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.     

The nonexistence of “hermaphoroditic” tracer systems

This communiction argues that so-called “hermaphroditic” tracer systems, which are neither open nor closed, do not exist physically. The argument is based on the assumption that any observable (possibly nonhomogeneous) macroscopic compartment can be approximated by a compartmentC with a finite number of entry points for the tracer, each associated with an abstract subcompartment ofC. It is shown that the “hermaphroditic” property requires that the mean waiting time be infinite in at least one of the subcompartments, or in a subcompartment elsewhere in the system. A subcompartment with infinite mean waiting time must have some sort of memory, of infinite duration, which knows how long a given particle has been retained, however long that is, and thereby determines its probability of departure. Assuming, as seems likely, that no physical basis exists for such an infinite memory, it follows that “hermaphroditic” systems do not exist. Supported in part by U.S. Public Health Service Research Grant GM 21269 from the National Institute of General Medical Sciences, and in part by Biomedical Research Support Grant S07 RR 05392 from the National Institutes of Health.     

Calculation of stable isotope enrichment tracer kinetic procedures

The choice of method of expressing isotopic enrichment in tracer kinetic experiments utilizing stable isotopes was found to affect the calculation of tracee pool size and half-life. The most commonly used definition, the difference between enriched and natural abundance, i.e. atom percent excess, was found to result in significant error in model systems when the dose of tracer was 10% of the pool size. Errors in determining first-order rate constants of efflux and in pool sizes decreased with decreasing ratio of tracer to tracee. Error in determining pool size increased with longer 'sampling' periods, while error in determining the rate constant increased with shorter sampling periods. Of three less frequently used expressions of isotopic enrichment two were found to yield the exact answers in model systems. The correct expressions of isotopic enrichment were linear functions of the quantity of tracer in the system. A practical example demonstrated the effect of choice of expression of enrichment on estimates of whole body copper pool size and turnover in dairy cattle.     

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.     

Fast tracer efflux from membrane vesicles; investigation by controlled elution

A method has been developed to study tracer efflux from membrane vesicles. Vesicles are trapped on filters, but in contrast to conventional filtration techniques tracer efflux is measured as such. A functional integration of a commercial fraction collector, a pulse generator, and a programmable repetitive pipet with a simple electronic circuit allows monitoring of complete efflux kinetics from seconds onward. The automatic control of discrete elution steps guarantees reproducible results and makes possible a correction for background release of tracer from the filter. The dependence of efflux data on selected combinations of filters is demonstrated. These experiments also shed some light on problems intrinsic to conventional filtration procedures. The performance of the controlled elution technique is shown with ²²Na efflux from Na channel-rich membrane vesicles.     

Immobilization and mineralization of tracer nitrogen in forest raw humus

Summary A series of laboratory incubation experiments was conducted to provide information about the effects of soil temperature on the nitrogen interchange in forest raw humus after addition of different forms of nitrogen fertilizers enriched with the N¹⁵-isotope.A positive correlation between temperature and immobilization of nitrogen (non-extractable inN KCl) added as urea-N¹⁵, was found at temperatures of 4°, 12°, and 20°C. When ammonium was added as the source of nitrogen the data indicated a gradual and continual immobilization of tracer nitrogen throughout the entire 90 days experimental period at temperatures of 4° and 12°C. At an incubation temperature of 20°C the amount of immobilized tracer nitrogen reached a relatively low but almost constant level within 10 days.A positive correlation between incubation temperature and the overall nitrogen turnover was found in the raw humus after the nitrate application. Within 3 days of incubation significant net re-mineralization of added tracer nitrate nitrogen took place at the highest temperature (20°C) used. The data show a negative correlation between incubation temperature and net accumulated nitrite-nitrate nitrogen after addition of urea, while no significant amount of nitrite-nitrate was detected in the humus after the ammonium application.At temperatures of 4° and 12°C the nitrogen added as ammonium as compared with nitrate was more rapidly used in supplying the needs of the micro-organisms decomposing forest raw humus. However, the results reveal that in spite of the presence of ammonium in the system, nitrate nitrogen is included in the pathway of the internal nitrogen cycle. Compared with the ammonium and the nitrate treatment the preferential utilization of nitrogen added as urea generally increased with increasing incubation time and temperature.Contribution from the Forest Soil Fertilization Research Group, Vollebekk, Norway. This work was supported by the Agricultural Research Council of Norway.     

