concentration to be decreased by one half is constant. It is impottant to understand that the half-life of chemicals that are eliminated by first-order kinetics is independent of dose. ... 

Figure 8.23 Predicted time courses of supersaturation and magma density (Wachi and Jones, 1992)...

The time course of the product formation is interesting. Consider product Y ... 

This is a very interesting result. The time course is identical in form with that given by Eq. (3-78) for Scheme IX, but in Eq. (3-87) the rate parameters a and P are not elementary rate constants instead they are composite quantities defined by Eqs. (3-85) and (3-86). 

Direct detection of an intermediate. A nice example, the pyridine-catalyzed hydrolysis of acetic anhydride, was discussed in Chapter 1. Spectroscopic techniques are of great value, because they do not perturb the kinetic system, and because they are selective and sensitive. If the intermediate can be detected, the time course of its appearance and disappearance may be followed. 

That is, the change in concentration of ES with time, t, is 0. Eigure 14.8 illustrates the time course for formation of the ES complex and establishment of the steady-state condition. 

E. M. Benson, A. J. Tomlinson and S. Nayloi, Time course analysis of a microsomal incubation of a therapeutic dmg using preconcenti ation capillary electrophoresis (Pc-CE) , 7. High Resolut. Chromatogr. 17 671-673 (1994). 

FIGURE 1.9 Time course for increasing concentrations of a ligancl with a Ka of 2 nM. Initially the binding is rapid but slows as the sites become occupied. The maximal binding increases with increasing concentrations as does the rate of binding. 

FIGURE 5.15 Different modes of response measurement, (a) Real time shows the time course of the production of response such as the agonist-stimulated formation of a second messenger in the cytosol, (b) The stop-time mode measures the area under the curve shown in panel A. The reaction is stopped at a designated time (indicated by the dotted lines joining the panels) and the amount of reaction product is measured. It can be seen that in the early stages of the reaction, before a steady state has been attained (i.e., a plateau has not yet been reached in panel A), the area under the curve is curvilinear. Once the rate of product formation has attained a steady state, the stop-time mode takes on a linear character. 

FIGURE 5.16 The effect of desensitization on stop-time mode measurements. Bottom panels show the time course of response production for a system with no desensitization, and one in which the rate of response production fades with time. The top dose response curves indicate the area under the curve for the responses shown. It can be seen that whereas an accurate reflection of response production is observed when there is no desensitization the system with fading response yields an extremely truncated dose-response curve. 

Growth, substrate utilisation and product formation time courses exhibit coincident maxima. 

Figure 8.7 gives a typical time course for the conversion of pyruvic acid to L-phenylalanine. 

Fig. 1.6 The time course of luminescence reaction initiated by the injection of ATP. The light intensity first rises rapidly, reaching a maximum in 0.3-0.5 sec, followed by relatively rapid decrease for the first few seconds and then a much slower decay that lasts for several minutes or more. From McElroy and Seliger, 1961, with permission from the Johns Hopkins University Press.

The luminescence of aequorin in terms of total light is efficient in a wide range of pH, from 4.5 to beyond 10 (Fig. 4.1.4). The light intensity is also optimum in a broad pH range of 7-8.5. The time course of the aequorin luminescence reaction is roughly the first order in the presence of various concentrations of Ca2+ (Fig. 4.1.5 Shimomura et al., 1963b). 

Fig. 4.1.5 The time course of aequorin luminescence measured with various concentrations of Ca2+. Calcium acetate solution (5 ml) was added to 10 pi of aequorin solution to give the final Ca2+ concentrations of 10 2 M (A), 10-4 M (B), 10-5 M (C), 10 6 M (D), and 10 7 M (E) at 25°C. The dashed line (F) represents the light emitted following the addition of deionized distilled water that had been redistilled in quartz. The concentration of EDTA derived from the aequorin sample was 10 7 M (final cone.). From Shimomura et al., 1963b, with permission from John Wiley Sons Ltd.

---