Analysis of tracer experiments in non-conservative steady-state systems

A method is developed for finding the transfer and localization rates and the volumes ofN compartment steady-state biological systems from experimental results. It is shown that a complete solution for certain systems in which the rates and volumes remain constant and in which there is access to all compartments can be obtained by using a single radioactive tracer. The information obtainable from experiments wherein some compartments are not accessible is analyzed for mammillary and catenary systems. Conservative systems are handled as special cases in which the localization is zero while anisotropic membranes separating compartments are shown to introduce no additional mathematical difficulty whenever all compartments are accessible. The limitations on the use of this method of multi-compartment tracer analysis are briefly discussed. Research supported by the Atomic Energy Commission, Contract AT (30-1)-1551.     

Analysis of tracer experiments: IV. The kinetics of generalN compartment systems

The methods of C. W. Sheppard and A. S. Householder (Jour. App. Physcis,22, 510–20, 1951), H. D. Landahl (Bull. Math. Biophysics,16, 151–54, 1954) and H. E. Hart (Bull. Math. Biophysics,17, 87–94, 1955;ibid.,19, 61–72, 1957;ibid.,20, 281–87, 1958) are employed in studying the kinetics of generalN compartment systems. It is shown that the nature of the transfer processes occurring in fluid flow systems and the chemical processes occurring in quadratic systems and in catalyzed quadratic systems can in principle be completely determined for all polynomial dependencies. Systems involving three-body and higher-order interactions can be completely solved, however, only if supplementary information is available. Research supported by the Atomic Energy Commission, Contract AT (30-1)-1551.     

Analysis of tracer experiments: VI. Determination of partitioned initial entry functions

It is shown that the partitioned initial entry functions previously introduced in multicompartment analysis can be directly and uniquely determined from the experimental data.     

On dispersion in tracer experiments

Extending the results of a previous paper (Rescigno, 1973), the dispersion between two compartments or through the cycle around a compartment is defined in terms of the transport time of the particles flowing through the system.Some of the properties of the dispersion are analyzed, and the method for computing it is described.     

Bacteriophage tracer experiments in groundwater

Three tracer experiments employing three different bacteriophage were performed at one groundwater site near Beverley, Humberside. In two of the experiments the bacteriophage were injected into the aquifer by a borehole at a distance of 366 m from the pumping borehole. In the other experiment they were injected at a distance of 122 m. Regular samples were taken of water abstracted at the pumping boreholes as well as from the injection boreholes. The objectives were to: (1) investigate the pattern of bacteriophage recovery from the aquifer; (2) calculate the total number of bacteriophage recovered and the rate of their migration; and (3) detect any differences in bacteriophage behaviour which could be directly related to the morphology of the three bacteriophage. In all experiments the pattern of recovery was similar, exhibiting a peak of high numbers reaching the pumping borehole soon after injection. The highest percentage of original inoculum recovered was 1.9%. In the majority of cases, however, recovery was usually one log₁₀ lower than this. The fastest migration rates were very rapid, reaching 2.8 cm/s in one experiment. No variation in percentage recovery or transit time could be directly attributed to morphology of bacteriophage. The most important factor governing the pattern of migration was undoubtedly the hydrogeological conditions.     

Bacteriophage tracer experiments in groundwater

Three tracer experiments employing three different bacteriophage were performed at one groundwater site near Beverley, Humberside. In two of the experiments the bacteriophage were injected into the aquifer by a borehole at a distance of 366 m from the pumping borehole. In the other experiment they were injected at a distance of 122 m. Regular samples were taken of water abstracted at the pumping boreholes as well as from the injection boreholes. The objectives were to: (1) investigate the pattern of bacteriophage recovery from the aquifer; (2) calculate the total number of bacteriophage recovered and the rate of their migration; and (3) detect any differences in bacteriophage behaviour which could be directly related to the morphology of the three bacteriophage. In all experiments the pattern of recovery was similar, exhibiting a peak of high numbers reaching the pumping borehole soon after injection. The highest percentage of original inoculum recovered was 1.9%. In the majority of cases, however, recovery was usually one log10 lower than this. The fastest migration rates were very rapid, reaching 2.8 cm/s in one experiment. No variation in percentage recovery or transit time could be directly attributed to morphology of bacteriophage. The most important factor governing the pattern of migration was undoubtedly the hydrogeological conditions.     

