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: 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.     

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.     

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.     

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:

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

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.     

Estimation of steady-state flux rates in metabolic systems by computer simulations of radioactive tracer experiments

The dynamics of radioactive tracers in metabolic systems canbe mathematically modelled by coupled systems of differentialequations for both the concentrations and the specific radio-activitiesof the metabolites involved. Computer simulations, i.e. directfitting of numerical solutions of these equations to observedtime-courses of metabolites and spec jflc radioactivities, enablesone to estimate unknown kinetic parameters of the system. Thetheoretical fundamentals of this approach and the main stepstowards the quantitative assessment of flux rates in stationarymetabolic systems are outlined. An application of the methodto the purine nucleotide metabolism of Ehrlich ascites twnorcells is given based on a simp4fied model of this pathway. Theobtained steady-state flux rates indicate a marked increasein the metabolism of the adenine nucleotides during the proliferatingphase in comparison to the resting phase of tumor growth.     

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.     

Calculation of physiological acid-base parameters in multicompartment systems with application to human blood.

A general formalism for calculating parameters describing physiological acid-base balance in single compartments is extended to multicompartment systems and demonstrated for the multicompartment example of human whole blood. Expressions for total titratable base, strong ion difference, change in total titratable base, change in strong ion difference, and change in Van Slyke standard bicarbonate are derived, giving calculated values in agreement with experimental data. The equations for multicompartment systems are found to have the same mathematical interrelationships as those for single compartments, and the relationship of the present formalism to the traditional form of the Van Slyke equation is also demonstrated. The multicompartment model brings the strong ion difference theory to the same quantitative level as the base excess method.     

Ultrastructural study of cholestasis induced by longterm treatment with estradiol valerate. I. Tight junctional analysis and tracer experiments

Over a period of 20 weeks estradiol valerate (1.5 mg/kg body weight/week) was administered subcutaneously to male Wistar rats from which the livers were examined at four week intervals employing a freeze-fracture technique and colloidal lanthanum tracer studies. In connection with intrahepatic cholestasis, distinct alterations in the tight junctions were observed, consisting of disorganization, rarification and proliferation. Disruption of the tight junctions was not seen and colloidal lanthanum did not penetrate into the bile canalicular lumen. Holding the view that the term "leakiness" of tight junctions should be defined with reference to the tracer employed, we conclude that in the liver one tight junctional strand is sufficient to prevent the escape of larger bile constituents such as bile acids and that a back diffusion of bile acids over the tight junctional barrier does not play a role in the pathogenesis of the estrogen-induced cholestasis. Interruptions of tight junctions, as described by other authors, are interpreted as a secondary mechanical effect. On the other hand, we consider an increased permeability of the tight junctions to water and small solute molecules as probable; possibly this increased permeability is brought about by alterations in the microfilaments. A model for the pathogenesis of the estrogen-induced intrahepatic cholestasis is proposed.     

Contributions to the treatment of tracer distribution equations in multicompartmental systems

Summary A tracer kinetic method is outlined for the treatment of multicompartmental non steady-state systems. Metabolic rates are considered as consisting of two components: one of them (exchange) is balanced by a reverse process of the same rate, and the other (transport) results in concentration change. Assuming the transport rates to be known, the method allows of excluding a lot of logically possible compartmental models as inconsistent with the experimental data. Thus the real compartment structure of the system can be approached.     

Numerical solutions of the Lamm equation. IV. Rotor slowing experiments

This paper presents the results of a numerical solution of the Lamm equation for roton slowing specified by ω² = ω₀² exp {– λτ}, for parameters relevant to equilibrium experiments. It. is shown that in the two-component system it is theoretically possible to deduce s/D from measurements of the difference of concentration across the. cell with rotor slowing, provided that the time at which the difference reaches a maximum is known.     

An antagonist treatment in combination with tracer experiments revealed isocitrate pathway dominant to oxalate biosynthesis in Rumex obtusifolius L.

Oxalate accumulates in leaves of certain plants such as Rumex species (Polygonaceae). Oxalate plays important roles in defense to predator, detoxification of metallic ions, and in hydrogen peroxide formation upon wounding/senescence. However, biosynthetic pathways of soluble oxalate are largely unknown. In the present study we analysed Rumex obtusifolius L. treated with itaconate (an antagonist to isocitrate). Comprehensive metabolome analysis using capillary electrophoresis-mass spectrometry showed that oxalate content of “new leaves” was notably down-regulated by itaconate, as opposed to the accumulation of citrate. The ¹³CO₂ feeding experiment revealed that oxalate accumulation in new leaves was affected by citrate translocation from stems. The results suggested that excess oxalate in new leaves of R. obtusifolius was synthesized primarily via the isocitrate pathway utilizing citrate delivered from stems.     

Structural stabilization and functional improvement of horseradish peroxidase upon modification of accessible lysines: experiments and simulation

Horseradish peroxidase (HRP) is an important heme enzyme with enormous medical diagnostic, biosensing, and biotechnological applications. Thus, any improvement in the applicability and stability of the enzyme is potentially interesting. We previously reported that covalent attachment of an electron relay (anthraquinone 2-carboxylic acid) to the surface-exposed Lys residues successfully improves electron transfer properties of HRP. Here we investigated structural and functional consequences of this modification, which alters three accessible charged lysines (Lys-174, Lys-232, and Lys-241) to the hydrophobic anthraquinolysine residues. Thermal denaturation and thermoinactivation studies demonstrated that this kind of modification enhances the conformational and operational stability of HRP. The melting temperature increased 3 degrees C and the catalytic efficiency enhanced by 80%. Fluorescence and circular dichroism investigations suggest that the modified HRP benefits from enhanced aromatic packing and more buried hydrophobic patches as compared to the native one. Molecular dynamics simulations showed that modification improves the accessibility of His-42 and the heme prosthetic group to the peroxide and aromatic substrates, respectively. Additionally, the hydrophobic patch, which functions as a binding site or trap for reducing aromatic substrates, is more extended in the modified enzyme. In summary, this modification produces a new derivative of HRP with enhanced electron transfer properties, catalytic efficiency, and stability for biotechnological applications.