Kinetic behavior of slowly equilibrating association-dissociation enzyme systems]

The shape of the plots of product accumulation versus time (t) has been analysed for slowly equilibrating association-dissociation enzyme systems of the types 2p in equilibrium P (P is enzyme oligomer which is able to dissociate reversibly forming two identical halves p) and M in equilibrium M2 in equilibrium M2 in equilibrium... (M is monomer which has two association sites overlapping with active sites). It is assumed that the rate of equilibration between oligomeric forms is comparable with the rate of over-all enzymatic reaction and that substrate-oligomer complexes are in rapid equilibrium with free components. It has been shown that characteristic feature of kinetic behavior of slowly equilibrating association-dissociation enzyme systems is that the value of tau depends on enzyme concentration (tau is the intercept on t-axis for linear asymptota of the curve of product concentration versus time at t leads to infinity).     

Plasma equilibrium in 3D magnetic confinement systems and soliton theory

Single-valued conformal flux (magnetic) coordinates can always be introduced on arbitrary toroidal magnetic surfaces. It is shown how such coordinates can be obtained by transforming Boozer magnetic coordinates on the surfaces. The metrics is substantially simplified and the coordinate grid is orthogonalized at the expense of a more complicated representation of the magnetic field in conformal flux coordinates. This in turn makes it possible to introduce complex angular flux coordinates on any toroidal magnetic surface and to develop efficient methods for a complex analysis of the geometry of equilibrium magnetic surfaces. The complex analysis reveals how the plasma equilibrium problem is related to soliton theory. Magnetic surfaces of constant mean curvature are considered to exemplify this relationship.     

Optimizing the sensitivity of enzyme systems to perturbations from equilibrium

Algebraic derivations and numerical examples illustrate how metabolite pool sizes and enzyme rate constants influence the rate at which a multireactant enzyme system, initially poised in a near-equilibrium steady state, responds to small perturbations in the concentrations of the reactants. Certain enzymes, such as those employing the ordered bi bi catalytic mechanism, become relatively insensitive to perturbations when the reactants are all present at high concentrations. Other enzymes, such as those employing the ping-pong bi bi mechanism, are most sensitive to perturbations at high reactant concentrations. The ratio of the reactant concentrations to one another significantly alters sensitivity to perturbations; equations are presented for calculation of the reactant concentrations yielding maximal sensitivity to perturbations. Natural selection could choose metabolite pool sizes and enzyme rate constants which would optimize the performance of these systems, but changing metabolic loads (naturally or experimentally imposed) constantly alter the sensitivity of these systems to perturbations, changing the relative strengths of various connections in metabolic control networks.     

Effects of diffusion on the electrophoretic behavior of associating systems: the Gilbert-Jenkins theory revisited

The Gilbert-Jenkins theory predicts the asymptotic shape of moving-boundary sedimentation and electrophoretic patterns and broad zone molecular sieve chromatographic elution profiles for the class of interacting systems, A + B in equilibrium C, in which two dissimilar macromolecules react reversibly to form a complex. A particularly provocative case is the one in which the complex has a greater migration velocity than that of either reactant, each of which has a different velocity. Depending upon conditions, this case predicts, for example, that in the asymptotic limit an ascending electrophoretic pattern or a frontal gel chromatographic elution profile can show two hypersharp reaction boundaries separated by a plateau. This prediction is now confirmed by numerical solution of transport equations which retain the second-order diffusional term and extrapolation of the computed patterns to zero diffusion coefficient. For finite diffusion coefficient, however, the two hypersharp reaction boundaries are separated by a weak negative gradient. These calculations are extended to an examination of the transitions between the three types of patterns admitted by the case under consideration in order to gain physical understanding and to define criteria for recognizing the transitions. Studies of this kind not only establish confidence in the Gilbert-Jenkins theory, but, in addition, they provide new insights which make for more effective application of the theory to real systems.     