On transfer times in tracer experiments

A compartment is defined as a pool of material whose behavior can be described by a deterministic or by a stochastic equation; these two equations are used to define the transit time through the compartment, the total residence time, the time of entrance and the time of exit.If in a complex system one or more compartments are accessible, the transport of material through it can be studied using a tracer. Then the transfer time between any two compartments, or through the cycle around a compartment, can be analyzed under certain hypotheses, even if the transport along the route considered cannot be described by compartment equations.     

Analysis of tracer experiments: VII. General multi-compartment systems imbedded in non-homogeneous inaccessible media

An integral equation analysis of generaln compartment steady state systems imbedded in static media of arbitrary complexity has been developed. A set of initial entry functions can be found which serve to determine a corresponding set of partitioned initial entry functions. The partitioned functions, in turn, can be used to predict the probabilities and time courses of various transport histories and to determine all steady state rates of flow between measured compartments. The method is quite general, being completely applicable, for example, to closed systems, to cyclic systems and to systems in which relatively rapid (but finite) exchange between compartments occurs.     

13C tracer experiments and metabolite balancing for metabolic flux analysis: comparing two approaches

Conventional metabolic flux analysis uses the information gained from determination of measurable fluxes and a steady-state assumption for intracellular metabolites to calculate the metabolic fluxes in a given metabolic network. The determination of intracellular fluxes depends heavily on the correctness of the assumed stoichiometry including the presence of all reactions with a noticeable impact on the model metabolite balances. Determination of fluxes in complex metabolic networks often requires the inclusion of NADH and NADPH balances, which are subject to controversial debate. Transhydrogenation reactions that transfer reduction equivalents from NADH to NADPH or vice versa can usually not be included in the stoichiometric model, because they result in singularities in the stoichiometric matrix. However, it is the NADPH balance that, to a large extent, determines the calculated flux through the pentose phosphate pathway. Hence, wrong assumptions on the presence or activity of transhydrogenation reactions will result in wrong estimations of the intracellular flux distribution. Using 13C tracer experiments and NMR analysis, flux analysis can be performed on the basis of only well established stoichiometric equations and measurements of the labeling state of intracellular metabolites. Neither NADH/NADPH balancing nor assumptions on energy yields need to be included to determine the intracellular fluxes. Because metabolite balancing methods and the use of 13C labeling measurements are two different approaches to the determination of intracellular fluxes, both methods can be used to verify each other or to discuss the origin and significance of deviations in the results. Flux analysis based entirely on metabolite balancing and flux analysis, including labeling information, have been performed independently for a wild-type strain of Aspergillus oryzae producing alpha-amylase. Two different nitrogen sources, NH4+ and NO3-, have been used to investigate the influence of the NADPH requirements on the intracellular flux distribution. The two different approaches to the calculation of fluxes are compared and deviations in the results are discussed. Copyright 1998 John Wiley & Sons, Inc.     

Single channel gating events in tracer flux experiments. II. Flux amplitude analysis

Measurement of tracer ion flux from or into a collection of closed membrane structures (CMS) constitutes a broadly applicable technique for studying ion channel gating by specialized gating molecules in biological membranes. The amplitudes for the flux process reflect the overall change in tracer content due to flux during a period in which channels on at least some of the CMS were open. In practice, the attainment of a time-invariant, finite overall tracer content, indicating a cessation of flux, need not imply that flux has reached completion, i.e., that the CMS internal and external tracer concentrations have fully reached equilibrium. Less than maximum flux amplitudes arise when binding of control ligands leads to an inhibition or inactivation of the channel gating molecules prior to a complete equilibration of tracer. Analysis of the dependence of the flux amplitudes on control ligand concentration permits determination of characteristic parameters of the CMS that may vary with the methods of preparation (e.g., the distributions of CMS size and CMS content of gating units). Knowledge of these parameters in turn permits evaluation of the mean single channel flux amplitude contribution, which is functionally dependent on the rate constant ratio (k'eff/ki), where k'eff and ki are, respectively, the effective rate constants for tracer flux and for gating unit inactivation.     

