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 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.     

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.     

Structural identifiability of compartmental systems with respect to data obtained from constant-infusion tracer experiments

The problem of structural identifiability of compartmental systems receiving constant input rates of tracer material is studied, and the relationship between this steady-state problem and that of identification using the impulse response is sought. Input connectability of the compartmental system allows exogenous inputs to produce arbitrary steady-state values anywhere in state space, resulting in sufficient conditions for the structural identifiability of the system when direct measurements can be made for every compartment. Because of the steady-state nature of the problem, the systems concept of output connectability is shown to play no role in this identification scheme. The importance of constant-infusion tracer experiments is demonstrated for a compartment model describing volatile fatty acid production and conversion in ruminants.     

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.

     

MMT--a pathway modeling tool for data from rapid sampling experiments

The identification of metabolic regulation is a major concern in metabolic engineering. Metabolic regulation phenomena depend on intracellular compounds such as enzymes, metabolites and cofactors. A complete understanding of metabolic regulation requires quantitative information about these compounds under in vivo conditions. This quantitative knowledge in combination with the known network of metabolic pathways allows the construction of mathematical models that describe the dynamic changes in metabolite concentrations over time. Rapid sampling combined with pulse experiments is a useful tool for the identification of metabolic regulation owing to the transient data they provide. Enzymatic tests in combination with ESI-LC-MS (Electrospray Ionization Liquid Chromatographic Tandem Mass Spectrometry) and HPLC measurements have been used to identify up to 30 metabolites and nucleotides from rapid sampling experiments. A metabolic modeling tool (MMT) that is built on a relational database was developed specifically for analysis of rapid sampling experiments. The tool allows to construct complex pathway models with information stored in the relational database. Parameter fitting and simulation algorithms for the resulting system of Ordinary Differential Equations (ODEs) are part of MMT. Additionally explicit sensitivity functions are calculated. The integration of all necessary algorithms in one tool allows fast model analysis and comparison. Complex models have been developed to describe the central metabolic pathways of Escherichia coli during a glucose pulse experiment.     

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.     

Single channel gating events in tracer flux experiments I. Theory

Tracer ion flux measurements are a commonly used method for studying ion transport through membranes of cellular systems, where the rate of ion flow is determined by gating processes which control the opening and closing of transmembrane channels. Due to recent advances in the theoretical analysis of tracer flux from or into closed membrane structures (CMS), the mechanism of gating reactions can, in principle, be derived from flux data. A physically well founded analysis is presented for the dependence of the total tracer ion content of a collection of CMS on the gating processes. For functionally uncoupled gating units a mean single channel flux contribution [equation, see text] can be defined, where k is the intrinsic single channel flux coefficient, t the time over which flux is measured, and p(tau,t) is the probability that a given channel was open for a total period tau during t. This quantity reflects the mean time course of the tracer content due to flux through a single channel. Expressions for are derived that explicitly take into account a distribution in the lifetime of open channels. On the basis of the results, kinetic and thermodynamic parameters of multiphasic gating reactions can be determined from the time course of the overall tracer content in a colleciion of CMS.     

Analysis of tracer experiments V: Integral equations of perturbation-tracer analysis

An integral equation approach to perturbation-tracer analysis in steady-state multicompartment systems is formulated. The theory is developed for δ function perturbation and tracer inputs and extended to the case of continuous small perturbations and continuous tracer inputs. It is shown that the first order dependence of the initial entry function can then be expressed by means of an integral equation:

$$B_1 (t) = \int_{t_2 = - \infty }^\infty {\int_{t_1 = - \infty }^\infty {P(t_1 )T(t_2 )B_1 (t - t_2 ,t_1 - t_2 )dt_1 dt_2 } } $$     

13CO2 as a universal metabolic tracer in isotopologue perturbation experiments

A tobacco plant was illuminated for 5h in an atmosphere containing (13)CO(2) and then maintained for 10 days under standard greenhouse conditions. Nicotine, glucose, and amino acids from proteins were isolated chromatographically. Isotopologue abundances of isolated metabolites were determined quantitatively by NMR spectroscopy and mass spectrometry. The observed non-stochastic isotopologue patterns indicate (i) formation of multiply labeled photosynthetic carbohydrates during the (13)CO(2) pulse phase followed by (ii) partial catabolism of the primary photosynthetic products, and (iii) recombination of the (13)C-labeled fragments with unlabeled intermediary metabolites during the chase period. The detected and simulated isotopologue profiles of glucose and amino acids reflect carbon partitioning that is dominated by the Calvin cycle and glycolysis/glucogenesis. Retrobiosynthetic analysis of the nicotine pattern is in line with its known formation from nicotinic acid and putrescine via aspartate, glyceraldehyde phosphate and alpha-ketoglutarate as basic building blocks. The study demonstrates that pulse/chase labeling with (13)CO(2) as precursor is a powerful tool for the analysis of quantitative aspects of plant metabolism in completely unperturbed whole plants.     

Design of experiments for predictive microbial modeling

Summary Good predictive microbial models can be built with appropriate data from well-designed experiments. Anyone setting up an experiment should consider the sources of variability, possible screening experiments, optimum spacing between points on a continuous scale, and the most appropriate type of design, e.g. factorial, screening, or central composite.     

The use of mean pool abundances to interpret 15N tracer experiments

Details are presented of a simple mathematical framework that allows ¹⁵N tracer experiments to be interpreted in terms of the main processes of the soil/plant nitrogen cycle. The calculations, all of which can be performed on a scientific calculator, yield the rates of gross mineralization and nitrification and the crop nitrogen uptake occurring as ammonium and nitrate. Two procedures are presented. One requires paired experiments with labelled ammonium and unlabelled nitrate as one treatment, and unlabelled ammonium and labelled nitrate as the other. The second procedure requires only the labelled ammonium, unlabelled nitrate treatment. Example calculations are presented using actual experimental data. The interpretative procedure uses the fact that the rate of isotopic dilution in an ammonium pool labelled with ¹⁵N is a function of the rate at which unlabelled ammonium is introduced into the pool via mineralization. Similarly, the rate of isotope dilution in an ¹⁵N labelled nitrate pool is a function of the rate at which unlabelled nitrate is introduced into the pool via nitrification.