Kinetic methods for the study of the enzyme systems of β-oxidation

Kinetic methods for studying the reactions of the “general” fatty acyl CoA dehydrogenase under three sets of substrate and enzyme concentration conditions have been developed. The reaction of butyryl-CoA and electron transfer flavoprotein (ETF) can be studied either under steady-state conditions with enzyme at catalytic concentration or under single-turnover conditions with enzyme in excess. Under the latter conditions, acyl-CoA dehydrogenase acts both as a catalyst and an ultimate electron-transfer acceptor. The reductive half-reaction of butyryl-CoA and enzyme can also be studied in a separate kinetic experiment. Comparison of the pH dependences of the rate constants and isotope effects of the steady-state reaction of butyryl-CoA and ETF with the same parameters for the reductive half-reaction is consistent with a mechanism involving transfer of electrons from butyryl-CoA to ETF within a ternary complex. An alternative mechanism in which the reductive half-reaction takes place prior to the binding and reaction of ETF seems unlikely because the pH 8.5 isotope effect on the reductive half-reaction is much larger than that on the complete reaction in spite of the fact that the rates of the reactions are comparable. The pH dependence of the K_m for substrate and K_I for inhibitor is consistent with a mechanism for transfer of electrons within the ternary complex which involves protonation of the C group of substrates. The protonation labilizes the C-2 proton and base catalysis of the removal of the C-2 proton results in the production of the active enzyme-substrate species, namely the C-2 anion of substrate.     

Effects of diffusion on the electrophoretic behavior of associating systems: The Gilbert-Jenkins theory revisited

The Gilbert-Jenkins theory predicts the asymptotic shape of moving-boundary sedimentation and electrophoretic patterns and broad zone molecular sieve chromatographic elution profiles for the class of interacting systems, A + B ⇄ C, in which two dissimilar macromolecules react reversibly to form a complex. A particularly provocative case is the one in which the complex has a greater migration velocity than that of either reactant, each of which has a different velocity. Depending upon conditions, this case predicts, for example, that in the asymptotic limit an ascending electrophoretic pattern or a frontal gel chromatographic elution profile can show two hypersharp reaction boundaries separated by a plateau. This prediction is now confirmed by numerical solution of transport equations which retain the second-order diffusional term and extrapolation of the computed patterns to zero diffusion coefficient. For finite diffusion coefficient, however, the two hypersharp reaction boundaries are separated by a weak negative gradient. These calculations are extended to an examination of the transitions between the three types of patterns admitted by the case under consideration in order to gain physical understanding and to define criteria for recognizing the transitions. Studies of this kind not only establish confidence in the Gilbert-Jenkins theory, but, in addition, they provide new insights which make for more effective application of the theory to real systems.     

NMR spin exchange kinetics at equilibrium in membrane transport and enzyme systems

A set of differential equations is formulated to describe the rapid exchange (time scale, approximately 0.01 to approximately 10 s) of a labelled solute across the membranes of cells in suspension. The labelling is achieved with nuclear magnetic resonance by exposure of the system to a high intensity radio-frequency pulse, and the excited nuclei relax to the equilibrium state with a short half life. An analytical expression for the decay of the magnetic resonance signal is presented; the solution involves the determination of eigenvalues, of an array of Laplace-Carson transformed differential equations, by use of the general solution of a quartic polynomial. Simulations of the behaviour of the exchange system using various conditions of cell number, rate constants and nuclear magnetic relaxation times are presented. The marked concentration dependence of the extent of reaction at a given time has not previously been reported for nuclear magnetic resonance exchange systems and is a feature anticipated from the known saturability of several membrane transport systems including glucose transport into human erythrocytes. The theory is readily generalized to other model systems by appropriate reinterpretation of the physical meaning of various parameters; the general form of the solution holds in many biological contexts other than membrane transport and includes equilibrium enzyme kinetics.     