Determination of stable molybdenum isotopes by thermionic mass spectrometry for tracer studies of molybdenum plant metabolism

A tracer technique based on multiple stable Mo isotopes and thermionic quadrupole mass spectrometry for isotopic analysis of plant tissue was developed and has been applied in the long-term study of foliar absorption of Mo by potato plants. As several tracers have been used the multivariate linear regression methods has been applied to calculate the portions of tracer Mo present in the potato samples from the isotopic ratios measured and to estimate their reproducibilities.In this paper solely the tracer portions transferred from the leaf into the tuber of the potato have been determined. Dependent on the time of contamination, tracer portions of 0.2 to 12% have been measured, corresponding to a maximum of 2.3% of the foliar application of the tracer molybdate. The reproducibilities of the tracer method as a whole (analytical determination and calculation of the tracer portions in the tracer plant samples) amounted to 7% at the maximum (with one exception); by contrast, the individual differences between the three plants investigated were much larger (up to 80%).     

Use of decreasing foliar carbon isotope discrimination during water limitation as a carbon tracer to study whole plant carbon allocation

Foliar carbon isotope discrimination (Δ) of C₃ plants decreases in water‐deficit situations as discrimination by the photosynthetic primary carboxylation reaction decreases. This diminished Δ in leaves under water deficit can be used as a tracer to study whole plant carbon allocation patterns. Carbon isotope composition (δ¹³C value) of leaf hot water extracts or leaf tissue sap represents a short‐term integral of leaf carbon isotope discrimination and thus represents the δ¹³C value of source carbon that may be distributed within a plant in water‐deficit situations. By plotting the δ¹³C values of source carbon against the δ¹³C values of sink tissues, such as roots or stems, it is possible to assess carbon allocation to and incorporation into sink organs in relation to already present biomass. This natural abundance labelling method has been tested in three independent experiments, a one‐year field study with the fruit tree species Ziziphus mauritiana and peach (Prunus persica), a medium‐term drought stress experiment with Ziziphus rotundifolia trees in the glasshouse, and a short‐term drought stress experiment with soybean (Glycine max). The data show that the natural abundance labelling method can be applied to qualitatively assess carbon allocation in drought‐stressed plants. Although it is not possible to estimate exact fluxes of assimilated carbon during water deficit the method represents an easy to use tool to study integrated plant adaptations to drought stress. In addition, it is a less laborious method that can be applied in field studies as well as in controlled experiments, with plants from any developmental stage.     

Multibreath tracer species dynamics in the lung

By studying the behavior of various tracer species in the lungs, one can assess many important characteristics which distinguish normal and abnormal function. Quantitative evaluation of function depends on the use of an appropriate model in conjunction with experimental data. A multi-compartment model is derived from mass balances to describe dynamic as well as (breath-averaged) steady-state transport processes between the environment and pulmonary capillary blood. The breathing cycle is divided into three time periods (inspiration, expiration, and pause) so that the model equations are discrete in time. No other model of tracer species transport in the lungs deals simultaneously with species dynamics, variable breathing pattern, distribution inhomogeneities, and non-equilibrium between alveolar gas and capillary blood. Models currently in the literature are shown to be special cases of the model presented here.     

Double isotope tracer method for measuring fractional zinc absorption: theoretical analysis

Several approaches for estimation of fractional zinc absorption (FZA) by calculating the ratio of oral to intravenous stable isotopic tracer concentrations (at an appropriate time) in urine or plasma after their simultaneous administration have been proposed in the last decade. These simple-to-implement approaches, often referred to as the double isotopic tracer ratio (DITR) method, are more attractive than the classical "deconvolution" method and the more commonly used single-tracer methods based on fecal monitoring and indicator dilution, after oral or intravenous tracer administration, respectively. However, the domain of validity of DITR for measuring FZA has recently been questioned. In this paper, we provide a theoretical justification of the validity of four different "approximate" formulations of the DITR technique by demonstrating mathematically that their accuracy is a consequence of the particular properties of zinc kinetics.     

Lithium as a non-radioactive tracer for roots of intercropped species

Summary A technique is described for investigating the rooting pattern of species when intercropped, using Lithium as a non-radioactive tracer. The technique was tested on pure stands and mixtures of barley (Hordeum sativum) and field beans (Vicia faba), with 10% LiCl solution placed at depths of 0, 10, 25 and 62 cm.Pure stands of the two crops had similar patterns of Li uptake with depth. Growing the crops in mixture did not significantly change the pattern of Li uptake with depth, but did change total uptake. The Li uptake (m^–2) by both species was reduced in mixtures, and was further reduced when the observed species was sown later than the other.The value of non-radioactive tracers, especially Li, in intercropping studies is discussed.     

