Step tracer experiment

Now that we have an understanding of the meaning of the RTD eurve from a pulse input, we will formulate a more general relationship between a time-varying tracer injeetion and the eorresponding eoneentration in the effluent. We shall state without development that the output eoneentration from a vessel is related to the input eoneentration by the eonvolution integral  

The inlet eoneentration most often takes the form of either perfeetpulse input (Dirae delta function), imperfectpulse injection (see Figme 13-4), or a step input. 

We will now analyze a step input in the traeer eoneentration for a system with a eonstant volmnetric flow rate. Consider a eonstant rate of traeer addition to a feed that is initiated at time t = 0. Before this time no traeer was added to the feed. Stated symbolically, we have 

The eoneentration of tracer in the feed to the reactor is kept at this level imtil the concentration in the effluent is indistinguishable from that in the feed the test may then be discontinued. A typical outlet concentration cmwe for this type of input is shown in Figme 13-4. 

Because the inlet concentration is a constant with time, Cq, we can take it outside the integral sign, that is. 

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Figure 11.11 Information obtainable from a step tracer experiment.

Thus, measurement of one readily gives the other. The washout experiment is generally preferred since IF(oo) = 0 will be known a priori but F(oo) = Cq must usually be measured. The positive step change will also be subject to possible changes in Co during the course of the experiment. However, the positive step change experiment requires a smaller amount of tracer since the experiment will be terminated before the outlet concentration fully reaches Cq. 

Tsunogai and Nozaki [6] analysed Pacific Oceans surface water by consecutive coprecipitations of polonium with calcium carbonate and bismuth oxychloride after addition of lead and bismuth carriers to acidified seawater samples. After concentration, polonium was spontaneously deposited onto silver planchets. Quantitative recoveries of polonium were assumed at the extraction steps and plating step. Shannon et al. [7], who analysed surface water from the Atlantic Ocean near the tip of South Africa, extracted polonium from acidified samples as the ammonium pyrrolidine dithiocarbamate complex into methyl isobutyl ketone. They also autoplated polonium onto silver counting disks. An average efficiency of 92% was assigned to their procedure after calibration with 210Po-210Pb tracer experiments. 

Stimulus-response experiments were used to evaluate the operation of a 1.465L laboratory stirred-tank reactor as a CSTR. The response curves were obtained (a) by using acetic acid (A, ca = 0.85 mol L-1) as a tracer chasing water in step-change experiments, and (b) by using a small pulse of glacial acetic acid (density = 1.05 g cm-3, M = 60 g mol-1) on a... 

In the first step lysine is decarboxylated to cadaverine. Then three cadaverine units are incorporated into the tetracyclic QA skeleton, such as in lupanine, which serves as a precursor for most of the other QA. Recent tracer experiments have been reviewed (, 7). In... 

Pathway of C02 in Gluconeogenesis In the first bypass step of gluconeogenesis, the conversion of pyruvate to phosphoenolpyruvate (PEP), pyruvate is carboxylated by pyruvate carboxylase to oxaloacetate, which is subsequently decarboxylated to PEP by PEP carboxykinase (Chapter 14). Because the addition of C02 is directly followed by the loss of C02, you might expect that in tracer experiments, the 14C of 14C02 would not be incorporated into PEP, glucose, or any intermediates in gluconeogenesis. 

Protoberberine Alkaloids.—In the course of the bioconversion of the proto-berberine scoulerine (65) into chelidonine (62) and phthalide-isoquinolines, e.g. narcotine (63), C-13 becomes oxidized.61 Ophiocarpine (68), with a hydroxy-group at C-13, represents an intermediate stage in the modification of the protoberberine skeleton, and results62 of tracer experiments have shown that scoulerine (65) is also to be included in the biosynthesis of this alkaloid. Tetrahydro-protoberberine (67) is also a precursor, its incorporation indicating that C-13 hydroxylation is a terminal step. As for other protoberberine derivatives,63 nandinine (64) was not assimilated,62 and it follows then that (65) is probably converted into (67) by way of isocorypalmine (66). 

Intracellular fluxes can be estimated more precisely through 13C tracer experiments. Following 13C feeding to a cell it is possible to analyze metabolic products, such as amino acids, and measure 13C enriched patterns, so to be able to reconstruct the flux distribution from the measured data [91]. To obtain flux data from the labeling patterns, two techniques can be applied NMR [92, 93] and MS [94, 95]. Due to the low intracellular concentration of metabolites, these are often difficult to measure therefore the analysis of the labeling pattern of amino acids in proteins is used as input for flux quantification. Here proteins are hydrolyzed to release labeled amino acids and further analyzed by NMR of GC-MS. Once NMR or MS spectra are recorded, the next step is the quantitative interpretation of the isotopomer data by using mathematical models that describe the relationship between fluxes and the observed isotopomer abundance [96, 97], Some of the mathematical approaches used include cumulative isotopomer (cumomers) [98], bondomers [99], and fractional labeling [100], For a more comprehensive review on the methods we refer to Sauer [91]. 