Quantitative comparison of 2D and 3D monitoring dimensions in fish behavior analysis

To improve the accuracy and efficiency of fish behavior assessment, this paper focuses on quantitatively exploring the variations and relationships between different monitoring dimensions. A systematic comparison was conducted between 3D and 2D behavioral factors using an infrared tracing system, during both day and night. Significant differences in swimming distance were observed among the different monitoring methods, as determined by two-way ANOVA and Tukey's test. A correction was applied to account for the disparities observed in 2D swimming distance, ensuring accurate measurements. These findings present a cost-effective and efficient approach for obtaining precise 3D distance data. Additionally, a kinematic factor called the “number of U-turns” was proposed to provide a more intuitive characterization of directional changes in fish swimming. Significant differences were observed between 2D and 3D data, with higher percentages of false U-turn counts and missing U-turn counts compared to correct counts in the 2D view. These findings suggest that reducing the monitoring dimension may impact the accurate estimation of swimming motion, potentially resulting in inaccurate outcomes. Finally, the statistical analyses of the non-linear properties of fractal dimension revealed significant differences among the various monitoring methods. This conclusion has practical implications for biologists and physicists, enabling them to improve the accuracy of behavioral phenotyping for organisms exhibiting 3D motion.     

Incorporating 2D tree-ring data in 3D laser scans of coarse-root systems

In times of global change biomass calculations and the carbon cycle is gaining in importance. Forests act as carbon sinks and hence, play a crucial role in worlds and forests carbon budgets. Unfortunately, growth models and biomass calculations existing so far mainly concentrate on the above-ground part of trees. For this reason, the aim of the present study is to develop an annually resolved 3D growth model for tree roots, which allows for reliable biomass calculations and can later be combined with above-ground models. A FARO scan arm was used to measure the surface of a tree-root segment. In addition, ring-width measurements were performed manually on sampled cross sections using WinDENDRO. The main goal of this study is to model root growth on an annual scale by combining these data sets. In particular, a laser scan arm was tested as a device for the realistic reproduction of tree-root architecture, although the first evaluation has been performed for a root segment rather than for an entire root system. Deviations in volume calculations differed between 5% and 7% from the actual volume and varied depending on the used modeling technique. The model with the smallest deviations represented the structure of the root segment in a realistic way and distances and diameter of cross sections were acceptable approximations of the real values. However, the volume calculations varied depending on object complexity, modeling technique and order of modeling steps. In addition, it was possible to merge tree-ring borders as coordinates into the surface model and receive age information in connection with the spatial allocation. The scan arm was evaluated as an innovative and applicable device with high potential for root modeling. Nevertheless, there are still many problems connected with the scanning technique which have an influence on the accuracy of the model but are expected to improve with technical progress.     

Stochastic and deterministic models for the kinetic behavior of certain structured enzyme systems II: consecutive two enzyme systems.

This paper contains extensions of results from a previous paper regarding structured one enzyme systems to a more complicated structured two enzyme system. A stochastic model and a deterministic model are developed for such systems and their steady state reaction kinetics are compared. These comparisons are in the form of graphs of the reaction kinetics versus substrate concentration. Two quantities are proposed as indications of lack of agreement between the two models. This lack of agreement corresponds to situations in which the model systems are more highly non-linear, in accord with Jensen's inequalities. Implications of these results, relative to experimental procedures are briefly discussed.     

The sedimentation equilibrium of heterogeneously associating systems and mixtures of non-interacting solutes: analysis without determination of molecular weight averages

Sedimentation equilibrium is first considered of a system in which a ligand of any size binds to an acceptor at p sites, the experimental result, obtained with either interference or absorption optics, being a distribution of total solute concentration as a function of radial distance. Theory illustrated by a numerical example, is presented which shows that this distribution may be analysed to give the activity of the unbound ligand as a function of total weight concentration. It is shown that this information may be used together with conservation of mass equations written in terms of the initial mixing composition to evaluate the equilibrium constant(s) relevant to the system. Correlation with composition evaluation by use of absorption optics (when possible) is also discussed. The procedure does not involve solution of simultaneous equations which are sums of exponentials nor differentiation of experimental results to obtain apparent weight-average molecular weights. It is general in that it leads to the evaluation of the activity of the species characterized by the smallest M(l-$\text{v}$π) product and, accordingly, is shown to be useful in the analysis of non-interacting as well as of interacting systems.