Revision of the theory of tracer transport and the convolution model of dynamic contrast enhanced magnetic resonance imaging

Counterexamples are used to motivate the revision of the established theory of tracer transport. Then dynamic contrast enhanced magnetic resonance imaging in particular is conceptualized in terms of a fully distributed convection–diffusion model from which a widely used convolution model is derived using, alternatively, compartmental discretizations or semigroup theory. On this basis, applications and limitations of the convolution model are identified. For instance, it is proved that perfusion and tissue exchange states cannot be identified on the basis of a single convolution equation alone. Yet under certain assumptions, particularly that flux is purely convective at the boundary of a tissue region, physiological parameters such as mean transit time, effective volume fraction, and volumetric flow rate per unit tissue volume can be deduced from the kernel.      

Heterogeneity of membrane transport quantified by the analysis of a unidirectional flux transient of charged tracer

A planar mosaic membrane consists of patches, each with a given area, diffusion coefficient, and mobility of charged tracer; a common electric field, constant in space and time, lies across all the patches. Given the properties of the patches, the transient of the total unidirectional flux (summed over the patches) is predictable. Here we deal with the inverse problem: Given only the observed transient of the total unidirectional flux (as defined experimentally by Ussing), the unknown transport heterogeneity of the mosaic membrane is to be analyzed. Results obtained previously for uncharged tracers are generalized to include effects of the field. In particular, the ratio of the arithmetic and harmonic means (both area-weighted) of the diffusion coefficients, evaluated over the membrane, is expressed in terms of only the observed transient and the field strength and is used to characterize the heterogeneity; and the unique exact solution of the inverse problem for two kinds of patches is recovered at any field strength. If the mosaic consists of n distinct kinds of patches, a sweep of the field strength from low to high values reveals (at most) n steplike shapes in the time course of the total unidirectional flux (normalized to its final steady value), which permit an approximate analysis of the heterogeneity by elementary means.     

Assessment of sigma-1 receptor occupancy in mice with non-radiolabelled FTC-146 as a tracer

Abstract

The use of liquid chromatography coupled with mass spectrometry (LC-MS/MS) is advantageous in in-vivo receptor occupancy assays at pre-clinical drug developmental stages. Relatively, its application is effective in terms of high throughput, data reproducibility, sensitivity, and sample processing. In this perspective, we have evaluated the use of FTC-146 as a non-radiolabelled tracer to determine the sigma-1 receptor occupancy of test drugs in mice brain. Further, the brain and plasma exposures of test drug were determined at their corresponding occupancies. In this occupancy method, the optimized tracer treatment (sacrification) time after intravenous administration was 30?min. The tracer dose was 3?µg/kg and specific brain regions of interest were frontal cortex, pons and midbrain. Mice were pretreated orally with SA4503, fluspidine, haloperidol, and donepezil followed by tracer treatment. Among the test drugs, SA4503 was used as positive control group at its highest test dose (7?mg/kg, intraperitoneal). There was a dose-dependent decrease in brain regional FTC-146 binding in pretreated mice. From the occupancy curves of SA4503, fluspidine, haloperidol, and donepezil the effective dose (ED₅₀) value ranges are 0.74–1.45, 0.09–0.11, 0.11–0.12, and 0.07–0.09?mg/kg, respectively. Their corresponding brain effective concentration (EC₅₀) values are 74.3–132.5, 3.4–3.7, 122.5–139.5, and 8.8–11.0?ng/g and plasma EC₅₀ values are 34.3–53.7, 0.08–0.10, 7.8–9.5, and 0.6–0.7?ng/mL. Brain regional distribution and binding inhibition upon pretreatment were comparable with data reported with labeled [¹⁸F]FTC-146. Drug exposures were simultaneously determined and correlated with sigma-1 occupancy from the same experiment. Wide category drugs can be assayed for sigma-1 receptor engagement and their correlation with exposures aid in clinical development.     

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.     

Simultaneous measurement of endogenous and deuterium-labeled tracer variants of choline and acetylcholine in subpicomole quantities by gas chromatography-mass spectrometry

A method is described for the simultaneous analysis of endogenous and d₄-labeled tracer variants of choline and acetylcholine by a gas chromatograph/mass spectrometer system operated in the specific ion detection mode, using d₉-labeled variants of both choline and acetylcholine as internal standards. The detection limit is approximately 10^?13 moles of both tracer and endogenous variants.     

A method for the synthesis of an oseltamivir PET tracer

A protocol applicable for the synthesis of an oseltamivir positron emission tomography (PET) tracer was developed. Acetylation of amine 3 with CH(3)COCl, followed by deprotection and aqueous workup, produced oseltamivir 4 from 3 within 10 min. The obtained 4 was sufficiently pure for PET studies. This method can be extended to PET tracer synthesis using CH(3)(11)COCl.     