Analysis of tracer experiments: VIII. Integro-differential equation treatment of partly accessible,partly injectable multicompartment systems

An integro-differential equation treatment of multi-compartment systems is developed which permits formal analysis of the incomplete data which is available from partly accessible, partly injectable systems. New transport functions are defined which can be obtained directly from the experimental data. These functions serve to characterize the communication and topology between different accessible compartments and also the reentrant contributions from inaccessible sites. The method gives solutions consistent with those of the differential equation approach when the system is uniformly contiguous and accessible, more complete solutions than those of the integral equation approach when all measured compartments are injectable, and in addition provides complete or partial solutions for certain otherwise analytically intractable systems. Detailed numerical illustrations of the method are given.     

Diver-operated versus remote-controlled chambers used in underwater tracer experiments

Summary 1. Two chambers, one diver-operated and the other remote-controlled, were developed for in situ feeding experiments.2. Both chambers have been used effectively in numerous experiments with vertically migrating copepods fed⁶⁵Zn-labeled microzooplankton.3. Laboratory results demonstrated no significant difference in recovered radioactivity due to differences in material or design of the two chambers.4. Diver-operated chambers are initially much less expensive and are generally more adaptable to changes in experimental design.5. Remote-operated chambers require less personnel and are necessary when determining effects of depth within the entire range common for vertically migrating zooplankton.

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Von Tauchern eingesetzte versus ferngesteuerte Kammern bei Unterwasser-Tracerexperimenten

Kurzfassung Zwei Verfahren, die in situ bei ernährungsbiologischen Untersuchungen an marinen Copepoden angewendet worden sind, werden beschrieben und kritisch verglichen. Die erste Methode erfordert den ständigen Einsatz von Tauchern. Sie bedienen Plastikbeutel, die in bestimmten Abständen von der Oberfläche bis zu 60 m Tiefe angebunden werden. In die Beutel werden die Versuchstiere eingesetzt, vor allemUndinula vulgaris. Mikrozooplankton, mit⁶⁵Zn markiert, dient den Copepoden als Nahrung. Nach Injektion markierter Nahrungstiere in die Plastikbeutel wird das Experiment durch Abtöten der Versuchstiere mit einem Plankton-Fixierungsmittel beendet. Das Maß der Ingestion und Defäkation der Nahrung wird danach anhand der Verteilung der Radioaktivität bestimmt. In einem zweiten Versuchsprogramm wird ein Behälter aus Plexiglas innerhalb eines PVC-Rahmens benutzt, der durch Fernsteuerung bedient werden kann. Dieser dient der Aufnahme der Copepoden und der Nahrungsorganismen. Nach Beendigung des Versuchs wird die Flüssigkeit durch ein Membranfilter abgelassen und die Verteilung der Radioaktivität in den Copepoden gemessen, die auf dem Filter zurückbleiben. Zwischen Oberfläche und 200 m Tiefe wurden mehrere derartige, an einem langen Draht befestigten Behälter eingesetzt. Vor- und Nachteile beider Verfahren werden diskutiert.

     

Note on the interpretation of tracer experiments in biological systems

It is shown that the results of C. W. Sheppard and A. S. Householder (1951) can be modified to include open systems which may or may not be in the steady state. Some conditions are given under which simple chemical reactions can be included.     

TFLUX: a general purpose program for the interpretation of radioactive tracer experiments.

TFLUX is a computer program which simulates radioactive tracer experiments using intact cells under steady-state conditions. It is designed for the naive computer user to use, providing English-like input. An example is described in which compartmentation and flux through the citric acid cycle in Dictyostelium discoideum are simulated.     

Enhanced benthic activity in sandy sublittoral sediments: Evidence from 13C tracer experiments

In situ and on-board pulse-chase experiments were carried out on a sublittoral fine sand in the German Bight (southern North Sea) to investigate the hypothesis that sandy sediments are highly active and have fast turnover rates. To test this hypothesis, we conducted a series of experiments where we investigated the pathway of settling particulate organic carbon through the benthic food web. The diatom Ditylum brightwellii was labelled with the stable carbon isotope ¹³C and injected into incubation chambers. On-board incubations lasted 12, 30 and 132 h, while the in situ experiment was incubated for 32 h. The study revealed a stepwise short-term processing of a phytoplankton bloom settling on a sandy sediment. After the 12 h incubation, the largest fraction of recovered carbon was in the bacteria (62%), but after longer incubation times (30 and 32 h in situ) the macrofauna gained more importance (15 and 48%, respectively), until after 132 h the greatest fraction was mineralized to CO₂ (44%). Our findings show the rapid impact of the benthic sand community on a settling phytoplankton bloom and the great importance of bacteria in the first steps of algal carbon processing.