Baumgartner and Hill s decontamination procedure was evaluated on more than 500 different hair samples that were externally contaminated in this laboratory. In the initial phases of this study we used four phosphate washes. In later phases, based upon the comments in Baumgartner and Hill, ° our procedure was modified to use between three and ten phosphate washes. However, in the radioactive tracer experiments we typically perform, it is possible to account for all radioactivity the sample is digested and no radioactivity is lost from any extraction step. Therefore, it is possible to calculate the effect of either three or four phosphate washes on the decontamination of the hair and on the various calculated criteria. No remarkable differences were found between our four-phosphate extraction process and the recalculated values for the equivalent three-phosphate extraction process. 

Two types of tracer experiments are commonly employed and they are the input of a pulse or a step function. Figure 8.2.1 illustrates the exit concentration curves and thus the shape of the (f)-curves (same shape as exit concentration curve) for an impulse input. Figure 8.2.2 shows the exit concentration for a step input of tracer. The (r)-curve for this case is related to the time derivative of the exit concentration. 

Vinyl alkyl ethers, RCH CHOR, are very rapidly hydrolyzed by dilute aqueous acid to form the alcohol R OH and the aldehyde RCH2CHO. Hydrolysis in H2 <0 gives alcohol R OH containing only ordinary oxygen. Outline all steps in the most likely mechanism for the hydrolysis. Show how this mechanism accounts not only for the results of the tracer experiment, but also for the extreme ease with which hydrolysis takes place. 

The reversibility of the reduction step (17) — (21) was examined by feeding [ll-3H]cinchonidine (21) to C. ledgeriana shoots and isolating the corresponding ketone (17) after addition of a carrier. The recovered cinchonidinone was radioactive, which proves that reversal does occur [i.e. (21)— (17)]. In view of this result, it is reasonable to suppose that all the late steps are reversible after generation of the quinoline system in (17) and (18) but obviously many more tracer experiments would be required to prove every detail implied in the scheme. 

Putting aside this general difficulty, Salmon s account can be applied to our example. We can mark an atom of a molecule in the model by giving it another color, say. The atom will still have the same color after a number of time steps. A Monte Carlo simulation, however, fails. Here the process described by the model, a random walk in conformational space, is not intended to be in time, and hence Salmon s criterion cannot even be applied. Salmon s early process account could, and in fact has been used by chemists to determine which, of a number of processes that might have occurred during a chemical reaction, is the real one. I refer to the technique of marking molecules with isotopes to find the underlying reaction mechanism. Such tracer experiments are a standard technique in chemistry. 

MK biosynthesis by the OSB pathway has been elucidated on the basis of isotopic tracer experiments, isolation of mutants blocked in the various steps, isolation and identification of intermediates accumulated by the mutants, and by enzyme assays. Early isotopic tracer experiments with various bacteria established that methionine and prenyl PPi contribute to the methyl and prenyl substituents of the naphthoquinone. The early isotopic tracer studies and other work have been reviewed by Bentley and Meganathan. " In 1964, Cox and Gibson observed that [G- " C] shikimate was incorporated into both MK and ubiquinone by E. coli, thus providing the first evidence for the involvement of the shikimate pathway." Chemical degradation of the labeled isolated menaquinone (MK-8) showed that essentially all of the radioactivity was retained in the phthalic anhydride. It was concluded that the benzene ring of the naphthoquinone (sic) portion of vitamin K2 arises from shikimate in E. coli The authors further suggested that shikimate was first converted to chorismate before incorporation into MK. A more complete chemical degradation of the MK derived from... 

Step response. Although we can in principle use any feed concentration time function to determine the RTD, some choices are convenient for ease of data analysis. One of these is the step response. In the step-response experiment, at time zero we abruptly change the feed tracer concentration from steady value co to steady value c/. For convenience we assume cq =. 0. Exercise. 8.4 shows, that, we can easily remove this... 

We next examine again the well-stirred reactor introduced in Chapter 4. Consider the following step-response experiment a clear fluid with flovvrate Q/ enters a well-stirred reactor of volume Vr as depicted in Figure 8.3. At time zero we start adding a small flow of a tracer to the feed stream and measure the tracer concentration in the effluent stream. 

The calculated values are those obtained by assuming the ratedetermining step to be abstraction of an allylic hydrogen with an isotope effect equal to the discrimination effect obtained from the retention of deuterium in the products. The observed kinetic isotope effects show clearly that this first abstraction is the slow step. The good agreement with the discrimination values gives excellent confirmation for the stepwise mechanistic scheme proposed. In the tracer experiments using deuterium it was found that appreciable propylene isomerization occurred unless ammonia was present. The oxidation rate was unaffected by the ammonia. This was taken to indicate that the initial oxidative abstraction reaction had no carbonium ion characteristic. However, this conclusion does not apply in the case of cuprous oxide, where ammonia very severely inhibited the oxidation reaction. 

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