The use of lead as an ionic tracer for investigating routes of passive fluid transfer

Several inorganic ions, including lead, barium, silver, and thallium, have been tested as possible tracers for demonstrating fluid-accessible channels in functional epithelia at the ultrastructural level. The most useful of the ionic tracers examined was the lead (plumbous) ion, administered for short time intervals (less than 2 min) and "captured" with phosphate used as the buffer in the fixative. Passive fluid and ion-accessible channels of rat parotid salivary gland have been examined with this method. At short tracer infusion times (0.5-1.0 min), localization of the tracer was primarily extracellular, although intracellular deposits were observed in the following sites: smooth membrane-delimited endocytic vesicles of both epithelial and connective tissue cells, inner Golgi cisternae, and occasional cisternae of rough endoplastic reticulum. The lead tracer readily penetrated tight junctions between parotid acinar cells but rarely passed through the tight junctions between intercalated duct cells and did not penetrate junctions of striated duct cells. Fat cells observed in the stroma of this gland were the only cells that exhibited lead tracer in the cytosol, suggesting that the plasmalemma of this cell type is more permeable to exogenous ions than the plasmalemma of other cell types present in this gland.     

Populations of strongyloid nematode infective stages in sheep pastures: Comparison between direct pasture sampling and tracer lambs as estimators of larval abundance

Waller P.J., Dobson R.J., Donald A.D. and Thomas R.J. 1981. Populations of strongyloid nematode infective stages in sheep pastures : comparison between direct pasture sampling and tracer lambs as estimators of larval abundance. International Journal for Parasitology11: 359–367. Over a 2-year period, numbers of infective larvae in samples of pasture herbage, and numbers of worms in previously worm-free “tracer” lambs allowed 4 weeks grazing, were compared as estimators of the abundance of infective larvae on pastures.Transformation of sample estimates of infective larval numbers per 100 g herbage dry matter (DM) and of worm numbers in tracer sheep, according to the expression y = log₁₀ (x+25), was effective in stabilizing variances. Estimates of error variance for each technique did not differ significantly among the genera Haemonchus, Ostertagia or Trichostrongylus and the pooled estimate for the tracer sheep method was 4 times greater than that for pasture sampling. From these results, more tracer sheep than pasture samples would be required to achieve the same level of precision with the two techniques. Using conventional statistical methods, the effects of numbers of pasture samples or tracer sheep on the size of the difference between two means which can be detected as significant and on the width of the confidence interval about a single mean, are illustrated. These can be used as a guide in the choice of sample sizes. Error variances for Nematodirus spp. were significantly less than for the other genera by pasture sampling, and greater by the tracer sheep technique. Possible reasons for this are discussed, but it is concluded that pasture sampling is likely to be much the more precise method for estimating Nematodirus spp. infective larval availability.Changes with time in infective larval abundance, for Haemonchus, Trichostrongylus and Nematodirus spp. which were present in moderate to low numbers, followed similar trends by both techniques. However, for Ostertagia spp. larvae, which were much more abundant, peak levels were defined more sharply and occurred earlier by pasture sampling than by the tracer method. It is suggested that worm counts from tracer sheep, especially those grazing for 4 weeks rather than shorter periods, may systematically underestimate the infective larval population on pasture at high levels of abundance owing to density-dependent worm loss.     

基于氘示踪剂和热扩散技术的栓皮栎水分运输速率与效率研究

利用同位素示踪和热扩散技术研究了不同胁迫处理栓皮栎的水分运输和储存差异。结果表明,注射氘同位素后,充分灌溉、轻度和重度胁迫处理的最大氘同位素比率分别升高到586.67‰、997.33‰和1364.89‰,处理间差异显著。轻度和重度胁迫处理的示踪速率分别为0.10 m/h和0.07 m/h,显著低于充分灌溉处理,但半减期和残留期显著高于充分灌溉。轻度和重度胁迫处理的枝条栓塞程度(PLC)比充分灌溉显著增加,液流通量、水势和蒸腾速率则显著减小。统计分析表明蒸腾作用强弱决定树体水分运输速率,PLC的增加和枝条水势的降低阻碍木质部水分运输。半减期和残留期内,轻度和重度胁迫处理的累积液流量显著高于充分灌水处理,运载相同体积的示踪剂,胁迫处理栓皮栎需要的水量增加,表明胁迫环境下受到PLC、蒸腾以及与树体储水交换的影响,水分运输效率下降。栓皮栎通过栓塞和储水交换来降低水分运输速率和效率,调控水分的收支平衡来适应干旱的环境。